Apparatus and method for measuring quality measure of phase noise waveform

[0002] The present invention relates to an apparatus and a method for measuring a quality measure of a clock signal that drives, for example, a microprocessor.

[0003] A jitter has traditionally been used as a measure for estimating quality of a clock signal of a microprocessor. Incidentally, there are two types of jitters, i.e., a period jitter and a timing jitter. As shown in FIG. 1A, in a jitter-free ideal clock signal, for example, an interval T_intbetween adjacent rising points is constant as indicated by a dotted line waveform, and in this case a period jitter is zero. In an actual clock signal, a rising edge fluctuates from an arrow toward leading side or trailing side, i.e., an interval T_intbetween adjacent rising points fluctuates, and this fluctuation of the interval is a period jitter. For example, in the case of a sine wave that does not have a rectangular waveform like a clock signal, a fluctuation of an interval T_intbetween zero crossing points is also a period jitter.

[0004] As shown in FIG. 1B, when a jitter-free square waveform is assumed to be a dashed line waveform, a deviation width Δφ of an actual rising point (solid line) from a normal rising point (dashed line) is a timing jitter in the case of a jittery square waveform.

[0005] A conventional measurement of a period jitter is performed by a time interval analyzer (hereinafter, this measuring method is referred to as a time interval method or a TIA method). This is shown in “Phase Digitizing Sharpens Timing Measurements”, by David Chu, IEEE Spectrum, pp. 28-32, 1988, and “Time Domain Analysis and Its Practical Application to the Measurement of Phase Noise and Jitter”, by Lee D. Cosart et al., IEEE Trans. Instrum. Meas., vol. 46, pp. 1016-1019, 1997. This time interval method is a method in which zero crossing points of a signal under test are counted, an elapsed time is measured, and a time fluctuation between zero crossing points is obtained to obtain a period jitter. In addition, a root-mean-square value of the period jitters is obtained.

[0006] There is a method, as a conventional timing jitter measurement, in which a timing jitter is measured by measuring a phase noise-spectrum in frequency domain, and those spectrums are summed to estimate a root-mean-square value of timing jitters.

[0007] The inventors of the present invention have proposed a method of measuring a jitter as described below in an article entitled “An Application of An Instantaneous Phase Estimating Method to A Jitter Measurement” in a technical report “Probo” pp. 9-16 issued by Probo Editorial Room of ADVANTEST CORPORATION, Nov. 12, 1999. That is, as shown in FIG. 2, an analog clock waveform from a PLL circuit under test (Phase locked loop) 11 is converted into a digital clock signal x_c(t) by an analog-digital converter 12, and the digital clock signal x_c(t) is supplied to a Hilbert pair generator 14 acting as analytic signal transforming means 13, where the digital clock signal x_c(t) is transformed into an analytic signal z_c(t).

[0008] Now, a clock signal x_c(t) is defined as follows.

[0009] x_c(t)=A_ccos(2πf_ct+θ_c+Δφ(t))

[0010] The A_cand the f_care nominal values of amplitude and frequency of the clock signal respectively, the θ_cis an initial phase angle, and the Δφ(t) is a phase fluctuation that is called a phase noise.

[0011] The clock signal x_c(t) is Hilbert-transformed by a Hilbert transformer 15 in the Hilbert pair generator 14 to obtain the following equation.

[0012] {circumflex over (x)}_c(t)=H[x_c(t)]=A_csin(2πf_ct+θ_c+Δφ(t))

[0013] Then, an analytic signal z_c(t) having x_c(t) and {circumflex over (x)}_c(t) as a real part and an imaginary part, respectively is obtained as follows. $\begin{array}{c}{z}_c\left(t\right)=x_c\left(t\right)+{\hat{x}}_c\left(t\right)\\ =A_c\cos (2\pi f_{c}t+{\theta }_c+\Delta \phi \left(t\right)+j{A}_c\sin \left(2\pi f_{c}t+{\theta }_c+\Delta \phi \left(t\right)\right)\end{array}$

[0014] From this analytic signal z_c(t), an instantaneous phase Θ(t) of the clock signal x_c(t) can be estimated by the instantaneous phase estimator 16 as follows.

