A new crystal radio design
A crystal radio is essentially a coil (inductor) connected in parallel with a capacitor, with values such that they will resonate together at the frequency of a desired AM broadcast radio station. Some of the energy resonating between the coil and the capacitor is tapped off, rectified by a germanium diode, and used to drive an earpiece or headset. If the coil is wound just the right way, the capacitor is naturally formed by the distribute capacitance between the turns of the coil, but it doesn't have to be that way.
When I tried to build the crystal radio project in my young son's electronics kit, I was faced with a problem: the radio circuit requires a connection to the Earth, the ground, recommended to be a copper cold water pipe. In my house, that meant tinkering in the laundry room in the basement. But the project also needed a long wire antenna outdoors, as high as possible. That was too hard to arrange from in the laundry room, and the radio didn't work.
Years later, as a ham radio enthusiast, I knew that my ham radio antenna, a dipole, didn't require an earth ground for operation. (Grounding for lightning safety is a separate issue.) The difference between the end-fed long wire and the dipole is characteristic impedance: high at the end of the long wire, low at the middle of the dipole. The middle of the dipole connects to a cable which runs into my basement radio room.
So, the new design provides for a low-impedance drive to the coil/capacitor resonator, and an audio impedance-matching transformer to convert ~1 k-ohms impedance from the diode to 8 ohms impedance of my ordinary earbuds or personal stereo headphones.
(To be continued).