Title:

United States Patent 7305025

Abstract:

A measuring apparatus for measuring reliability against jitter of an electronic device, including: a jitter tolerance estimator operable to estimate a jitter tolerance of the electronic device based on an output signal output from the electronic device according to an input signal input through a transmission line of which the transmission length is shorter than a predetermined length so that it does not generate a deterministic jitter; a jitter tolerance degradation quantity estimator operable to estimate a quantity of degradation of the jitter tolerance which deteriorates by the deterministic jitter caused in the input signal by transmission through the long transmission line when the input signal is input into the electronic device through the transmission line, of which the transmission length is longer than a predetermined length so that it may cause the deterministic jitter; a system jitter tolerance estimator operable to estimate a jitter tolerance of the electronic device and a jitter tolerance of a system including the long transmission line and the electronic device based on quantity of degradation of the jitter tolerance, is provided.

Inventors:

Yamaguchi, Takahiro (Tokyo, JP)

Ishida, Masahiro (Tokyo, JP)

Soma, Mani (Seattle, WA, US)

Ishida, Masahiro (Tokyo, JP)

Soma, Mani (Seattle, WA, US)

Application Number:

10/925870

Publication Date:

12/04/2007

Filing Date:

08/25/2004

Export Citation:

Assignee:

Advantest Corporation (Tokyo, JP)

Primary Class:

Other Classes:

375/371

International Classes:

Field of Search:

375/227, 375/346, 375/285, 375/226, 375/371, 375/224

View Patent Images:

US Patent References:

7012982 | Method and system for de-jittering of transmitted MPEG-2 and MPEG-4 video | 2006-03-14 | Basch et al. | 375/371 |

Foreign References:

JP08050156 | February, 1996 | JITTER RESISTANCE MEASURING DEVICE | ||

JP08248078 | September, 1996 | |||

JP11083924 | March, 1999 | |||

JPH1183924A | 1999-03-26 | |||

JPH0850156A | 1996-02-20 | |||

JPH08248078A | 1996-09-27 |

Other References:

U. S. Office Action issued in corresponding U.S. Appl. No. 10/776,926 dated May 14, 2007 (24 pages).

Patent Abstract s of Japan, publication No. 11-083924, date of publication Mar. 26, 1999; 1 page.

Patent Abstracts of Japan, publication No. 08-050156, date of publication Feb. 20, 1996, 1 page.

Japanese International Search Report, dated May 6, 2003.

PCT Patent Abstract, publication No. 03/073115 A1, publication date Sep. 4, 2003, 1 page.

Patent Abstracts of Japan, publication No. 08-248078; publication date Sep. 27, 1996, 1 page.

Patent Abstract s of Japan, publication No. 11-083924, date of publication Mar. 26, 1999; 1 page.

Patent Abstracts of Japan, publication No. 08-050156, date of publication Feb. 20, 1996, 1 page.

Japanese International Search Report, dated May 6, 2003.

PCT Patent Abstract, publication No. 03/073115 A1, publication date Sep. 4, 2003, 1 page.

Patent Abstracts of Japan, publication No. 08-248078; publication date Sep. 27, 1996, 1 page.

Primary Examiner:

BAYARD, EMMANUEL

Attorney, Agent or Firm:

OSHA BERGMAN WATANABE & BURTON LLP (HOUSTON, TX, US)

Parent Case Data:

The present application is a CIP application of
PCT/JP03/01523 filed on Feb. 14, 2003 which claims priority
from PCT/US02/05901 filed on Feb. 26, 2002 and U.S. Ser. No.
10/265,349 filed on Oct. 4, 2002, the contents of which are
incorporated herein by reference.

Claims:

What is claimed is:

1. A measuring apparatus for measuring reliability against jitter of an electronic device, comprising: a jitter tolerance estimator operable to estimate a jitter tolerance of the electronic device based on an output signal output from the electronic device according to an input signal input through a transmission line which does not generate a deterministic jitter; a jitter tolerance degradation quantity estimator operable to estimate a quantity of degradation of the jitter tolerance which deteriorates by the deterministic jitter caused in the input signal due to transmission through the long transmission line when the input signal is input into the electronic device through the long transmission line which causes the deterministic jitter; a system jitter tolerance estimator operable to estimate a jitter tolerance of a system including the long transmission line and the electronic device based on a jitter tolerance of the electronic device and also based on quantity of degradation of the jitter tolerance.

2. The measuring apparatus as claimed in claim 1, further comprising: a timing jitter estimator operable to estimate an output timing jitter sequence of the output signal based on the output signal; and a jitter transfer function measuring apparatus operable to measure the jitter transfer function in the electronic device based on the output timing jitter sequence, wherein said jitter tolerance estimator estimates a jitter tolerance of the system based on a gain of the jitter transfer function.

3. The measuring apparatus as claimed in claim 2, wherein said jitter tolerance estimator estimates a jitter tolerance of the system further based on a phase of the jitter transfer function.

4. The measuring apparatus as claimed in claim 1, further comprising: a timing jitter estimator operable to estimate an output timing jitter sequence of the output signal based on the output signal; and a jitter distortion estimator operable to estimate a jitter distortion of a timing jitter of the output signal based on the output timing jitter sequence, wherein said jitter tolerance estimator estimates a jitter tolerance of the system based on the jitter distortion.

5. The measuring apparatus as claimed in claim 4, wherein said jitter distortion estimator estimates the jitter distortion based on a spectrum of a timing jitter of the output signal.

6. The measuring apparatus as claimed in claim 2, wherein said timing jitter estimator comprises: an instantaneous phase noise estimator operable to calculate an instantaneous phase noise of the output signal based on the output signal; and a resampler operable to generate said output timing jitter sequence obtained by resampling the instantaneous phase noise at predetermined timings.

7. The measuring apparatus as claimed in claim 6, wherein said instantaneous phase noise estimator comprises: an analytic signal transformer operable to transform the output signal to a complex analytic signal; an instantaneous phase estimator operable to estimate an instantaneous phase of the analytic signal based on the analytic signal; a linear instantaneous phase estimator operable to estimate a linear instantaneous phase of the output signal based on an instantaneous phase of the analytic signal; and a linear trend remover operable to calculate an instantaneous phase noise obtained by removing the linear instantaneous phase from the instantaneous phase based on the instantaneous phase and the linear instantaneous phase.

8. The measuring apparatus as claimed in claim 2, wherein said timing jitter estimator comprises: a period jitter estimator operable to estimate a period jitter sequence of the output signal; an ideal edge timing estimator operable to estimate average period of the period jitter sequence; and an edge timing error estimation unit operable to estimate the output timing jitter sequence based on the average period of the period jitter sequence and the period jitter sequence.

9. The measuring apparatus as claimed in claim 1, further comprising an input signal generating unit operable to generate the input signal to which a plurality of timing jitters are applied, wherein frequencies of the timing jitters are different from one another.

10. The measuring apparatus as claimed in claim 1, further comprising a bit error rate estimator operable to detect a bit error of the output signal based on the output signal of the electronic device, wherein said input signal generating unit sequentially inputs the plurality of input signals on which the timing jitters are applied into the electronic device, wherein the amplitudes of the timing jitters are different from one another, and said jitter tolerance estimator estimates a peak-to-peak value of the timing jitter, in which said bit error rate estimator does not detect a bit error of the output signal, as the jitter tolerance.

11. The measuring apparatus as claimed in claim 10, wherein said bit error rate detector detects the bit error by sampling the data signal output from the electronic device outputs by a clock signal output by the electronic device, detecting each bit of the data signal, and comparing each bit of the detected data signal with each bit of the given reference signal.

12. A measuring apparatus for measuring reliability against jitter of an electronic device, comprising: a jitter tolerance estimator operable to estimate a jitter tolerance of a system including a predetermined transmission line and the electronic device based on an output signal output from the electronic device according to an input signal input through the transmission line; a jitter tolerance degradation quantity estimator operable to estimate a quantity of jitter tolerance degradation based on the input signal, wherein the jitter tolerance degradation is caused by a deterministic jitter generated in the input signal due to a transmission through the transmission line; and a device jitter tolerance estimator operable to estimate a jitter tolerance of the electronic device by correcting a jitter tolerance of the system estimated by said jitter tolerance estimator based on the quantity of jitter tolerance degradation estimated by said jitter tolerance degradation quantity estimator.

13. The measuring apparatus as claimed in claim 12, further comprising an input signal generating unit operable to generate the input signal and provides an input signal to the electronic device through the transmission line, wherein said jitter tolerance degradation quantity estimator compares the input signal input into the transmission line from said input signal generating unit with the input signal input into the electronic device from the transmission line, and estimates the quantity of jitter tolerance degradation by the deterministic jitter based on the comparison result.

1. A measuring apparatus for measuring reliability against jitter of an electronic device, comprising: a jitter tolerance estimator operable to estimate a jitter tolerance of the electronic device based on an output signal output from the electronic device according to an input signal input through a transmission line which does not generate a deterministic jitter; a jitter tolerance degradation quantity estimator operable to estimate a quantity of degradation of the jitter tolerance which deteriorates by the deterministic jitter caused in the input signal due to transmission through the long transmission line when the input signal is input into the electronic device through the long transmission line which causes the deterministic jitter; a system jitter tolerance estimator operable to estimate a jitter tolerance of a system including the long transmission line and the electronic device based on a jitter tolerance of the electronic device and also based on quantity of degradation of the jitter tolerance.

2. The measuring apparatus as claimed in claim 1, further comprising: a timing jitter estimator operable to estimate an output timing jitter sequence of the output signal based on the output signal; and a jitter transfer function measuring apparatus operable to measure the jitter transfer function in the electronic device based on the output timing jitter sequence, wherein said jitter tolerance estimator estimates a jitter tolerance of the system based on a gain of the jitter transfer function.

3. The measuring apparatus as claimed in claim 2, wherein said jitter tolerance estimator estimates a jitter tolerance of the system further based on a phase of the jitter transfer function.

4. The measuring apparatus as claimed in claim 1, further comprising: a timing jitter estimator operable to estimate an output timing jitter sequence of the output signal based on the output signal; and a jitter distortion estimator operable to estimate a jitter distortion of a timing jitter of the output signal based on the output timing jitter sequence, wherein said jitter tolerance estimator estimates a jitter tolerance of the system based on the jitter distortion.

5. The measuring apparatus as claimed in claim 4, wherein said jitter distortion estimator estimates the jitter distortion based on a spectrum of a timing jitter of the output signal.

6. The measuring apparatus as claimed in claim 2, wherein said timing jitter estimator comprises: an instantaneous phase noise estimator operable to calculate an instantaneous phase noise of the output signal based on the output signal; and a resampler operable to generate said output timing jitter sequence obtained by resampling the instantaneous phase noise at predetermined timings.

7. The measuring apparatus as claimed in claim 6, wherein said instantaneous phase noise estimator comprises: an analytic signal transformer operable to transform the output signal to a complex analytic signal; an instantaneous phase estimator operable to estimate an instantaneous phase of the analytic signal based on the analytic signal; a linear instantaneous phase estimator operable to estimate a linear instantaneous phase of the output signal based on an instantaneous phase of the analytic signal; and a linear trend remover operable to calculate an instantaneous phase noise obtained by removing the linear instantaneous phase from the instantaneous phase based on the instantaneous phase and the linear instantaneous phase.

8. The measuring apparatus as claimed in claim 2, wherein said timing jitter estimator comprises: a period jitter estimator operable to estimate a period jitter sequence of the output signal; an ideal edge timing estimator operable to estimate average period of the period jitter sequence; and an edge timing error estimation unit operable to estimate the output timing jitter sequence based on the average period of the period jitter sequence and the period jitter sequence.

9. The measuring apparatus as claimed in claim 1, further comprising an input signal generating unit operable to generate the input signal to which a plurality of timing jitters are applied, wherein frequencies of the timing jitters are different from one another.

10. The measuring apparatus as claimed in claim 1, further comprising a bit error rate estimator operable to detect a bit error of the output signal based on the output signal of the electronic device, wherein said input signal generating unit sequentially inputs the plurality of input signals on which the timing jitters are applied into the electronic device, wherein the amplitudes of the timing jitters are different from one another, and said jitter tolerance estimator estimates a peak-to-peak value of the timing jitter, in which said bit error rate estimator does not detect a bit error of the output signal, as the jitter tolerance.

11. The measuring apparatus as claimed in claim 10, wherein said bit error rate detector detects the bit error by sampling the data signal output from the electronic device outputs by a clock signal output by the electronic device, detecting each bit of the data signal, and comparing each bit of the detected data signal with each bit of the given reference signal.

12. A measuring apparatus for measuring reliability against jitter of an electronic device, comprising: a jitter tolerance estimator operable to estimate a jitter tolerance of a system including a predetermined transmission line and the electronic device based on an output signal output from the electronic device according to an input signal input through the transmission line; a jitter tolerance degradation quantity estimator operable to estimate a quantity of jitter tolerance degradation based on the input signal, wherein the jitter tolerance degradation is caused by a deterministic jitter generated in the input signal due to a transmission through the transmission line; and a device jitter tolerance estimator operable to estimate a jitter tolerance of the electronic device by correcting a jitter tolerance of the system estimated by said jitter tolerance estimator based on the quantity of jitter tolerance degradation estimated by said jitter tolerance degradation quantity estimator.

13. The measuring apparatus as claimed in claim 12, further comprising an input signal generating unit operable to generate the input signal and provides an input signal to the electronic device through the transmission line, wherein said jitter tolerance degradation quantity estimator compares the input signal input into the transmission line from said input signal generating unit with the input signal input into the electronic device from the transmission line, and estimates the quantity of jitter tolerance degradation by the deterministic jitter based on the comparison result.

Description:

1. Field of the Invention

The present invention relates to a measuring apparatus and a measuring method for measuring an electronic device. More particularly, the present invention relates to a measuring apparatus and a measuring method that measure a jitter transfer function, a bit error rate and jitter tolerance of the electronic device under test. The present application also relates to the United States patent application described as below.

2. Description of the Related Art

Jitter testing is an important item to a serial-deserial communication device. For example, Recommendations and Requirements from International Telecommunication Union and Bellcore ((1) ITU-T, Recommendation G.958: Digital Line Systems Based on the Synchronous Digital Hierarchy for Use on Optical Fibre Cables, November 1994, (2) ITU-T, Recommendation O.172: Jitter and Wander Measuring Equipment for Digital Systems Which are Based on the Synchronous Digital Hierarchy (SDH), March 1999, (3) Bellcore, Generic Requirements GR-1377-Core: SONET OC-192 Transport System Genetic Criteria, December 1998) define measurements of jitter tolerance, jitter generation and jitter transfer function.

Therefore, VLSIs for serial communication have to satisfy the values described in the above specifications. Especially, in the jitter tolerance measurement of a deserializer, (a) a sinusoidal jitter is added to zero-crossings of an input bit stream, then (b) the deserializer samples the serial bit stream at times in the vicinity of decision boundaries (sampling instants) and outputs the serial bit stream as parallel data. (c) one port is connected to a Bit Error Rate Tester and its error rate is calculated. (d) This decision boundary or sampling instant has to be obtained from a recovered clock or a clock extracted from the data stream, in which the zero-crossings have jitter. Thus, it is apparent from the above that the jitter tolerance measurement is one of the most difficult measurements.

First, a conventional measuring apparatus that measures a jitter transfer function of the device under test is described. FIG. 74 explains a case of measuring the jitter transfer function by using a network analyzer. The network analyzer measures the jitter transfer function of the deserializer as the device under test. A signal generator generates a sinewave (reference carrier) having frequency f_{a }supplied to the deserializer. The network analyzer phase modulates the reference carrier by a sinusoid having f_{b}. The modulated carrier clocks a pulse pattern generator. The pulse pattern generator supplies a bit stream to the deserializer.

The deserializer performs serial-parallel conversion for input serial bit stream so as to output the converted data as recovered data of a plurality of bits. The data clock of the pattern is subjected to phase modulation by the sinusoidal wave supplied from the network analyzer.

A recovered clock in the recovered data output from the deserializer is compared to a reference clock in phase by being mixed with the reference clock.

The network analyzer measures the jitter transfer function of the deserializer based on phase noise spectra in the digital signal input to the deserializer and phase noise spectra in the recovered data. In a case of measuring the jitter transfer function based on a ratio of the phase noise spectra, however, the phase noises in a region other than the edges of the waveform are included. These phase noises prevent the high-precision measurement of the jitter transfer function.

FIG. 75 explains a case of measuring the jitter transfer function of the deserializer by means of a jitter analyzer. The jitter analyzer generates a clock having a predetermined frequency. A synthesizer modulates this clock. A clock source supplies the clock phase modulated by the sinusoid generated by the synthesizer to a pattern generator. The pattern generator supplies data and clock to the deserializer in accordance with the received clock. The deserializer outputs output data and recovered clock in accordance with the received data. The jitter analyzer receives the input clock and the output recovered clock of the deserializer and samples the input clock and output recovered clock. Note that the band-pass filter eliminates both clock and high frequency jitter components (e.g. see Recommendation G.825).

Next, discuss the measurement problem associated with periodic sampling. The jitter analyzer samples one sample per M periods of the input data. The jitter analyzer also performs each sampling at a timing shifted by a small phase. That is, assuming the period of the input data to be T, the sampling period of the jitter analyzer is MT+T_{ES}. Since both the input data and the output data are periodic waveforms having a period of multiples of T, the result of the sampling are substantially equivalent to that obtained in a case of sampling at a sampling period T_{ES}.

The jitter analyzer calculates a ratio of the instantaneous phase spectra of the input data to the instantaneous phase spectra of the output data based on the sampling result and then measures the jitter transfer function of the deserializer based on the thus calculated spectra ratio. However, the jitter analyzer performs the sampling at the sampling period of MT+T_{ES }and extracts data equivalent to the data of one period. Thus, it takes long time to measure the jitter transfer function.

Moreover, the jitter analyzer generates the waveform equivalent to one period data from approximately MT/T_{ES }samples. Therefore, it is difficult to measure the fluctuation of the period between adjacent edges in the waveform of the input data or the output data. The period fluctuation in the waveform generated by the sampling is a mean value of the period fluctuations between the adjacent edges in M periods of the input data or the output data. Therefore, the jitter analyzer cannot precisely measure the instantaneous phases of the input data and the output data, so that it is difficult to precisely measure the jitter transfer function.

