Piezoelectric Transducer

in this lecture, we are going to learn about the Piezoelectric Transducer, the derivation of induced voltage by the piezoelectric effect, the expression for voltage sensitivity, and the properties of the Piezoelectric Transducer, and the last, we will discuss the application of the Piezo Electric Transducer. So let’s discuss the definition of Piezo Electric Transducer.

Piezoelectric Transducer

• This type of transducer works on the principle of the “piezoelectric effect”.

• A piezoelectric transducer crystal is one in which an electric voltage is developed across a certain surface when dimensions are changed by applying mechanical force. The potential is produced by the displacement of charges. This effect is reversible i.e. conversely if a variable voltage 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 the “piezoelectric effect”.

• The materials that exhibit a significant and useful piezoelectric effect are divided into two categories:

1. Natural Group: Quartz and Rochelle salt are examples.
2. Synthetic Group: Lithium sulfate and ethylene diamine tartrate belong to this group.

• The piezoelectric effect can be made to respond to mechanical deformations of the material in many modes. This mode can be thickness expansion, transverse expansion, thickness-shear, and face shear.

Expression for Voltage sensitivity of Piezoelectric Transducer

• Mechanical deformation generates a charge and this charge appears as a voltage across the electrodes.

• Charge Induces, Q \propto F ,

\Rightarrow Q= d\; \times \;F …… Eq. 1

where d is the charge sensitivity of crystal.

• Force (F) cause a change in thickness (t) of crystal = \frac{AE}{t}. \Delta t

• Young’s Modulus = E=\frac{S}{\epsilon}

E=\frac{F}{A}. \frac{t}{\Delta t}

• From Equation.1,

Q=d \;AE\times \left ( \frac{\Delta t}{t}\right )

\because Capacitance of crystal in between electrodes= C_P

C_P=\frac{\epsilon_0 \epsilon_r A}{t}

where t is the thickness of crystal and A is the area of crystal =W \times l

• \therefore Voltage induce at output is E₀ so,

E_0=\frac{Q}{C_P}=\frac{d \times F}{\frac{\epsilon_0 \epsilon_r A}{t}}

E=\frac{dAE \left ( \frac{\Delta t}{t}\right ) \times t }{\epsilon_0 \epsilon_r A}=\frac{dE \Delta t}{\epsilon_0 \epsilon_r}= \frac{d}{\epsilon_0 \epsilon_r}. \left ( \frac{F}{A}\right )t

\boxed{E_0= g\; t \;p }

where,

g=\frac{d}{\epsilon_0 \epsilon_r}= Voltage sensitivity of crystal (Vm/N)

P= stress or pressure applied=\frac{F}{A}(N/m²)

Now, g= \frac{E_0}{t \times p}= \frac{E_0/t}{p}= \frac{Electric\; field}{Stress}

\boxed{g= \frac{\epsilon}{p}}

Also, \boxed{Charge \; sensitivity (d) = g \epsilon_0 \epsilon_r}

Equivalent Circuit of Piezoelectric Transducer

The source is a charge generator. The value of the charge is Q= d \times F. The charge generated is across the crystal’s capacitance, C_p, and its leakage resistance is R_p. The charge generator can be replaced by an equivalent voltage source having a voltage of,

\boxed{E_0=\frac{Q}{C_p}=\frac{d \times F}{C_p}}

Properties of Piezoelectric Crystal

• The desirable properties of piezoelectric material are stability, high output insensitivity to temperature and humidity, and the ability to be formed into the most desirable shape. “Quartz“ is the most stable piezoelectric material and its output is quite small.

• Rochelle salt provides the highest output but it can be worked over a limited humidity range and has to be protected against moisture. The highest temperature is limited to 45^oC.

• Barium titanate has the advantage that it can be formed into a variety of shapes and sizes since it is polycrystalline. It has also a higher dielectric constant.

• Natural crystals possess the advantages that they have higher mechanical and thermal stability, can withstand higher stresses have low leakage volume resistivity and have a good frequency response.

• The synthetic material, in general, has a higher voltage sensitivity.

Uses of Piezoelectric materials and Transducers

• Quartz is commonly used for stabilizing electronic oscillators because of its stability. The use of piezoelectric transducer elements is confirmed primarily by dynamic measurements.

• The voltage developed by applications of strain is not held under static conditions. Hence, the elements are primarily used in the measurement of such quantities as surface roughness and in accelerometers and vibration pickups.

• Ultrasonic generator elements also use barium titanate, a piezoelectric material. Such elements are used in industrial cleansing apparatus and also in underwater detection systems known as “SONAR“.

Frequently Asked Questions on Piezoelectric Transducer