The next question to ask becomes, “Is it ever wise to use a thru-calibration method?” The answer is shown by looking at Figure 10 and Table 4, which exhibits two measurements across a 49.9Ω DUT and a 1Ω DUT after a thru-calibration with the 0805 probe tip.

Here we see the impedance across the 49.9Ω DUT remains fairly consistent across the current frequency range; however, the impedance on the 1Ω DUT starts to become more inductive at 20 MHz, which indicates that the effects of the inductive coupling are impacting our measurement. This would indicate when we make low impedance measurements less than 1Ω we will start to see errors caused by the inductive coupling in our measurement. It is also important to keep in mind that the physical size of the DUT comes with inherent inductance. In other words, to fully differentiate how much of the inductive curve appearing at 20MHz is inductive coupling versus the DUT’s package inductance, we need to know the inductance of the resistor.

Fig. 10 - 49.9Ω DUT (Green) and 1Ω DUT (Red) Measurement with 0805 P2102A-2X Probe Tip on Bode 100.

Table 4 - Results Summary - 49.9 ohm DUT (Green) and 1 ohm DUT (Red) Measurement with 0805 P2102A-2X Probe Tip on Bode 100.

Now let’s circle back to the isolation calibration discussion. For this topic, we need to switch to a different VNA. For our example we are going to use the Rohde & Schwarz ZNL6 VNA [5], which includes multiple calibration options. For now we will focus on only three calibration methods available on the ZNL6: 1) the Transmission Normalization (Trans Norm for short), which is a thru-calibration; 2) the Trans Norm with isolation, which is a thru-calibration that allows an isolation error correction during calibration; and lastly, 3) the Through-Open-Short-Match (TOSM) calibration method, which not only includes an isolation calibration, but also ensures the highest accuracy with a 12-term error correction model by requiring 7 standard measurements, as depicted by Figure 12. For reference, the ZNL6 measurement setup is shown below, in Figure 11.

Fig. 11 - Measurement Setup after Calibration with ZNL6.

Fig. 12 - TOSM Calibration Steps Completed on ZNL6.

 Figure 13 provides a depiction of the various calibration points that are necessary to complete the Trans and TOSM calibrations with the P2102A probe on the ZNL6.

 Fig. 13 - P2102A 2-port Calibration Open (top left), Short and Isolation (top right), Through (bottom left) and Match/Load (bottom right) with ZNL6.

With reference to Figure 14, we can see that the Trans Norm starts becoming inductive much sooner than the Trans Norm with isolation and the TOSM calibration method. In fact, the Trans Norm started exhibiting an inductive error around 20 kHz, whereas the Trans Norm with isolation does not start exhibiting an inductive error until around 10 MHz. The isolation calibration is what is correcting for the mutual inductance in the probe tip until around 10 MHz on the Trans Norm isolation.

When comparing the two Trans Norm calibrations to each other, we see that they are hovering around 1 mΩ to 1.8 mΩ from 10 kHz to 200 kHz; however, the TOSM calibration shows an even lower measurement that varies from 819 µΩ to 112 µΩ from 10 kHz to 200 kHz. This lower value is due to the better TOSM error correction model. 

Lastly, let’s compare the Trans Norm with isolation to the TOSM calibration. While ignoring the magnitude difference, we see that the isolation calibration is correcting for the mutual inductance in the probe tip until around 10 MHz, which also follows the TOSM calibration curve. We start to see the benefits of having the additional error terms included in the TOSM calibration by observing a 4.7 mΩ delta at 20 MHz and a 14.8 mΩ delta at 60 MHz. 

Fig. 14 - Short Impedance Measurement with P2102A-2X, 0603 Probe Tip on ZNL6 - Trans Norm Calibration (Black), Trans Norm Calibration with Isolation (Green), TOSM (includes Isolation) Calibration (Orange).

If all measurements are equal, then when we measure the same 0805 capacitor with a P2102A probe or with SMA connections to the DUT, the measured curve should be the same; however, in reality that is never the truth. In reference to Figure 15, an 0805 capacitor that was measured with the P2102A 0805 probe tip using the SOL calibration on the Bode 100 and compared to SMA 2-port shunt-through calibration, we can clearly see the mutual inductance in the P2102A probe tip causing a measurement error in comparison to SMA measurement with the Bode 100. The 0805 capacitor was mounted on a Picotest decoupling board, so the 4-point contact was made on the top side of the Picotest board, but measured from the SMA, since the SMA uses the same surface trace. 