[0015] Θ(T)=[2πf_ct+θ_c+Δφ(t)] mod 2π

[0016] A linear phase is removed from this instantaneous phase Θ(t) by a linear phase remover 17 to obtain a phase noise waveform Δφ(t). That is, in the linear phase remover 17, a continuous phase converting part 18 applies a phase unwrap method to the instantaneous phase Θ(t) to obtain a continuous phase θ(t) as follows.

[0017] θ(t)=2πf_ct+θ_c+Δφ(t)

[0018] The phase unwrap method is shown in “A New Phase Unwrapping Algorithm” by Jose M. Tribolet, IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-25, pp. 170-177, 1977 and in “On Frequency-Domain and Time-Domain Phase Unwrapping” by Kuno P. Zimmermann, Proc. IEEE. vol. 75, pp. 519-520, 1987.

[0019] A linear phase [2πf_ct+θ_c] of a continuous phase θ(t) is estimated by a linear phase evaluator 19 using a linear trend estimating method. This estimated linear phase [2πf_ct+θ_c] is subtracted from the continuous phase θ(t) by a subtractor 21 to obtain a variable term Δφ(t) of the instantaneous phase Θ(t), i.e., phase noise waveform as follows.

[0020] θ(t)=Δφ(t)

[0021] The phase noise waveform Δφ(t) thus obtained is inputted to a peak-to-peak detector 22, where a difference between the maximum peak value max (Δφ(k)) and the minimum peak value min (Δφ(1)) of the Δφ(t) is calculated to obtain a peak value Δφ_ppof timing jitters as follows. $\Delta {\phi }_{\mathrm{pp}}=\underset{k}{\max }\left(\Delta \phi \left(k\right)\right)-\underset{l}{\min }\left(\Delta \phi \left(1\right)\right)$

[0022] In addition, the phase noise waveform Δφ(t) is inputted to a root-mean-square detector 23, where a root-mean-square value of the phase noise waveform Δφ(t) is calculated using following equation to obtain a root-mean-square value Δφ_RMSof timing jitters. $\Delta {\phi }_{\mathrm{RMS}}=\sqrt{\frac{1}{N}\sum _{k=0}^{N-1}\Delta {\phi }^2\left(k\right)}$

[0023] A method for obtaining, in this manner, a peak value of timing jitters and/or a root-mean-square value of timing jitters from the phase noise waveform Δφ(t) is called a Δφ method. According to the Δφ method, a jitter measurement can be performed in a test time of 100 millisecond order since measuring points are not limited to zero crossing points. Further, in FIG. 2, the analytic signal transforming means 13, the instantaneous phase estimator 16 and the linear phase remover 17 compose phase noise detecting means 25.

[0024] In the case of a jitter that each rising edge of a clock signal fluctuates in the same direction with substantially same quantity, a microprocessor driven by this clock signal is not influenced so much by the jitter. In a design of a PLL circuit that generates a clock signal, a correlation coefficient between rising edges of the clock signal is important. The correlation coefficient takes a vale of −1 to +1. If, for example, this value is 0.6, it can be seen that the PLL circuit has room for improvement in correlation coefficient by 0.4. It can be deemed that a fluctuation between adjacent rising edges of a clock signal consists of a linear fluctuation (signal) in which a fluctuation of a following rising edge depends on a fluctuation of an immediately leading rising edge and a fluctuation (noise) in which a fluctuation of a following rising edge does not relate to a fluctuation of an immediately leading rising edge, whereby a signal to noise ratio of a fluctuation of a rising edge can be defined. Such a correlation coefficient or a signal to noise ratio can clarify more correctly than a root-mean-square value of period jitters or a root-mean-square value of timing jitters can as to whether or not, for example, a PLL circuit operates in the performance close to its theoretical limit. In addition, if such a correlation coefficient or a signal to noise ratio can be measured, those are effective for a test of a PLL circuit or the like. However, a method for measuring such a correlation coefficient or a signal to noise ratio between zero crossings of a signal, namely a quality measure of a phase noise waveform has not been proposed up to today.

