There are some who insist that it is not possible to make practical measurements of a common mode choke using a one port analyser, and recommend the ‘S21 method'

## S21 method

The ‘S21 method' means different things to different people.

Above, (Agilent 2009) describe the common methods of impedance measurement using a VNA. The first method is often supported with direct display of R,X, and possibly a Smith chart presentation of Γ.

These are not the only methods, others include the classic Q meters of decades ago, and the so-called RF I-V method, neither of which will be discussed here.

One port analysers are usually based on the first method, though some cannot detect the sign of the argument of Γ, or equivalently, the sign of reactance X so they display |X|, |arg(Z)|, and |Z|.

The second and third methods, two port shunt and series-through provide better configurations for measuring very low and very high impedances, and whilst they are straight forward enough to implement, the instruments are often not direct reading, so there is scope for error in translating the complex S21 measurement to R,X.

To complicate the field, G3TXQ describes a ‘S21 method' for high Z measurements, a method that is a combination of the shunt and series-through method in that the unknown is connected as in the series-through configuration and port one also has a shunt 50+j0 loadΩ. It is not clear that this delivers any benefit for high Z measurements, but it does introduces another element of uncertainty (the value of that shunt load), and it decreases the level reaching port two by up to 6dB.

Above is G3TXQ's diagram of his ‘different' method.

Above is a plot after Figure 6 of (Agilent 2009) of S21 vs a range of Runknown using both configurations, and G3TXQ's method delivers a lower signal to port , 6dB lower as Z becomes very high. This would decrease S/N in the port two detector, which would seem a disadvantage.

Of course, the formulas given in Agilent's graphic above do not apply to G3TXQ's ‘S21 method'.

Above is G3TXQ's formula for R for his variant of the ‘S21 method' (but as noted later, it is incorrect).

Though I have seen a derivation of the formulas, I have not seen an uncertainty analysis or any other argument as to why it is better.

In this confusing environment, I recently saw an online post responding to this challenge:

Magnitude of the common mode Z = 50(10^(dB/20)-1). Using 44 dB from G3TXQ's S21 example, Z = about 7.9 K.

For a start S21 is negative for this type of measurement, hams seem to like to disregard the sign of dB values. The above formula ignores phase, -48° in the challenge, and the results are wrong.

The problem actually posed by G3TXQ was:

Here's a typical S21 measurement for that balun at 10MHz: S21=-44.3dB, S21phase=-48 degrees calculate Rs from those S21 measurements and let us know what result you get.

Solving this, Rs using G3TXQ's formula Rs=50*10^(-|S21|/20)/(1+(tan(θ)^2)^0.5-75=-75Ω, obviously wrong. The – in the exponent is wrong (only a small error, but an error nonetheless), so fixing that error Rs=50*10^(|S21|/20)/(1+tan(θ)^2)^0.5-75=5414Ω.

Perhaps a clearer expression of the formula might be Rs=50*10^(-S21dB/20)/(1+tan(θ)^2)^0.5-75 where s21dB=20log(|S21|) and θ is the argument (or angle) of S21.

In the same form as the expressions in Figure 1, in G3TXQ's variant S21=50/(Zx+75) where Zx is a complex quantity (having real and imaginary parts) and of course S21 is a complex quantity. Rearrange that expression to make Zx the subject, we get Zx=50/S21-75 and for G3TXQ's example, using python's interactive prompt with S21=0.00408-j0.00453:

>> 50/(0.00408-0.00453j)-75

(5413.695708324252+6094.066558507075j)

So Zx=5414+j6094Ω. This demonstrates that it is simpler to calculate using the cartesian form of S21 rather than the dB magnitude and phase.

As I mentioned, – signs seem to often challenge hams. Working as a team of one also has its challenges.

Can you see the advantage of one port measurements with direct R,X display?

## 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.

Footnote: G3TXQ published a revised method more in line with the Agilent AN in Feb 2018, and revised his spreadsheet to use the new methods. There are now two G3TXQ methods, the original and the 2018 version. The formulas discussed above are applicable to the test configuration shown in the figure above.