Fig. 15 - P2102A 0805 Probe Tip SOL Cal No Isolation (Grey) vs. SMA 2-port Calibration (Black) with Copper Mountain Technologies S5085 VNA.

Conclusions

We have explored the tradeoffs for various calibration methods and considerations to making accurate sub-milliohm impedance measurements.

Other factors that were not discussed (and may be shown in a future article), were calibrations at higher frequencies, bending of the cables, and phase-matched cables. 

As a parting thought on the importance of these calibration methods to measure impedances < 40 MHz, let’s consider if we were measuring a VRM’s output impedance to import into our simulation model, to make the model power-aware: how much would this impedance measurement error, due to improper calibration, affect the eye diagram in our power-aware signal integrity model? This question will be further explored in our next article.

Appendix

Fig. 16 - Picotest PDN Cables®, adapters, calibration substrate, P2102A probe, P2102A probe tips, and probe holder for measurement.

Table 5 - Test Equipment List for Measurements.

5.0 References

1. Ultra-low Impedance (20 micro ohm) Measurement using 2-Port Shunt-Through - https://www.picotest.com/images/download/Ultra-low.pdf
2. Inductance. (2020, December 30). Retrieved February 08, 2021, from https://en.wikipedia.org/wiki/Inductance
3. 100uOhm Probing Methods, Brian Hostetler, EDICON 2018
4. S. M. Sandler, "Extending the usable range of the 2-port shunt through impedance measurement," 2016 IEEE MTT-S Latin America Microwave Conference (LAMC), Puerto Vallarta, 2016, pp. 1-3, doi: 10.1109/LAMC.2016.7851286.
5. S. M. Sandler, “Measuring pH and fF with a TDR using a cursor measurement,” Signal Integrity Journal, January 2021.
6. OMICRON Lab Bode 100 - https://www.picotest.com/products_BODE100.html
7. Rohde & Schwarz ZNL6 Vector Network Analyzer - https://www.rohde-schwarz.com/us/product/znl-productstartpage_63493-432704.html
8. Picotest P2102A - 2-Port PDN Transmission Line Probe - https://www.picotest.com/products_PDN_Probe.html
9. Picotest J2102B-N - Common Mode Transformer - https://www.picotest.com/products_J2102B.html
10. Picotest PDN Cable - https://www.picotest.com/pdn-cable.html
11. Pasternack PE9081 - SMA Female to N Male Adapter - https://www.pasternack.com/sma-female-n-male-straight-adapter-pe9081-P.aspx
12. Pasternack PE9073 - SMA Female to BNC Male Adapter - https://www.pasternack.com/sma-female-bnc-male-straight-adapter-pe9073-p.aspx
13. Pasternack PE9002 - N Male to BNC Female Adapter - https://www.pasternack.com/n-male-bnc-female-straight-adapter-pe9002-p.aspx
14. Keysight 3D Probe Positioner - N2787A https://www.keysight.com/en/pd-1643963-pn-N2787A/3d-probe-positioner?cc=US&lc=eng
15. Rohde & Schwarz ZNL Vector Network Analyzers User Manual https://scdn.rohde-schwarz.com/ur/pws/dl_downloads/pdm/cl_manuals/user_manual/1178_5966_01/ZNL_ZNLE_UserManual_en_10.pdf
16. Copper Mountain Technologies S5085 VNA - https://coppermountaintech.com/vna/s5085-compact-2-port-vna/
17. Tektronix MSO6B Oscilloscope https://www.tek.com/oscilloscope/6-series-mso-mixed-signal-oscilloscope
18. Picotest TDR J2151A PerfectPulse - https://www.picotest.com/products_J2151A.html
19. 2-Port impedance Measurement using the P2102A Probe and Bode 100 VNA - https://www.picotest.com/images/download/ApplicationNote-2-PortImpedanceMeasurementusingP2102AProbeandBode100VNA.pdf
20. 2-Port impedance Measurement using the P2102A Probe and ZNL6 VNA - https://www.picotest.com/images/download/ApplicationNote-2-PortImpedanceMeasurementusingP2102AProbeandZNL6VNA.pdf
21. Pathwave Advanced Design System - https://www.keysight.com/us/en/products/software/pathwave-design-software/pathwave-advanced-design-system.html