This article demonstrates the use of a nanoVNA to select a ferrite core material and sufficient primary turns for a low InsertionVSWR 50Ω broadband RF transformer.
Simple low frequency equivalent circuit
Above is a very simple approximation of an ideal 1:1 transformer where the effects of flux leakage and conductor loss are ignored. A 1:n transformer can be modelled the same way, as if flux leakage and conductor loss are ignored, the now ideally transformed secondary load becomes 50Ω.
This simple equivalent circuit does contain the elements that are most important to low frequency performance, the inductor and resistor represent the magnetising impedance as a parallel equivalent circuit of the magnetising inductance and core loss.
Let's simulate that circuit.
Above is a simulation of the |s11| and |s21| we would expect to measure for our simplified transformer.
The design object is:
- low |s11|; and
- high |s21|.
In this case, at the low frequency end, |s11| increases, and |s21|decreases, both due to the combined effects of the winding inductance and core loss.
Now ferrite cores yield a frequency dependent inductance and core loss. There are many articles on this website explaining how to design with ferrite cores using the published core characteristics, but this article is about using a nanoVNA to validate such a design, or even to find a combination by cut and try.
Most failed published ham designs failed to provide sufficient magnetising impedance to deliver adequate low frequency performance.
Let's measure a couple of examples by winding the primary winding alone, and measuring it in shunt with a through connection from Port 1 to Port 2 (nanoVNA CH0 and CH1). As always, the fixture is very important.
Let's try a FT240-43 core with a 2t winding connected in shunt with a through connection from VNA Port 1 to Port 2.
Above is a plot of |S21|, and recall that InsertionLoss=-|s21|.
Without capturing the effects of a secondary winding and flux leakage, the primary winding is not at all suitable for a low InsertionVSWR broadband transformer, it has low magnetising impedance, a result of the combination of ferrite characteristic and the number of turns.
Let's try a FT240-43 core with a 4t winding connected in shunt with a through connection from VNA Port 1 to Port 2.
Above is a plot of |S21|, a huge improvement on the 2t case.
Above is a plot of |s11| which tells us there is some mismatch at the lowest frequencies, but mismatch is unlikely to make a large contribution to the InsertionLoss in this case.
Above is a plot of InsertionVSWR, another presentation of the |s11| measurement.
We can calculate the Loss from the s11 and s21 measurements recorded in the saved .s2p file at 3.5MHz.
As suggested, the main contribution to InsertionLoss is Loss (conversion of RF energy to heat) in the core material and winding, mainly the core material in this case.
Increasing turns increases magnetising impedance and reduces losses, but more turns means longer conductors which compromises high frequency performance, so for a broadband transformer, you need sufficient turns for low frequency response, but no more.
Stacking cores increases magnetising impedance, reduces losses and increases surface are, but longer turns means longer conductors which compromises high frequency performance, so for a broadband transformer, you need sufficient turns for low frequency response, but no more.
Based on measurement results, you may choose different turns and / or different core material.
This measurement does not capture all the important influences on transformer performance, but it does provide a very useful first step for selection / screening / validation test to select a ferrite core material and sufficient primary turns for a low InsertionVSWR 50Ω broadband RF transformer.
If a DUT does not pass muster, it is going to be worse when built with a secondary winding and load.