13 Jul 2026

Coupling Coefficient of a Piezoelectric Crystal

practical ug-vi piezoelectricity crystal coupling

Experimental arrangement

The piezoelectric crystal is connected between electrodes, driven by the oscillator, and monitored for resonance and anti-resonance.

Aim

To determine the electromechanical coupling coefficient of a piezoelectric crystal from its resonance and anti-resonance frequencies.

Apparatus

Piezoelectric crystal, oscillator, frequency meter, electrodes, and CRO.

Theory

The coupling coefficient measures conversion between electrical and mechanical energy. If $f_r$ and $f_a$ are the resonance and anti-resonance frequencies,

\[k^2=\frac{\pi^2}{8}\frac{f_a-f_r}{f_r}\]

for the standard small-coupling approximation used in the experiment.

Observations

Trial	Resonance $f_r$ (kHz)	Anti-resonance $f_a$ (kHz)
1	31.20	32.05
2	31.18	32.04
3	31.21	32.06

Calculation

Using $f_r=31.20\,\text{kHz}$ and $f_a=32.05\,\text{kHz}$,

\[k=\sqrt{\frac{\pi^2}{8}\frac{32.05-31.20}{31.20}}=0.183.\]

Result

\[\boxed{k=0.183}.\]

Precautions

1. Keep the crystal firmly mounted but free from mechanical stress.
2. Sweep frequency slowly near resonance.
3. Avoid excessive drive voltage.

Viva Questions

1. What is piezoelectricity? It is the coupling between mechanical strain and electric polarisation in certain crystals.
2. What is resonance? It is the condition of maximum response at a natural frequency.
3. Why is anti-resonance observed? Electrical and mechanical responses combine to give a minimum current at a nearby frequency.