55 years ago I was taught to get maximum voltage out I want the load Z to be 10 times the source Z. Testing the theory I set the load to 500K. I now have the gain of 30 I asked for. So to recap with Zin = Zout I get maximum POWER transfer at the cost of half the voltage. Half the voltage being dropped internal to the source is a high price to pay when I am not looking for voltage on the output. Let's add a second stage and try the above test with a second stage.
In summary we Z match I/O to get maximum POWER transfer. We set the output Z at least 10 times the source Z for minimum power consumption and highest voltage output.
This is our main problem with RF circuits. The input Z drops as the frequency increases because of circuit capacitance. The same transistor may have a Z of 1kOhm at 1 KHz and 50 Ohms at 30 Mhz.
Food for though:
Based on the above data how would you " Z match " the input to and antenna circuit which is power limited?
Same question reworded, In a receiver would you want to send a higher voltage or power from the antenna?