Draw the circuit diagram of crystal oscillator and explain its working.
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To excite a crystal for operation in the series-resonant mode it may be connected as a series element in a feedback path, the crystal impedance is the smallest and the amount of positive feedback is the largest. Resistor R1, R2 and RE provide a voltage-divider stabilized dc bias circuit, the capacitor CE provides ac bypass of the emitter resistor RE and the radio-frequency coil (RFC) provides for dc bias -while decoupling any ac signal on the power lines from affecting the output signal. The voltage feedback signal from the collector to the base is maximum when the crystal impedance is minimum . The coupling capacitor Cc has negligible impedance at the circuit operating frequency but blocks any dc between collector and base. The circuit shown in figure is generally called the Pierce crystal. The resulting circuit frequency of oscillations is set by the series resonant frequency of the crystal. Variations in supply voltage, transistor parameters, etc. have no effect on the circuit operating frequency which is held stabilized by the crystal. The circuit frequency stability is set by the crystal frequency stability, which is good. 

The resonant frequency is given as 

Fo = 1/( 2 π √LC ) 

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