Before we can examine a detector we must define the type - high level or low level? The diode has 3 sections in its characteristic curve. It can be cut-off, conducting or in the twilight zone called the square law region.
In a high level detector the diode is switched on and off. Then the RF is filtered to develop the audio. We would see this type detector in a tube or transistor radio with the signal amplified before being detected.
The following screen shots show the small and large signal detectors.
Now the Z match in one page.
Notice when the Zin matches Zout half the power is lost in the generator. In a crystal set working in the micro volt range this would be a problem. See the alternate definition of Z matching on the right hand column.
Look at the load on the printouts. This chart relates a 100 Ohm source to loads from 1 Ohm to 10000 Ohms. The 10k load receives a higher %age of the power. This would be good for the small signal detector. The higher the better?
Look back at the large signal detector. It could drive a high Z head phone?
So the first step is define the project and stick with the design. Don't talk apples and oranges.
A crystal set is limited by the signal and power levels. A TRF or superhet would be a different animal.
While you are thinking about these things consider the antenna system and feeder system. A transmitter hookup would require a large signal approach. A receiver could be more small signal approach.
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