A simplified design for small broadband RF transformers using medium µ ferrite core for receiving use.
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 4t primary and 12t secondary for a nominal 1:9 50:450Ω transformer.
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°.
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 4t primary is probably good enough down to 1.8MHz, depending on one’s limit for InsertionVSWR. We are not being too fussy here… this is not an application that demands InsertionVSWR < 1.2.
Above is a plot of expected R and X for a 4t winding using my common mode choke design tool. Z at 1.8MHz is 49+j199Ω, or Y=0.00117-j0.00474S. (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=0.02117-j0.00474S, and plugging that in to calculate VSWR…
…we have InsertionVSWR=1.27, that is fine for our application.
But, we better measure a real inductor to confirm our estimates.
Above is the test inductor with 4t of wire wrap wire, plugged into a test fixture that has been OSL calibrated (mentioned elsewhere on the site).
The measurement indicates permeability is a bit higher than the datasheet value, that happens, these things have wide tolerances… they are anything but 1% parts.
Now lets calculate the frequency at which high end roll off is likely to start.
The winding is 22mm per turn, the 12t winding is 264mm which is 15° around 7m wl or 43MHz. So we expect this transformer will be good from 1.8-40MHz.
The next step is to make one up and measure it, keep watching.