Accuracy of the Measurement Setup

The standard jitter measurement set-up, described in chapter III, was used to measure jitter in several Token Ring products. However, the accuracy of these measures was unknown. In order to increase the confidence in the numbers obtained, it was necessary to study the set-up and understand the phenomena that influenced the jitter measurement process.

Fig. 4.1 illustrates some typical results obtained by using the IOL standard jitter measurement set-up and procedure. This example shows the filtered jitter measured for 6 stations. PLOT B shows the filtered jitter for Trace 1 (test point A) for 15 different acquisitions while PLOT C shows the filtered jitter for Trace 2 (test point B). PLOT A shows the average of the 15 acquisitions for both test points while PLOT D shows the FAPS for the two test points. PLOT D is obtained by differentiating PLOT A. On close examination of PLOT B and PLOT C one notices the variance associated with the 15 jitter measurements. These are measures obtained for the same configuration. One question that cropped up was whether this variance was of an acceptable level i.e. whether it was comparable to the inherent accuracy of the test set-up.

If this was not true, then it was uncertain whether this variance in the measurements was caused by some jitter source in the test set-up like crosstalk or reflections or whether it was a characteristic of the device under test. To answer these questions, it was necessary to study the accuracy of the test set-up. It was also necessary to identify the source of the variance.

4.1. Study of the Accuracy of the Measurement Set-Up

To study the accuracy of the test set-up, a list of possible sources of error was made. An attempt was made to quantify the inaccuracy introduced by each source. These errors were first classified as procedural errors and instrumentation errors.

4.1.1. Procedural errors

• 4.1.1.1. Interpolation error - This is the error introduced by performing linear interpolation (rather than sinusoidal) between two sample points of opposite polarity to determine the time stamp for a zero crossing (refer to section 3.2). After looking closely at the interpolation process, it was found that by performing linear interpolation one is assuming that sin(A) = A, where A is small and in radians. Since in this case the sample interval is 2 ns and the highest frequency of interest is 16 MHz, the worst-case assumption made is that sin(2*pi*16MHz*2 ns) ÷ 2 ns * pi/31.25 ns. The above approximation works out to be 1.986 ns ÷ 2 ns or an error of the order of 14 picoseconds. Since this source of error was much smaller than other sources, it was neglected in the final analysis.

4.1.1.2. Floating point error - This is the error due to rounding off of double precision floating point numbers in the post-processing steps in jitter calculations on the PC. Since instrumentation errors were significantly greater than this error, it was neglected.

4.1.2. Instrumentation Errors

Since the procedure for measuring jitter is such that the jitter added by the TJ-16 is subtracted out, the only instrument that has to be investigated is the DSO. After examining the specifications of the LeCroy 9354 M, the following possible sources of errors were identified.

1. Quantization Error or Vertical resolution
2. Sampling Clock inaccuracy
3. Timing skew between channels
4. Sampling rate

A program was written in MATLAB to simulate the effect of quantization error on the jitter measurement. The resulting inaccuracy in measuring jitter due to quantization error was calculated by simulating the sampling process of the DSO for a worst-case data pattern and then calculating jitter from the digitized samples. All jitter calculations were based on the same post-processing steps as outlined in section 3.2. The calculated jitter was compared to the actual jitter that was programmed into the same data pattern.

 

The key parameters studied using this program were the vertical resolution which is determined by the Volts/div. setting on the DSO and the signal amplitude, the sampling rate of the DSO, the clock inaccuracy or the sampling inaccuracy of the DSO, and timing skew between channels. These parameters were studied individually. First the parameters were set equal to the specifications and settings of the LeCroy 9354M being used in the standard test set-up and then they were varied to observe the effect on the measurements.

 

The LeCroy 9354 M has a vertical resolution of 8 bits which gives 255 quantization bins. The clock inaccuracy or the sampling inaccuracy is specified as +/- 10 ps which is the uncertainty in the occurrence of a sampling edge in the DSO. The maximum time skew between channels is specified as less then 100 ps.

 

The maximum peak to peak amplitude of the AC coupled Token Ring differential Manchester encoded waveform that one can expect is 3.3 V. However, it was stated earlier in section 3.1 that the Volts/div. setting of the DSO was set to 1 V/div. thus giving a full scale range of 10 V. The reason for doing so is as follows: A number of Token Ring devices that were tested were found to transmit with a large (10 Vp-p ) common mode component. Though this signal component was not differential, (i.e. it was common mode), the voltage difference in the set-up was computed only after sampling the signal on individual wires of the pair. The 60 Hz component was thus canceled only after channel differencing (Channel A - Channel B) inside the DSO. Hence individual channels had to be set at 1 V/div. to provide the required dynamic range.

