# Crystal Detector Basics | Crystal Detector Circuit

This page describes **crystal detector basics** including crystal detector circuit,
crystal detector characteristics and mathematical equations.

The crystal detector is widely used in Rf and microwave field due to their sensitivity and simple design.
Following are the applications of crystal detector.

• Used as video detector which produces DC output based on input signal frequency (unmodulated or modulated).

• Used in RF mixers for super heterodyne circuit.

The semiconductor chip and metal whisker are two essential parts of a crystal detector. Microwave crystal detector uses silicon chip (1/16 inch square) and tungsten whisker wire (3/1000 inch diameter). Other part is required to support chip & whisker and to couple electric energy to detector.

Crystal detectors are useful at microwave frequencies due to their smaller size. This crystal size limits power handling capabiliy of crystal detector to about 100 mWatt.

The figure-1 depicts crystal detector circuit with its characteristics.

## Crystal Detector Characteristics

The curve is square law in nature and hence output voltage is proportional to square of input voltage. This law has been mathematically explained in the below section. This curve shows that large variation of output voltage results into minor variation in input voltage. This refers to higher sensitivity of the crystal detector.

This curve is approximated by Taylor series as shown by following equation-1.

i = a0 + a1*v + a2*v^{2} + a3*v^{3} ...Equation-1

Let v = A*cos(w*t) ...Equation-2

Where, A = Amplitude

w = 2*π*f

After putting equation-2 in equation-1 we will get,

i = a1*(A*cos(w*t)) + a2*(A*cos(w*t))^{2} + a3*(A*cos(w*t))^{3} ... Equation-3

For extreme small signals, all terms except the first one are negligible.
This results into following equation.

i = a1*(A*cos(w*t))

Hence current is proportional to the applied voltage. Here crystal behaves as simple resistor with negligible amount of
DC current flowing through milliampere meter.

For larger signals, second term must be included in the equation and we get following equation.

i = a1*(A*cos(w*t)) + a2*(A*cos(w*t))^{2}

= a1*(A*cos(w*t)) + a2* (A^{2}/2) *(1+cos(2*w*t)) ... Equation-4

• The current includes DC component i.e. a2*A^{2}/2, which flows through mA meter.

• Second component i.e. a2* (A^{2}/2)*cos(2*t) flows through capacitor (C).

• Hence, milliampere meter indicates reading which is proportional to
square of amplitude A of microwave voltage.

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