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 200Ω 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 10t secondary for a nominal 1:4 50:200Ω 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 hints that a 5t primary on a BN43-202 core is probably good enough down to 0.5MHz, depending on one’s limit for InsertionVSWR. We are not being too fussy here… this is not an application that demands InsertionVSWR < 1.5.
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 with terminals for antenna field test.
Above is a VNA sweep of a prototype wound with 0.25mm ECW.
The load resistance is a resistor with DC resistance of 148.6Ω in series with the VNA 50Ω input port. InsertionLoss at less than 0.2dB is quite within expectation.
Above is a disaggregation of InsertionLoss into TransmissionLoss (or simply Loss) and MismatchLoss. It can be seen that MismatchLoss is worse at the lowest and highest frequencies, it is what limits the VSWR bandwidth.
The response is quite acceptable for the application (a very low gain, ie lossy, antenna). The compensated transformer is slightly better at the high end.
Update 23/01/2022
The transformer was revised to add a centre tap to the secondary winding for optional grounding for feed line common mode current mitigation.
The transformer is wound by forming a trefoil bundle of wires and winding five turns, but one wire is split out at the start end to tuck a further half turn in, and at the other end, the same wire is split out of the last half turn so that one five turn winding has its terminals at one end, and the other two windings have their ends at the other end so that they can be joined start to finish to produce a centre tapped secondary of 10 turns. This construction is to minimise leakage reactance, the enemy of broadband transformers.
Above is the equivalent series inductance of the transformer with short circuit termination.
Above is the measured InsertionVSWR of the uncompensated transformer.
Above is a calibrated Simsmith model of the rewound transformer with optimal compensation. A 33pF capacitor was added to the prototype.
Above, the revised transformer assembly with compensation capacitor installed.
Above is InsertionVSWR for the revised transformer with 200Ω load.
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.