Diagnosis of a 9:1 transformer from NanoVNA plot

A chap recently posted online a question:

I have added two 1:9 transformer (2T/6T) back to back (high side together) and measured with the nanovna – 2 port measurement, as the binocular core I am not confident BN73 or not.

Also I swiped with one port S11, with one transformer where the high side is terminated with a 470ohm resistor load.

Please advise if it can be used for beverage antenna for 160/80m.

Let’s focus on the second test, and assume that the measurements are valid (and that is often an issue), that the 470Ω resistor is close enough to 450+j0Ω and the connections are short.

Above is his s11 sweep from 1 .5-7MHz.

I suspect this is actually #43 material.

Note how the curve is almost a perfect arc, much like a mirror image of the R=50 arc, ie much like the G=1/50S arc. This is a strong hint of why the InsertionVSWR (a radially scaled parameter, a function of the distance of a point from the centre) is poor (VSWR almost 3 at 1.8MHz).

InsertionVSWR is an interesting parameter as it gives us an indication of how ideal (or not) is the transformation ratio… nominally 9:1.

The chart above is from a Simsmith model of a simple circuit, in this case the curve follows the G=1/50S exactly and is quite similar to the poster’s measurement. The simple circuit is a 4µH inductor in shunt with a 50Ω resistor.

In poster’s case, a first approximation of the transformer response is an ideal transformer with a shunt inductance. The shunt inductance is the magnetising inductance of the transformer core, and it is too low to give low InsertionVSWR at 1.8MHz. The combination of core geometry, material and number of turns is a poor choice.

This is a simplified model that represents the magnetising impedance as simply a constant inductance. A more complete model considers the magnetising impedance as having reactance and resistance, and it has loss (by virtue of the non-zero resistance. Ferrite cored transformers with low magnetising impedance tend to have higher core loss, see RF transformer design with ferrite cores – initial steps.

In the absence of a quantitative requirement (eg a maximum InsertionVSWR specification), whether it “works” or is “good enough” is a personal choice.

I would not be surprised if this implementation may be a copy of a popular ‘design’, well… but for perhaps using #43 material.