Common mode choke measurement – length matters #2 discussed the effect that even quite short pigtails might have on the measurement of a high value resistor.

This article documents an experiment to measure a DUT comprising two 1206 0.1% 10kΩ resistors soldered to a 2w section of turned pin male header strip.

Above is the measurement fixture with the 5kΩ DUT, and the parts used to calibrate the fixture. The LOAD resistor measured 50.185Ω at DC, and that was entered into the NanoVNA for improved calibration accuracy.

The fixture is a 3w section of female turned pin header soldered to a male end launch SMA connector.

## What to expect?

Even small resistors like these are not perfect.

Above is the equivalent circuit proposed by (Vishay 2009). Note that the resistor is inside the dot-dash box. The parts outside the box are a model of their fixture.

Above is a table from (Vishay 2009). The resistors used were not Vishay, and at 1206 size, they were twice the size of the 0603 parts listed. We might extrapolate and estimate that for 2 x 1206 resistors in parallel, C is of the order of 120fF and L is of the order of 0.01nH.

Above is a SimNEC model of the assumed equivalent circuit of the parallel pair of 10kΩ resistors. Note the Smith chart plot follows a constant G circle (Zref=5kΩ). For such high resistance and at relatively low frequencies, the result is dominated by the shunt capacitance.

So without the long connections shown in Common mode choke measurement – length matters #2 there is still a departure that we should be able to measure, even with the humble NanoVNA with a suitable fixture and care.

## Measured

Let’s measure the DUT shown above, and import the s1p file into SimNEC for analysis.

Above is a Smith chart polot of a sweep from 1 to 101MHz, the reference impedance (ie chart centre) is 5kΩ. Note that the sweep locus is circular, and approximately follows a constant G circle.

The measured result is not greatly different to the expected response given earlier.

Above is a plot of S11 admittance from 1 to 101 MHz.

Note that G is approximately constant (equivalent to R=5.8kΩ), and that susceptance B is close to a straight line proportional to frequency rising to 72e-6S at 100MHz, equivalent to \(C=\frac{B}{2 \pi f}=114 \text{ fF}\).

G is a little different to expectation for unknown reasons, the resistor measured 5001Ω at DC. Perhaps the current distribution is not uniform at RF, some kind of skin effect?

So, the DUT is looking like a resistance of about R=5.8kΩ in parallel with a capacitance C=114fF.

R||C is one explanation for the curve we see.

There are other possible explanations, contributions of different effects, but considering the equivalent circuit laid out earlier, it would be naive to expect to observe and ideal resistor response, even with a quite good fixture.

## Conclusions

There are challenges in measuring extreme impedances with a reflection measurement instrument, the DUT is key to success.

Assertions that reflection measurement instruments are worthless for measurements of impedances much above perhaps 200Ω are not well informed, and if based on experiment, speak to experiment shortcomings.

## References

- Feb 2009. Vishay. Frequency response of thin film chip resistors (60107).