Next, a conventional method for measuring the bit error rate and a conventional method for measuring the jitter tolerance are described. According to an eye-diagram measurement, the performance of the communication device can be tested easily. FIG. 76 shows an eye diagram. The horizontal eye opening provides a peak-to-peak value of the timing jitter, while the vertical eye opening provides noise immunity or a signal-to-noise ratio (Edward A. Lee and David G. Messerschmitt, Digital Communication, 2nd ed., pp. 192, Kluwer Academic Publishers, 1994). In the measurement of the jitter tolerance, however, the zero-crossings of an input bit stream are caused to fluctuate by the timing jitter having a peak-to-peak value of 1 UI (Unit Interval, 1 UI is equal to the bit period T_{b}) or more. (For example, Recommendation (1) defines 1.5 UI_{PP}.) As a result, the eye-diagram measurement can measure only a closed eye pattern. Therefore, it is found that the eye diagram cannot be applied to the jitter tolerance measurement.

The jitter tolerance measurement is an extension of the bit error rate test. FIG. 77 shows the arrangement of the jitter tolerance measurement of the deserializer. The deserializer performs serial-parallel conversion for the input serial bit stream, and outputs the resultant data as, for example, 16-bit recovered data. The instantaneous phase Δθ[nT] of the input bit stream to the deserializer to be measured is made to fluctuate by the sinusoidal jitter. Please note that T is a data rate. A bit error rate tester delays the output recovered clock with an appropriate time delay so as to obtain the optimum timing instants, and samples the output recovered data at those instants. By comparing the sampled values of the recovered data and expected values corresponding thereto, the bit error rate of the deserialized data is obtained. However, since the output recovered clock is extracted from the serial bit stream in which edges fluctuate, it becomes difficult to sample the output recovered data at the optimum sampling instants under the condition of the large amplitude of the applied jitter. On the other hand, according to the method in which the clock is extracted from the recovered data stream, the bit error rate tester has to include a high-performance clock recovery unit. This is because the clock recovery unit, which has larger jitter tolerance than that of the clock recovery unit included in the deserializer under test, is required for measuring the jitter tolerance of the deserializer under test. In other words, in the jitter tolerance measurement using the bit error rate tester, it is likely to underestimate the jitter tolerance. Therefore, in order to perform the measurement with excellent repeatability, high measurement skill or know-how is required.

Moreover, in the jitter tolerance measurement, while the applied jitter amount is increased with the jitter frequency ƒ_{J }fixed, the minimum applied jitter amount that causes the occurrence of the bit error is obtained. For example, in order to perform the bit error rate test for a 2.5 Gbps serial communication device by using a pseudo-random binary sequence having a pattern length of 2^{23}-1, the test time of 1 sec is required. Therefore, in order to measure the jitter tolerance by changing the jitter amplitude to be supplied 20 times, the test time of 20 sec is required.

Timing degradation of the input bit stream as well as amplitude degradation increases the bit error rate. The timing degradation corresponds to the horizontal eye opening in the eye-diagram measurement, while the amplitude degradation corresponds to the vertical eye opening. Therefore, by measuring the degrees of the timing degradation and amplitude degradation, the bit error rate can be calculated. Please note that the jitter tolerance measurement corresponds to the horizontal eye opening in the eye-diagram measurement. For example, degradation of the amplitude of the received signal of ΔA=10% corresponds to the reduction of the signal-to-noise ratio of 20 log 10(100-10)/100=0.9 dB Therefore, the bit error rate increases by 0.9 dB. As for the timing degradation ΔT, the similar calculation can be performed. Please note that the % value of the ratio and the dB value are relative values, not absolute values. In order to obtain an accurate value of the bit error rate, calibration is required. Here, the definition of ΔA and ΔT by J. E. Gersbach (John E. Gersbach, Ilya I. Novof, Joseph K. Lee, “Fast Communication Link Bit Error Rate Estimator,” U.S. Pat. No. 5,418,789, May 23, 1995) is used. The apparatus disclosed in the above patent uses the following equation

to calculate an instantaneous bit error rate from ΔA, ΔT, a local clock period T and the maximum value A of the samples at the optimum sampling instants. However, the aforementioned apparatus merely provides a method for estimating the bit error rate by measuring the timing degradation by a Gaussian noise jitter. The apparatus described in the aforementioned patent obtains a histogram of data edges, performs a threshold operation and obtains ΔT. This operation is effective to the Gaussian noise jitter having a single peak. The sinusoidal jitter used in the jitter tolerance test has two peaks at both ends of the distribution. Therefore, ΔT cannot be obtained only by performing the simple threshold operation. Moreover, in the jitter tolerance measurement, the zero-crossings are caused to fluctuate by the timing jitter of 1 UI_{PP }or more. As a result, the histogram has the distribution in which the probability density functions of adjacent edges overlap each other. From such a histogram, it is difficult to obtain ΔT. It is known that this histogram operation cannot secure a sufficient measurement precision unless about 10000 samples or more are obtained (T. J. Yamaguchi, M. Soma, D. Halter, J. Nissen, R. Raina, M. Ishida, and T. Watanabe, “Jitter Measurements of a PowerPC™ Microprocessor Using an Analytic Signal Method,” Proc. IEEE International Test Conference, Atlantic City, N.J., Oct. 3-5, 2000). Therefore, it is hard to reduce the measurement time. Moreover, K in the above equation does not have an ideal value. Therefore, by calibrating the instantaneous bit error rate with the actual bit error rate, the initial value for K has to be given. Also, a correction value ΔK has to be calculated from the difference between the long-term mean value of the instantaneous bit error rate and the actual bit error rate. Therefore, the conventional apparatus is poor in efficiency, requiring the longer test time.

Therefore, it is an object of the present invention to provide a measuring apparatus and a measuring method which are capable of overcoming the above drawbacks accompanying the conventional art. The above and other objects can be achieved by combinations described in the independent claims. The dependent claims define further advantageous and exemplary combinations of the present invention.

To solve the foregoing problem, according to a first aspect of the present invention, there is provided a measuring apparatus for measuring reliability against jitter of an electronic device, including: a jitter tolerance estimator operable to estimate a jitter tolerance of a system including a transmission line and an electronic device based on the output signal output from the electronic device in response to an input signal input through a predetermined transmission line; a jitter tolerance degradation quantity estimator operable to estimate a quantity of jitter tolerance degradation which deteriorates by the deterministic jitter caused in the input signal by transmission through the transmission line based on the input signal, and a device jitter tolerance estimator operable to estimate a jitter tolerance of the electronic device by correcting the jitter tolerance of the system estimated by the jitter tolerance estimator based on the quantity of jitter tolerance degradation estimated by the jitter tolerance degradation quantity estimator.

The measuring apparatus may further include: a timing jitter estimator operable to estimate an output timing jitter sequence of the output signal based on the output signal; and a jitter transfer function measuring apparatus operable to measure the jitter transfer function in the electronic device based on the output timing jitter sequence, where the jitter tolerance estimator may estimate a jitter tolerance of the system based on a gain of the jitter transfer function.

The jitter tolerance estimator may estimate a jitter tolerance of the system further based on a phase of the jitter transfer function.

The measuring apparatus may further include: a timing jitter estimator operable to estimate an output timing jitter sequence of the output signal based on the output signal; and a jitter distortion estimator operable to estimate a jitter distortion of a timing jitter of the output signal based on the output timing jitter sequence, where the jitter tolerance estimator may estimate a jitter tolerance of the system based on the jitter distortion.

The jitter distortion estimator may estimate the jitter distortion based on a spectrum of a timing jitter of the output signal.

The timing jitter estimator may include: an instantaneous phase noise estimator operable to calculate an instantaneous phase noise of the output signal based on the output signal; and a resampler operable to generate the output timing jitter sequence obtained by resampling the instantaneous phase noise at predetermined timings.

The instantaneous phase noise estimator may include: an analytic signal transformer operable to transform the output signal to a complex analytic signal; an instantaneous phase estimator operable to estimate an instantaneous phase of the analytic signal based on the analytic signal; a linear instantaneous phase estimator operable to estimate a linear instantaneous phase of the output signal based on an instantaneous phase of the analytic signal; and a linear trend remover operable to calculate an instantaneous phase noise obtained by removing the linear instantaneous phase from the instantaneous phase based on the instantaneous phase and the linear instantaneous phase.

The timing jitter estimator may includes: a period jitter estimator operable to estimate a period jitter sequence of the output signal; an ideal edge timing estimator operable to estimate average period of the period jitter sequence; and an edge timing error estimation unit operable to estimate the output timing jitter sequence based on the average period of the period jitter sequence and the period jitter sequence.

The measuring apparatus may further include an input signal generating unit operable to generate the input signal to which a plurality of timing jitters are applied, wherein frequencies of the timing jitters are different from one another.

The measuring apparatus may further include a bit error rate estimator operable to detect a bit error rate of the output signal based on the output signal of the electronic device, wherein the input signal generating unit sequentially inputs the plurality of input signals on which the timing jitters are applied into the electronic device, wherein the amplitudes of the timing jitters are different from one another, and the jitter tolerance estimator estimates a peak-to-peak value of the timing jitter, in which the bit error rate estimator does not detect a bit error of the output signal, as the jitter tolerance.

The jitter tolerance estimator may receive the recovered clock signal output from the electronic device in response to the input signal as the output signal, and may estimate thee jitter tolerance of the system based on the recovered clock signal.

According to a second aspect of the present invention, there is provided a measuring apparatus for measuring reliability against jitter of an electronic device, including: a jitter tolerance estimator operable to estimate a jitter tolerance of an electronic device based on the output signal output from the electronic device according to the input signal input through the transmission line of which the transmission length is shorter than predetermined length, and does not cause a deterministic jitter; a jitter tolerance degradation quantity estimator operable to estimate a quantity of jitter tolerance degradation which deteriorates by the deterministic jitter caused in the input signal by transmission through a long transmission line when an input signal is input into the electronic device through the long transmission line longer than the transmission line and does cause a deterministic jitter; and a system jitter tolerance estimator operable to estimate the jitter tolerance of the system including a long transmission line and an electronic device based on the jitter tolerance of the electronic device and also based on the quantity of degradation of jitter tolerance.

The summary of the invention does not necessarily describe all necessary features of the present invention. The present invention may also be a sub-combination of the features described above.

FIG. 1 illustrates an exemplary structure of a measuring apparatus **100** according to the present invention.

FIG. 2 is a flowchart showing an exemplary measuring method according to the present invention.

FIG. 3 shows an exemplary structure of the jitter transfer function measuring apparatus **101**.

FIG. 4 is a flowchart of an example of jitter transfer function estimation step S**201**.

FIG. 5 illustrates another exemplary structure of the jitter transfer function measuring apparatus **101**.

FIG. 6 is a flowchart of another example of jitter transfer function estimation step S**201**.

FIG. 7 shows a flow chart of an example of jitter transfer function estimation step S**223**.

FIG. 8 shows an example of the relationship between the input timing jitter value and the output timing jitter value.

FIG. 9 shows an example of the structure of the timing jitter estimator **501**.

FIG. 10 is a flowchart of an example of step of timing jitter estimation S**221**.

FIG. 11 shows an example of the output signal x(t) output from the DUT.

FIG. 12 shows an example of the analytic signal z(t) generated by the analytic signal transformer **701**.

FIG. 13 shows an example of the instantaneous phase φ(t) calculated by the instantaneous phase estimator **702**.

FIG. 14 shows an example of the unwrapped instantaneous phase φ(t).

FIG. 15 shows an example of the instantaneous linear phase φ(t).

FIG. 16 shows an example of the instantaneous phase noise Δφ(t).

FIG. 17 shows an example of the timing jitter sequence Δφ[n].

FIG. 18 shows an exemplary real part of the analytic signal z(t).

FIG. 19 shows an example of the bit error rate calculated by the bit error rate estimator **102**.

FIG. 20 shows the alignment jitter in the worst case.

FIG. 21 shows an exemplary relationship between the frequency of the input timing jitter and the jitter tolerance.

FIG. 22 shows an example of the phase noise spectra.

FIG. 23 shows another example of the structure of the timing jitter estimator **501**.

FIG. 24 is a flowchart showing an example of step of timing estimation S**221**.

FIG. 25 shows an example of the signal received by the timing jitter estimator **501**.

FIG. 26 shows an example of the signal from which the amplitude modulation components have been removed.

FIG. 27 shows still example of the other structure of the timing jitter estimator **501**.

FIG. 28 is a flowchart showing another example of step of timing estimation S**221**.

FIG. 29 shows another example of the structure of the timing jitter estimator **501**.

FIG. 30 is a flowchart showing another example of the timing jitter estimation S**221**.

FIG. 31 shows an exemplary structure of the analytic signal transformer **701**.

FIG. 32 is a flowchart showing an example of analytic signal transforming step S**801**.

FIG. 33 shows another exemplary structure of the analytic signal transformer **701**.

FIG. 34 is a flow chart showing another example of analytic signal transforming step S**801**.

FIG. 35 shows an example of the signal received by the analytic signal transformer **701**.

FIG. 36 shows an example of the signal X(f) in frequency domain.

FIG. 37 shows a signal Z (f) in frequency domain of which the bandwidth was limited.

FIG. 38 shows the analytic signal z(t) for which the bandwidth was limited.

FIG. 39 shows another example of the structure of the analytic signal transformer **701**.

FIG. 40 is a flowchart of another example of analytic signal transforming step S**801**.

FIG. 41 shows a flowchart of an example of phase difference estimation step S**2301** described referring to FIG. 7.

FIG. 42 is a flowchart of another example of phase difference estimation step S**2301** described referring to FIG. 7.

FIG. 43 illustrates another exemplary measuring apparatus **100**.

FIG. 44 is a flow chart of another example of the measuring method according to the present invention.

FIG. 45 illustrates another exemplary measuring apparatus **100**.

FIG. 46 is a flow chart of another example of the measuring method according to the present invention.

FIG. 47 shows an exemplary structure of the DUT.

FIG. 48 illustrates another exemplary measuring apparatus **100**.

FIG. 49 shows exemplary input and output signals.

FIG. 50 is a flow chart of another example of the measuring method according to the present invention.

FIG. 51 illustrates an exemplary structure of the timing estimator **3100**.

FIG. 52 is a flowchart of an example of timing estimation step S**3201**.

FIG. 53 shows an example of the ideal and actual signals of the output signal.

FIG. 54 shows the test time of the measuring apparatus **100** and that of a conventional bit error rate measuring apparatus.

FIG. 55 shows an exemplary relationship between the number of times the applied jitter amount was changed and the measured jitter tolerance in the measuring apparatus **100**.

FIG. 56 illustrates another exemplary measuring apparatus **100**.

FIG. 57 illustrates examples of pattern data generated by a pattern generator **4012**.

FIG. 58 illustrates another exemplary structure of the timing jitter estimator **501** of the jitter transfer function measuring apparatus **101**.

FIG. 59 is a flowchart showing another example of step of the timing jitter estimation S**221**.

FIG. 60 is an example of a curve of bit error rate.

FIG. 61 is an exemplary measurement of the jitter tolerance.

FIG. 62 is another exemplary structure of a jitter tolerance measuring apparatus as an example of the measuring apparatus **100**.

FIG. 63 is a flowchart showing an example of measuring method for measuring DUT **3000**.

FIG. 64 is an exemplary measurement of the jitter tolerance.

FIG. 65 is an exemplary structure of a jitter distortion estimator **4100**.

FIG. 66 is another exemplary measurement of the jitter tolerance.

FIG. 67 is another example of jitter spectrum of an output timing jitter of an output signal which is to be output from the DUT **3000** in a case where a sinusoidal jitter is applied to the input signal.

FIG. 68 is a jitter histogram of the output timing jitter in a case where amplitude of the sinusoidal jitter, applied to the input signal, is in linear domain, described referring to FIG. 64.

FIG. 69 is a jitter histogram of the output timing jitter in a case where amplitude of the sinusoidal jitter, applied to the input signal, is in nonlinear domain, described referring to FIG. 64.

FIG. 70 is another exemplary structure of a jitter tolerance measuring apparatus as an example of the measuring apparatus **100**.

FIG. 71 shows yet another example of a configuration of the measuring apparatus **100**.

FIG. 72 shows an example of a configuration of a jitter tolerance degradation quantity estimator **390**.

FIG. 73 shows an example of an operation of the measuring apparatus **100**.

FIG. 74 explains a case of measuring the jitter transfer function by using a network analyzer.

FIG. 75 explains a case of measuring the jitter transfer function of the deserializer by means of a jitter analyzer.

FIG. 76 shows an eye diagram.

FIG. 77 shows the arrangement of the jitter tolerance measurement of the deserializer.

The invention will now be described based on the preferred embodiments, which do not intend to limit the scope of the present invention, but exemplify the invention. All of the features and the combinations thereof described in the embodiment are not necessarily essential to the invention.

FIG. 1 illustrates an exemplary structure of a measuring apparatus **100** according to the present invention. The measuring apparatus **100** calculates a bit error rate of a circuit, electronic device or system under test (hereinafter, simply referred to as DUT). The measuring apparatus **100** includes a jitter transfer function measuring apparatus **101** operable to measure jitter transfer function of the DUT, and a bit error rate estimator **102** operable to estimate the bit error rate of the DUT based on the jitter transfer function measured by the jitter transfer function measuring apparatus **101**. The bit error rate estimator **102** estimates the bit error rate of the DUT based on the gain of the jitter transfer function, for example. The bit error rate estimator **102** may estimate the bit error rate of the DUT further based on the phase of the jitter transfer function or further based on the internal noise of the DUT.

FIG. 2 is a flowchart showing an exemplary measuring method according to the present invention. First, the jitter transfer function of the DUT is estimated in jitter transfer function estimation step S**201**. Step S**201** has the same or similar function as/to the jitter transfer function measuring apparatus **101** described referring to FIG. 1. Step S**201** may be performed by using the jitter transfer function measuring apparatus **101**. Then, the bit error rate of the DUT is estimated based on the jitter transfer function of the DUT in bit error rate estimation step S**202**. Step S**202** has the same or similar function as/to the bit error rate estimator **102** described referring to FIG. 1. Step S**202** may be performed by using the bit error rate estimator **102**.

FIG. 3 shows an exemplary structure of the jitter transfer function measuring apparatus **101**. The jitter transfer function measuring apparatus **101** includes a timing jitter estimator **501** that calculates an output timing jitter sequence indicating the output timing jitter of an output signal output from the DUT in response to an input signal input to the DUT, and a jitter transfer function estimator **103** that calculates the jitter transfer function of the DUT based on the output timing jitter sequence. The timing jitter estimator **501** may receive a recovered clock signal corresponding to the output signal of the DUT, as the output signal of the DUT. The details of the timing jitter estimator **501** are described later. Moreover, the timing jitter estimator **501** may calculate an output instantaneous phase noise of the output signal based on the output signal. Even in this case, the jitter transfer function measuring apparatus **101** can calculate the jitter transfer function using the output instantaneous phase noise instead of the output timing jitter sequence.

