# An experiment with NanoVNA and series through impedance measurement

## s21 series through impedance measurement

HP and their successors describe this technique in many publications, the following is from 5988-0728EN.pdf.

Note in the second formula the use of 2Zo and 100 synonymously. The formula depends on the Port 1 source being a Thevenin source with source impedance Zo and the Port 2 input impedance Zo (which they take to be 50+50Ω).

Derivation of the expression for the unknown impedance in an s21 series through measurement shows that the critical value is actually Zsource+Zload or Zs+Zl. If Zs+Zl ≠ 100 then that formula is not correct, the measurements will have error.

## The experiment

This article reports an experiment to determine whether assuming Zs+Zl = 100 is sound.

A NanoVNA-H4 v4.3 was used with a SDR-kits test jig pictured above. The setup was SOLIT calibrated from 1 to 101MHz, the reference plane is in the middle of the test jig. The picture shows a 200Ω 1% SM resistor in the series through path for measurement using the s21 series through method (as described above).

## Find Zx assuming Zs+Zl=100Ω

Above is a plot of R and X components of Zx calculated using the formula set out above.

Above is a screenshot from the NanoVNA displaying the R and X components of Zx using the formula set out above.

Note the lack of reconciliation at the marker of s11 and the calculated Zx. If Zin of Port 2 (Zl) was 50+j0Ω, we would expect s11 reflection measurement of Z to be 20+200=250+j0Ω… but it reads 243.3-j37.08Ω implying Zx=193.3-j37.08Ω and Zx from s21 reads 212.3-j25.64Ω.

Why is it so?

## Find Zs+Zl assuming Zx=200Ω

Since we know Zx, let’s turn it around and find Zs+Zl implied by Zx=200+j0Ω.

Above is calculation of Zs+Zl from the measurement.

The error in Zs+Zl is a large contribution to the failure of the calculation of Zx assuming Zs+Zl=100Ω.

## How about KISS, an s11 reflection measurement of the nominal 200Ω resistor used above?

Above, s11 reflection of the 200Ω 1% SM resistor.

Above, s11 reflection presented as equivalent impedance components.

## Is the series pi (so-called Y21) method the answer?

See NanoVNA-H4 – a ferrite cored test inductor impedance measurement – s11 reflection vs s21 series vs s21 pi for explanation / discussion of this method which I prefer to call the s21 pi method.

Above is a comparison of:

• s11 shunt (s11 reflection);
• s21 series through; and
• s21 π.

Both s21 based method are very poor.

## Conclusions

The NanoVNA-H4 v4.3 and Dislord firmware v1.2.30 using 5 term calibration does not appear to give good accuracy on series through measurement of impedance.

## References

• Agilent. Feb 2009. Impedance Measurement 5989-9887EN.
• Agilent. Jul 2001. Advanced impedance measurement capability of the RF I-V method compared to the network analysis method 5988-0728EN.