Transducers use the piezoelectric effect to measure physiological variables in medical instrumentation. The piezoelectric effect occurs in certain natural and man-made crystals, where an electric charge is produced when mechanical stress is applied. Piezoelectric transducers are used as microphones to detect heart sounds and in ultrasound devices due to their ability to convert mechanical energy to electrical signals. The capacitive properties of piezoelectric transducers interact with the input impedance of amplifiers, affecting the transducer response. Piezoelectric constitutive equations describe the relationships between stress, strain, electric field, and electric charge in piezoelectric materials.

1. Transducer Principles
The Piezoelectric Effect

2.  Major function of medical instrumentation is the measurement of physiological
variables.
 Variable- A quantity whose value changes with time
 Physiological variables- Variables associated with physiological properties of the body.
For example: body temperature, electrical activity of heart (ECG), arterial blood
pressure, and respiratory air flow.
Many forms of physiological variables:
 Ionic potential and currents
 Mechanical movements
 Hydraulic pressure and flows
 Temperature variations
 Chemical reactions and so on….

3. Topics to be covered:
Transducer
Input-output relationship
Active vs. Passive transducer
The piezoelectric effect
• Natural and man-made crystals
• Bimorph configuration
• Interaction of the capacitive property with the input impedance to affect transducer
response (Circuit and Traces)
• Applications: -Microphones or heart sounds or other acoustic signals from within the body
-Ultrasonic instruments; Typical acoustic-electric system
-Ultrasound dental scalers
-Ultrasonic surgery instruments
-Ultrasound scanners
• Piezoelectric constitutive equation

4. The Piezoelectric Effect:
Natural materials- Slices from crystals of quartz or Rochelle salt cut at a certain angle with
respect to the crystal axis, cane sugar, topaz, tourmaline, bone (apatite crystals)- biological
force sensors
Man-made materials- Wafers of barium titanate by heat-treating them in the presence of
strong electric field; PZT (Lead Zirconate Titanate); More pronounced effect

5.  The capacitive property of the piezoelectric transducer interacting with the input impedance of the
amplifier to which they are connected affect the response of the transducer.
 Voltage measured at the input of the amplifier depends on the capacitance and amplifier input
impedance with respect to the duration of the force, T.
Applications
(Acoustic-Electric Systems)
24-36 KHz
55 KHz
2 – 18 MHZ;
Pregnancy monitoring: 3-5 MHz
Ultrasonic dental scalers Ultrasound scanners
Ultrasonic surgical instruments

6. Piezoelectric Constitutive Equations
Hooke’s Law and Dielectrics
S = s. T
D = ∈. E
Combining these two seemingly different constitutive equations:
S = sE. T + dt.T
D = d.T + ∈T. E
S = sE. T + gt.D
D = (-g).T + [∈T]-1. D

7. Symbol Object type Size Units Meaning
T Vector 6X1 N/m2 Stress components
S Vector 6X1 m/m Strain components
E Vector 3X1 N/C Electric field components
D Vector 3X1 C/m2 Electric charge density
s Matrix 6X6 m2/N Compliance coefficients
c Matrix 6X6 N/m2 Stiffness coefficients
∈ Matrix 3X3 F/m Electric permittivity
d Matrix 3X6 C/N Piezoelectric coupling coefficient for strain-charge form
e Matrix 3X6 C/m2 Piezoelectric coupling coefficient for stress-charge form
g Matrix 3X6 m2/C Piezoelectric coupling coefficient for strain-voltage form
q Matrix 3X6 N/C Piezoelectric coupling coefficient for stress-charge form