over 100 simple radio circuits.
http://www.intio.or.jp/jf10zl/index.html
The first transistor acts as a reflex stage. A 10 millihenry choke sends the RF to the diode detector and the audio to the output stage.
http://www.techlib.com/electronics/crystal.html#Twotransistorreflex
It is constructed by NE612 balanced modulator. It is direct conversion receiver.
http://www.intio.or.jp/jf10zl/neof.htm
The crystal radio works best with a long, high outdoor antenna. This page describes different such radios and amplifiers.
http://www.techlib.com/electronics/crystal.html
This is normal superheterodyne radio receiver. It does not use any coils. It uses a filter and oscillator made by OP-AMP. Converter is also constructed by a OP-AMP detector.
http://www.intio.or.jp/jf10zl/opraio.htm