Moreover, the jitter transfer function estimator **103** has the jitter gain estimator **502** that estimates the gain of the jitter transfer function based on the output timing jitter sequence. In this example, the bit error rate estimator **102** calculates the bit error rate of the DUT based on the gain of the jitter transfer function. A method for calculating the gain of the jitter transfer function is described later.

The jitter gain estimator **502** estimates the gain of the jitter transfer function of the DUT based on a timing jitter in the input signal and a timing jitter in the output signal. The jitter gain estimator **502**, for example, receives information indicative of the input timing jitter in the input signal, and the output timing jitter sequence calculated by the timing jitter estimator **501**.

The jitter gain estimator **502** estimates the gain of the jitter transfer function of the DUT based on the received information indicative of the input timing jitter and the thus estimated output timing jitter sequence. In this case, the jitter gain estimator **502** calculates the output timing jitter value from the timing jitter sequence of the output signal. For example, the jitter gain estimator **502** calculates peak values or RMS values of the output timing jitter as the output timing jitter values based on the output timing jitter sequences. Alternatively, the jitter gain estimator **502** may receive the timing jitter sequence of the input signal and the timing jitter sequence of the output signal, and estimate gain of the jitter transfer function. In this case, the jitter gain estimator **502** may calculate the input timing jitter values from the input timing jitter sequences and may calculate the output timing jitter values from the output timing jitter sequences.

FIG. 4 is a flowchart of an example of jitter transfer function estimation step S**201**. Step S**201** calculates the timing jitter sequence of the output signal in timing jitter estimation step S**221**. Step S**221** have the same or similar function as/to the timing jitter estimator **501** described referring to FIG. 3, and may be performed by the timing jitter estimator **501**. Step S**221** may calculate the timing jitter sequence of the input signal.

Then, in step of calculating a timing jitter value S**222**, the timing jitter value is calculated based on the timing jitter sequence. Step S**222** may calculate the timing jitter values based on the output timing jitter sequences, or may calculate both the timing jitter values of the output signal and the timing jitter values of the input signal based on the input timing sequences and the output timing jitter sequences. For example, step S**222** may calculate the root-mean-square value or the peak-to-peak value of the timing jitter sequence as the timing jitter value.

Then, in jitter transfer function estimation step S**223**, the jitter transfer function is calculated. Step S**223** have the same or similar function as/to the jitter transfer function estimator **103** described referring to FIG. 3, and may be performed by the jitter transfer function estimator **103**.

FIG. 5 illustrates another exemplary structure of the jitter transfer function measuring apparatus **101**. In the jitter transfer function measuring apparatus **101** of this example, the jitter transfer function estimator **103** includes the structure of that described referring to FIG. 3 and a jitter phase difference estimator **503**. Moreover, the jitter transfer function measuring apparatus **101** includes a plurality of timing jitter estimators **501**. One timing jitter estimator **501** calculates the input timing jitter sequence of the input signal, while the other timing jitter estimators **501** calculate the output timing jitter sequences.

The jitter phase difference estimator **503** calculates the phase difference between the input timing jitter and the output timing jitter based on the input timing jitter sequence and the output timing jitter sequence. That is, the jitter phase difference estimator **503** calculates the phase of the jitter transfer function. For example, the jitter phase difference estimator **503** calculates the phase of the jitter transfer function based on the following equation.

The bit error rate estimator **102** calculates the bit error rate of the DUT further based on the phase of the jitter transfer function. The method of calculating the bit error rate based on the phase of the jitter transfer function is described later.

In the measuring apparatus **100** using jitter transfer function measuring apparatus **101** of this example, the bit error rate estimator **102** calculates the bit error rate of the DUT based on the gain and phase of the jitter transfer function.

FIG. 6 is a flowchart of another example of jitter transfer function estimation step S**201**. Step S**201** calculates the input timing jitter sequence in input timing jitter sequence estimation step S**241**. Then, in step of calculating the input timing jitter value, S**242**, the input timing jitter value is calculated. Then, the output timing jitter sequence is calculated in output timing jitter sequence estimation step S**243** and thereafter the output timing jitter value is calculated in output timing jitter value calculation step S**244**. Then, in jitter transfer function estimation step S**245**, the jitter transfer function is estimated. Steps S**241** and S**243** calculate the timing jitter sequences in a similar manner to timing jitter estimation step S**221** described referring to FIG. 4. Moreover, steps S**242** and S**244** calculate the timing jitter values in a similar manner to timing jitter value calculation step S**222** described referring to FIG. 4. Furthermore, step S**245** calculates the jitter transfer function in a similar manner to jitter transfer function estimation step S**223** described referring to FIG. 4.

FIG. 7 shows a flow chart of an example of jitter transfer function estimation step S**223**. In jitter gain estimation step S**261**, the gain of the jitter transfer is calculated based on the input timing jitter sequence and the output timing jitter sequence. Step S**261** calculates the gain of the jitter transfer function by using the same or similar method as/to the jitter gain estimator **502** described in FIG. 5. Step S**261** may be performed by the jitter gain estimator **502**.

Moreover, in phase difference estimation step S**2301**, phase of the jitter transfer function is calculated based on the input timing jitter sequence and the output timing jitter sequence. Step S**2301** calculates the phase of the jitter transfer function by using the same or similar method as/to the jitter phase difference estimator **503** described in FIG. 5. Step S**2301** may be performed by the jitter phase difference estimator **503**.

Moreover, in the jitter transfer function estimation step S**223**, either of the jitter gain estimation step S**261** and the phase difference estimation step S**2301** may be performed prior to the other, or may be performed simultaneously.

FIG. 8 shows an example of the relationship between the input timing jitter value and the output timing jitter value. The jitter gain estimator **502** calculates a plurality of input timing jitter values and a plurality of output timing jitter values based on input timing jitter sequences of a plurality of input signals respectively having different jitter amounts and the output timing jitter sequence in the output signal corresponding to the respective input signal. For example, the jitter gain estimator **502** calculates the root-mean-square value or peak-to-peak value of the timing jitter sequence as the timing jitter value.

The jitter gain estimator **502** estimates the gain of the jitter transfer function. More specifically, input signals having different jitter amounts are supplied to the DUT one after another, and the jitter gain estimator **502** estimates the gain of the jitter transfer function based on the input timing jitter sequence of each input signal and the output timing jitter sequence corresponding to that input signal.

The jitter gain estimator **502** performs linear fitting for the relationship between a plurality of input timing jitter values and the output timing jitter values, as shown in FIG. **8**, and then calculates a slope of the straight line as the gain of the jitter transfer function of the DUT, given a linear relationship between the two. In the following description, the jitter transfer function of the DUT is described.

When an input instantaneous phase noise of the input signal Δθ(nT_{s}) and an output instantaneous phase noise of the output signal Δφ(nT_{s}) are transformed into the frequency domain by Fourier transform, the following phase noise spectra is obtained.

where ƒ_{J }is a jitter frequency (frequency offset from the clock frequency), and T_{S }is a sampling period.

In a case where the sampling period T_{S }is made equal to the clock period T of the clock recovery unit of the DUT and the instantaneous phase noises in the vicinity of the zero-crossings (rising edges or falling edges) are sampled, the input timing jitter Δθ[nT] and the output timing jitter Δφ[nT] are obtained. When Δθ[nT] and Δφ[nT] are transformed into the frequency domain by using Fourier transform, the following timing jitter spectra

are obtained. Since the timing jitter is wide-sense cyclostationary with a period T, the timing jitter spectra is more effective to analysis of a modulation noise source than phase noise spectra. However, when the timing jitter is made to pass through a narrow band-pass filter, the wide-sense cyclostationary signal can be transformed to a stationary signal,

ΔΘ(ƒ_{J})≈ΔΘ[ƒ_{J}] (5)

ΔΦ(ƒ_{J})≈Δφ[ƒ_{J}] (6)

are satisfied. That is, by using the narrow band-pass filter, sampling jitter signal at its zero-crossings (i.e., the time-dependent operation associated with the wide-sense cyclostationary signal) can be avoided.

The jitter transfer function of the DUT is defined as follows:

The jitter transfer function is given as a frequency response function of a constant-parameter linear system. The output timing jitter spectra of the clock recovery unit of the DUT is represented by using the jitter transfer function as follows:

ΔΦ[ƒ_{J}*]=H*_{J}(ƒ_{J})ΔΘ[ƒ_{J}] (10)

From the assumption of the linearity, a peak-to-peak value of the input timing jitter is also amplified by the gain of the jitter transfer function, so that the resultant value is given as a peak-to-peak value of the output timing jitter. Next, a method for measuring the gain of the jitter transfer function in frequency domain and time domain is discussed.

When |ΔΘ(ƒ_{J})| is not zero, the gains corresponding to the peak jitter and the RMS jitter can be estimated in frequency domain by the following equations, respectively.

Since the jitter transfer function is given as the frequency response function of the constant-parameter linear system, the jitter transfer function is not a function of the applied input amplitude. Based on this fact, the procedure in which the jitter transfer function is estimated in time domain is described. First, the peak-to-peak value of the input timing jitter is set in a segment in which the operation of the DUT is linear, and then the input/output relationship between Δθ[nT] and Δφ[nT] are measured for plural times. Thereafter, the input/output relationship between Δθ[nT] and Δφ[nT] shown in FIG. 8 is subjected to a least squares fit of a straight line. The gains of the jitter transfer function are estimated from the slope of the straight line.

Please note that the worst-case value in a certain time period corresponds to the peak-to-peak value (the peak value in frequency domain).

From the assumption of the linearity, a peak-to-peak value of the input jitter is amplified by the gain |H_{j}(ƒ_{J})| of the jitter transfer function, so as to provide a peak-to-peak value of the timing jitter of the recovered clock. The jitter transfer function can be estimated from a ratio of the peak values or mean values of the input and output jitters. Next, a method for measuring the gain of the jitter transfer function in frequency domain and time domain is discussed.

When |ΔΘ(ƒ_{J})| is not zero, the gain of the jitter transfer function can be estimated in frequency domain from the peak values or mean values of the timing jitter spectra (phase noise spectra) as follows:

Since the jitter transfer function is given as the frequency response function of the constant-parameter linear system, the jitter transfer function is not a function of the applied input amplitude to the system. Based on this fact, the procedure in which the jitter transfer function is estimated in time domain is described. First, the peak-to-peak value of the input timing jitter is set in a region in which the operation of the clock recovery device under test is a linear operation, and then the input/output relationship between Δθ[nT] and Δφ[nT] are measured for plural times. Thereafter, when the input/output relationship of the peak-to-peak jitter or the RMS jitter between Δθ[nT] and Δφ[nT] is subjected to linear fitting, as shown in FIG. 8, the gain of the jitter transfer function is obtained from the slope of the line as follows:

For example, in order to obtain the gain of the jitter transfer function by linear fitting, the measuring apparatus **100** may measure the input/output relationship between the input timing jitter sequence Δθ[nT] and the output timing jitter sequence Δφ[nT] about four times.

FIG. 9 illustrates an exemplary structure of the timing jitter estimator **501**. The timing jitter estimator **501** includes the instantaneous phase noise estimator **700** and the resampler **901**. The instantaneous phase noise estimator **700** includes an analytic signal transformer **701** that transforms the received signal to an analytic signal, that is a complex signal, an instantaneous phase estimator **702** that estimates the instantaneous phase of the analytic signal based on the analytic signal, a linear phase estimator **703** that estimates an instantaneous linear phase of the signal received by the analytic signal transformer **701** based on the instantaneous phase of the analytic signal, and a linear trend remover **704** that calculates an instantaneous phase noise by removing the linear instantaneous phase from the instantaneous phase based on the instantaneous phase and the linear instantaneous phase. The instantaneous phase noise estimator **700** may calculate the instantaneous phase noise in the output signal of the DUT, or may calculate both the instantaneous phase noise in the output signal of the DUT and the instantaneous phase noise in the input signal to the DUT. The timing jitter estimator **501** may calculate the output timing jitter in the output signal of the DUT, or may calculate the output timing jitter sequence in the output signal of the DUT and the input timing jitter sequence in the input signal to the DUT. Moreover, the analytic signal transformer **701** may generate the analytic signal based on predetermined frequency components of the received signal.

Referring to FIGS. 16 and 17, the resampler **901** outputs the timing jitter sequence that was obtained by sampling of the instantaneous phase noise generated by the linear trend remover **704** at the zero-crossing timings. By sampling the instantaneous phase noise at the zero-cross timings, the phase noise at the edges of the signal can be detected. Thus, the gain of the jitter transfer function can be calculated with high precision.

FIG. 10 is a flowchart of an example of step of timing jitter estimation S**221**. Timing jitter estimation step S**221** transforms the signal received to the analytic signal in analytic signal transforming step S**801**. Step S**801** performs the transform in a similar manner to the analytic transformer **701** described referring to FIG. 9. Step S**801** may be performed by using the analytic signal transformer **701**.

Next, step of instantaneous phase estimation S**802** estimates the instantaneous phase of the analytic signal. Step S**802** performs the estimation in the similar manner to the instantaneous phase estimator **702** described referring to FIG. 9, and may be performed by using the instantaneous phase estimator **702**.

Next, step of linear instantaneous phase estimator S**803** estimates the linear component of the instantaneous phase of the signal received in step S**801**. Step S**803** estimates the linear component of the instantaneous phase of the received signal in a similar manner to the linear phase estimator **703** described referring to FIG. 9. Step S**803** may be performed by using the linear phase estimator **703**.

Next, linear trend removal step S**804** removes the linear component from the instantaneous phase so as to calculate the instantaneous phase noise. Step S**804** performs the calculation in a similar manner to the linear trend remover **704** described referring to FIG. 9. Step S**804** may be performed by using the linear trend remover **704**.

Next, Resampling step S**1001** generates the timing jitter sequence obtained by sampling of the instantaneous phase noise. Step S**1001** generates the timing jitter sequence in a similar manner to that of the resampler **901** described referring to FIG. 9. Moreover, step S**1001** may be performed by using the resampler **901**.

FIG. 11 shows an example of the output signal x(t) output from the DUT. In the present example, the timing jitter estimator **501** estimates the output timing jitter sequence of the output signal. The output signal is jittery. The analytic signal transformer **701** transforms the output signal to a complex analytic signal. In this example, the analytic signal transformer **701** performs such transform by using Hilbert transform that is described later.

FIG. 12 shows an example of the analytic signal z(t) generated by the analytic signal transformer **701** which generates an analytic signal having a real part and an imaginary part by using Hilbert transform. In FIG. 12, the real part of the analytic signal is shown with a solid line while the imaginary part is shown with a broken line. The instantaneous phase estimator **702** calculates the instantaneous phase of the analytic signal. The details of the calculation of the instantaneous phase are described later.

FIG. 13 shows an example of the instantaneous phase φ(t) calculated by the instantaneous phase estimator **702**. The instantaneous phase estimator **702** unwraps the instantaneous phases to remove discontinuities from it and get a continuous phase.

FIG. 14 shows an example of the unwrapped instantaneous phase φ(t). The linear phase estimator **703** calculates the linear component of the instantaneous phase of the signal received by the timing jitter estimator **501**, based on the unwrapped instantaneous phase. The linear phase estimator **703** performs a least squares fit of a straight line to the unwrapped instantaneous phase to get the linear instantaneous phase.

FIG. 15 shows an example of the instantaneous linear phase φ(t). The linear trend remover **704** calculates the instantaneous phase noise by removing the linear component from the unwrapped instantaneous phase. That is, the linear trend remover **704** calculates the difference between the unwrapped instantaneous phase shown in FIG. 14 and that of the instantaneous linear phase shown in FIG. 15 as the instantaneous phase noise.

FIG. 16 shows an example of the instantaneous phase noise Δφ(t). The resampler **901** calculates the timing jitter values of the signal received by the timing jitter estimator **501** based on the instantaneous phase noise. The resampler **901** performs sampling of the instantaneous phase noise waveform Δφ(t) at the closest timings to the respective zero-crossings of the real part x(t) of the analytic signal z(t), that are called as approximated zero-crossing timings, so as to calculate the instantaneous phase noise at the zero-crossing timing nT_{0}, i.e., the timing jitter sequence Δφ[n](=Δφ(nT_{0})). By estimating the gain of the jitter transfer function from timing jitter sequences (the instantaneous phase noises at the zero-cross timings), the gain of the jitter transfer function can be calculated precisely.

FIG. 17 shows an example of the timing jitter sequence Δφ[n]. The jitter gain estimator **502** calculates the RMS value and peak-to-peak value of the timing jitter based on the timing jitter sequence. The RMS timing jitter Δφ_{RMS }is the mean square value of the timing jitter sequence Δφ[n] and is calculated by the jitter gain estimator **502** in accordance with the following equation.

N is the number of samples of the timing jitter that were measured. On the other hand, the peak-to-peak timing jitter Δφ_{PP }is the difference between the maximum value and the minimum value of Δφ[n] and is calculated by the jitter gain estimator **502** based on the following equation.

Next, the detection of the zero-crossings is described.

FIG. 18 shows an exemplary real part of the analytic signal z(t). First, where the maximum value and the minimum value of the real part of the analytic signal of the input signal to be measured is assumed to be 100% level and 0% level, respectively. Thus a 50% level value V_{50% }can be calculated. Then, the difference between each of the adjacent sampled values of the real part of the analytic signal and the 50% level value V_{50%}, (x(j−1)−V_{50%}) and (x(j)−V_{50%}) is obtained, and thereafter the product of the thus obtained values, (x(j−1)−V_{50%})×(x(j)−V_{50%}) is calculated. When x(t) crosses the 50% level, that is, the zero-crossing level, the signs of the adjacent sampled values (x(j−1)−V_{50%}) and (x(j)−V_{50%}) change from negative to positive or from positive to negative. Thus, when the above product value is negative, it is determined that x(t) has crossed the zero-crossing level. Therefore, the time j−1 or j that corresponds to one of the sampled values (x(j−1)−V_{50%}) and (x(j)−V_{50%}). Thus, x(j−1) or x(j) that has the smaller absolute value than the other is determined as the approximated zero-crossing. In FIG. 18, circles respectively represent the closest points to the rising zero-crossings, i.e., the approximated zero-crossings, that were detected.

The jitter gain estimator **502** described referring to FIG. 3 calculates the gain of the jitter transfer function of the above-described DUT based on the RMS value or the peak-to-peak value of the input and output timing jitter described above. Moreover, jitter phase difference estimator **503** described referring to FIG. 5 calculates the phase of the jitter transfer function of the above-described DUT from the input timing jitter sequence and the output timing jitter sequence. Next, the calculation of the bit error rate, which the bit error rate estimator **102** described referring to FIG. 1 calculates based on the gain of the jitter transfer function, is described.

