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

Measured | Predicted | |

Loss (dB) | 0.32 | 0.35 |

InsertionVSWR | 1.15 | 1.21 |

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