Measurement uncertainty in VNAs vs. TDRs, Part 2
Paul Pino- September 20, 2012Editor’s Note: See Part 1 here
In the first round of testing, involving 60 measurements (six samples x five repeat tests x two rounds), an initial review of the results indicated that one sample consistently performed better than the others in both TDR and VNA testing. A second experiment was created to gather information on measurement uncertainty under best-case conditions. The instruments, conditions, and configuration were identical to those used in the initial experiments on multiple assemblies. The details of the experiment were as follows:
• Repeat testing of 22 consecutive measurements without disconnecting/disturbing the DUT and test system.
• Reproducibility testing of 22 connect/disconnect cycles of the DUT, with measurements taken at each connect/disconnect cycle.
The number of measurements (22) was determined through a confidence interval calculation. This number assured a 98 percent confidence that the sample mean in the experiment would be within +/- 0.08 ps of the actual population mean, based upon an estimated standard deviation of 0.16 ps.
The objective was to observe measurement uncertainty under more closely controlled conditions. Towards that end, during TDR testing, the 3.5mm precision open was left in place during all 22 connect/disconnect measurements; the sample assembly connection was cycled at the TDR sampling head only. Likewise, during VNA testing, the sample assembly connection was cycled at port one only. This strategy, although not representative of production testing, introduced a disturbance into the test system such that the outcome could be observed.
For this portion of the analysis, TDR and VNA measurement uncertainty was divided into three categories:
• Instrument uncertainty — uncertainty associated with the instrument platform itself, measured through repeat testing, i.e., 22 consecutive measurements without disconnecting the DUT from the instrument.
• Total uncertainty — uncertainty resulting from the cumulative effects of instrument characteristics, test fixture, test conditions, and operator influences. Measured through connect/disconnect cycling, included instrument uncertainty
• Test uncertainty — resulting from operator error, test fixture influences and prevailing environmental conditions at time of test. Measured indirectly.
Because of the best-case uncertainty for Sample 6 (see Figure 8), test uncertainty values were expected to be similar in the TDR and VNA due to similarities in test configurations.
Figure 8: ±3 sigma uncertainty analysis of sample 6 measurements
Test uncertainty was measured indirectly. Based upon the previous definitions, test uncertainty was derived in the following way:
Total uncertainty = Test uncertainty + Instrument uncertainty
Test uncertainty = Total uncertainty – Instrument uncertainty
Best-Case Performance Results
With this information, the best-case uncertainty associated with each instrument platform could be assessed. 22 percent of the total measurement uncertainty for the VNA is associated with the instrument itself, as compared to 61 percent for the TDR (see Figure 9). This was a repeating theme throughout the experiment. This significant difference was determined to mean that even under ideal test conditions, i.e., minimal test fixture, operator, and environmental influences, the gap in TDR/VNA measurement uncertainty remained, as it was inherent to instrument performance.
Figure 9: Total measurement uncertainty broken down by test and instrument uncertainty
Some may be concerned about the external processing of the s-parameter data (see VNA Time Delay Measurement Method), thinking this aided in the VNA’s reduced instrument uncertainty. In practice, a time delay value delivered directly from the VNA was calculated by applying a smoothing aperture, essentially a variable length, moving average filter. The aperture was adjustable to encompass the entire swept frequency range or a small portion of it. Comparisons of the VNA manufacturer’s standard method with Gore’s method used for this experiment indicated similar instrument uncertainty results. The Gore post-processing method was used primarily for reasons of convenience in data collection.
The 22 connect/disconnect measurements of Sample 6 (see Figure 10) showed that the VNA measurements had a range spanning 0.0983 ps as compared to the TDR’s range of 0.275 ps. Both data sets clearly trended downward, i.e., a progressively shorter device delay.
Figure 10: Connect/disconnect measurements in sequence, illustrating the change in time delay with respect to the first measurement
The TDR data indicated a potential repeatability issue with the 3.5mm connector on the TDR sampling head (see Figure 11); this variability was associated with the instrument itself, not with the connector.
Figure 11: TDR repeatability: connect/disconnect vs. consecutive measurements with un-disturbed DUT
The data showed instrument variability influencing the connect/disconnect TDR measurements. An identical test was conducted using a second TDR, similarly equipped and from the same manufacturer. The outcome was comparable to the initial findings. As a point of comparison, VNA data is shown in Figure 12.
Figure 12: VNA repeatability: connect/disconnect vs. consecutive measurements with undisturbed DUT
The downward-trending behavior may be attributed to burnishing of SMA/3.5mm-mated interfaces. Recalling the VNA test configuration, a 3.5mm connector was used as the calibrated reference plane to which the test sample’s SMA was mated.
Insertion loss for sample 6 decreased over a series of 22 connect/disconnect cycles (see Figure 13). Connecting and disconnecting the SMA interface in succession (without cleaning between cycles, as was done in the experiment) had the potential to burnish the mated connector interface components. It was theorized that over the course of 22 test cycles, the mated interfaces were sufficiently abraded to experience improved electrical contact, as evidenced by a reduction in insertion loss and electrical length.
Figure 13: Sample 6 insertion loss over 22 connect/disconnect cycles, indicated reduction in loss
It is of some interest to compare the absolute time delay values for sample 6 as measured by the TDR and VNA. An examination of repeat testing (22 consecutive measurements made without disturbing the DUT) produced an average time delay of 0.817364 ns for the VNA and 0.849754 ns for the TDR; a difference of 32.5 ps. This discrepancy was unexpected and an attempt was made to obtain closer agreement between the two instruments.
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