[0025] It is an object of the present invention to provide an apparatus and a method that can measure a quality measure of a phase noise waveform.

[0026] According to a method of the present invention, an input signal is transformed into a complex analytic signal, and an instantaneous phase of the analytic signal is obtained. A linear phase is removed from the instantaneous phase to obtain a phase noise waveform, and a correlation coefficient and/or a signal to noise ratio of the phase noise waveform, i.e., a quality measure of the phase noise waveform is obtained from the phase noise waveform. That is, according to the present invention, a quality measure is obtained by the aforementioned Δφ method.

[0027] A signal to noise ration is obtained from the correlation coefficient. There will be explained below a principle for obtaining a correlation coefficient, and also for obtaining a signal to noise ratio from the correlation coefficient.

[0028] A correlation coefficient ρ_tt(T) between adjacent zero crossing points nT and (n+1)T of an instantaneous timing jitter {Δφ(nT)} (T is a period of a clock signal) is obtained as follows.

[0029] A period jitter J_pis obtained from a difference between two timing jitters Δφ(nT) and Δφ((n+1)T) of an input signal each being spaced apart from one another by a period T. A variance σ_p²(T) of this period jitter J_pis obtained by the following equation as an expected value of the period jitter J_p. $\begin{array}{c}{\sigma }_p^2\left(T\right)=E\left({\left\{\Delta \phi \left(\left(n+1\right)T\right)-\Delta \phi \left(T\right)\right\}}^2\right)\\ =E\left({\left\{\Delta \phi \left(\left(n+1\right)T\right)\right\}}^2\right)-2E\left(\Delta \phi \left(\left(n+1\right)T\right)\Delta \phi \left(T\right)\right)+E\left({\left\{\Delta \phi \left(T\right)\right\}}^2\right)\\ ={\sigma }_t^2-2\frac{E\left(\Delta \phi \left(\left(n+1\right)T\right)\Delta \phi \left(T\right)\right)}{{\sigma }_t{\sigma }_t}{\sigma }_t{\sigma }_t+{\sigma }_t^2\end{array}$

[0030] In this case, σ_t²is a variance of timing jitter Δφ(T).

[0031] From equations (7-6) and (7-8) in page 150 of “Probability, Random Variables, and Stochastic Processes” by A. Papoulis, 2nd Edition, McGraw-Hill Book Company, and from a fact that each of Δφ(nT) and Δφ((n+1)T) is a deviation from an average value, $\frac{E\left(\Delta \phi \left(\left(n+1\right)T\right)\Delta \phi \left(T\right)\right)}{{\sigma }_t{\sigma }_t}$

[0032] is a correlation coefficient ρ_ttbetween Δφ(nT) and Δφ((n+1)T). Therefore, the following equation is obtained.

[0033] σ_p²(T)=2(1−ρ_tt(T))σt²(T)  (1)

[0034] This can be re-written as follows. $\begin{array}{cc}{\rho }_{\mathrm{tt}}\left(T\right)=1-\frac{{\sigma }_p^2\left(T\right)}{2{\sigma }_t^2\left(T\right)}& \left(2\right)\end{array}$

[0035] In the above equation, σ_p(T) is a root-mean-square value of period jitters J_p, and σ_t,(T) is a root-mean-square value of timing jitters Δφ(T).

[0036] Alternatively, a correlation coefficient σ_tt(T) can be obtained, from the definition of a correlation coefficient, by the following equation using a timing jitter {Δφ(nT)}. $\begin{array}{cc}{\rho }_{\mathrm{tt}}\left(T\right)=\frac{{\sigma }_{\mathrm{tt}}}{{\sigma }_t{\sigma }_t}=\frac{\sum _i\left\{\Delta \phi \left(\mathrm{iT}\right)-\Delta {\phi }^{\prime }\right\}\left\{\Delta \phi \left(\left(i+1\right)T\right)-\Delta {\phi }^{\prime }\right\}}{\sum _i{\left(\Delta \phi \left(\mathrm{iT}\right)-\Delta {\phi }^{\prime }\right)}^2}& \left(3\right)\\ =\frac{\sum _i\Delta \phi \left(\mathrm{iT}\right)\Delta \phi \left(\left(i+1\right)T\right)-\Delta {\phi }^{\prime 2}}{\sum _i{\left(\Delta \phi \left(\mathrm{iT}\right)-\Delta {\phi }^{\prime }\right)}^2}& \left(4\right)\end{array}$

[0037] In the above equation, Δφ′ is an average value of the Δφ(nT).

