Piezoelectric Effect –

It is used for producing ultrasonic waves and is explained as –

When a quartz crystal is subjected to mechanical compression or tension across its faces than voltage having magnitude directly proportional to pressure is induced across the crystal. Its polarities are opposite for compression and tension. This phenomenon is called the direct piezoelectric effect. Conversely, if an a.c. voltage is applied across the crystal surface, it vibrates at the frequency of a.c voltage. This is called inverse piezoelectric effect.

The vibrator of max amplitude will occur at the resonance frequency of crystal.

The frequency is given by,

$F= \dfrac {n}{2L} \sqrt{\dfrac {Y}{\rho}} $

a) Diagram:

The circuit consist of centre tap transformer connected to quartz crystal in secondary & a frequency generating tank circuit consisting of variable capacitor C & primary coil L2. The grid of triode is positively coupled to tank circuit.

b)  Working –

When the H.T. supply is switched ON, current flows in the tank circuit setting up the oscillation whose frequency is –

$f_{1} =\dfrac {1}{2\pi \sqrt{L_{2}C}} $

These oscillation are fed into the secondary due to mutual  inductance between it & L3. The crystal now starts vibrating due to increase pizoelectric effect causing a back e.m.f across L1 this emf is stopped up by the transformer & fed back positively into tank circuit where the oscillations are sustained. The variable capacitor C is so adjusted that the quartz crystal starts vibrating with its natural frequency given by –

$f_{2}=\dfrac {\eta}{2L}\sqrt{\dfrac {Y}{\rho}}$

where $\left\{ \begin{array} {l l}n=1,2,.....integers\\ L=Rod\ length \end{array} \right\}$

The vibrations of crystal will be maximum when it is set at resonance i.e. when

$f_1=f_2$