# Calculate Loss from s11 and s21 – convenient online calculator

I often need to calculate loss from marker values on a VNA screen, or extracted from a saved .s2p file.

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 $$loss=\frac{PowerIn}{PowerOut}=\frac{\frac{PowerIn}{P_{fwd}}}{ \frac{PowerOut}{P_{fwd}}}=\frac{1-|s11|^2}{|s21|^2}$$

Noelec makes a small transformer, the Balun One Nine, pictured above and they offer a set of |s11| and |s12| curves in a back to back test. (Note: back to back tests are not a very reliable test.)

Let’s work an example.

From the chart marker at 0.2MHz, |s11|=-2.59dB and |S21|=-6.00dB, enter the data into Calculate Loss from s11 and s21.

Above, the calculation. The magnitude of each of s11 and s21 is required by the calculator, the angle of each is not used.

One can approximate the loss of a single transformer by dividing this loss equally between the two cascaded transformers, giving a loss of 1.3dB per transformer.

The MismatchLoss is also calculated. In this case, |s21| (-6dB) has two main components, MismatchLoss (3.476dB) and Loss (2.524dB). If you were to hook this up between a 50Ω signal generator and 50Ω power meter, inserting the back to back transformer power would reduce the power meter reading 6dB (over a direct connection, partly due to MismatchLoss and partly due to Loss (conversion of RF to heat in the core and windings).