AM is quite easy (a diode and a capacitor can be enough), an FM receiver need a local oscillator that require some active elements (transistors) and a more complex circuit.
> The aerial is connected to the grounded inductor. The coil has an internal parasitic capacitance which, along with the capacitance of the antenna forms a resonant circuit (tuned circuit) with the inductance of the coil, resonating at a specific resonant frequency. The coil has a high impedance at its resonant frequency, and passes radio signals from the antenna at that frequency along to the detector, while conducting signals at all other frequencies to ground. By varying the inductance with a sliding contact arm, a commercial crystal radio can be tuned to receive different frequencies. Most of these wartime sets did not have a sliding contact and were only built to receive one frequency, the frequency of the nearest broadcast station. The detector and earphones were connected in series across the coil, which applied the radio signal of the received radio station. The detector acted as a rectifier, allowing current to flow through it in only one direction. It rectified the oscillating radio carrier wave, extracting the audio modulation, which passed through the earphones. The earphones converted the audio signal to sound waves.
If you are building an AM crystal radio. [1] You will also need a high-impedance speaker [2] if you want to operate it without a power supply, otherwise you will need an amplifier. You can avoid using a commercial diode by making your own point contact diode as done in Foxhole radios [3] and you can make your own piezoelectric speaker from Rochelle salt [4]. Here [5] is one personal projects site touching all those topics.
In conclusion, you should be able to build a simple radio from copper wire, aluminium foil, a pencil, a razor blade, and baking powder.
AM peak detector is probably the easiest and primitive AM demodulator: it's basically made by a diode, a capacitor and a resistance. I implemented it when I was in the high school and I was making the first physics experiments.
The idea behind this demodulator is quite easy: the diode filters out all of the negative part of the signal, then the positive signal charge the capacitor and the energy is released in a quite constant way (R*C must be several order of magnitude higher than 1/f where f is the carrier frequency) during the negative signal "hole".
In theory. Reception of FM works much like AM except you need an FM detector before turning the signal into audio. A circuit a little more fancy, than a diode (or rusty razor blade and wire) used in AM. But not that much more fancy. There are many ways to detect FM. Most methods actually use the phase - the immediate relative change in the frequency - and not the actual frequency. While the modern technique is a phase-locked loop, it can be much simpler.
A classic passive RC or LC or RL filter, will cause a phase shift. Take the difference between two phases effectively decodes FM. No active elements required. With only RL filters it would be very inefficient. So you may need to be standing next to the transmitter if you don't have at least one transistor or tube. But one such tube or transistor would be plenty for a strong local broadcast.
If you have some capacitors, it gets easier. Maybe paper and tinfoil rolled tightly, or flakes of glass or mica between thin slices of wood. Check out the slope detector circuits here [1] (fig 3, 4); the article is a good introduction to FM detection in general.
