broadband transistor test fixture for high power applications

Can anyone explain how standing wave is used to separate DC bias from AC. And what tools or phenomenon is used to make it work in a modern communication system, any help would be greatly appreciated

If you feed the DC bias into the base of a transistor via a quarter wave line which is decoupled at the DC end, to the RF it looks like an open circuit. A quarter wave line is a transformer at its working frequency a short circuit at one end appears as a open circuit at the other, and vice versa.
Frank

hi, thank you for your help, but can you please clear out where the standing wave comes into the picture? thanks

Modern telecomm system use freq less than 5GHz, in such low freq, the 1/4 lamda is a little long, so normally use inductor to bias current. For DC, the inductor has little resistance, say 0.5 ohm; but for RF, the resistance is greatly more than 50R, say 300R, so the RF leakage through the inductor is very little.

Because after the inductor, there is several capacitors shunt to GND to short the RF to GND, for VSWR, in Smith chart, it is equal to shunt the inductor to GND for RF. Normally after shunt the inductor to GND, the VSWR become worse, and you need to re-tune the match component.

Standing wave. If you have a transmission line that is terminated correctly, the voltage along it will be the same. If the termination is wrong, some of the RF energy travelling down it will be reflected and travel backwards down to line towards the source. This is called the standing wave because at different points down the line, the "backwards" wave will subtract from the "forward" wave causing the voltage on the line to be lower then expected at other points the "backward" wave will add to the "forward" wave and the voltage will increase. With a quarter wave line with a short circuit on it ALL the power is rejected, no current loads of voltage, i.e. it is a high impedance. If it was terminated in a 50 ohm load the input side would look like 50 ohms too. [ input voltage = output voltage and as power the same, input current = output current]
Frank

if an inductor also stops RFac from flowing into the DC stem why use a quarterwave transformer instead. What happens to inductor at RF do its characteristics change?

If you lay down a quarterwave line on a PCB track, saves making a RF choke and soldering it in. Inductors always have stray capacity so they have a resonent frequency, i.e. they must be made and tried out to ensure that they have the desired impedance at the operating frequency.
Frank