# Crystal Oscillator

### Crystal Oscillator:-

In LC oscillators the frequency of oscillation fo depends on the tank circuit parameters  L & C, whereas L & C values change with respect to time, temperature, aging etc. Therefore fo does not remain constant so at high frequencies LC oscillators are unsuitable because of instability. Crystal oscillators are more suitable at high frequencies and uses crystal as oscillatory element.

Piezo-electric effect:-

It is the ability of certain materials to generate an electric charge when mechanical stress is applied and vice-versa ( vice-versa is called Reverse Piezo electric effect).

i.e, If mechanical pressure is applied across x-axis, the electric charges appear perpendicular to x-axis  that is along y-direction. similarly if electric field is applied along x-direction mechanical strain is produced along y-direction.

working of quartz crystal:-

In this circuit crystal is placed between two metal plates then it acts as a capacitor with dielectric material as crystal between two metal plates.

i.e, when a.c  voltage is applied across these plates the crystal vibrates at a frequency of the applied a.c voltage . when fi = fo resonance takes place and crystal vibrates with it’s natural frequency almost of constant value.

Equivalent circuit of crystal:-

when crystal is not vibrating it is equivalent to a capacitance Cm.

when it is vibrating it is equivalent to series R-L-C circuit as shown below

and the series resonant frequency is given by $\left&space;|&space;X_{L}&space;\right&space;|&space;=&space;\left&space;|X_{C}&space;\right&space;|$

$\omega&space;L&space;=\frac{1}{\omega&space;C}$

$f_{s}=\frac{1}{2\pi&space;\sqrt{LC}}$

Parallel resonance $\left&space;|&space;X_{L}+X_{C}&space;\right&space;|=\left&space;|&space;X_{Cm}&space;\right&space;|$

$\omega&space;L-\frac{1}{\omega&space;_{C}}=\frac{1}{\omega&space;_{Cm}}$

$\omega&space;^{2}=\frac{1}{L}\sqrt{\frac{1}{c}+\frac{1}{C_{m}}}$

$f_{p}=\frac{1}{2\pi&space;}\sqrt{\frac{1}{L}(\frac{1}{c}+\frac{1}{C_{m}})}$Crystal Oscillator has two modes of operation Series $f_{s}$ resonance mode and parallel resonance mode $f_{p}$.

Crystal Oscillator with BJT:-

using crystal oscillator can be built up as follows

In this circuit crystal acts as a parallel tuned circuit at parallel resonance, the crystal impedance is maximum that is maximum voltage drop is there across C1 this allows that maximum energy transfer through feedback network through fp. BJT offers a phase shift of 180o further 180o is produced by the capacitor voltage. Oscillations are possible only through fp, which provides stable oscillations.

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