FIG. 19 shows an example of the bit error rate calculated by the bit error rate estimator **102**. In FIG. 19, the horizontal axis represents the peak-to-peak value of the input timing jitter while the vertical axis represents the bit error rate. In the shown example, a sinusoidal jitter is used to fluctuate the clock of the input bit stream to be supplied to the DUT.

The instantaneous phase Δθ[nT] of the bit clock is modulated by a sine wave cos (2πƒ_{PM}t). The data stream input to the DUT has the following timing jitter.

Δθ[*nT]=K*_{i }cos(2πƒ_{PM}*t*)|_{t=nT} (21)

In this equation, 2K_{i }is the peak-to-peak value of the input jitter, while ƒ_{PM }is the phase modulation frequency. When the sinusoidal jitter that is sufficiently larger than the internal jitter generated by the DUT itself is applied to the DUT, the output timing of the recovered clock becomes

Δφ[*nT]=K*_{i}*|H*_{J}(ƒ_{PM})|exp(−*j<H*_{J}(ƒ_{PM}))cos(2πƒ_{PM}*t*)|_{t=nT} (22)

Where H_{J}(ƒ_{PM}) is the jitter transfer function of the DUT. The DUT has a clock recovery unit, and H_{J}(ƒ_{PM}) corresponds to the jitter transfer function of the clock recovery unit. From Equations (21) and (22), the peak-to-peak values of the sinusoidal jitter are bounded, namely,

Δθ_{PP}<M_{1}, Δφ_{PP}<M_{2} (23)

The jitter frequency ƒ_{J }is represented by the phase modulation frequency ƒ_{PM}.

ƒ_{J}=ƒ_{PM} (24)

Thus, the worst-case value and the mean value of the peak jitter at the jitter frequency ƒ_{J }are obtained as follows:

Moreover, the peak-to-peak jitter value and the RMS value in time domain are obtained as follows:

Δφ_{PP}=max{(Worst[|ΔΦ[ƒ_{J}]^{2}])^{0.5 }exp(*j*2πƒ_{J}*k*)}−min{(Worst[|ΔΦ[ƒ_{J}]^{2}])^{0.5 }exp(*j*2πƒ_{J}*k*)} (27)

σ_{Δφ}=√{square root over (1*/L*{(mean[|ΔΦ[ƒ_{J}]^{2}])^{0.5 }exp(*j*2πƒ_{J}*k*)
}^{2})}{square root over (1*/L*{(mean[|ΔΦ[ƒ_{J}]^{2}])^{0.5 }exp(*j*2πƒ_{J}*k*)
}^{2})} (28)

In the above equations, |X|^{2 }or (|X|^{2})^{0.5 }can be calculated as |X|. From the above equations, when the sinusoidal jitter is applied to the input signal, the sinusoidal jitter provides deterministic jitter to the DUT. Moreover, the probability density function of the sinusoidal jitter corresponds to the worst case. The details of the sinusoidal jitter are described later.

Next, a bit error rate equation is derived considering the fluctuation of the rising edges of the input data stream due to the applied input jitter. When the timings t_{zero-crossing }of the adjacent rising edges cross t_{decision}, respectively, the preceding bit or the next bit is discriminated at t_{decision}. That is, an erroneous decoding occurs. Since the probability of error for the preceding bit is equal to that for the next bit, the bit error rate is given as follows:

*BER*=ƒ(Δalign_{PP})=½*P*_{e}(*t*_{decision}*<t*_{zero-crossing})+½*P*_{e}(*t*_{zero-crossing}*<t*_{decision}) (29)

For simplification, t_{decision }is regarded as the optimum sampling instant and the timing fluctuation Δφ[nT] at this optimum sampling instant can be incorporated into the fluctuation of the input data stream, Δθ[nT]. It follows that only calculating the bit error rate caused by the alignment jitter is sufficient to get the desired estimates. Moreover, due to the symmetry of sinusoidal jitter distribution, Equation (29) can be re-written as:

*BER*=ƒ(Δalign_{PP})=*P*_{e}(*t*_{decision}*<t*_{zero-crossing}) (30)

Here, an alignment jitter is described. The alignment jitter is defined by P. R. Trischitta, and represents an alignment error between the timing jitter of the input signal and the timing jitter of the output signal (recovered clock). The alignment jitter is defined by the following equation.

Δalign[*nT*]=|(Δφ[*nT]−Δθ[nT*])| (31)

Δθ[nT] is the timing jitter of the input signal to the DUT and Δφ[nT] is the timing jitter of the output signal input.

From Equation (31), when the probability density function of the alignment jitter is obtained by substituting Equations (21) and (22) for terms in Equation (31), the following equation is obtained.

Δalign[*nT]=|K*_{i}*{|H*_{J}(ƒ_{PM})|exp(−*j<H*_{J}(ƒ_{PM}))−1}cos(2πƒ_{PM}*t*)|_{t=nT} (32)

When a certain value is given as the phase modulation frequency ƒ_{PM}, K_{i}{|H_{J}(ƒ_{PM})exp(−j<H_{j}(ƒ_{PM})−1)} becomes constant. Therefore, in the case of the sinusoidal jitter input, the probability density function of the alignment jitter follows a sinusoidal distribution.

Here, X=K_{i}{|H_{J}(ƒ_{PM})|−1}. For simplification, the above sinusoidal distribution is approximated as a uniform distribution.

where X=Δφ_{P}=Δθ_{P}{|H_{J}(ƒ_{PM})|−1}.

FIG. 20 shows the alignment jitter in the worst case. The minimum input jitter 0.5 UI_{PP }makes the recovered bit swing between 0 UI and 0.5 UI. From Equation (30), the probability of error that the random variable following the uniform distribution exceeds t_{decision }is given by

The sampling instant t_{decision }should be at the center of the bit time interval or as 0.5 UI (Unit Interval). Thus, the bit error rate becomes:

The bit error rate estimator **102** may calculate the bit error rate of the DUT based on Equation (36). In other words, based on the gain H_{J}(ƒ_{PM}) of the jitter transfer function of the DUT, the relationship between the input timing jitter and the bit error rate shown in FIG. 19 can be calculated.

The measuring apparatus **100** may calculate a jitter tolerance of the DUT. Please note that the jitter tolerance means the threshold amount of the input timing jitter above which the erroneous bit decoding happens. For example, the jitter tolerance may be the minimum amount of the input timing jitter above which the bit error rate larger than zero occurs.

The bit error rate of the DUT can be calculated in accordance with Equation (36). The lower limit of the jitter tolerance is given from Equation (36) as follows:

Since |H_{J}(f_{PM})| is generally less than 1, the bit error rate and the jitter tolerance may be calculated by ||H_{J}(f_{PM})|−1|=1−|H_{J}(f_{PM})| in Equations (36) and (37).

The measuring apparatus **100** of this example calculates the bit error rate and the jitter tolerance based on the alignment errors of the input and output signals that are based on the gain of the jitter transfer function, as described associated with Equations (36) and (37). Since Equations (36) and (37) calculate the bit error rate and the jitter tolerance while considering the internal noise in the DUT to be zero, the bit error rate and the jitter tolerance represented by Equations (36) and (37) are the best-case values thereof. The measuring apparatus **100** may calculate the bit error rate and the jitter tolerance represented by Equations (36) and (37) as the best-case values of the bit error rate and jitter tolerance of the DUT or as the approximated values thereof.

The measuring apparatus **100** may calculate the bit error rate and jitter tolerance further based on the phase of the transfer function as described referring to FIG. 5. When the phase of the jitter transfer function is introduced into the bit error rate and jitter tolerance represented by Equations (36) and (37),

are obtained. The measuring apparatus **100** may calculate the bit error rate and jitter tolerance in accordance with Equations (38) and (39). Since the internal noise in the DUT is considered to be zero in Equations (38) and (39) as well as in Equations (36) and (37), the bit error rate and jitter tolerance represented by Equations (38) and (39) are also the best-case values of the bit error rate and jitter tolerance of the DUT. The measuring apparatus **100** may calculate the bit error rate and jitter tolerance represented by Equations (38) and (39) as the best-case values of the bit error rate and jitter tolerance of the DUT or as the approximated values thereof. Moreover, since

*Re*(|*H*_{J}(ƒ_{PM})|exp(−*j<H*_{J}(ƒ_{PM})))

is generally less than 1, the bit error rate and the jitter tolerance may be calculated by

∥*H*_{J}(ƒ_{PM})|exp(−*j<H*_{J}(ƒ_{PM}))−1|=1*−Re*(|*H*_{J}(ƒ_{PM})|exp(−*j<H*_{J}(ƒ_{PM})))

in Equations (38) and (39).

Moreover, the measuring apparatus **100** may calculate the bit error rate and jitter tolerance of the DUT based on the following equations.

Where β is a correction constant which indicates performance degradation of the DUT, and is given in advance by measurement etc.

Moreover, the measuring apparatus **100** may calculate the bit error rate and jitter tolerance of the DUT further based on the internal noise in the DUT. In a case where the DUT includes a PLL for generating the recovered clock and the recovered clock is received as the output signal of the DUT, for example, the measuring apparatus **100** may calculate the bit error rate and the jitter tolerance of the DUT further based on the internal nose in the PLL.

The phase noise caused by the PLL internal noise is given as follows:

|1*−H*_{J}(ƒ_{PM})exp(−*j<H*_{J}(ƒ_{PM}))|^{2}|ΔΦ(ƒ_{PM})|^{2 }(ƒ_{PM}<ƒ_{b}) (40)

ƒ_{b}=ƒ_{0}/2*Q* (41)

In the above, ƒ_{b }is the upper limit frequency of the band of the output signal of the DUT. For example, in a case where the DUT outputs the recovered clock as the output signal thereof, ƒ_{b }is the upper limit of the pass band of the PLL loop for generating that recovered clock. ƒ_{b }can be obtained from the clock frequency ƒ_{0 }in accordance with Equation (41). Alternatively, f_{b }can be obtained from the maximum value of the phase factor of the jitter transfer function.

When the term related to the phase noise in Equation (40) is added to the bit error rate represented by Equation (38), the following equation is obtained.

Therefore, the bit error rate and the lower limit of the jitter tolerance are obtained, respectively.

Note that, for ƒ_{PM}<ƒ_{b}, |H_{J}(ƒ_{PM})|≈1.0. Thus, it is found that the lower limit of the jitter tolerance below ƒ_{PM}=ƒ_{b }is degraded to about ½ of the lower limit of the jitter tolerance above ƒ_{PM}=ƒ_{b}. Moreover, since

*Re*(|*H*_{J}(ƒ_{PM})|exp(−*j<H*_{J}(ƒ_{PM})))

is generally less than 1, the bit error rate and the jitter tolerance may be calculated by

∥*H*_{J}(ƒ_{PM})|exp(−*j<H*_{J}(ƒ_{PM}))−1|=1*−Re*(|*H*_{J}(ƒ_{PM})|exp(−*j<H*_{J}(ƒ_{PM})))

in Equations (43) and (44).

The measuring apparatus **100** may calculate the bit error rate and jitter tolerance of the DUT in accordance with Equations (43) and (44). Since this calculation is further based on the internal noise in the DUT, the bit error rate and jitter tolerance of the DUT can be calculated more precisely.

As described above, the lower limit of the jitter tolerance can be obtained only from the jitter transfer function. For ƒ_{PM}<ƒ_{b}, the measurement of the jitter tolerance corresponds to a test of the effects of the phase noise. Since the jitter transfer function can be calculated simply by a computer, the bit error rate and the lower limit of the jitter tolerance can be calculated from Equations (36), (37), (38), (39), (43) and (44). Therefore, the bit error rate estimator **102** may calculate the bit error rate of the DUT in accordance with any of Equations (36), (38) and (43).

FIG. 21 shows an exemplary relationship between the frequency of the input timing jitter and the jitter tolerance. In FIG. 21, the vertical axis represents the jitter tolerance while the horizontal axis represents the frequency of the input timing jitter. Moreover, in FIG. 21, solid line shows an exemplary specification of the DUT while circles show exemplary values actually measured. The jitter tolerance in FIG. 21 corresponds to Equation (44). In addition, when the frequency of the input timing jitter is high, the jitter tolerances calculated in accordance with Equations (39) and (44) are equal to each other. Furthermore, when the frequency of the input timing jitter is higher, Equation (44) approximates to Equation (37). On the other hand, the frequency region of ƒ_{PM}<ƒ_{b }in Equation (44) corresponds to a slope region on the low-frequency side in FIG. 21.

FIG. 22 shows an example of the phase noise spectra. The slope of the phase noise spectra shown in FIG. 22 corresponds to the slope of the jitter tolerance shown in FIG. 21. From FIGS. 21 and 22, the phase noise spectra and the jitter tolerance have the same slope region over the low jitter frequencies.

FIG. 23 shows another example of the structure of the timing jitter estimator **501**. In FIG. 23, the components labeled with the same reference numeral as those in FIG. 9 have the same or similar functions and structures as/to those described referring to FIG. 9. The timing jitter estimator **501** in this example includes the structure of the timing jitter estimator **501** described referring to FIG. 9, and further includes a waveform clipper **1701**.

The wave form clipper **1701** removes the amplitude modulation components from the signal received by the timing jitter estimator **501**. The waveform clipper **1701** replaces the signal value that is larger than a predetermined first threshold value with the first threshold value and also replaces the signal value that is smaller than a predetermined second threshold value with the second threshold value, so as to remove the amplitude modulation component of the signal. Moreover, the timing jitter estimator **501** described in the other examples may include the waveform clipper **1701** as in the present example. Since the waveform clipper **1701** removes the amplitude modulation components from the signal, the jitter transfer function can be calculated precisely.

FIG. 24 shows another example of step of timing jitter estimation S**221**. In FIG. 24, the steps having the same reference numerals are the same or similar as/to those described referring to FIG. 10. Timing jitter estimation step S**221** in this example includes timing jitter estimation step S**221** described referring to FIG. 10 and further includes waveform clipping step S**1801**.

Waveform clipping step S**1801** removes the amplitude modulation components from the signal. Analytic signal transforming step S**801** generates an analytic signal of the signal from which the amplitude modulation components have been removed. Step S**1801** removes the amplitude modulation components in a similar manner to that of the waveform clipper **1701** described referring to FIG. 23. Moreover, step S**1801** may be performed by using the waveform clipper **1701**.

FIGS. 25 and 26 are diagrams for explaining the removal of the amplitude modulation components by the waveform clipper **1701**. FIG. 25 shows an example of the signal received by the timing jitter estimator **501**. The waveform clipper **1701** multiplies the signal value of the analogue or digital input signal by a constant, replaces the resultant signal value that is larger than the predetermined first threshold value with the first threshold value, and replaces the resultant signal value that is smaller than the predetermined second threshold value with the second threshold value. Please note that the first threshold value is assumed to be larger than the second threshold value. FIG. 26 shows an example of the signal from which the amplitude modulation components have been removed.

FIG. 27 shows still another example of the structure of the timing jitter estimator **501**. In FIG. 27, the components labeled with the same reference numerals as those in FIG. 9 have the same or similar functions and structures as/to those described referring to FIG. 9. The timing jitter estimator **501** in this example includes the structure of the timing jitter estimator **501** described referring to FIG. 9, and further includes a low frequency component remover **1901**. The low frequency component remover **1901** extracts frequency components in a desired band from the instantaneous phase noise and outputs the extracted components. The low frequency component remover **1091** may remove the low frequency components from the instantaneous phase noise and output the instantaneous phase noise with no low frequency component. By removing the low frequency components of the instantaneous phase noise, the gain of the jitter transfer function can be calculated more precisely.

FIG. 28 shows another example of step of timing estimation S**221**. In FIG. 28, the steps having the same reference numerals are the same or similar as/to those described referring to FIG. 10. Timing jitter estimation step S**221** includes timing jitter estimation step S**221** described referring to FIG. 10 and further includes step of removing low frequency component S**2001**.

Low frequency component removal step S**2001** removes the low frequency components from the signal. Step S**2001** removes the low frequency components in a similar manner to that of the low frequency component remover **1901** described referring to FIG. 27. Step S**1801** may be performed by using the low frequency component remover **1901**.

FIG. 29 shows another example of the structure of the timing jitter estimator **501**. In FIG. 29, the components labeled with the same reference numerals as those in FIG. 9 have the same or similar functions and structures as/to those described referring to FIG. 9. The timing jitter estimator **501** in this example includes the structure of the timing jitter estimator **501** described referring to FIG. 9, and further includes an analogue-to-digital (AD) converter **9901**.

AD converter **9901** converts the analogue signal received by the timing jitter estimator **501** to a digital signal. AD converter **9901** supplies the digital signal to the analytic signal transformer **701**, and the analytic signal transformer **701** generates the analytic signal based-on the digital signal. AD converter **9901** may use a high-speed AD converter, a digitizer, or a digital oscilloscope. Alternatively, the timing jitter estimator **501** described in the other examples may include the AD converter **9901** same as the timing jitter estimator **501** of this example.

FIG. 30 is a flowchart showing another example of the timing jitter estimation step S**221**. In FIG. 30, the steps having the same reference numerals are the same or similar as/to those described referring to FIG. 10. Timing jitter estimation step S**221** in this example includes timing jitter estimation step S**221** described referring to FIG. 10 and further includes AD conversion step S**9801**.

AD conversion step S**9801** converts the analogue signal to a digital signal. Analytic signal transforming step S**801** generates the analytic signal of the converted digital signal. Step S**9801** converts the analogue signal to the digital signal in a similar manner to that of the AD converter **9901** described referring to FIG. 29. Step S**9901** may be performed by using the AD converter **9901**.

FIG. 31 shows an exemplary structure of the analytic signal transformer **701**. The analytic signal transformer **701** includes a band-pass filter **1101** that generates a band-limited signal obtained by extracting the frequency components in the vicinity of the fundamental frequency of the signal received by the timing jitter estimator **501**, and a Hilbert transformer **1102** that performs Hilbert transform of the band-limited signal so as to generate a Hilbert pair of the signal.

The band-pass filter **1101** may be an analogue filter or a digital filter, or may be implemented by using digital signal processing such as FFT. Moreover, the band-pass filter **1101** may be construed so as to allow the bandwidth in which the components are allowed to pass to be varied freely. According to the analytic signal transformer **701** of this example, the analytic signal corresponding to the fundamental component of the received signal can be generated. Thus, the gain of the jitter transfer function can be calculated precisely. The generation of the analytic signal using the Hilbert transform is described below.

The analytic signal z(t) of the real signal x(t) is defined by the following complex signal.

