Select a ferrite core material and sufficient primary turns for a low InsertionVSWR 50Ω broadband RF transformer – comparison of measured and predicted

Select a ferrite core material and sufficient primary turns for a low InsertionVSWR 50Ω broadband RF transformer – nanoVNA described a method of using a nanoVNA to select by trial possible core and turns combinations for a transformer.

This article compares the results for the FT240-43 example at 3.5MHz with calculation using tools on this web site.

Simple low frequency equivalent circuit

Above is a very simple approximation of an ideal 1:1 transformer where the effects of flux leakage and conductor loss are ignored. A 1:n transformer can be modelled the same way, as if flux leakage and conductor loss are ignored, the now ideally transformed secondary load becomes 50Ω.

Calculation

First step is to find the complex permeability of the core material.

Next, calculate the RF impedance and admittance at 3.5MHz of a 4t winding.

The real part of Y is the magnetising conductance Gm (the inverse of the equivalent parallel resistance).

We can calculate core magnetising loss as \(Loss_m=10 log \left(1 + \frac{Gm }{0.02}\right)=10 log \left(1 + \frac{0.00168}{0.02}\right)=0.35 \; dB\).

We can calculate InsertionVSWR using Ym+0.02 S as the load admittance.

Above, InsertsionVSWR is 1.21.

Reconciliation

Given the tolerance of ferrite cores, the reconciliation is very good.