 

A worst-case data pattern was synthesized with a programmed amount of correlated jitter. The rounding function was used to simulate the quantization process. The data pattern was sampled at a rate of 500 Mega samples/s and the samples were then quantized. Jitter was then calculated using the normal post-processing steps. The calculated FAJ and FAPS was compared to the actual jitter programmed into the data pattern.

• 4.1.2.1. Quantization Error - To study the effects of the quantization error, two sets of jitter measurements were obtained using the simulations. The first set was obtained by making the assumption in the simulation that true differential DSO measurement before quantization of the data pattern whereas the second set of jitter measurements was obtained by numerical differencing of single ended DSO measurements.
• Figures 4.2, 4.3 and 4.4 show the effect of quantization on the measures when a data signal with a peak to peak amplitude of 2.5 V was used and the Volts/div. setting was set to a full scale of 5 volts. This simulation was done assuming that there was a differential amplifier used to perform the differential measurement rather than calculating the numerical difference of channels (channel A - channel B approach). With this approach, measurements could be made with the Volts/div. setting set to a full scale of 5 volts or less because of rejection of common mode noise (including the 60 Hz power line noise) by the amplifier before the quantization occurs.

  Fig. 4.2 shows the actual AJ and the calculated AJ for the MATLAB simulation program. The calculated AJ shows the effect of quantization. Fig. 4.3 shows the actual Filtered AJ and calculated FAJ. On comparing Fig. 4.2 and Fig. 4.3, it was observed that the error due to quantization is significantly reduced by the low pass filtering of the jitter. FAJ is calculated by observing the phase of the long string of zeros and subtracting from it the observed phase of the ones after the phase has settled after the transition. Hence this 'observed' phase is basically obtained by a further low pass filtering of the jitter. Hence the FAJ calculated in Fig 4.3 is very close to the actual FAJ and the error is negligible.

• Fig 4.4 shows the actual FAPS and the calculated FAPS. The calculated FAPS shows an inaccuracy of about 0.00025 ns/ns. However, an interesting phenomenon that was observed was that the calculated maximum FAPS was very close to the actual maximum FAPS and the two were within 0.00005 ns/ns of each other. This was consistent when other data patterns with different jitter steps were analyzed.

  In the next simulation, two channels (channel A - channel B) were used to make one differential measure. This meant that the difference of the two signals was calculated after quantization, thereby giving a reduced CMRR. Fig 4.5 shows the simulation results for the error in calculating FAJ. As explained earlier, in this configuration the full scale vertical range had to be set to 10 V. The peak to peak signal voltage was set to 2.5 V and the sampling rate was set to 500 Mega samples/s. In Fig. 4.5, it can be observed that the average error in calculating FAJ is less than +/- 50 ps.. However, on comparing the results of Fig 4.3 and Fig 4.5, it can be clearly seen that using a differential amplifier would provide more accurate results than the 2 channel approach.

   

  Fig 4.6 shows the actual FAPS and the calculated FAPS for the same simulation described above. The error due to quantization in calculating FAPS is significantly high (+/- 0.002 ns/ns). However, even in this scenario the error in calculating maximum FAPS is relatively small (0.0005 ns/ns). On comparing the results of Fig 4.6 and 4.4, we observe that by taking true differential measures, the increase in the accuracy in measuring FAPS is significant as compared to the accuracy obtained by taking numerical differences of two single ended measurements.

• 4.1.2.2. Sampling Clock inaccuracy - To introduce the effects of the sampling clock inaccuracy, the program used for section 4.1.2.1 was modified. The sampling intervals were generated by adding a uniformly distributed zero mean perturbation to the 2 ns interval. However, it was found that the error in the jitter measurements due to sampling clock inaccuracy was negligible as compared to the error due to quantization.

• 4.1.2.3. Timing Skew between channels - This simulation studied the effect of having a possible timing skew of up to 100 ps between the two channels A and B on the jitter measures. Timing skew in this context means the difference in sampling times for the two channels. This also includes the difference in times taken by the signal traveling from the point of probing on the twisted pair of cable to the actual quantization point for the two channels in the DSO.