*z*(*t*)≡*x*(*t*)+*j{circumflex over (x)}*(*t*) (45)

In the above equation, j is imaginary unit, and the imaginary part {circumflex over (x)}(t) of the complex signal z(t) is obtained by Hilbert transform of the real part x(t).

On the other hand, Hilbert transform of the time-domain waveform x(t) is defined by the following equation.

{circumflex over (x)}(t) is convolution of functions x(t) and (1/πt). In other words, Hilbert transform is equivalent to the output obtained by making x(t) pass through an all pass filter. Please note that the phase of the output {circumflex over (x)}(t) is shifted by π/2 although the magnitude of the components in the frequency domain is left unchanged.

The analytic signal and Hilbert transform are described in, for example, A. Papoulis, Probability, Random Variables, and Stochastic Processes, 2nd edition, McGraw-Hill Book Company, 1984.

The instantaneous phase φ(t) of the real signal x(t) is obtained from the analytic signal z(t) by using the following equation.

Next, algorithm for estimating the instantaneous phase using Hilbert transform is described. First, the signal to be measured shown in FIG. 11

is subjected to Hilbert transform so as to obtain a signal corresponding to the imaginary part of the complex signal

thereby the signal under test x(t) is transformed to the analytic signal,

shown in FIG. 12.

The obtained analytic signal has been subjected to the band-pass filtering by the band-pass filter **1101**. Therefore, the jitter corresponding to the fluctuation of the fundamental frequency of the signal to be measured can be calculated precisely.

Then, the instantaneous phase estimator **702** estimates the phase function φ(t) shown in FIG. 13 from the analytic signal z(t) by using Equation (47).

φ(t) represents the principal value of the phase, and has discontinuous points −π and π. Finally, by unwrapping the discontinuous phase function φ(t) (that is, appropriately adding integral multiples of 2π to the principal value φ(t)), the discontinuities can be removed, so that the instantaneous phase φ(t) shown in FIG. 14 is obtained.

The analytic signal transformer **701** may compensate the real part for delay time τ, as represented by the following equation.

*z*(*t*)=*x*(*t*−τ)+*j{circumflex over (x)}*(*t*) (53)

As represented by Equation (53), the high accuracy analytic signal can be obtained in a case where the delay time τ corresponding to the filter delay is observed in the Hilbert transforming procedure by the analytic signal transformer **701** generating the analytic signal. Moreover, the timing jitter estimator **501** may calculate the instantaneous phase φ(t) after the linear phase term has been removed, in accordance with the following equation.

Moreover, the timing jitter estimator **501** may calculate the instantaneous phase φ(t) after compensating the delay time τ caused by the Hilbert transform, in accordance with the following equation.

Please note that ƒ_{J }represents the jitter frequency of the signal x(t). By removing the linear phase term, the instantaneous phase noise of the signal x(t), shown in FIG. 16, can be detected.

FIG. 32 is a flowchart showing an example of analytic signal transforming step S**801**. Analytic signal transforming step S**801** generates a band-limited signal obtained by extracting the frequency components in the vicinity of the fundamental frequency of the signal received by the timing jitter estimator **501**, in band-pass filtering step S**1201**. Step S**1201** generates the band-limited signal in the similar manner to that of the band-pass filter **1101** described referring to FIG. 31. Step S**1201** may be performed by using the band-pass filter **1101**.

Then, in Hilbert transforming step S**1202**, the band-limited signal is subjected to Hilbert transform so as to generate a Hilbert pair. Step S**1202** performs the generation of the Hilbert pair in a similar manner to that of the Hilbert transformer **1102** described referring to FIG. 31. Step S**1202** may be performed by using the Hilbert transformer **1102**.

Then, in output step S**1203**, the band-limited signal is output as the real part of the analytic signal, and the band-limited signal after being subjected to Hilbert transform is output as the imaginary part of the analytic signal.

FIG. 33 shows another exemplary structure of the analytic signal transformer **701**. The analytic signal transformer **701** includes a time-domain to frequency-domain transformer **1301** that transforms the signal received by the timing jitter estimator **501** to a two-sided spectra in frequency domain, a bandwidth limiter **1302** that extracts the frequency components in the vicinity of the positive fundamental frequency in the two-sided spectra in frequency domain, and a frequency-domain to time-domain transformer **1303** that transforms the output of the bandwidth limiter **1302** to a signal in time domain. The time-domain to frequency-domain transformer **1301** and the frequency-domain to time-domain transformer **1303** may be implemented by using FFT and inverse FFT, respectively. Moreover, the bandwidth limiter **1302** may have the same or similar function and structure as/to the band-pass filter **1101** described referring to FIG. 31. The band where the signal components are allowed to pass through the bandwidth limiter **1302** is freely variable. The details of the operation of the analytic signal transformer **701** in this example are described later.

FIG. 34 is a flowchart showing another example of analytic signal transforming step S**801**. Analytic signal transforming step S**801** transforms the signal received by the timing jitter estimator **501** to a signal in frequency domain in step S**1401**. Step S**1401** generates the signal in frequency domain in a similar manner to that of the time-domain to frequency-domain transformer **1301** described referring to FIG. 33. Step S**1401** may be performed by using the time-domain to frequency-domain transformer **1301**.

Then, in negative frequency component removal step S**1402**, negative frequency components in the two-sided spectra in frequency domain are removed. Step S**1402** may have a similar function to that of the bandwidth limiter **1302** described referring to FIG. 33. Step S**1403** may be performed by using the bandwidth limiter **1302**.

Then, in bandwidth limiting step S**1403**, the frequency components in the vicinity of the positive fundamental frequency in the transformed signal in frequency domain are extracted. Step S**1403** may have a similar function to that of the bandwidth limiter **1302** described referring to FIG. 33. Step S**1403** may be performed by using the bandwidth limiter **1302**.

The signal in frequency domain is then transformed to a signal in time domain in step S**1404**. Step S**1404** may generate the signal in time domain in a similar manner to that of the frequency-domain to time-domain transformer **1303** described referring to FIG. 33. Step S**1404** may be performed by the frequency-domain to time-domain transformer **1303**. Next, the details of the operation of the analytic signal transformer **701** that generates the analytic signal by using Fast Fourier transform are described.

FIG. 35 shows an example of the signal received by the analytic signal transformer **701**. The analytic signal transformer **701** receives the digitized signal x(t) shown with circles in FIG. 35. The time-domain to frequency-domain transformer **1301** performs FFT operation for the signal x(t), thereby transforming the signal x(t) to the signal X(f) in frequency domain.

FIG. 36 shows an example of the signal X(f) in frequency domain. The bandwidth limiter **1302** sets the data other than the data in the vicinity of the fundamental frequency in the positive frequency components of the spectra X(f) to zeros so as to leave only the data in the vicinity of the fundamental frequency in the positive frequency components, and then doubles the positive frequency components. These operations in frequency domain correspond to the bandwidth limiting of the signal to be measured in time domain and the transform of the signal after band limiting to the analytic signal.

FIG. 37 shows a signal Z(f) in frequency domain of which the bandwidth was limited. The frequency-domain to time-domain transformer **1303** performs inverse Fourier transform operation on the signal Z(f) so as to generate the analytic signal z(t) for which the bandwidth was limited.

FIG. 38 shows the analytic signal z(t) for which the bandwidth was limited. Please note that the operation for doubling the positive frequency components can be omitted in a case where the object is the instantaneous phase estimation.

In the analytic signal transformer **701** described referring to FIG. 33, the period of the signal x(t) does not correspond to the number of the points of Fast Fourier transform in some cases. In these cases, it is necessary to multiply the digitized signal x(t) by a window function. The analytic signal transformer **701** in the cases of multiplying the signal x(t) by the window function is described below.

FIG. 39 shows another example of the structure of the analytic signal transformer **701**. The analytic signal transformer **701** includes a buffer memory **1501** that stores the received signal, a waveform data selector **1502** that selects a waveform from the signal stored in the buffer memory **1501**, a window function multiplier **1503** that multiplies the signal waveform section selected by the waveform data selector **1502** by a predetermined window function, a time-domain to frequency-domain transformer **1504** that transforms the waveform data multiplied by the window function to the spectra in frequency domain, a bandwidth limiter **1505** that extracts the frequency components in the vicinity of the positive fundamental frequency of the given spectra, a frequency-domain to time-domain transformer **1506** that transforms the frequency components extracted by the bandwidth limiter **1505** to a signal in time domain, and an amplitude corrector **1507** that multiplies the signal in time domain by a reciprocal of the window function so as to generate the analytic signal. Please note that the wave form data selector **1502** selects a finite duration waveforms by overlapping the waveform sections partially.

In the case where the signal components of the signal x(t) were multiplied by the window function, the signal x(t) is subjected to amplitude modulation. According to the analytic signal transformer **701** of this example, however, the amplitude modulation of the signal x(t) can be corrected by performing multiplication by a reciprocal of the window function in the amplitude corrector **1507**.

The window function multiplier **1503** outputs the signal x(t) w(t) obtained by multiplying the signal x(t) by the window function w(t) to the time-domain to frequency-domain transformer **1504**. The time-domain to frequency-domain transformer **1504** transforms the received signal to a signal in frequency domain. The bandwidth limiter **1505** outputs the spectra Z(f) obtained by replacing the negative frequency components of that signal with zeros.

The frequency-domain to time-domain transformer **1506** outputs a signal IFFT [Z(f)] obtained by transforming the spectra Z(f) to a signal in time domain. In this example, the analytic signal transformer **701** may output the real part and the imaginary part of the signal output from the frequency-domain to time-domain transformer **1506** as the real part and the imaginary part of the analytic signal. The real part x_{real}(t) and the imaginary part x_{imag}(t) of the analytic signal are the real part Re{IFFT[Z(f)]} and the imaginary part Im{IFFT[Z (f)]} of the output signal from the frequency-domain to time-domain transformer **1506**, respectively.

*w*′(*t*)*x*_{real}(*t*)=*Re{IFFT[Z*(ƒ)]}

*w*′(*t*)*x*_{imag}(*t*)=*Im{IFFT[Z*(ƒ)]} (56)

w′ (t) represents the transformed window function w(t) from the spectra Z(f). The real part x_{real}(t) and the imaginary part x_{imag}(t) of the analytic signal are influenced by the amplitude modulation by the window function w(t) to approximately the same degree. Therefore, the instantaneous phase represented by Equation (54) is represented by the following equation.

In a case of calculating the instantaneous phase of the signal x(t) in this example, as represented by Equation (57), the phase estimation errors caused by the amplitude modulation by the window function can be cancelled in the real part and the imaginary part. On the other hand, if the amplitude modulation by the window function occurs, it results in the phase estimation error as given by the following equation.

Since the phase estimation errors associated with x_{real}(t) and x_{imag}(t) can be cancelled with each other in this example, it is possible to calculate the instantaneous phase with no phase estimation error caused by the amplitude modulation by the window function. In other words, as is apparent from Equations (56) and (57), in a case that the real part Re{IFFT[Z(f)]} and the imaginary part Im{IFFT[Z(f)]} of the output signal of the frequency-domain to time-domain transformer **1506** are output as the real part and the imaginary part of the analytic signal, the instantaneous phase estimator **702** can calculate the instantaneous phase of the signal x(t) precisely.

Moreover, as shown in FIG. 39, when the real part and the imaginary part of the signal from which the amplitude modulation components by the window function were removed are output as the real part and the imaginary part of the analytic signal in the amplitude corrector **1507**, it is possible to efficiently perform other analysis and test of the DUT, and the like, by using the analytic signal.

The time-domain to frequency-domain transformer **1504**, the bandwidth limiter **1505** and the frequency-domain to time-domain transformer **1506** have the same or similar functions and structures as/to those of the time-domain to frequency-domain transformer **1301**, the bandwidth limiter **1302** and the frequency-domain to time-domain transformer **1303** described referring to FIG. 33.

Next, the operation of the analytic signal transformer **701** of the present invention is described. First, the buffer memory **1501** stores the signal to be measured. The waveform data selector **1502** then extracts waveform section of the signal stored in the buffer memory **1501**. The window function multiplier **1503** then multiplies the waveform section selected by the waveform data selector **1502** by the window function. Then, the time-domain to frequency-domain transformer **1504** performs FFT operation on the waveform section multiplied by the window function, so that the signal in time domain is transformed to the two-sided spectra in frequency domain. Next, the bandwidth limiter **1505** replaces the negative frequency components of the two-sided spectra in frequency domain with zeros, so as to obtain one-sided spectra. The bandwidth limiter **1505** then replaces the frequency components of the one-sided spectra other than those around the fundamental frequency of the signal to be measured with zeros so as to leave the frequency components around the fundamental frequency of the signal to be measured only, thereby the bandwidth of the signal in frequency domain is limited. Then, the frequency-domain to time-domain transformer **1506** performs inverse FFT on the band limited one-sided spectra, so that the signal in frequency domain is transformed to a signal in time domain. The amplitude corrector **1507** multiplies the signal in time domain by the reciprocal of the window function so as to generate the band limited analytic signal. The analytic signal transformer **701** then checks whether or not the buffer memory **1501** stores the waveform data that has not been processed. If the unprocessed waveform data is determined to be left in the buffer memory **1501**, the waveform data selector **1502** selects the next waveform section. After the waveform data selector **1502** extracts the waveform section so that it partially overlaps the previously extracted waveform section, the analytic signal transformer **701** repeats the aforementioned operations.

FIG. 40 is a flowchart of another example of analytic signal transforming step S**801**. Step S**801** stores the signals to be measured in buffer memory step S**1601**. Step S**1601** has the same or similar function as/to that of the buffer memory **1501** described referring to FIG. 39. Step S**1601** may be performed by using the buffer memory **1501**.

Then, waveform data selection step S**1602** selects a part of the signal to be measured, that was stored in buffer memory step S**1601**, and extracts the selected waveform section as the waveform data. Step S**1602** has the same or similar as/to that of the waveform data selector **1502** described referring to FIG. 39, and may be performed by using the waveform data selector **1502**.

Then, in window function multiplying step **1603**, the waveform data extracted in step S**1602** is multiplied by a predetermined window function such as Hanning function. Step S**1603** has the same or similar function as/to that of the window function multiplier **1503** described referring to FIG. 39, and may be performed by the window function multiplier **1503**.

Then, in time-domain to frequency-domain transforming step S**1604**, the waveform data multiplied by the window function is transformed to a signal in frequency domain. Step S**1604** has the same or similar function as/to that of the time-domain to frequency-domain transformer **1504** described referring to FIG. 39.

Then, in negative frequency component removal step S**1605**, the negative frequency components of the signal transformed into frequency domain are removed. Step S**1605** has the same or similar function as/to that of the bandwidth limiter **1505** described referring to FIG. 39, and may be performed by the bandwidth limiter **1505**.

Then, in bandwidth limiting step S**1606**, the frequency components of the signal transformed into frequency domain in the vicinity of the fundamental frequency thereof are extracted. Step S**1606** has the same or similar function as/to that of the bandwidth limiter **1505** described referring to FIG. 39, and may be performed by the bandwidth limiter **1505**.

Then, in frequency-domain to time-domain transforming step S**1607**, the signal having the limited bandwidth is transformed to a signal in time domain. Step S**1607** has the same or similar function as/to that of the frequency-domain to time-domain transformer **1506** described referring to FIG. 39 and may be performed by the frequency-domain to time-domain transformer **1506**.

Then, in amplitude correction step S**1608**, the amplitude modulation components of the signal transformed into time domain are removed. Step S**1608** has the same or similar function as/to that of the amplitude corrector **1507** described referring to FIG. 39, and may be performed by the amplitude corrector **1507**.

Next, in decision step S**1609**, it is determined whether or not there is any unprocessed data of the signal to be measured that was stored in step S**1601**. If the unprocessed data is left, waveform data selection step S**1601** extracts the next part of the signal in such a manner that it partially overlaps the previously extracted part. Step S**1610** has a similar function to step S**1602**. When it is determined in step S**1609** that there is no unprocessed waveform data, the procedure is finished.

Next, a method of estimating the phase of the jitter transfer function is described below. FIG. 41 shows a flowchart of an example of phase difference estimation step S**2301** described referring to FIG. 7. First, in input timing jitter spectra estimation step S**2604**, timing jitter spectra of the input signal is estimated by applying Fourier transform to the input timing jitter sequence, estimated in input timing jitter sequence estimation step S**241** described referring to FIG. 6. Next, in output timing jitter spectra estimation step S**2605**, timing jitter spectra of the output signal is estimated by applying Fourier transform to the output timing jitter sequence, estimated in output timing jitter sequence estimation step S**243** described referring to FIG. 6. Then, in jitter phase difference estimation step S**2606**, phase differences between the input and output timing jitter sequence is estimated from the timing jitter spectra estimated in steps S**2604** and S**2605**, and the procedure is finished.

The jitter phase difference estimator **503** estimates the timing jitter spectra of the input signal by using Equation (3) in step S**2604**, which estimates the timing jitter spectra from the input timing jitter. Moreover, the jitter phase difference estimator **503** estimates the timing jitter spectra of the output signal by using Equation (4) in step S**2605**, which estimates the timing jitter spectra from the output timing jitter. Moreover, the jitter phase difference estimator **503** estimates the phase difference between the input and output timing jitters by using Equation (9) in step S**2606**, which estimates differences between the input and output timing jitter from the timing jitter spectra. Furthermore, jitter phase difference estimator **503** may estimate the phase difference between the input and output timing jitter by calculating the arctangent of the ratio of imaginary part to real part of the jitter transfer function (i.e. Im/Re) in step S**2606**.

The phase difference between the input and output timing jitters may be calculated by calculating the timing difference between the zero-cross timing of the input instantaneous phase noise waveform and that of the output instantaneous phase noise, calculating a ratio of the calculated timing difference to the period of the applied jitter (reciprocal of the jitter frequency) and multiplying the calculated ratio by 2π (rad) (or 360 degrees). Similarly, it may be calculated by calculating the timing difference between the zero-cross timing of the input timing jitter waveform and that of the output timing jitter waveform, calculating the ratio of the calculated timing difference to the period of the applied jitter (the reciprocal of the jitter frequency) and multiplying the calculated ratio by 2π (rad) (or 360 degrees).

Moreover, the phase of the jitter transfer function may be calculated by the instantaneous phase noise waveform of the input and output signal. FIG. 42 is a flowchart of another example of phase difference estimation step S**2301** described referring to FIG. 7. The instantaneous phase noise waveform of the input signal to be supplied to the DUT is calculated in input instantaneous phase noise wave form estimation step S**2502**. Next, The instantaneous phase noise waveform of the output signal output from the DUT is calculated in output instantaneous phase noise waveform estimation step S**2503**. Next, the phase noise spectra of the input signal is calculated by applying Fourier transform to the instantaneous phase noise waveform of the input signal in input phase noise spectra estimation step S**2504**. Next, the phase noise spectra of the output signal is calculated by applying Fourier transform to the instantaneous phase noise waveform of the output signal in output phase noise spectra estimation step S**2505**. Then, in jitter phase difference estimation step S**2506**, the phase difference between the instantaneous phase noises from the phase noise spectra calculated in steps S**2504** and S**2505**, and the procedure is finished.