[0038] Further, since Δφ(iT) itself is a deviation from the linearity according to the definition of a timing jitter, Δφ′ is zero and hence this may be omitted from the equations (3) and (4). In addition, since Δφ′/σ_tis a small value such as Δφ′/σ_t≡{fraction (6/1000)} from an experiment, Δφ′ may be omitted from the equations (3) and (4).

[0039] A timing jitter variance σ_tt²of Δφ((n+1)T) that fluctuates against a timing jitter Δφ(nT) based on only a linear relationship with its fluctuation can be expressed by the following equation.

[0040] σ_tt²=ρ_tt²σ_t(n+1)²  (5)

[0041] A timing jitter variance σ_t,n²of Δφ((n+1)T) that fluctuates against a timing jitter Δφ(nT) based on other noises including a nonlinear relationship with its fluctuation can be expressed by the following equation.

[0042] σ_t,n=(1−ρ_tt²)σ_t(n+1)²  (6)

[0043] The equations (5) and (6) are shown in equations (3.10) and (3.11) in page 43-47 of “Engineering Applications of Correlation and Spectral Analysis” by J. S. Bendat & A. G. Piersol, John Wiley & Sons, 1980.

[0044] From the equations (5) and (6), a ratio of a linear fluctuation (signal component) of a timing jitter {Δφ((n+1)T)} based on a fluctuation of Δφ(nT) to a fluctuation (noise) not related to a fluctuation of the Δφ(nT), i.e., a noise to signal ratio SNR_tcan be obtained by the following equation. $\begin{array}{cc}{\mathrm{SNR}}_t=\frac{{\sigma }_{t,t}^2}{{\sigma }_{t,n}^2}=\frac{{\rho }_{\mathrm{tt}}^2}{1-{\rho }_{\mathrm{tt}}^2}& \left(7\right)\end{array}$

[0045] Incidentally, if a timing jitter variance σ_tis large, 1/SNR_tis also large, and if a timing jitter variance σ_tis small, 1/SNR_tis also small. That is, σ_tis proportional to 1/SNR_t. Therefore, if σ_t²in the right side of the equation (1) is multiplied by 1/SNR_tas a proportional coefficient, and the both sides are extracted and then the both sides are divided by T, the following equations can be obtained. $\begin{array}{cc}\frac{{\sigma }_p}{T}\propto \sqrt{2\left(1-{\rho }_{\mathrm{tt}}\right)}·\frac{\sqrt{\frac{{\sigma }_t^2}{{\mathrm{SNR}}_t}}}{T}& \left(8\right)\end{array}$

[0046] As mentioned above, by obtaining a period jitter variance σ_pand a timing jitter variance σ_t, a correlation coefficient ρ_ttof a timing jitter, i.e., a phase noise waveform Δφ(t) can be obtained. In addition, a correlation coefficient ρ_ttcan be obtained from the equations (3) and (4) using a timing jitter Δφ(nT). Furthermore, a signal to noise ratio SNr_tof a phase noise waveform Δφ(t) can be obtained from the equation (7) using the correlation coefficient ρ_tt.

[0047] In the present invention, a quality measure such as a correlation coefficient ρ_ttor a signal to noise ratio SNR_tis obtained by such a method using the Δφ(t).

