A simplified design for small broadband RF transformers using medium µ ferrite core for receiving use. The specific application is an impedance transformer for a nominally 450Ω antenna to a 50Ω receiver input. Intended frequency range is from 0.5 to 15MHz.

The characteristic of typical medium µ ferrite mixes, particularly NiZn, are well suited to this application.

This article continues with the design discussed at BN43-2402 balun example, but using a BN43-202 with 5t primary and 15t secondary for a nominal 1:9 50:450Ω transformer (though at high ratios, the transformation is only nominal).

Lets consider a couple of simple starting points for low end and high end rolloff.

## Low end roll off

A simple model for these devices with low flux leakage is an ideal transformer with primary shunted by the magnetising impedance. To obtain low InsertionVSWR, we want the magnetising impedance in shunt with 50+j0Ω to have a low equivalent VSWR.

Typically complex permeability changes in-band, and although it tends to decrease, increasing frequency means that the critical point for magnetising impedance is the low end.

## High end roll off

At the high end, transformation departs from ideal usually when the length of wire in a winding exceeds about 15°.

## Going forward

A small core makes for short windings to obtain high frequency performance, and sufficient turns are needed for low end… but not too many as it restricts the high end.

There are lots of rules of thumb for minimum magnetising impedance, most treat the inductor as an ideal inductor and these ferrites are not that.

A quick analysis using the method in BN43-2402 balun example

Above is a plot of expected magnetising R and X for a 5t winding using my common mode choke design tool. Z at 0.5MHz is 3.6+j172Ω, or Y=0.0001216-j0.005811S. (If your design tools are not giving you similar values, you might consider validating them.) Adding the shunt 50Ω (Y=0.02), we get Yt=0.0201216-j0.005811S, and plugging that in to calculate VSWR…

…we have InsertionVSWR=1.33, that is fine for our application. This is only a rough indication of suitability, the final test is a VNA sweep of a prototype.

The next step is to make one up and measure it.

Above, the prototype.

Above is a VNA sweep of a prototype wound with 0.25mm ECW.

The load resistance is a resistor with DC resistance of 386Ω in series with the VNA 50Ω input port. Because of the power division between that resistor and the input port, we expect that |S21| of a matched lossless transformer would be 10*log(50/436)=-9.41dB. The input impedance mid band implies a mismatch loss of around 0.1dB, and around 0.1dB of loss in the transformer, the measured |S21| is quite within expectation.

Above is the VNA plot of InsertionLoss.

The response is quite acceptable for the application (a very low gain, ie lossy, antenna).

## References / links

- Duffy, O. 2015. A method for estimating the impedance of a ferrite cored toroidal inductor at RF. https://owenduffy.net/files/EstimateZFerriteToroidInductor.pdf.
- Snelling, E C. Soft ferrites properties and applications. Iliffe books 1969.