In step S**2504**, where the phase noise spectra is obtained from the input instantaneous phase noise, the jitter phase difference estimator **503** estimates the phase noise spectra of the input signal by using Equation (1). Moreover, the jitter phase difference estimator **503** estimates the phase noise spectra of the output signal by using Equation (2) in step S**2505** where the phase noise spectra is obtained from the output instantaneous phase noise. Furthermore, the jitter phase difference estimator **503** obtains the phase difference between the input and output instantaneous phase noises by using Equation (9) in step S**2506**, where phase difference between the instantaneous phase noises is obtained from the phase noise spectra, and estimates phase of the jitter transfer function.

FIG. 43 illustrates another exemplary measuring apparatus **100**. In FIG. 43, the components having the same reference numerals as those in FIG. 1 have the same or similar functions and structures as/to those described referring to FIG. 1. The measuring apparatus **100** of this example includes the structure of that shown in FIG. 1 and also includes a signal input means **301** and a jitter tolerance estimator **302**.

The signal input means **301** supplies a signal obtained by applying a desired jitter to the input signal to be input to the DUT. The signal input means **301** applies sinusoidal jitter to the input signal, for example. By applying the sinusoidal jitter, the bit error rate can be calculated precisely. The details in the case of applying the sinusoidal jitter are described later.

The jitter tolerance estimator **302** estimates a jitter tolerance of the DUT based on the jitter transfer function of the DUT. The jitter tolerance estimator **302** may estimate the jitter tolerance based on the gain of the jitter transfer function as described above. Moreover, the jitter tolerance estimator **302** may estimate the jitter tolerance further based on the phase of the jitter transfer function. Moreover, the jitter tolerance estimator **302** may estimate the jitter tolerance further based on the internal noise of the DUT.

The jitter tolerance estimator **302** may calculate the jitter tolerance of the DUT in accordance with Equation (37), (39) or (44). Moreover, the jitter tolerance estimator **302** may calculate the best-case value of the jitter tolerance of the DUT as described above.

The jitter transfer function measuring apparatus **101** estimates the jitter transfer function of the DUT based on the input timing jitter that the signal input means **301** applies to the input signal and the output timing jitter in the output signal of the DUT. The signal input means **301** applies input timing jitters having different jitter amplitude to the input signal one after another. In this example, the jitter transfer function measuring apparatus **101** receives the signal input to the DUT and the signal output from the DUT.

FIG. 44 is a flowchart of another example of the measuring method according to the present invention. In FIG. 44, the steps labeled with the same reference numeral as those in FIG. 2 have the same or similar functions as/to those described referring to FIG. 2. First, in signal input step S**401**, a desirable jitter is applied to the input signal, and the jittery input signal is supplied to the DUT. Step S**401** has the same or similar function as/to the signal input means **301** described referring to FIG. 43. Step S**401** may be performed by using the signal input means **301**.

Next, the jitter transfer function is calculated in step S**201**. Step S**201** is the similar step to jitter transfer function estimation step S**201** in FIG. 2. Next, the bit error rate is calculated in step S**202**. Step **202** is the similar step to bit error rate estimation step S**202** in FIG. 2.

Next, the jitter tolerance of the DUT is calculated in jitter tolerance estimation step S**402**. Step S**402** has the same or similar function as/to the jitter tolerance estimator **302** described referring to FIG. 43. Step S**402** may be performed by using the jitter tolerance estimator **302**.

FIG. 45 illustrates another exemplary measuring apparatus **100**. In FIG. 45, the components having the same reference numerals as those in FIG. 1 have the same or similar functions and structures as/to those described referring to FIG. 1. The measuring apparatus **100** of this example includes the structure of that shown in FIG. 1 and also includes a clock recovery unit **2101**.

The clock recovery unit **2101** generates a recovered clock signal of the output signal based on the output signal of the DUT. The jitter transfer function measuring apparatus **101** receives the recovered clock as the output signal from the DUT and calculates the jitter transfer function of the DUT based on the recovered clock signal.

FIG. 46 is a flowchart of another example of a measuring method according to the present invention. In clock recovery step S**2201**, the recovered clock signal of the output signal of the DUT is generated. Step S**2201** has the same or similar function as/to that of the clock recovery unit **2101** described referring to FIG. 45, and may be performed by using the clock recovery unit **2101**.

Then, in jitter transfer function estimation step S**201**, the jitter transfer function of the DUT is calculated. Step S**201** has the same or similar function as/to that of the jitter transfer function measuring apparatus **101** described referring to FIG. **45**, and may be performed by using the jitter transfer function measuring apparatus **101**.

Then, in bit error rate estimation step S**202**, the bit error rate of the DUT is calculated. Step S**202** has the same or similar function as/to that of the bit error rate estimator **102** described referring to FIG. 45, and may be performed by using the bit error rate estimator **102**.

FIG. 47 shows an exemplary structure of the DUT. The DUT accepts serial data as an input signal and outputs parallel data as an output signal. The DUT includes a flip-flop **3001**, a clock recovery unit **3003** and a serial-parallel converter **3002**.

The clock recovery unit **3003** receives the input signal (serial bit stream) and generates the recovered clock for outputting the output signal based on the input signal (serial bit stream) received. In the present example, the clock recovery unit **3003** has a phase-locked-loop (PLL).

The flip-flop **3001** supplies the input signal to the serial-parallel converter **3002**. The serial-parallel converter **3002** receives the recovered clock and converts the serial input signal to the parallel output signal based on the timings of the recovered clock.

The measuring apparatus **100** receives the recovered clock generated by the clock recovery unit **3003** as the output signal of the DUT, and then calculates the bit error rate and/or jitter tolerance of the DUT based on the recovered clock.

FIG. 48 illustrates another exemplary measuring apparatus **100**. In FIG. 48, the components having the same reference numerals as those in FIG. 1 have the same or similar functions and structures as/to those described referring to FIG. 1. The measuring apparatus **100** of this example includes a timing estimator **3100**, a timing difference estimator **3102** and a bit error estimator **102**.

The timing estimator **3100** estimates a timing error sequence of the input signal for testing the DUT and a timing error sequence of the output signal that the DUT outputs in response to the input signal. The timing difference estimator **3102** calculates the timing differences between the timing error sequence of the input signal and that of the output signal. The timing difference estimator **3102** may calculate the timing differences based on the peak values or the RMS values of the input timing error sequences and the output timing error sequences. The bit error rate estimator **102** estimates the bit error rate of the DUT based on the thus calculated timing differences. Equations indicating the relationship between the timing differences and the bit error rate may be given in advance to the bit error rate estimator **102**. Also, Tables indicating the relationship between the timing differences and the bit error rate may be given in advance to the bit error rate estimator **102**.

FIG. 49 shows exemplary input and output signals. In the shown example, the DUT outputs the recovered clock as the output signal. The timings of the data stream input to the DUT and the timings of the recovered clock are shown with arrows in FIG. 49. The input data stream and the recovered clock have the timing differences shown in FIG. 49. The bit error rate estimator **102** calculates the bit error rate based on such timing differences.

FIG. 50 is a flowchart of another example of a measuring method according to the present invention. In timing estimation step S**3201**, the timing error sequences of the input and output signals are obtained. Step S**3201** has the same or similar function as/to that of the timing estimator **3100** described referring to FIG. 48, and may be performed by using the timing estimator **3100**.

Then, in timing difference estimation step S**3202**, the timing differences between the input and output signals are calculated. Step S**3202** has the same or similar function as/to that of the timing difference estimator **3102** described referring to FIG. 48, and may be performed by using the timing difference estimator **3102**.

Then, in bit error rate estimation step S**3203**, the bit error rate of the DUT is calculated. Step S**3203** has the same or similar function as/to that of the bit error rate estimator **102** described referring to FIG. 48, and may be performed by using the bit error rate estimator **102**.

FIG. 51 illustrates an exemplary structure of the timing estimator **3100**. In FIG. 51, the components having the same reference numerals as those in FIG. 9 have the same or similar functions and structures of those shown in FIG. 9. The timing estimator **3100** includes an analytic signal transformer **701** that transforms the input and output signals to complex analytic signals, an instantaneous phase estimator **702** that calculates the instantaneous phase of the analytic signal, an ideal timing estimator **3301** that calculates the initial phase angles and average frequencies of the instantaneous phases and estimates the ideal timings of the input and output signal, a resampler **3304** that resamples the instantaneous phase and generates the input timing sequence of the input signal and the output timing sequence of the output signal, and a timing error calculator **3305** that calculates a timing error sequence of the input signal and a timing error sequence of the output signal based on the ideal timings and the timing sequences.

The resampler **3304** may supply the timing n of the timing error sequences Δφ[nT] to the ideal timing estimator **3301**. Moreover, the resampler **3304** may sample the instantaneous phase at the zero-crossing timing of the waveform of the real part of the analytic signal. Furthermore, the resampler **3304** may supply the sampling timing in the resampler **3304** to the ideal timing estimator **3301** as the timing n. The ideal timing estimator **3301** calculates the ideal timings of the input and output signal based on the timing n supplied by the resampler **3304**.

The analytic signal transformer **701**, the instantaneous phase estimator **702**, and the resampler **3304** have the same or similar functions and structures as/to the analytic signal transformer **701**, the instantaneous phase estimator **702**, and the resampler **901** shown in FIG. 11.

The ideal timing estimator **3301** calculates the initial phase angles and average frequencies of the linear instantaneous phase of the input and output signals, that is shown in FIG. 14, so as to calculate the ideal timings of the input and output signals. In this case, the ideal timing estimator **3301** may include the linear phase estimator **703**. The ideal timing estimator **3301** may output the values of the linear phase, which is generated at the timing n, as the ideal timings. The timing error calculator **3305** generates the timing error sequence of each of the input and output signals based on the ideal timing and the result of the resampling of instantaneous phase noise by the resampler **3304**. The measuring apparatus **100** of the present example calculates the bit error rate based on an alignment error (timing difference) caused by the jitters in the input and output signals. The alignment error is described later.

FIG. 52 is a flowchart of an example of timing estimation step S**3201**. First, in analytic signal transform step S**3400**, the input and output signal are transformed to the analytic signal. Step S**3400** has the same or similar function as/to the analytic signal transformer **701** described referring to FIG. 51, and may be performed by using the analytic signal transformer **701**. Next, in instantaneous phase estimation step S**3401**, the instantaneous phases of the input and output signals are calculated. Step S**3401** has the same or similar function as/to the instantaneous phase estimator **702** described referring to FIG. 51, and may be performed by using the instantaneous phase estimator **702**.

Then, in resampling step S**3402**, the input and output timing jitter sequences are generated by sampling the instantaneous phase noise of the input and output signal. Step S**3402** has the same or similar function as/to that of the resampler **3304** described referring to FIG. 51, and may be performed by using the resampler **3304**.

Then, in ideal timing estimation step S**3403**, the initial phase angles and average frequencies of the input and output signals are calculated, and the ideal timings of the input and output signals are also calculated. Step S**3403** has the same or similar function as/to that of the ideal timing estimator **3301** described referring to FIG. 51, and may be performed by using the ideal timing estimator **3301**.

Then, in timing error calculation step S**3406**, the timing sequences of the input and output signals are generated. Step S**3406** has the same or similar function as/to the timing error calculator **3305** described referring to FIG. 51, and may be performed by using the timing error calculator **3305**.

Next, the alignment jitter is described. An alignment jitter is defined by P. R. Trischitta, and represents the alignment error between the timing jitter of the input signal and the timing jitter of the output signal (recovered clock). The alignment jitter is defined by the following equation.

Δalign[*nT*]=|(Δφ[*nT]−Δθ[nT*])| (31)

Δθ[nT] and Δφ[nT] are the timing jitter sequence of the input signal to the DUT and that of the output signal of the DUT, respectively. The peak-to-peak value and the RMS value of the alignment jitter are represented as follows:

Δalign_{PP}=|(Δφ−Δθ)_{PP}| (58)

σ_{Δalign}=√{square root over (σ_{Δφ}^{2}+σ_{Δθ}^{2}−2ρσ_{Δφ}σ_{Δθ})} (59)

ρ is a correlation coefficient between the timing jitter of the recovered clock and the timing jitter of the data input to the DUT. For example, it is assumed that the timing jitter of the recovered clock is strongly correlated with the timing jitter of the input data of the DUT. In this case, ρ can be considered to be 1.0, and the following relationship is established.

σ_{Δalign}≈√{square root over ((σ_{Δφ}−σ_{Δθ})^{2})}=|σ_{Δφ}−σ_{Δθ}|

Thus, the alignment error between the input data and the recovered clock can be minimized. At this time, the clock recovery unit has the minimum bit error rate. On the other hand, when the timing jitter of the recovered clock is completely uncorrelated with the timing jitter of the input data of the clock recovery unit, ρ can be considered to be 0.0, and the following relationship is satisfied.

σ_{Δalign}=√{square root over (σ_{Δφ}^{2}+σ_{Δθ}^{2})}

Because of the alignment error between the input data and the recovered clock, this DUT has the bit error rate that is not neglectable. Moreover, the peak-to-peak value of the timing jitter of the recovered clock is given as follows:

Δφ_{PP}=Δθ_{PP}√{square root over (max[|*H*_{J}(ƒ_{J})|^{2}])} (60)

The peak-to-peak value of the alignment jitter is obtained as follows:

Δalign_{PP}=Δθ_{PP}{|√{square root over (max[|*H*_{J}(ƒ_{J})|^{2}])}−1|} (61)

Next, the case where the sinusoidal jitter is applied to the input signal to the DUT is described. An input data signal x(t) is phase modulated with the timing jitter Δθ[nT]. The recovered clock signal y(t) is also phase modulated with the timing jitter Δφ[nT].

*x*(*t*)=*A *sin(2πƒ_{b}*t+Δθ[t*]) (62)

*y*(*t*)=*B *sin(2πƒ_{b}*t+Δφ[t*]) (63)

In the above equations, ƒ_{b }is a bit rate (bit clock frequency). When the instantaneous phase noises of the bit clock Δθ[nT] and Δφ[nT] are made to correspond to the sine wave cos(2πƒ_{PM}t), the sinusoidal jitter is obtained. On the other hand, when the sinusoidal jitter is demodulated, the sine wave is obtained. Since this sine wave corresponds to a line spectrum in frequency domain, the jitter frequency ƒ_{J }is given by a single frequency ƒ_{PM}. Therefore, a ratio of the demodulated sine wave at the frequency of ƒ_{PM }provides the jitter transfer function expressed by Equation (8).

On the other hand, when Δθ[nT] and Δφ[nT] are adapted to correspond to Gaussian noise n_{g}(t), the Gaussian noise jitter is obtained. When the Gaussian noise jitter is demodulated, the Gaussian noise wave is obtained. Since the Gaussian noise corresponds to wide band spectrum in frequency domain, the jitter frequency ƒ_{J }is given by a frequency band (F_{lower}, F_{upper}). Therefore, the ratio of the input and output spectrum in this frequency band gives the jitter transfer function.

It is known that, when the truncated Gaussian distribution jitter and the sinusoidal jitter are compared to each other at the same peak-to-peak value, the sinusoidal jitter results in the bit error rate with penalty of about 1 dB larger than that of the Gaussian distribution. In other words, the sinusoidal jitter can provide the worst-case jitter distribution to the DUT. Therefore, in the case where the measuring apparatus **100** applies the sinusoidal jitter to the input signal, the test of the bit error rate and jitter tolerance can be performed precisely.

Next, the jitter tolerance is described. The measurement of the jitter tolerance is extension of the bit error test. More specifically, the timing jitter Δθ[nT] of the input data to the DUT is made to fluctuate by the sinusoidal jitter or the like, thereby testing the bit error rate. While the jitter frequency ƒ_{J }is fixed and the applied jitter amount is increased, the minimum applied jitter amount that causes the occurrence of the bit error rate is obtained. Next, the relationship between the sinusoidal jitter and the bit error rate is described. First, a decision boundary or sampling instant is described. In the description of the decision boundary, it is assumed that the bit stream has no timing jitter.

FIG. 53 shows an example of the ideal and actual signals of the output signal. As shown in FIG. 53, the optimum decision boundary t_{decision }is a halfway point between two adjacent zero-crossings (that is, a rising edge and a falling edge). The period of the optimum decision boundaries is given by the period of bits T_{b}=1/ƒ_{b}. (a) A conventional measuring apparatus performs sampling of the bit stream output from the DUT at the optimum decision boundaries t_{decision}. In a case where the DUT is a serializer, for example, the output bit stream from the serializer is sampled at t_{decision }that is given by the bit period. In another case where the DUT is a deserializer, data multiplexed with a ratio **1**:L is output. Therefore, the output bit stream from the deserializer is sampled at t_{decision }that is given by the data period per channel of LT_{b}. (b) Then, the conventional measuring apparatus compares the sampled values with a threshold value, and discriminates logical values “1” or “0” of the output bit stream of the DUT. (c) The conventional measuring apparatus compares the logical values determined from the sampled values with expected values corresponding thereto, so as to calculate the error rate.

Let consider a test time required for the bit error rate test. For example, the application of a pseudo-random binary sequence having a pattern length of 2^{15}-1 that is phase-modulated with the jitter frequency of 5 MHz in order to perform the jitter tolerance test for a 2.5 Gbps serial communication device requires only 13 μsec. Moreover, the application of a pseudo-random binary sequence having a pattern length of 2^{23}-1 requires only 3.4 msec. On the other hand, the test for the bit error rate of 10^{−9 }requires 0.4 sec. Thus, this test time is independent of the pattern length. Moreover, in order to test the bit error rate of 10^{−12}, 400 sec is required. Moreover, when the applied jitter amount is increased, the PLL circuit in the DUT may not work correctly. In particular, as the bit clock frequency increases, this type of bit error may occur in a case that the applied jitter amount is slightly increased. From the above, according to the method in which the occurrence of the bit error is detected, it is hard to obtain a measurement having good repeatability or to shorten the test time. Therefore, it is necessary to find a method which does not require direct detection of the bit error occurrence to shorten the test time.

