# Estimating the Insertion VSWR in a ferrite cored RF transformer

The article Estimating the magnetising or core loss in a ferrite cored RF transformer discussed a first cut approach to determining the minimum magnetising impedance from a core loss viewpoint.

This article considers the effect of magnetising impedance on VSWR.

For medium to high µ cored RF transformers, flux leakage should be fairly low and the transformer can be considered to be an ideal transformer of nominal turns ratio shunted at the input by the magnetising impedance observed at that input winding.

A good indication of the nominal impedance transformation of the combination is to find the VSWR of the magnetising impedance in shunt with the nominal load (eg 50+j0Ω in many cases), and to express this as InsertionVSWR when the transformer is loaded with a resistance equal to n^2*that nominal load (eg 50+j0Ω in many cases). This model is better for low values of n than higher, but it can still provide useful indication for n as high as 8 if flux leakage is low.

Magnetising impedance can be estimated using one of the following calculators, but keep in mind that there are quite wide tolerances on ferrite cores.

Magnetising impedance can be measured (eg with an analyser), but it should be measured with only the measured winding on the core. Did I mention the wide tolerance of ferrites?

## Example – FT240-43 3t @ 3.6MHz

You might ask the question is 3t sufficient for the primary of an EFHW transformer that delivers a 50+j0Ω load to a transmitter.

### Estimation from published datasheets

Estimating with a calculator, we get the following. Let’s work with admittance, it is easier for shunt circuits.

We will take the magnetising admittance above and add the admittance of the load transformed to 50+j0Ω (G=1/50=0.02S). (Use another value for G if it is more appropriate.) So we want to calculate the VSWR of a load with Y=0.02305-j0.0064S. Above, InsertionVSWR=1.39. Not apalling, but not wonderful, up to the designer whether it is acceptable.

### Estimation from measurement

Measuring a core with a 3t winding using very short wires to the AA-600 coax socket, the following results were obtained. Let’s work with admittance, it is easier for shunt circuits.

We will take the magnetising R|| and X|| above, convert each component to admittance (1/397.4+1/j234.9=0.002516-j0.004257S) and add the admittance of the load transformed to 50+j0Ω (Y=1/50=0.02S). So we want to calculate the VSWR of a load with Y=0.022516-j0.004257S. Depending on your InsertionVSWR criteria, the 3t winding might be adequate on 3.6MHz. On the other hand you might be tempted to test 4t, but there is a limit as more turns tends to compromise the higher frequency performance, especially on a large core.

A follow up article will look at first pass compensation of InsetionVSWR for optimised broadband response.