Crystal detectors are widely used in the microwave field because of their sensitivity and simplicity. They are used as video detectors to provide either a dc output when unmodulated microwave energy is applied or a low frequency ac output up to tens of MHz or higher when the microwave signal is modulated. They are also used as mixers in superhetrodyne systems specifically at microwave frequencies where other mixers, such as vacuum tubes, are insufficient or inefficient.
The essential parts of the crystal detector are a semiconducting chip and a metal whisker, which contacts the chip. A typical microwave crystal detector uses a silicon chip about 1/16-inch square and a pointed tungsten whisker wire about 3/1,000 inch in diameter. The other part of the crystal detector or mount is needed simply to support the chip and the whisker and to couple electrical energy to a detector. Crystal detectors are successful at microwave frequencies partly because of their extremely small size, these dimensions also limit their power handling capability; just 100 mW is sufficient to damage crystals.
Square Law of Crystal Detectors :-
Square law of crystal detectors states that the output voltage is proportional to the square of the input voltage. Relatively large variations in output voltage result from minor variations inn the input voltage and the sensitivity of this type of detector is therefore relatively high.
Figure 1 : Idealized crystal detector circuit
Figure 2 : Square law characteristics of a crystal detector circuit
Consider the idealized circuit shown in Figure 21, in which a sinusoidal microwave voltage is applied to flow to the milliammeter. A typical crystal detector has a current voltage characteristic similar to that shown in Figure 2. Any such curve can always be approximated by a Taylor series consisting of terms involving powers of, that is,
If the operating point is the origin (v=0,i=0) then ao=0 . Let
where A is the amplitude, ω is equal to 2πf, and f is the microwave frequency. Substituting in Equation 1 yields
For extremely small signals, all terms in Equation 1 except the first are negligible. And i= a1(Acos(ωt). The current is simply proportional to the applied voltage, and the crystal behaves as a simple resistor with negligible dc current flowing through the milliammeter. However, for somewhat larger signals, the second term must be included to obtain reasonable accuracy.
The current now includes the dc component (a2A2)/2, which flows through the milliammeter, and the second harmonic component (a2A2)/2 Cos 2t , which flows through C. Thus, the milliammeter indication is proportional to the square of the amplitude A of the microwave voltage.