The measuring apparatus **100** described referring to FIGS. 1 to 47 calculates the jitter transfer function of the DUT and then calculates the bit error rate and/or the jitter tolerance of the DUT based on the thus calculated jitter transfer function. Therefore, as compared with the conventional measuring apparatus, the test time can be reduced. Moreover, although the measuring apparatus **100** described referring to FIGS. 1 to 47 calculates the jitter transfer function of the DUT, the measuring apparatus **100** in other examples may calculate the bit error rate and/or jitter tolerance of the DUT based on the jitter transfer function that was supplied to the measuring apparatus **100** in advance.

In other words, the measuring apparatus **100** may include the bit error rate estimator that estimates the bit error rate of the DUT based on the jitter transfer function of the DUT given in advance. Moreover, the measuring apparatus **100** may include the jitter tolerance estimator that estimates the jitter tolerance of the DUT based on the gain of the jitter transfer function of the DUT given in advance. In this case, the bit error rate estimator and jitter tolerance estimator may have the same or similar functions and structures as/to the bit error rare estimator **102** and the jitter tolerance estimator **302** mentioned above.

The measuring apparatus **100** described referring to FIGS. 48 to 52 calculates the timing differences between the input and output signals and then calculates the bit error rate of the DUT based on the thus calculated timing differences. Therefore, as compared with the conventional measuring apparatus, the test time can be reduced. Moreover, the measuring apparatus described referring to FIGS. 48 to 52 may include the jitter tolerance estimator that estimates the jitter tolerance of the DUT. The jitter tolerance estimator calculates the jitter tolerance of the DUT based on the timing difference between the input and output signals.

FIG. 54 shows the test time of the measuring apparatus **100** and that of a conventional bit error rate measuring apparatus. FIG. 55 shows an exemplary relationship between the number of times the applied jitter amplitude was changed and the measured jitter tolerance in the measuring apparatus **100**. As shown in FIG. 54, the conventional bit error rate measuring apparatus requires the test time of 20 sec in order to change the applied jitter amplitude 20 times and perform 1-sec bit error rate test for each of 20 different jitter amplitudes. On the other hand, the aforementioned measuring apparatus **100** can estimate the jitter tolerance with high precision by changing the applied jitter amplitude the minimum number times (for example, four times) and obtaining the jitter gain, as shown in FIG. 55. The measuring apparatus **100** can calculate the jitter tolerance with high precision by changing the applied jitter amplitude, for example, four times and performing the measurement for the respective applied jitter amplitude, as shown in FIG. 55. In the measuring apparatus **100**, the jitter measurement for each jitter amount requires about 0.5 msec. Thus, the measuring apparatus **100** can obtain the jitter gain of the DUT in about 2 sec. That is, the measuring apparatus **100** can obtain the jitter tolerance in the test time that is about 1/10 of the test time of the conventional measuring apparatus.

FIG. 56 illustrates another exemplary measuring apparatus **100**. The measuring apparatus **100** of this example includes the same structure of that described referring to FIG. 43 and a selector **4020***a *and a selector **4020***b *(hereinafter, simply referred to as selectors **4020**). The selectors **4020** select either an input data signal given to the electronic device or an input data clock signal for generating the input data signal, and supply it to the jitter transfer function measuring apparatus **101** as an input signal of the DUT **3000**. Moreover, the selectors **4020** select either an output data signal output from the DUT **3000** in response to the input data signal, or a recovered clock signal output from the DUT **3000** in response to the input data signal, and supply it to the jitter transfer function measuring apparatus **101** as an output signal of the DUT **3000**.

The jitter transfer function measuring apparatus **101** measures the jitter transfer function between the received input signal and the received output signal. Operation of the jitter transfer function measuring apparatus **101** is the same as the operation of the jitter transfer function measuring apparatus **101** described referring to FIG. 43. Moreover, operation of the bit error rate estimator **102** and the jitter tolerance estimator **302** is the same as the operation of the bit error rate estimator **102** and the jitter tolerance estimator **302** described referring to FIG. 43.

Moreover, the signal input means **301** generates the input data signal supplied to the DUT **3000**, and includes a pattern generator **4012**, a timing generator **4014**, and a serializer **4010**. The pattern generator **4012** supplies pattern data for generating the input data signal to the serializer **4010**, and the timing generator **4014** supplies the input data clock signal for generating the input signal to the serializer **4010**. The serializer **4010** generates the input data signal based on the received pattern data and the received input data clock. For example, the serializer **4010** outputs each data of the received pattern data one after another in response to a timing of edges of the received input data clock signal.

Moreover, as explained in. FIG. 43, the signal input means **301** applies a desired timing jitter to the input data signal. The signal input means **301** may apply the timing jitter to the input data signal by applying the timing jitter to the input data clock signal.

As the output signal, when the recovered clock signal is selected, the jitter transfer function measuring apparatus **101** can measure the jitter transfer function in the clock recovery unit **3003** described referring to FIG. 47. In this case, either the input data signal or the input data clock signal maybe selected as the input signal.

Moreover, as the output signal, when the output data signal is selected, the jitter transfer function measuring apparatus **101** can measure the jitter transfer function in all the structure of the DUT **3000** described referring to FIG. 47. Also in this case, either the input data signal or the input data clock signal may be selected as the input signal. That is, by selecting the input signal, it can be determined that which part of the DUT **3000** is to be measured.

Moreover, also in the measuring method described referring to FIG. 44, there may be a step for selecting either the input data signal or the input data clock signal as the input signal, and a step for selecting either the output data signal or the recovered clock signal as the output signal, between S**401** and S**201**. These steps may be performed by using the selectors **4020**.

FIG. 57 illustrates examples of pattern data generated by the pattern generator **4012**. For example, the pattern generator **4012** may generate a signal of pseudo-random binary sequence as shown in data A. Moreover for example, the pattern generator **4012** may generate pattern data as shown in data B, in which a bit of the pattern data corresponding to a certain output pin of the DUT **3000** repeats 1 (high) and 0 (low) by turns. In this case, the amount of the input data signal and the input data clock signal input to the DUT **3000** are equalized for the certain output pin of the DUT **3000**. Thereby, the jitter transfer function measuring apparatus **101** can measure the jitter transfer function more precisely.

Moreover, the pattern generator **4012** may generate pattern data as shown in Data C, in which 1 and 0 is repeated for every bit number same number as the output pins. Also in this case, the jitter transfer function can be measured more precisely same as the Data B, and the pattern data can be generated easily.

FIG. 58 illustrates another exemplary structure of the timing jitter estimator **501** of the jitter transfer function measuring apparatus **101**. The timing jitter estimator **501** of this example includes a signal capturing unit **4062**, a period jitter estimator **4004**, an ideal edge timing estimator **4006**, and an edge timing error estimator **4008**. For example, the timing jitter estimator **501** in this example is a conventional oscilloscope.

The signal capturing unit **4062** captures the output signal of the DUT. Moreover, the signal capturing unit **4062** measures a period of the captured output signal etc.

The period jitter estimator **4004** estimates a period jitter sequence of the output signal based on the measurement result in the signal capturing unit **4062**. Here, the period jitter sequence may indicate length of each cycle of the output signal, and may indicate timing of each edge of the output signal.

The ideal edge timing estimator **4006** estimates an average period of the output signal based on the period jitter sequence. For example, when the period jitter sequence indicates the length of each cycle of the output signal, the ideal edge timing estimator **4006** estimates an average of each value of the period jitter sequence as an average period of the output signal.

Next, the edge timing error estimator **4008** estimates the output timing jitter sequence based on the average period of the period jitter sequence, and the period jitter sequence. For example, the output timing jitter may be estimated by calculating an ideal edge timing sequence indicating ideal timing of each edge of the output signal, and calculating difference between the ideal edge timing sequence and the period jitter sequence indicating timing of each edge of the output signal, based on the average period of the output signal.

The timing jitter sequence of the output signal can be estimated by the structure of the timing jitter estimator **501** in this example as well as the timing jitter estimators **501** of the other examples. Moreover, the timing jitter sequence of the input signal of the DUT may be estimated.

FIG. 59 is a flowchart showing another example of step of the timing jitter estimation S**221**. The timing jitter estimation step S**221** in this example may be performed by the timing jitter estimator **501** described referring to FIG. 58.

First, the signal, from which the timing jitter is to be estimated, is captured in signal capturing step S**8000**. The step S**8000** may be performed by using the signal capturing unit **4062** described referring to FIG. 58.

Next, the period jitter sequence of the captured signal is estimated in a period jitter sequence estimation step S**8002**. The step S**8002** may be performed by using the period jitter estimator **4004** described referring to FIG. 58.

Next, the average period of the signal is estimated in ideal edge timing estimation step S**8004**. The step S**8004** may be performed by using the ideal edge timing estimator **4006** described referring to FIG. 58.

Next, the timing jitter sequence of the signal is estimated in the edge error estimation step S**8006**. The step S**8006** may be performed by using the edge timing error estimator **4008** described referring to FIG. 58.

FIG. 60 shows an example of a curve of a bit error rate. In FIG. 60, circles show measurement points of bits measured by a conventional measuring apparatus, and a solid line shows the bit error rate curve measured by the measuring apparatus **100**. According to the measuring apparatus **100**, the bit error rate curve which is compatible with the conventional method can be obtained. Moreover, as described referring to FIG. 56, in order to obtain the bit error rate curve as shown in FIG. 60, either the input data signal or the input data clock signal may be selected as the input signal, and either the output data signal or the recovered clock signal as the output signal.

FIG. 61 is an exemplary measurement of the jitter tolerance.

In FIG. 61, a horizontal axis shows frequency of the input timing jitter, and a vertical axis shows the jitter tolerance. Moreover, in FIG. 61, circles show the jitter tolerance measured by the conventional measuring apparatus, and square marks show the jitter tolerance measured by the measuring apparatus **100**. In this example, the measuring apparatus **100** measures the jitter tolerance using the Equation (39). As shown in FIG. 61, the measuring apparatus **100** can measure the jitter tolerance which is compatible with the conventional method. Moreover, as described referring to FIG. 56, in order to obtain the jitter tolerance as shown in FIG. 61, either the input data signal or the input data clock signal may be selected as the input signal, and either the output data signal or the recovered clock signal may be selected as the output signal.

Moreover, the measuring apparatus **100** may measure the jitter tolerance using Equation (39.2). The more accurate jitter tolerance can be measured by substituting, for example, 0.75 for 8 in this case.

FIG. 62 is another exemplary structure of a jitter tolerance measuring apparatus as an example of the measuring apparatus **100**.

The measuring apparatus **100** includes a signal input means **301**, a timing jitter estimator **501**, a jitter distortion estimator **4100**, and a jitter related transmission penalty estimator **4102**. The signal input means **301** has the same function and the same structure as the signal input means **301** described referring to FIG. 56, and the timing jitter estimator **501** has the same function and the same structure as the timing jitter estimator **501** described referring to FIG. 3.

The jitter distortion estimator **4100** estimates the jitter distortion of the output timing jitter sequence. Here, the jitter distortion of the output timing jitter sequence is distortion of the output timing jitter of the output signal which the DUT **3000** actually outputs in response to the input signal, against the ideal timing jitter of the output signal which the DUT **3000** is to output in response to the input signal.

The jitter related transmission penalty estimator **4102** estimates reliability of the DUT **3000** against jitter based on the jitter distortion. For example, the jitter related transmission penalty estimator **4102** estimates the jitter tolerance of the DUT **3000**. Moreover, the jitter related transmission penalty estimator **4102** may estimate whether the DUT **3000** operates normally in response to the input timing jitter of a predetermined amplitude. That is, the signal input means **301** may apply the input timing jitter of desired amplitude to the input signal, and may supply it to the DUT **3000**, and the jitter related transmission penalty estimator **4102** may estimate the reliability of the DUT **3000** against jitter for the amplitude of the input timing jitter.

FIG. 63 is a flowchart showing an example of measuring method for measuring the DUT **3000**. First, in the jitter frequency setting step S**4500**, frequency of the input timing jitter, applied to the input signal to the DUT **3000**, is set up.

Next, in a jitter amplitude setting step S**4502**, amplitude of the input timing jitter, applied to the input signal to the DUT **3000**, is set up. The steps S**4500** and S**4502** may be performed using the signal input means **301** described referring to FIG. 62.

Next, in a timing jitter sequence measurement step S**4504**, the output timing jitter sequence is measured based on the output signal of the DUT **3000**. The step S**4504** may be performed using the timing jitter estimator **501** described referring to FIG. 62.

Next, in a jitter distortion measurement step S**4506**, the jitter distortion of the timing jitter of the output signal, which DUT **3000** actually outputs, against the timing jitter of the output signal which DUT **3000** is to output in response to the input signal, is measured. The step S**4506** may be performed using the jitter distortion estimator **4100** described referring to FIG. 62.

Next, in a judging step S**4508**, it is judged whether the jitter distortion is larger than a predetermined value. The step S**4508** may be performed using the jitter related transmission penalty estimator **4102** described referring to FIG. 62.

In the step S**4508**, if the jitter distortion is smaller than the predetermined value, the sequence returns to the step S**4502** again, where the input signal, to which input timing jitter of larger amplitude than the previous time is applied, inputs to the DUT **3000**, and the processing of the steps S**4502**-S**4508** is repeated until the jitter distortion in the step **4508** becomes larger than the predetermined value.

If the jitter distortion is larger than the predetermined value in the step S**4508**, the jitter tolerance of the DUT **3000** is estimated in the jitter tolerance estimation step S**4510**. In the step S**4510**, the amplitude of the input timing jitter may be estimated as a jitter tolerance of the DUT **3000** at the frequency of the input timing jitter, when being judged in the step S**4508** that the jitter distortion is larger than the predetermined value. Moreover, the step S**4510** may be performed using the jitter related transmission penalty estimator **4102** described referring to FIG. 62.

Next, in a step S**4512**, it is judged whether there is any input timing jitter of another frequency which is to be measured further. If there is another input timing jitter frequency (or frequencies) which is to be measured, the frequency is set up in the S**4500** and the processing of the steps S**4500**-S**4510** is repeated. Moreover, if there is no input timing jitter frequency (or frequencies) to be measured any more, the measurement of the jitter tolerance is ended. That is, the signal input means **301** supplies the input signal, to which a plurality of sinusoidal jitters having different frequency are applied, to the DUT **3000** for example, and the jitter related transmission penalty estimator **4102** estimates the reliability of the DUT against the jitter for every frequency of the sinusoidal jitters. Moreover, the signal input means **301** may supply the input signal, to which the input timing jitters having a plurality of frequency components is applied, to the DUT **3000**. In this case, the reliability of the DUT **3000** against the jitters is measured for every frequency components.

FIG. 64 is an exemplary measurement of the jitter tolerance. In FIG. 64, a horizontal axis shows the amplitude of the input timing jitter having a predetermined frequency, and a vertical axis shows the amplitude of the output timing jitter.

As described referring to FIG. 63, the signal input means **301** of the measuring apparatus **100** supplies a plurality of input signals, having different amplitudes of the input timing jitter, to the DUT **3000**, and the jitter related transmission penalty estimator **4102** estimates the jitter tolerance of the DUT **3000** based on the jitter distortion of each of the output timing jitters against the plurality of input signals.

That is, as shown in the circles of FIG. 63, the jitter distortion estimator **4100** estimates the amplitude of the output timing jitters in response to a plurality of input timing jitters having different amplitudes, and the jitter related transmission penalty estimator **4102** estimates the jitter tolerance based on the amplitude of the input timing jitters, where the amplitude of the output timing jitter, in response to the amplitude of the input timing jitter, becomes nonlinear.

As described referring to FIG. 47, in the DUT **3000**, the clock recovery unit **3003** generates a recovered clock in response to the input signal, and the flip-flop **3001** and the serial-parallel converter **3002** output the received signal in response to the recovered clock. Therefore, when the amplitude of the input timing jitter in the input signal is small, the output timing jitter has a linear relation to the amplitude of the input timing jitter. However, when the amplitude of the input timing jitter becomes larger than the bit width of the input signal etc., for example, there is a possibility that the flip-flop **3001** and the serial-parallel converter **3002** output a different bit value from the bit value which is to be output. Therefore, the amplitude of the output timing jitter becomes nonlinear in response to the amplitude of the input timing jitter. In this case, as mentioned above, since the output signal may output a different bit value from the original bit value, the jitter tolerance of the DUT **3000** can be measured easily by detecting the region where the amplitude of the output timing jitter becomes nonlinear in response to the amplitude of the input timing jitter.

FIG. 65 is an exemplary structure of a jitter distortion estimator **4100**. In this example, the jitter distortion estimator **4100** measures the jitter distortion of the output timing jitter based on the spectrum of the output timing jitter sequence. The jitter distortion estimator **4100** includes a timing jitter spectrum estimator **4104** and a jitter distortion calculator **4106**. Moreover, in this example, the signal input means **301** applies the input timing jitter having a predetermined frequency, like a sinusoidal jitter for example, to the input signal.

The timing jitter spectrum estimator **4104** receives the output timing jitter sequence, and estimates the jitter spectrum of the output timing jitter sequence. For example, the timing jitter spectrum estimator **4104** estimates the jitter spectrum with Fourier transformation.

The jitter distortion calculator **4106** calculates the jitter distortion of the output timing jitter based on the jitter spectrum.

For example, the jitter distortion calculator **4106** calculates the distortion of the jitter spectrum of the output timing jitter in the output signal output from the DUT **3000**, against the jitter spectrum of the output timing jitter in the output signal which is to be output from the DUT **3000**.

FIG. 66 is another exemplary measurement of the jitter tolerance. FIG. 66 shows an example of the jitter spectrum of the output timing jitter of the output signal which the DUT **3000** is to output, when a sinusoidal jitter is applied to the input signal. In FIG. 66, a horizontal axis shows jitter frequency and a vertical axis shows the magnitude of the jitter at the jitter frequency. When the input timing jitter is applied to the input signal, the output timing jitter is determined by the jitter transfer function of the sinusoidal jitter and the DUT **3000**.

For example, when the sinusoidal jitter having a predetermined frequency is applied to the input signal, the spectrum of the output timing jitter has a peak at the fundamental frequency of the sinusoidal jitter, and having the magnitude according to the jitter transfer function.

When the amplitude of the applied input sinusoidal jitter is in the linear response region described referring to FIG. 64, the spectrum of the output timing jitter shows the spectrum according to the sine wave, as described referring to FIG. 66. That is, the levels of harmonics are low enough compared with the level of the fundamental.