[0048] FIG. 1A is a diagram for explaining a period jitter;

[0049] FIG. 1B is a diagram for explaining a timing jitter;

[0050] FIG. 2 is a block diagram showing a functional configuration of an apparatus for measuring a jitter based on the proposed Δφ method;

[0051] FIG. 3 is a block diagram showing a functional configuration of an embodiment of an apparatus for measuring a quality measure according to the present invention;

[0052] FIG. 4 is a diagram showing a relationship among zero crossing points of a real part x_c(t), a phase noise waveform and period jitters of an input signal;

[0053] FIG. 5 is a block diagram showing a functional configuration of another embodiment of the present invention;

[0054] FIG. 6 is a block diagram showing a modified example of analytic signal transforming means 13;

[0055] FIG. 7 is a block diagram showing another modified example of the analytic signal transforming means 13;

[0056] FIG. 8 is a graph showing experimental results; and

[0057] FIG. 9 is a diagram showing their numeric values.

[0058] FIG. 3 shows an embodiment of the present invention. Portions in FIG. 3 corresponding to those in FIG. 2 have the same reference numerals affixed thereto as those in FIG. 2. In the present invention, similarly to the case shown in FIG. 2, an input signal from a PLL circuit under test 11 or the like is converted into a digital signal by an AD converter 12. This digital signal is inputted to phase noise detecting means 25, by which a phase noise waveform Δφ(t) is extracted therefrom. This phase noise waveform Δφ(t) is supplied to timing jitter root-mean-square value detecting means 31 and period jitter root-mean-square value detecting means 32. In the timing jitter root-mean-square value detecting means 31, a root-mean-square value Δφ_RMSof the inputted phase noise waveform Δφ(t) is calculated. In the period jitter root-mean-square value detecting means 32, a root-mean-square value J_RMSof the period jitters J_pis calculated from the inputted phase noise waveform Δφ(t).

[0059] In the timing jitter root-mean-square value detecting means 31 and the period jitter root-mean-square value detecting means 32, in this example, the phase noise waveform Δφ(t) is sampled by a zero crossing sampler 33 at a timing closest to a zero crossing point of a real part x_c(t) of an analytic signal z_c(t).

[0060] That is, a waveform of a real part x_c(t) of an analytic signal is shown in FIG. 4A, and a sampling point (arithmetic processing point) closest to a zero crossing point of the rising (or falling) edge of the waveform is detected by a zero crossing point detecting part 34. In FIG. 4A, a point closest to the detected zero crossing point is indicated by a mark ◯. This point is called an approximate zero crossing point. As shown in FIG. 4B, a value of the phase noise waveform Δφ(t) indicated by a mark ◯ is extracted by a zero crossing sampler 33 as a sample value at the approximate zero crossing point. Each of the extracted sample values (re-sampled phase noise waveform) is a deviated quantity from an ideal timing (zero crossing point) of a real part x_c(t) of a jitter-free analytic signal. Regarding the sample values of the Δφ(t), when a difference between each sample value and its immediately previous sample value is obtained, this difference is a fluctuation between zero crossings, i.e., a period jitter J_p. A period jitter J_pcan be obtained from nth sample value Δφ_nand (n+1)th sample Δφ_n+1of the Δφ(t) in FIG. 4B as J_pΔφ_n+1−Δφ_n. The J_pthus obtained is shown in FIG. 4C.

[0061] A detecting method of an approximate zero crossing point in the zero crossing point detecting part 34 will be explained. The maximum value of a waveform of an inputted real part x_c(t) is defined as 100% level, and the minimum value is defined as 0% level to calculate 50% level V (50%) of the difference between the 100% level and the 0% level as a zero crossing level. A difference between a sample value and 50% level V (50%) and a difference between its adjacent sample value and 50% level V (50%), i.e., (x_c(j−1)−V (50%)) and (x_c(j)−V (50%)) are calculated, and further a product of those difference values (x_c(j−1)−V(50%))×(x_c(j)−V (50%)) is calculated. When the x_c(t) crosses 50% level, i.e., zero level, the sign of its sample value x_c(j−1) or x_c(j) changes from a negative sign to a positive sign or from a positive sign to a negative sign. Therefore, when the product is negative, it is detected that the x_c(t) has passed the zero level, and a time point j−1 or j at which a smaller absolute value of the sample value x_c(j−1) or x_c(j) is detected is obtained as an approximate zero crossing point.

