I'm doing a power amplifier with 2 stages but I'm with doubts about how to do the inter-stage matching.
Do I need to find the z optimum (in the stage of gain) and after that match the output to 50 ohm and after that match with the input of the second stage?
Is this correct?
How can I simulate it to be sure if the match is correct?
If the two stages are close one to the other and not use 50 ohms transmission lines between them, you do not need to go to 50 ohms. Just use a matching network to match the output impedance of the first stage to the input impedance of the second stage. Designing the matching network have to take into consideration the bandwidth of your two-stage amplifier.
This is how one engineer designed her 10MHz 2-stage power amp with 10nH and 45 Ohms on the drain of 1st stage. She suggests a lower output impedance for more Pout.
Keep in mind stripline tracks.
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This paper describes how to use negative feedback for impedance matching using Rogers laminate 0~3GHz
If you are playing with a simulator, try doing what you say , i.e. matching the Zout to 50 and the Zin to 50. As said you do not need the 50 ohm point at all, so the last component of the Zout matching network can be combined with the first component of the Zin network. Giving a virtual 50 ohm point, but the Zout to Zin match will be OK.
Frank