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# I

## Short notes on Piezoelectric transducers

Piezoelectric effect:Piezoelectricity is the charge that accumulates in certain solid materials such as crystals, certain
ceramics etc. in response to applied mechanical stress. Due to displacement of charges, an
electric potential appears across certain surfaces of the crystal. The word piezoelectricity means
electricity resulting from pressure. Piezo is a Greek word which means to squeeze or press.
Piezoelectricity was discovered in 1880 by French physicists Jacques and Pierre Curie. The
piezoelectric effect is a reversible process i.e. conversely, if a varying potential is applied to the
proper axis of the crystal, it will change the dimensions of the crystal, thereby deforming it. This
effect is known as piezoelectric effect. Elements exhibiting piezoelectric effect are called as
electro resistive elements. A piezoelectric element used for converting mechanical motion into
electrical signal can be considered as a charge generator and capacitor. Mechanical deformation
generates a charge and this charge appears as a voltage across the electrodes.
The voltage is E =

Q
C

Piezoelectric effect is direction sensitive i.e. a tensile force produces a voltage of one polarity
while compressive voltage produces a voltage of opposite polarity. Piezoelectric effect can be
made to respond to mechanical deformations of the materials in many different modes- thickness
expansion, transverse expansion, thickness shear, face shear. The mode of motion affected
depends on shape of body relative to crystal axis and location of electrodes.
Advantages:1. The transducer needs no external power and is therefore self generating (active type).
2. It has a very good high frequency response.
Disadvantages:1. Piezoelectric transducers cannot measure static pressures. They respond only to changing
pressures.
2. The output of the transducer is affected by changes in temperature. Therefore,
temperature compensating devices have to be used.

Piezoelectric materials: - There are about 40 crystalline materials which exhibit piezoelectric
properties. Eg: - Rochelle salt, ammonium dihydrogen phosphate, lithium sulphate, dipottassium
tartarate, potassium dihydrogen phosphate, quartz etc.
Piezoelectric materials

Natural group
Quartz, Rochelle salt

Synthetic group
lithium sulphate, ethylene diamine tartarate

## Properties of Piezoelectric crystals

The desirable properties of piezoelectric materials are stability, high output insensitivity to
temperature and humidity and the ability to be formed into most desirable shape.
Quartz is the most stable piezoelectric material. However its output is very small. Rochelle salt
provides the highest output but it can be worked over a limited humidity range and has to be
protected from moisture. The highest temperature is limited to 45oC. Barium titanate can be
formed into a variety of shapes and sizes since it is polycrystalline. It has also a higher dielectric
constant.
Natural crystals have higher mechanical and thermal stability, can withstand higher stresses, have
low leakage and have a good frequency response. The synthetic materials, in general, have a
higher voltage sensitivity.

II

## Derive expression for crystal voltage sensitivity and charge sensitivity.

The magnitude and polarity of induced surface charges are proportional to the magnitude and
direction of applied force F. The polarity of induced charges depends on the direction of applied
force.
Charge Q = d X F (1)
Whered is the charge sensitivity of the crystal in C/N (constant for a given crystal) and F is
the applied force in N.
The force F causes a change in thickness of the crystal.
F=

AE
t t Newton (2)

Where A= area of crystal in m2, t= thickness of crystal in m and E= Youngs Modulus in N/m2
Youngs Modulus E=

stress
strain

= (F/A).

1
t /t

Ft
A t

N/m2 (3)

## Area A= wl where w= width of crystal in m and l = length of crystal in m

From Eqns. (1) & (2) we have,
Charge Q= dAE(t/t) (4)
The charge at the electrode gives rise to an output voltage Eo.
Voltage

## Where Cp= Capacitance between electrodes, F.

Capacitance between electrodes, Cp= roA/t (6)
From Eqns. (1), (5) & (6),
Eo=

Q
Cp =

dF
dt F
r o A /t = r o A

(7)

## F/A=P= pressure or stress in N/m2

d
Eo= r o tP (8)
= gtP (9)
Where g =

d
ro

(10)

g is the voltage sensitivity of the crystal. This is constant for a given crystal cut. Unit is Cm/N
g=

Eo
Eo /t
=
tP
P

(11)

g=

## electric field intensity

=
stress

(12)

Crystal voltage sensitivity, g, can be defined as the ratio of electric field intensity to pressure
(stress). Unit is Vm/N.
From Eqn. (10),
Charge sensitivity d= rog C/N (13)

III

## Equivalent Circuit of Piezoelectric Transducers

Cp

Cp

Rp
Output

Fig (a)

Eo

Rp

Output

Fig (b)

Basic Equivalent Circuit of piezoelectric transducer is shown in fig (a). The source is a charge
generator. The value of Q=dF. The charge generated is across the capacitance, Cp, of the crystal
and its leakage resistance is Rp.
The charge generator can be replaced by an equivalent voltage source having a voltage of
Q
dF
Eo= Cp = Cp
in series with a capacitance, Cp, and resistance, Rp, as shown in fig (b).
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