   

  Fig 4.7 shows the FAJ when the time skew between two channels was set to 100 ps and zero time skew. These results clearly indicate the effect of time skew between two channels. Fig 4.8 shows the FAPS for the same configuration. It is evident that the time skew between the two channels did not affect the FAPS measure.

• 4.1.2.4. Sampling rate - Fig 4.9 shows the calculated FAJ when sampling at a rate of 2 Giga samples/s, while Fig. 4.10 shows the calculated FAPS. The approach used here was that of a differential amplifier with the vertical range set to 5 V, similar to Fig 4.3 and Fig 4.4 for which the sampling was done at 500 Mega samples/s. On comparing with the actual FAJ and FAPS, the resulting error is negligible. On comparing Fig 4.3 with Fig 4.9 and Fig 4.4 with Fig 4.10, it can be concluded that by increasing the sampling rate from 500 Mega samples/s to 2 Giga samples/s, the gain in the accuracy of the FAPS measure is noticeable but not significant. Hence, for practical purposes, a sampling rate of 500 Mega samples/s seems to be sufficient.

4.1.3. Summary of the study of the accuracy of the jitter measurement set-up

From the discussion in section 4.1.2 the following conclusions were reached:

1. Low pass filtering of the jitter at 360 kHz reduces the quantization induced FAJ error significantly (compare Fig. 4.2 and 4.3).
2. Using the present DSO configuration in IOL, the filtered jitter at individual zero crossings can be calculated to an accuracy of approximately +/-50 ps. However, considering the extra low pass filtering necessary to come up with a figure for FAJ, the error becomes insignificant (Fig. 4.5).
3. Quantization induced error in calculating FAPS was high. At individual zero crossings it could be as high as +/-0.001 ns/ns. But the observed maximum FAPS had a smaller error range of +/-0.0005 ns/ns (Fig 4.6).
4. The effect of sampling clock inaccuracy was not noticeable. On the other hand time skew between channels showed up in the FAJ measures only (Fig 4.7).
5. High accuracy can be obtained by taking true differential measures which in turn allows the vertical range to be set to less than 5 Volts full scale for increased vertical resolution (refer to Fig 4.3 and 4.4).
6. Increasing the sampling rate to 2 Giga samples/second improves the measurements but the improvement is not significant.

 

Fig. 4.12 shows actual jitter measurements taken at the end of a short cable terminated in 100 ohm resistor. The source for the worst-case pattern was the TJ-16. Fig 4.11 shows the configuration used to make the measurements. 15 measures were taken and averaged. Four channels were used to make the same differential measurement at the transmit pair of the TJ 16. Probes for channel A and channel C were connected physically to the same point on one wire and probes for channel B and channel D were connected to the same point on the other wire forming the twisted pair.

Fig. 4.11. Measurement set-up for Fig. 4.12

On close observation of Fig. 4.12 the following can be noticed.

1. The FAJ time series in all the 15 measurements at most of the zero crossings was within +/-100 ps (refer to the second and third sub plot, jitter a and jitter b).
2. Timing skews between channels showed up in the average of the fifteen measures for the two sets of measurements when plotted together at the top of the graph.
3. The FAJ and FAPS for the string of ones (after the transition point) has a greater variance from the mean as compared to the string of zeros. This can be confirmed in all simulation results (Fig 4.2 - Fig. 4.10).

The error in the jitter measurements due to the various contributing sources can be tabled as follows.

It should be noted that in Table 4.1, filtered jitter refers to the maximum error at any one value in a sequence of jitter values obtained by filtering the jitter calculated at each zero crossing in the worst-case data pattern. FAJ measurement refers t o a single number obtained from the filtered jitter. FAPS refers to the sequence of values obtained by differentiating the filtered jitter and max.|FAPS| refers to a single number obtained as the maximum absolute value in the FAPS sequence.

 

From the above table, it can be concluded that using the present test set-up to measure FAJ, a conservative figure of +/-150 ps can be quoted as the accuracy of the set- up.

For max.|FAPS| measurements, the accuracy of the setup is better than +/-0.001 ns/ns. To improve on this test set-up, true differential channels in DSO should be used to make these measurements thus allowing better vertical resolution and less quantization error.

Another important conclusion was that the observed variance in the jitter seen in Fig 4.1 is not within the resolution of the measurement test set-up. Hence the source of this considerably larger variance in measurements had to be identified.

< Chapter 3, Chapter 5 >