An online expert discussing broadband RF transformers recently opined “… if you measure k, the correlation of k and performance is excellent” whatever “performance” means.
Presumably he means k as in the flux coupling coefficient of two flux coupled inductors, ie inductors with mutual inductance (meaning changing current in one inductor induces an EMF in the other inductor). k is the proportion of flux due to current in one inductor that cuts the turns of the other inductor, it is usually stated pu (per unit) but sometimes in % (per cent or per 100).
A common metric for the performance of a broadband transformer is its InsertionVSWR. Other factors might be considered, but InsertionVSWR is commonly most ranked. Note that to describe a transformer as 1:49 implicitly invokes InsertionVSWR as a measure of its performance.
One of the enemies of broadband performance is flux leakage, k less than unity. The equivalent leakage reactance is usually the main contirubutor to high frequency roll off (an increase in InsertionVSWR at high frequencies) in good designs.
Let’s explore the ‘magic’ using the calibrated model used at 1:49 EFHW transformer using a Jaycar LO1238 core – design workup.
Above is a chart from that model showing:
- InsertionVSWR (magenta solid line);
- k (dotted blue line); and
- 1-k (dashed magenta line).
This is a good 1:49 transformer (see the referenced article) with low InsertionVSWR (<1.5) from below 2MHz to 25MHz.
Study the k line, does it jump out as a performance indicator? Is there an apparent “correlation of k and performance?”
k needs to be very close to unity for a good broadband transformer. In fact, it is more revealing to examine the departure of k from unity, ie to plot 1-k (dashed magenta line).
Some things to note:
- 1-k is clearly frequency dependent in this model (and of course so is k, but less so);
- whilst leakage reactance is the main contributor to high frequency roll off, and k is one of the influences on leakage reactance, the relationship is not a simple one trivial (ie there is no obvious correlation between the roll off of InsertionVSWR at high or low end of the chart above.
Conclusions
k is an important design parameter for broadband ferrite cored RF transformers, but there is not a simple and strong correlation between k and InsertionVSWR.