[0062] The re-sampled phase noise waveform from the zero crossing sampler 33 is inputted to a Δφ_MRS(root-mean-square value) detector 35, where its root-mean-square value is calculated by the following equation to obtain a timing jitter root-mean-square value Δφ_RMS, i.e., σ_t. $\Delta {\phi }_{\mathrm{RM}S}={\sigma }_t=\sqrt{\frac{1}{N}\sum _{n=0}^{N-1}\Delta {\phi }^2\left(\mathrm{nT}\right)}$

[0063] In addition, in the period jitter root-mean-square value detecting means 32, regarding the sample values from the zero crossing sampler 33, a difference between each sample value and its immediately previous sample value is obtained by the differential circuit 36 in the sequential order to obtain a period jitter J_p. Regarding a series of obtained period jitters J_p, a root-mean-square value is calculated by a J_RMS(root-mean-square value) detector 37. That is, a differential waveform of a re-sampled phase noise waveform from the zero crossing sampler 33 is calculated by the differential circuit 36, and the differential phase noise waveform is supplied to the root-mean-square value detector 37, where the following equation is calculated. $J_{R\mathrm{MS}}={\sigma }_p=\sqrt{\frac{1}{N}\sum _{n=0}^{N-1}{J}_p^2\left(n\right)}$

[0064] In this manner, a period jitter root-mean-square value J_RMS, i.e., a period jitter variance σ_pcan be obtained.

[0065] The timing jitter root-mean-square value Δφ_RMS(timing jitter variance σ_t) and the period jitter root-mean-square value J_RMS(period jitter variance σ_p) obtained as mentioned above are inputted to quality measure estimating means 38. In the quality measure estimating means 38, the equation (2) is calculated by correlation coefficient (ρ_tt) calculator 39 based on the σ_tand the σ_pto obtain a correlation coefficient ρ_tt. In this example, this correlation coefficient ρ_ttis inputted to a signal to noise ratio (SNR_t) calculator 41, by which the equation (7) is calculated based on this ρ_ttto obtain the SNR_t. The correlation coefficient ρ_ttand/or the signal to noise ratio SNR_tare outputted from an output terminals 42 and/or an output terminal 43 as quality measures, respectively.

[0066] FIG. 5 shows another embodiment of the present invention. Portions in FIG. 5 corresponding to those in FIG. 3 have the same reference numerals affixed thereto as those in FIG. 3. In this embodiment, the equation (3) from which the Δφ′ is omitted is calculated by the correlation coefficient (ρ_tt) calculator 39 with respect to the re-sampled phase noise waveform from the zero crossing sampler 33. That is, two series of re-sampled phase noise waveforms having a time difference of period T between them are inputted to a product-sum calculator 45, by which a product-sum between the Δφ(iT) and the Δφ((i+1)T) is calculated. In addition, one series of the re-sampled phase noise waveforms from the zero crossing sampler 33 is inputted to a square-sum calculator 46, by which a sum of Δφ(iT)²is calculated. The product-sum ΣΔφ(iT)Δφ((i+1)T) calculated by the product-sum calculator 45 is divided by the calculated square-sum ΣΔφ(iT)²in a divider 47 to obtain a correlation coefficient ρ_tt. This correlation coefficient ρ_ttis outputted, if necessary, from the output terminal 42. In addition, this correlation coefficient ρ_ttis inputted to the signal to noise ratio calculator 41, by which a calculation of the equation (7) is performed, and the calculated result SNR_tis outputted to an output terminal 43.

