Low level crystal detector Vs high level detector And a dab of Z matching.

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.

 

The vacuum tube has the same three regions which may be used for high or low level detection. In this case we see a low level detector operating in 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.