relation between reflexion coefficient and power ratio

Question

Assume you have an intermediate input/outpout device connected to a coaxial line. For example, the device may be a DC-bloc, a bias tee, or simply a PCB microstrip transmission line.

Using a signal generator (e.g. YIG oscillators), you can generate a continuous wave and feed the input of the device.

At a given frequency, you have measured the power of the oscillator dissipated in the 50ohm input load of your spectrum analyzer (without connecting the device), and noted the value, e.g. P1 = 20dbm. Then you connect the device between the oscillator and the spectrum analyzer and measure again the power, say P2 = 15dbm.

I would like a mathematical relation between P1 and P2 and the reflection coefficient (or equivalently the VSWR) caused by the device. Is it possible ?

Answer 1

The device you're connecting has at least 2 properties (there are others, but let's stay simple), the amount of power it transmits, and the amount it reflects. That's two unknowns.

However, you've only measured the amount it transmits. That means you have one equation, and two unknowns, so you can't solve for both unknowns.

Consider a perfectly matched 5dB attenuator. That would transmit 15dBm with 20dBm incident on it, and reflect nothing, as it absorbs the remaining power.

Alternatively you might have something non-dissipative, like a shunt capacitor, which with 20dBm incident allows 15dBm to pass to a load, and reflects 18.35dBm back to the source (do the sums carefully!) absorbing nothing.

You can't tell these two situations apart using a simple power transmission measurement.

This is why a network analyser measures both transmission (S21) and reflection (S11), and if the load has any reflection, we need to take account of the device's output match (S22) and reverse transmission (S12) as well. These are call S, for Scattering, parameters. There's plenty to read on the interwebs, once you know the name to search for.