Learn Instrumentation: Piezo electric effect

Electrical charges are produced on the opposite surfaces of some crystals when subjected to force or torsion. The electrical charge produced is proportional to the effective force. By application of force, dimension of the crystal changes causing a displacement of charge. Piezoelectric effect is reversible, i.e. if a varying potential is applied to the crystal, it will change the dimension of the crystal along a certain axis.

It must be remembered that a piezoelectric crystal can convert a changing force into a changing electrical signal, whereas a steady-state force produces no electrical response.

Piezo-electric crystals are available in two forms- natural and man-made. Quartz and ceramic are examples of naturally available piezo-electric crystals whereas Rochelle salts, Lithium sulphate, Ammonium dihydrogen phosphate etc are examples of man-made crystals. Quartz is considered as one of the most stable piezo-electric crystal and is known for its ability
to perform accurate measurement for time and frequency. Its output is independent of temperature variation. They have low voltage sensitivity but high charge sensitivity.

Description of operation

The piezoelectric effect causes a realignment and accumulation of positively and negatively charged electrical particles, or ions, at the opposed surfaces of a crystal lattice, when that lattice undergoes stress. The number of ions that accumulate is directly proportional to the amplitude of the imposed stress or force.

PE transducers use a spring-mass system to generate a force proportional to the amplitude and frequency of the input quantity. The stress imposed upon the piezoelectric material is the direct result of a physical input such as acceleration, force, or pressure. To accomplish this, a mass is attached to the crystal, which, when accelerated, causes force to act upon the crystal. The mass, also known as a seismic mass, creates a force directly proportional to acceleration according to Newton’s law of motion, F=ma. Thin metallic electrodes collect the accumulated ions. Small lead wires interconnect the electrodes to an electrical connector or feed-through, to which cabling is attached. An advantage of PE materials is that they are self-generating and require no external power source.

A piezo-elecric crystal can be considered as charge generator and a capacitor. External force generates a charge and this charge appears as voltage across the electrodes.

The voltage V=Q/C . The voltage polarity depends on the direction of applied force.

The amount and polarity of charge produced is proportional to the magnitude and direction of force.

Charge Q = k_q x F Coulomb, (1)

where k_q is the charge sensitivity of the crystal; C/N and F is applied force; N

From Hooke’s Law, the Young’s modulus Y of the crystal is given as

Where A = area of crystal; t = thickness of crystal; Y = Young’s modulus; A = area of crystal;

From above equations,

The voltage output V_o is given as

Where C is the capacitance between the electrodes;

From above equations,

Where P = F/A= stress or pressure, N/m²

Electrical analysis of Piezo-electric crystals

Piezo-electric crystal can be considered a charge generator. The amount of charge is q= k_q x F.

The charge appears across capacitance C_p of the crystal. R_p is the leakage resistance of the crystal. The equivalent circuit with voltage source id shown above. The voltage

V=q/C_p = k_q x F/C_p

If a load is connected at the output, the load capacitance C_L and resistance R_L will make the loaded circuit as below.

We can consider Rp as very large (open).

The equivalent impedance of load is

The total impedance is

Displacement measurement using Piezo-crystal

At steady state when ω=0, M=0. Hence piezo-crystals are not suitable for static measurements.

Uses

They are used in numerous applications such as environmental stress screening, vibration control, active vibration reduction, flight testing, wind tunnel testing, structural testing, modal analysis, seismic vibration, package testing, shock, motion and attitude detection and stabilization, ride quality response and simulation, acoustic testing and noise, harshness and vibration testing. Fast response, ruggedness, high stiffness, extended range, and the ability to also measure quasi-static forces are standard features associated with PE sensors.

Gate Questions
GATE-2008