Principle:

• Resonance is obtained between a natural frequency of suitable cut piezoelectric crystal and with a suitable frequency superimposed on it that is generated by an oscillator.

Construction:

• In the diagram we have a thin plate of piezoelectric crystal cut on such axis so that we get inverse piezoelectric effect that is on application of high frequency electric field, it can vibrate in resonance.
• Natural frequency of crystal slab cut is given by:$\eta = \dfrac k {2t} \sqrt {\dfrac Y {\rho}}$
  where, t = Thickness of crystal slab
  Y = Young's modulus
  $\rho = Density$
  k= 1, 2, 3, ... which represent order or harmonic. We take k = 1 that is fundamental frequency.
• It is important to know that natural frequency$\eta$ is inversely proportional to thickness t.
• Hence for higher frequency, t has to be reduced. But very small thickness of slab without fracturing it is very difficult to cut.
• Hence for frequencies above 20 MHz, we make use of higher overtones.

Working:

• Function of the oscillator is very much similar to magnetostriction oscillator.
• When the current through coil L2, changes it causes a corresponding change in the magnetisation of the rod, due to magnetostriction effect a small change in the kength of rod will be noticed.
• This change in length will give rise to change of flux linked with the coil L1 and it will induce an voltage.
• This induce voltage will change grid voltage. The changed grid voltage will be amplified and come out at plate circuit, and cycle will continue.
• Oscillator circuit will develop the frequency:$f = \dfrac 1 {2\pi} \sqrt {\dfrac 1 {L_2C}}$
• Electric field of frequency f is transfered to plates A and B through coil L2 and L.
• Between plates A and B, a crystal of natural frequency$\eta$ is fixed.
• For resonance we take, f =$\eta$, under this condition crystal will generate oscillations with highest amplitude.

Advantages:

• It has higher frequency range.
• It is small in size and economical.
• It has better waveform.