At nanoVNA-H – measure ferrite transformer I gave an example of using a nanovna to measure loss of a ferrite cored transformer.

Noelec makes a small transformer, the Balun One Nine, pictured above and they offer a set of |s11| and |s12| curves.

These curves fuel online discussions about the loss, InsertionLoss, TransmissionLoss and ReturnLoss… often given in -ve dB values (it is a hammy sammy thing), and without correct application of the terms (again).

Lets calculate the loss of the pair of transformers back to back as shown from the marker data. Firstly, loss means PowerIn/PowerOut, and can be expressed in dB as 10log(PowerIn/PowerOut). For a passive network, loss is always greater than unity or +ve in dB.

\(loss=\frac{PowerIn}{PowerOut}\\\)Some might also refer to this as Transmission Loss to avoid doubt, but it is the fundamental meaning of loss which might be further qualified.

So, lets find the two quantities in the right hand side using ‘powerwaves’ as used in S parameter measurement.

s11 and s21 are complex quantities, both relative to port 1 forward power, so we can use them to calculate relative PowerIn and relative PowerOut, and from that PowerIn/PowerOut.

### PowerIn

PowerIn is port 1 forward power less the reflected power at port 1, \(PowerIn=P_{fwd} \cdot (1-|s11|^2)\).

### PowerOut

PowerOut is port 2 forward power times less the reflected power at the load (which we take to be zero as under this test it is a good 50Ω termination), \(PowerOut=P_{fwd} \cdot |s21|^2 \).

### Loss

So, we can calculate \(loss=\frac{PowerIn}{PowerOut}=\frac{\frac{PowerIn}{P_{fwd}}}{ \frac{PowerOut}{P_{fwd}}}=\frac{1-|s11|^2}{|s21|^2}\)

Let’s work an example.

From the chart marker at 0.2MHz, |s11|=-2.59dB=0.742 and |S21|=-6.00dB=0.501.

So \(\frac{PowerIn}{PowerOut}=\frac{1-0.742^2}{0.501^2}=1.486\) which we can write as \(10log(1.486)=1.719dB\).

Online experts are inclined to divide the loss equally between the two back to back transformers, but that is only an approximation, and a poor approximation if the flux level is likely to be significantly different (as in this case).

In this case for back to back transformer network, InsertionLoss is 6.00dB, ReturnLoss is 2.59dB, and loss is 1.79dB.

Another quantity often used is MismatchLoss, \(MismatchLoss=\frac{P_{fwd}}{PowerIn}=\frac1{(1-|s11|^2)}\). In this example \(MismatchLoss=2.23=3.47dB\).

It is important to understand the meaning of the various loss metrics, and the appropriate metric for the application.