FIG. 67 is another example of jitter spectrum of the output timing jitter of the output signal which is to be output from the DUT **3000** in a case where a sinusoidal jitter is applied to the input signal. In FIG. 67, a horizontal axis shows the jitter frequency and a vertical axis shows the magnitude of the jitter at the jitter frequency. When the amplitude of the sinusoidal jitter, which is applied to the input signal, is in the nonlinear response region described referring to FIG. 64, distortion appears in the spectrum of the output timing jitter, as shown in FIG. 67, against the spectrum shown in FIG. 66. That is, the levels of harmonics increase. The jitter distortion estimator **4100** described referring to FIG. 65 estimates the distortion. For example, based on the ratio of the level of the fundamental at the jitter frequency of input sinusoid, and the level of the harmonic in the jitter spectrum, or the jitter distortion of the output timing jitter is estimated. In this example, the jitter distortion estimator **4100** estimates that the output timing jitter is distorted, when the ratio of the level of the primary harmonic to the level of the fundamental is larger than a predetermined value. When jitter distortion arises in the output timing jitter, a bit error may occur in the output signal of the DUT **3000**.

According to the jitter distortion estimator **4100** in this example, it can be judged that whether a bit error occurs in the output signal of the DUT **3000** by the applied input timing jitter. Moreover, the jitter tolerance of the DUT **3000** can be estimated by performing the same estimation for a plurality of input timing jitters having different amplitude.

FIGS. 68 and 69 illustrate other examples for the measurement of the jitter tolerance. FIGS. 68 and 69 show jitter histograms of the amplitude of the output timing jitter when a sinusoidal jitter is applied as the input timing jitter. In FIGS. 68 and 69, a horizontal axis shows the amplitude of the output timing jitter by Unit Interval, and a vertical axis shows the frequency of occurrence at each amplitude.

FIG. 68 is a jitter histogram of the output timing jitter in a case where the amplitude of the applied sinusoidal jitter is in linear response region described referring to FIG. 64. In this example, when the amplitude of the input sinusoidal jitter is in-the linear response region, the DUT **3000** outputs the output timing jitter which has two peaks at the both ends of the jitter histogram, as shown in FIG. 68.

FIG. 69 is a jitter histogram of the output timing jitter in a case where the amplitude of the applied sinusoidal jitter is in nonlinear response region described referring to FIG. 64.

When the amplitude of the sinusoidal jitter, which is applied to the input signal, is in the nonlinear response region described referring to FIG. 64, the jitter histogram of the output timing jitter shown in FIG. 69 has distortion, against the jitter histogram shown in FIG. 68.

In this example, the jitter distortion estimator **4100** generates the jitter histogram of the output timing jitter sequence, and estimates the jitter distortion of the output timing jitter based on the jitter histogram. For example, the jitter distortion estimator **4100** may estimate the distortion of the output timing jitter against the input sinusoidal jitter based on whether there are two peaks at the both ends of a jitter histogram.

FIG. 70 is another exemplary structure of a jitter tolerance measuring apparatus as an example of the measuring apparatus **100**. In addition to the composition of the measuring apparatus **100** described referring to FIG. 62, the measuring apparatus **100** in this example further includes a jitter transfer function measuring apparatus **101** and a jitter tolerance estimator **302**. The jitter transfer function measuring apparatus **101** and the jitter tolerance estimator **302** have the same or similar function and structure as/to the jitter transfer function measuring apparatus **101** and the jitter tolerance estimator **302** described referring to FIG. 43.

First, the measuring apparatus **100** in this example measures the jitter tolerance by the method described referring to FIG. 44 using the timing jitter estimator **501**, the jitter transfer function measuring apparatus **101**, and the jitter tolerance estimator **301**. Next, the signal input means **301** supplies a first test signal to the DUT **3000**, where the timing jitter of amplitude according to the jitter tolerance estimated by the jitter tolerance estimator **302** is applied to the first test signal.

The jitter distortion estimator **4100** estimates the jitter distortion of the output timing jitter of the output signal output from the DUT **3000** in response to the first test signal, against the ideal timing jitter of the output signal which the DUT **3000** is to output in response to the first test signal.

Then, the jitter related transmission penalty estimator **4102**, which is an example of the judging unit judges whether the jitter tolerance estimated by the jitter tolerance estimator **302** is the right value based on the jitter distortion estimated by the jitter distortion estimator **4100**.

When the jitter related transmission penalty estimator **4102** judges that the jitter tolerance is not the right value, the signal input means **301** supplies a second test signal to the DUT **3000**, where the timing jitter having smaller jitter amplitude than the first test signal is applied on the second test signal, and the jitter distortion estimator **4100** estimates the jitter distortion of the output timing jitter of the output signal which DUT **3000** outputs in response to the second test signal, against the ideal timing jitter of the output signal which DUT **3000** is to output in response to the second test signal. And the jitter related transmission penalty estimator **4102** newly estimates the jitter tolerance based on the jitter distortion corresponding to the second test signal estimated by the jitter distortion estimator **4100**. For example, the jitter tolerance may be estimated newly by the processing of the steps of S**4502**-S**4508** described referring to FIG. 63.

According to the measuring apparatus **100** in this example, the jitter tolerance of the DUT **3000** can be measured precisely and rapidly. That is, since the jitter tolerance is measured by each method described referring to FIGS. 44 and 63, the jitter tolerance can be measured precisely. For example, even if there is a tendency that the jitter tolerance measured by the method explained in FIG. 44 shows a larger value, the jitter tolerance can be measured with a still more sufficient precision. Moreover, the jitter tolerance can be measured at high speed by the method described referring to FIG. 63 by estimating the coarse value of the jitter tolerance by the method described referring to FIG. 44 at first. Moreover, like the measuring apparatus **100** explained in FIG. 56, the measuring apparatus **100** in this example may select either the input data signal or the input data clock signal as the input signal, and may select either the output data signal or the recovered clock signal as the output signal.

FIG. 71 shows yet another example of a configuration of the measuring apparatus **100**. The measuring apparatus **100** in this example measures the jitter tolerance on which the effect of the deterministic jitter caused by a transmission line connected to an input terminal of the electronic device **3000** being used is included, and the jitter tolerance of the electronic device **3000** on which no effect of the deterministic jitter is included.

Here, the deterministic jitter means timing variation in delay of each edge of the input signal which deviates according to the signal pattern of the input signal. That is, the deterministic jitter means the variation in delay time of the edges caused by, for example, a time interval between the edges of the input signal.

Since the transmission line includes an inductance component, a capacitance component, etc., a difference occurs in rising or falling time of each edge by the edge interval of the input signal. Therefore, the jitter (deterministic jitter) occurs at the timing of the rising edge or the timing of the falling edge of the input signal with respect to the ideal edge timing. The deterministic jitter is defined by the pattern of the input signal, the property of the transmission line per unit length, and the length of the transmission line.

Conventionally, in measurement of the jitter tolerance of the electronic device **3000**, the deterministic jitter generated by the transmission line during propagation has not been taken into consideration. Therefore, the jitter tolerance value under the actual condition deteriorates more than the measured jitter tolerance.

Moreover, for example, some standard specifies a relatively long transmission line, which might be connected to the electronic device **3000** conventionally. In this conventional measurement case, since the transmission line injects the deterministic jitter into the input signal, the measured bit error rate and the jitter tolerance are suffered from this additional deterministic jitter. That is, the estimated bit error rate or the jitter tolerance value of the system includes both the effects of transmission line and the BER or the jitter tolerance value of the electronic device. However, the measured result has been regarded as the bit error rate and the jitter tolerance of the electronic device **3000** only. Therefore, the bit error rate and jitter tolerance of the electronic device **3000** has not been able to be measured with sufficient accuracy.

The measuring apparatus **100** in this example measures the jitter tolerance with the effects of the deterministic jitter being excluded, and the jitter tolerance including the effects of the deterministic jitter. Therefore, the jitter tolerance of the system, which includes a long transmission line causing the deterministic jitter under the actual conditions, can be measured. Moreover, the jitter tolerance of only the electronic device **3000** can be measured with sufficient accuracy. For example, even if it is tested in the environment where the length of transmission lines differ, the repeatable test of the jitter tolerance of the electronic device **3000** can be performed.

For example, as shown in FIG. 71, the measuring apparatus **100** includes a jitter transfer function measuring apparatus **101**, a jitter related transmission penalty estimator **4102**, a system jitter tolerance estimator **392**, a jitter tolerance degradation quantity estimator **390**, and an input signal generating unit **388**.

The input signal generating unit **388** generates the input signal which is input into the electronic device **3000**. The input signal is a digital signal which includes a desired pattern. Moreover, the input signal generating unit **388** applies a desired input timing jitter on the input signal. That is, the input signal generating unit **388** has similar function to the signal input means **301** described with reference to FIG. 43.

The input signal is input into the electronic device **3000** through a transmission line, and the electronic device **3000** outputs the output signal corresponding to the input signal. In this example, the length of the transmission line is shorter than a predetermined length thereby the transmission line does not inject into the input signal being transmitted. Alternatively, the output signal may be the recovered clock described with reference to FIG. 47.

The jitter transfer function measuring apparatus **101** and the jitter related transmission penalty estimator **4102** include the same or similar function and configuration as/to those of the jitter transfer function measuring apparatus **101** described with reference to FIG. 43 and the jitter related transmission penalty estimator **4102** described with reference to the FIG. 62. The jitter related transmission penalty estimator **4102** in this example includes a bit error rate estimator **102** and a jitter tolerance estimator **302** described with reference to FIG. 43. Moreover, although the jitter related transmission penalty estimator **4102** estimates reliability of the jitter based on the gain and the phase of the jitter transfer function, the jitter related transmission penalty estimator **4102** may estimate the reliability of the jitter based on the jitter distortion of the output timing jitter of the output signal in another example. In this case, the measuring apparatus **100** includes the timing jitter estimator **501** and the jitter distortion estimator **4100** described with reference to FIG. 62 instead of the jitter transfer function measuring apparatus **101**. Moreover, in this example, since the transmission line does not cause a deterministic jitter, the jitter related transmission penalty estimator **4102** estimates the reliability of the jitter of the electronic device **3000**.

Here, the jitter tolerance inf(Δθ_{pp}) of the system including the transmission line and the electronic device **3000** is expressed by the following Equation.

Where, Δτ_{pp}(l) is the deterministic jitter in the input signal when the signal is transmitted through a transmission line which has length 1. That is, the first term of the right-hand side of Equation (65) gives the jitter tolerance of the electronic device, and the second term of the right-hand side gives the quantity of the degradation of the jitter tolerance deteriorated in the transmission line by the deterministic jitter.

Moreover, when the transmission line is shorter than a predetermined length l_{th}, the quantity of the degradation of the jitter tolerance by the deterministic jitter in the input signal transmitted in the transmission line is negligible. Therefore, the jitter tolerance inf(Δθ_{pp}) of the system can be expressed by the following Equation.

Where, u(l) is a unit-step function, which is one when 1 is greater than zero, and is zero when 1 is equal to or less than zero.

Moreover, the jitter tolerance inf(Δθ_{pp}) of the system can be expressed by the following Equation.

Where, Δθ_{MOD }is equal to or substantially equal to 0.5 UI.

The jitter tolerance degradation quantity estimator **390** estimates the quantity of the jitter tolerance caused by the degradation of the deterministic jitter in the input signal transmitted through the transmission line based on the input signal. That is, the jitter tolerance degradation quantity estimator **390** estimates the second term of the right-hand side of Equation (65), Equation (66), or Equation (67). The detail of estimation of the quantity of degradation will be described hereinafter with reference to FIG. 72.

In this example, the jitter tolerance degradation quantity estimator **390** estimates the quantity of jitter tolerance degradation in the long transmission line during use. At this time, the pattern of the input signal, the property of the long transmission line per unit length, and the length of the long transmission line during use of the electronic device **3000** are input into the jitter tolerance degradation quantity estimator **390**, thereby the quantity of jitter tolerance degradation by the deterministic jitter of the long transmission line during use will be estimated based on the result.

The system jitter tolerance estimator **392** estimates the jitter tolerance of the system including the long transmission line and the electronic device **3000** during use by correcting the jitter tolerance estimated by the jitter tolerance estimator **302** based on the quantity of jitter tolerance degradation estimated by the jitter tolerance degradation quantity estimator **390**. For example, the jitter tolerance of the system is estimated using Equation (65), Equation (66), and Equation (67).

Moreover, even if the measuring apparatus **100** connects the long transmission line, which causes the deterministic jitter, to the electronic device **3000** at the time of the test of the electronic device **3000**, it can estimate the jitter tolerance of the system including the long transmission line and the electronic device **3000** during use. In this case, the jitter tolerance degradation quantity estimator **390** estimates the difference between the deterministic jitter in the transmission line at the time of the test and the deterministic jitter in the transmission line during use. Then, the system jitter tolerance estimator **392** corrects the jitter tolerance estimated by the jitter tolerance estimator **302** computed based on the difference. When measuring the jitter tolerance of only the electronic device **3000** via the transmission line causing the deterministic jitter at the time of the test of the electronic device **3000**, the jitter tolerance degradation quantity estimator **390** estimates the quantity of jitter tolerance degradation in the transmission line at the time of the test, and the system jitter tolerance estimator **392** functions as a device jitter tolerance estimator which estimates the jitter tolerance of the electronic device **3000** based on the jitter tolerance of the electronic device **3000** estimated by the jitter tolerance estimator **302** and also based on the quantity of jitter tolerance degradation estimated by the jitter tolerance degradation quantity estimator **390**. In this case, the device jitter tolerance estimator computes the jitter tolerance of the first term of the right-hand side using Equation (64), Equation (65), and Equation (66).

Moreover, although the jitter tolerance estimator **302** estimates the jitter tolerance based on the gain, phase, or jitter distortion of the jitter transfer function in this example, the bit error rate estimator **102** may directly detect the bit error of the output signal, and the jitter tolerance estimator **302** may estimate the amplitude of the input timing jitter, by which the bit error rate estimator **102** detects the bit error, as the jitter tolerance in another example. In this case, the input signal generating unit **388** sequentially inputs a plurality of input signals, on which the input timing jitter having increasing amplitude is applied, into the electronic device **3000**, and the jitter tolerance estimator **302** detects the amplitude of the input timing jitter by which the bit error is detected.

An example of operation of the bit error rate estimator **102** in this case will be explained hereinafter.

When the electronic device **3000** is a deserializer as shown in FIG. 47, the bit error rate estimator **102** receives at least one of parallel data signals output from the electronic device **3000** and recovered clock output from the electronic device, and digitizes them. The sampling rate is preferably three or more times of the frequency of the digitized signal.

Next, the digitized signal is binarized by a comparator means or the like, and the binarized parallel signal is sampled at the rising edge of the digitized recovered clock. A generated binary series and the reference pattern signal are compared with each other, and then the bit error is detected.

Incidentally, in a 15-stage PRBS (pseudo random binary sequence), there exists at least one portion where consecutive “1” bits form the run, which has length 15, in a serial bit stream. Therefore, the binary series and the standard PRBS are aligned with each other by pattern matching the portion corresponding to such maximum length. Finally, the error of the binary series is detected by comparing them bit-by-bit.

FIG. 72 shows an example of the configuration of the jitter tolerance degradation quantity estimator **390**. The jitter tolerance degradation quantity estimator **390** includes an input signal spectrum estimator **394**, the transmission line property estimator **396**, and the deterministic jitter estimator **398**.

The input signal spectrum estimator **394** receives the input signal to be input into the transmission line from the input signal generating unit **388**, and estimates the spectrum of the input signal. The transmission line property estimator **396** estimates transmission property in the transmission line for every frequency band. For example, it is preferable that the transmission line property estimator **396** stores the transmission property per unit length in advance for every kind of the transmission line. In this case, the kinds and lengths of the transmission lines are input into the transmission line property estimator **396**, and the transmission property in the transmission line is estimated based on the kinds and lengths of the transmission line.

The deterministic jitter estimator **398** estimates the jitter tolerance deteriorated due to the deterministic jitter in the input signal transmitted through the transmission line based on the spectrum of the input signal estimated by the input signal spectrum estimator **394** and the transmission property of the transmission line. The deterministic jitter can be estimated because the quantity of delay of each edge of the input signal can be estimated based on the spectrum component of the input signal and the passage property for every frequency band of the transmission line. Moreover, the deterministic jitter estimator **398** may estimate the peak value of the amplitude of the deterministic jitter as the quantity of jitter tolerance degradation.

Moreover, in another example of the jitter tolerance degradation quantity estimator **390**, the quantity of jitter tolerance degradation can be estimated by the deterministic jitter caused in the input signal which is transmitted through the transmission line by comparing the input signal input into the transmission line from the input signal generating unit **388** with the input signal input into the electronic device **3000** from the transmission line. The quantity of jitter tolerance degradation caused in the transmission line can be estimated by comparing the signal input into the transmission line with the signal output from the transmission line.

FIG. 73 is a flow chart exemplary showing an operation of the measuring apparatus **100**. First, in S**4300**, the frequency of the input timing jitter, which is applied on the input signal supplied by the input signal generating unit **388** to the electronic device **3000**, is set.

Next, in S**4302**, the amplitude of the input timing jitter applied on the input signal is set. Then, in S**4304**, it is detected whether there is a bit error in the output signal output from the electronic device in response to the input signal.

When a bit error is not detected in the output signal, the amplitude of the input timing jitter is made to increase and S**4302**-S**4306** are repeated. When a bit error is detected in the output signal, the amplitude of the input timing jitter at this time is defined as the jitter tolerance (S**4308**). As mentioned above, the measuring apparatus **100** estimates the jitter tolerance of the system and the jitter tolerance of the electronic device **3000** at the frequency of the input timing jitter.

Then, it is judged whether there remains any frequency band to be tested (S**4310**), and the process ends when the jitter tolerance is computed about all the jitter frequencies that are to be tested. When there remains the jitter frequency to be tested, the steps of S**4300**-S**4310** will be repeated.

By the above-mentioned steps, at all the frequencies of the input timing jitter, the jitter tolerance of the system, and the jitter tolerance of the electronic device **3000** can be estimated.

Although the present invention has been described by way of exemplary embodiments, it should be understood that those skilled in the art might make many changes and substitutions without departing from the spirit and the scope of the present invention which is defined only by the appended claims. Also, it should be understood that the measuring apparatus and measuring method of the present invention might also measure or test network system including optical devices. That is, network system including circuits, electronic devices, optical devices, and other systems may be included in the scope of the electronic device of the present invention which is defined only by the appended claims. Moreover, circuits, electronic devices, and systems, which include devices such as optical devices inside, may be included in the scope of the electronic device of the present invention which is defined only by the appended claims.

As is apparent from the above, according to the present invention, the jitter transfer function, the bit error rate and the jitter tolerance of the DUT can be calculated efficiently. Moreover, the system jitter tolerance including the influence of the deterministic jitter and the device jitter tolerance which does not include the influence of the deterministic jitter can be measured easily.