[0067] In the embodiment shown in FIG. 3, the phase noise waveform is sampled by the zero crossing sampler 33 at a timing close to a zero crossing point of a rising edge. However, in general, the phase noise waveform may be sampled by the zero crossing sampler 33 at an interval of integer multiple of a time duration between a zero crossing point of a rising edge and a zero crossing point of a falling edge, and at a timing close to a zero crossing point. In addition, the re-sampled phase noise waveform to be supplied to the Δφ_RMSdetector 35 may be an output of the zero crossing sampler 33, or a sampler 51 may be separately provided as indicated by a dashed line and the phase noise waveform may be sampled by the sampler 51 the timing of the same period as the period nT/2 (n is an integer) of the re-sampled phase noise waveform to be supplied to the differential circuit 36 to supply the sampled phase noise waveform to the Δφ_RMSdetector 35. Regarding a sampling timing in this case, since the period T of the input signal is known, the phase noise waveform may be sampled at an interval of integer multiple of the sampling period t of the AD converter 12, and at a timing closest to nT/2.

[0068] In addition, since σ_p²and σ_t²are involved in the calculation of the equation (2), calculation results before extraction of the square root in the Δφ_RMSdetector 35 and J_RMSdetector 37, respectively may be supplied to a correlation coefficient calculator 39.

[0069] Also in the embodiment of FIG. 5, the sampling timing of the zero crossing sampler 33 may be close to nT/2. In addition, as indicated by a dotted line, a sampler 52 may be provided instead of the zero crossing sampler 33 to set a sampling period T′, and the phase noise waveform may be sampled at a timing close to each arbitrary period T′. Alternatively, without providing the sampler 33 or 52, the phase noise waveform Δφ(t) from the phase noise waveform detecting means 25 may be directly supplied to the correlation coefficient calculator 39. In the calculation of the correlation coefficient calculator 39, the Δφ′, i.e., an average value of the inputted phase noise waveform may be calculated to perform the faithful calculations of the equations (3) and (4).

[0070] As indicated by a dashed line in FIG. 3, a clock signal from the PLL circuit under test 11 may be supplied to the AD converter 12 via a clipper 53 so that the amplitude of the clock signal is made constant, whereby the phase noise waveform Δφ(t) is not influenced by an amplitude modulation component, and hence a jitter can correctly be measured. This processing facility for making the amplitude of an input signal constant may be provided in output side of the AD converter 12.

[0071] In the means 13 for transforming an input signal into an analytic signal z_c(t), as shown in FIG. 6, an inputted digital signal is Fourier-transformed by an FFT part 66, and negative frequency components are cut off from the transformed output by a bandpass filter 67 to extract a fundamental wave only of the input clock signal. Then the output of the bandpass filter 67 is inverse-Fourier-transformed by an inverse FFT part 68 to obtain an analytic signal z_c(t).

[0072] Alternatively, as shown in FIG. 7, an input clock signal x_c(t) is mixed with cos(2π(f_c+Δf)t+θ) and sin(2π(f_c+Δf)t+θ) in frequency mixers 71aand 71b, respectively. Then difference frequency components are extracted from the outputs of the low pass filters 72aand 72b, respectively to obtain an analytic signal z_c(t) expressed by the following equation. $z_c\left(t\right)=\left(A_c/2\right)\left[\cos \left(2\pi \Delta \mathrm{ft}+\left(\theta -{\theta }_c\right)-\Delta \phi \left(t\right)\right)+j\sin \left(2\pi \Delta \mathrm{ft}+\left(\theta -{\theta }_c\right)-\Delta \phi \left(t\right)\right)\right]$

[0073] A real part and an imaginary part of the above equation are converted into digital signals by AD converters 73aand 73brespectively, and those digital signals are supplied to an instantaneous phase estimator 16.

[0074] In the aforementioned configuration, a comparator may be used instead of the AD converter. That is, as indicated by a dashed line in FIG. 6 for example, a comparator 74 may be used to convert the input signal to a signal representing that the input signal is equal to or greater than a reference level or the input signal is smaller than the reference level, namely to one bit digital signal. In addition, as indicated by dashed lines in FIG. 7, comparators 74aand 74bmay be used instead of the AD converters 73aand 73b,respectively.

