To begin with, a crystal radio works just like any other radio, but without the amplifiers for radio/audio frequency signals, or local oscillators as used in the common superheterodyne radio.
Let's begin with the transmitted signal, which is a carrier wave at the transmitting radio frequency of the station, say, 1000 kiloHertz (thousands of cycles per second). For an AM (amplitude modulation) broadcast station, the carrier signal is modulated by an audio frequency signal ranging up to several thousand Hertz, which causes the signal to vary in amplitude at the frequency of the audio signal(my explanation, see the FAQ link for the other one) (with FM (frequency modulation) stations the audio signal varies the frequency of the carrier).
When the modulated wave reaches the antenna of the receiver, some of its energy is captured by the antenna. Ideally, the antenna is resonant at the radio frequency of interest, that is, at least a quarter wavelength long. (by comparison, a tuning fork is a quarter wavelength long at its resonant frequency). Generally, the longer and more tuned to resonance the receiving antenna is, the more signal from the station is available to be heard.
The received signal is carried to a tank circuit, typically an inductor (coil of wire), and a capacitor (parallel metal plates). The inductor and capacitor are connected in parallel or in series with each other, usually in parallel. The tank circuit acts as a band pass filter, and when it is resonant at the frequency of the received signal, it will "ring", just as a tuning fork does, storing the energy of the signal. Signals of different frequencies will not be stored in the tank circuit, but will pass on to "ground". Some simple sets, such as the Oatbox, use only a coil of wire with taps on it for the tank circuit, and rely on the self capacitance between the turns of wire in conjunction with the inductance of the coil to achieve a resonant condition. Tuning this circuit is done by selecting different taps for the antenna, bringing different amounts of inductance (and capacitance) into play.
Next, a portion of the energy in the tank circuit is taken by the detector, which is a rectifier, allowing the signal through on only half of its alternating cycle, rejecting the other half; this changes the ac signal to a pulsating direct current. Were it not for the detector, the positive and negative halves of the alternating current signal on reaching the headphones would essentially cancel each other out .
The headphone circuit is next. A diaphragm in the earphone, which moves the air to transfer the sound to your ear, can mechanically follow the audio frequency changes in the amplitude of the signal but not the rf signal, which moves too fast, and passes the rf signal on to ground. Some references would have you believe that the radio frequency and audio frequency signals are split apart by the detector - not true; that really takes place in the headphones. With magnetic type earphones, sometimes a capacitor of about 0.01 pF across the terminals of the headphone will improve the bass response of the phones and give an increase in the volume of the signal heard, working in conjunction with the inductance of the coils of the headphones to act as an audio filter. With the piezo electric earphones, supplied with many kits, a resistor of about 47 kohms is often used across the terminals of the earphone and works in a similar manner, bleeding off a dc voltage buildup across the earphone element, which looks like a capacitor electrically, improving the volume and bass response as well as reducing distortion on strong signals.
You can go from here to more complex circuits, such as those using full wave rectification instead of half wave as the single detector provides, and multiple tuned circuits which filter out unwanted stations better. Note that the simple rectifying action of the detector will not allow you to listen to unmodulated signals, such as those used for sending morse code (cw); for that you need to provide a local signal a few hundred Hz different from the received signal which mixes with the incoming signal- the difference frequency between the received signal and the local oscillator signal, or beat note, is then heard in the headphones. Incidentally, with a very strong local signal, all you need is some sort of antenna, a detector, and phones. Using the resonant circuits allow you to hear weaker signals (sensitivity), and to separate stations (selectivity). For a crystal set, the real challenge is to have as efficient a receiving system as possible, which includes a largish antenna tuned to resonance, low-loss components, good impedance matching from antenna to receiver to the detector and audio circuits, and sensitive headphones.
There are a number of good book sources on crystal sets as well as several on the web. Go to the Xtal Set Society new page for some more good info. How A Crystal Radio Works for Beginners
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