# Comment on KN5L on balun CMRR – coax example

One of the ham fashions of proposed solutions to characterising a balun is to find the Common Mode Rejection Ratio (a term carried over from other applications, eg voltage driven operational amplifiers).

(Anaren 2005) explains a method of finding balun CMRR. Anaren gives a definition of CMRR:

Common Mode Rejection Ratio is defined and the ratio between the differential mode insertion loss/gain versus the common mode signal loss or gain.

Note that in a passive system, CMRR (or CMR) in dB will usually be positive, and the larger the better. You might even think that the plain English meaning of the words Common Mode Rejection Ratio would suggest that a large ratio (or high +ve dB value) would mean most rejection, goodness. Such a meaning would be quite consistent with that of CMRR (CMR) applied to operation amplifiers (for a very long time).

Anaren does not mention applying the CMRR statistic to antenna systems. I have commented elsewhere on the lack of utility of CMRR in analysing common antenna systems.

Then immediately after the above definition, they give a formula which implies the inverse:

$$CMRR=\frac{S_{1c}}{S_{1d}}$$ and goodness would be a tiny fractional value, or a small (-ve) dB value.

John, KN5L, has published his own solution to balun characterisation in some online forums.

Let's look at his example with a 7t RG174 winding on a FT140-43 core in his recommended test fixture. He does not give a schematic of the test fixture, but it can be gleaned from his pic.

At the left is VNA Port 1 connection, the coax connects shield to the coax connector outer, and coax inner to connector inner. At the right hand end of the coax, the shield connects to the connector inner via a series 25Ω resistor, and the coax inner connects to the connector inner via another series 25Ω resistor, both coax connector outers are connected to the PCB copper plane, and the right hand coax connector connects to the VNA Port 2. He gives no explanation of why such a test fixture was chosen.

Above is his published VNA sweep. Analysing his published .s2p file reveals that the curves labelled “RG174 CMRR” is in fact |s21|… so he has implied his own meaning for CMRR, he does not give a clear definition other than this implication. The negative values of “RG174 CMRR” sound a warning.

John publishes a Simsmith model comparing a theoretical model of the balun in his test fixture with measurement. His Simsmith model of the balun in fixture is flawed, so I will use my own.

In this case, I have tweaked the number of turns a little to get a closer fit between model and measurement, ferrite has quite wide tolerance and the model is simple so we should not expect exact reconciliation.

Also calculated is the expected balun common mode impedance Zcm, in this case 1063+j617Ω @ 14MHz.

Above is my chart of his published measurement file. The curve “s21 dB” is simply |s21| from Port 1 to Port 2 through his test fixture, it is not in accord with Anaren's definition of CMRR as he labels his plots.

The curves “t2s(s21) real Z” and “t2s(s21) real Z” mimic a calculation John gives on some other examples. The function t2s is documented in the VNWA help.

t2s is a VNWA built in function intended to solve the so-called s21 series through fixture for impedance measurement of two terminal Zx connected between Port 1 and Port 2.

Looking at the marker values on my chart, they indicate Zx=5554+j4366Ω @ 14MHz. Is that the true common mode impedance? Hhe seems to be saying that:

ALL previous NEC Balun CM current models using a single inductor to
simulate two flux coupled inductors, of the same value, are flawed.

Well, applying the t2s function to data from a different test fixture circuit is invalid, the results are invalid, conclusions drawn from it are invalid.

NEC is quite capable of modelling the common mode current path separately to a TL element (which models only the differential mode), the appropriate value to load the common mode conductor path with is the calculated Zcm (which is frequency dependent).

## Conclusions

The test fixture used seems inspired by the theme ‘more complicated is naturally better'.

## 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.
• Anaren. May 2005. Measurement Techniques for Baluns.
• Skelton, R. Nov 2010. Measuring HF balun performance in QEX Nov 2010.