[0075] In order to supply a clock signal with its decreased frequency to the analytic signal transforming means 13, as indicated by dashed lines in FIGS. 6 and 7, the clock signal frequency may be frequency-divided by a frequency divider 75 to supply the frequency-divided clock signal to the analytic signal transforming means 13. Alternatively, although not illustrated, the clock signal may be converted, using substantially jitter-free local signal, into a difference frequency signal between those signals by a frequency converter to supply the difference frequency signal to the analytic signal transforming means 13. One or more functions of each functional configuration of the apparatus shown in FIGS. 3, 5, 6 and 7 may also be performed by decoding and executing programs in a computer.

[0076] In the aforementioned description, there has been explained, as a signal under test, a case of clock signal of a microprocessor. However, the present invention can be applied to an estimation of a quality measure such as a correlation coefficient, a signal to noise ratio, or the like of a phase noise waveform of a clock signal or another signal such as a sine wave signal or the like used in other devices.

[0077] A relationship between a period jitter variance σ_p²of a clock signal and an SNR_tof the {Δφ(nT)} has been verified by an experiment. In the experiment, a microprocessor was used. Its internal PLL circuit can generate a clock signal having a frequency of 200 NHz-600 MHz. The clock quality was estimated by placing the PLL circuit under two extreme conditions. One of the extreme conditions is quiet mode, i.e., a case of non-active state of a microprocessor. In the non-active state, when the personal computer waits for a user instruction, only a PLL circuit outputting a clock signal by giving thereto a phase base based on a reference clock from a reference clock generator operates, wherein the best state that the clock is not influenced by the operation of the personal computer is provided. The other extreme condition is noisy mode, i.e., a case of extremely active state of a microprocessor. In the noisy mode, a level 2 memory, a core bus and branch predictor units in a personal computer are all in full operation, wherein toggle operation of the microprocessor is maximized by those operations and a test program. That is, a state that the clock is most influenced by the operation of the personal computer is provided.

[0078] FIG. 8 shows a relationship between a correlation coefficient |ρ_tt(T)| obtained from the equation (2) or (3) and an SNR_tobtained from the equation (7). The axis of abscissas represents the SNR_tand the axis of ordinates axis represents the σ_p/T. The solid line indicates theoretical values obtained from the equation (8), and a mark ◯ indicates a experimental value. It can be seen that the experimental value is present on the theoretical curve, and hence the experimental value coincides with the theoretical value. FIG. 9 shows measured values in this case.

[0079] As mentioned above, according to the present invention, a correlation coefficient ρ_ttand a noise to ratio SNR_tbetween zero crossing points of an input signal can be obtained. In the design and the trial manufacturing, ρ_tt≡1 gives an upper limit of the SNR_t. Therefore, it is possible to ascertain, by a simulation at the design time or by measuring the ρ_ttor the SNR_tof an article made on an experimental basis, as to how much the clock quality can be improved more. When a ρ_ttis measured by individually operating each of core blocks to be packaged with a PLL circuit, and when the measured result indicates a small ρ_ttvalue, it can be considered that the PLL circuit receives relatively large influence from the noise or the like generated by the core block. Therefore, it can be seen that there is a necessity to provide a shield or the like between the core block and the PLL circuit so that the PLL circuit is not influenced from the core block.

[0080] Moreover, since the Δφ method is used in the present invention, (σp, σ_t) and quality measures (SNR_t, ρ_tt) can be measured at the same time as test items in the test of a microprocessor or the like.

[0081] In addition, in the case of obtaining a ρ_ttfrom the equation (3) or (4), it is sufficient to use a timing jitter Δφ(t) only. An occurrence of a timing jitter is based on its probability, and in general, the positive side maximum fluctuation value Δφ_max⁺ from an ideal timing is equal to the negative side maximum fluctuation value Δφ_max⁻ from the ideal timing. Therefore, the case of obtaining a correlation coefficient ρ_ttfrom the equation (3) or (4) requires shorter time than the case of obtaining a correlation coefficient ρ_ttfrom the equation (2) that uses a period jitter variance σ_p. Moreover, in the case of obtaining a ρ_ttfrom a computer simulation, the calculation in the equation (3) is simpler and more convenient than the case of the equation (2). Further, the equation (2) can obtain a ρ_ttin higher accuracy than the equation (3) can.