# Comment on KN5L on balun CMRR – series through impedance fixture

In recent articles, I flagged that on some of John’s VNWA plots he showed flawed impedance calculations using VNWA’s t2s inbuilt function.

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.

None of John’s test fixtures were equivalent to the circuit above required for valid t2s transformation.

What if we modify the Simsmith simulated circuit, does series through impedance measurement work?

Above is a minimum change to the simulation circuit to comply with the series through test fixture requirement. The two 25Ω resistors are made 0Ω, and at the other end of the transmission line, both wires are connected together. More on the now redundant elements later.

The figure above is from (Agilent 2009) and it shows the expression for calculation of s21 in the series through configuration. A rearrangement gives $$Z_x=\frac{100}{s_{21}}-100$$, which is used in the Simsmith model below.

Above is the simulation showing the calculations used for key values. In element A, Zcm is calculated as 1.413K+j1.04K, and in the G element Plots, Zx is calculated using the algorithm.

Not surprisingly, Zx reconciles with Zcm when the correct test fixture is used.

The dodgy fixture also inflates the calculated CMRR (a bogus metric when used in the context of antenna systems).

The simulation circuit above with minimal modification to comply with the series through test requirement now contains redundanct components.

Above, the simulation circuit with the redundant parts removed. It produces exactly the same results, and demonstrates that balun common mode impedance can be measured by connecting the transmission line wires at each end and measuring between the ends. If the transmission line is coax, it is sufficient to measure between the shield ends with the inner conductors left disconnected.

KISS!

The same is true of the simpler s11 reflection method for impedance measurement.

## 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.