Determining Resonance Frequency
When exposed to an AC electric field, a piezoelectric ceramic element changes dimensions cyclically, at the cycling frequency of the field. The frequency at which the ceramic element vibrates most readily, and most efficiently converts the electrical energy input into mechanical energy, is the resonance frequency.
the frequency at which
impedance in an electrical circuit describing the element is
zero, if resistance caused by mechanical losses is ignored. The
minimum impedance frequency also is the resonance frequency, f_{r}.
The composition of the ceramic material and the shape and volume
of the element determine the resonance frequency  generally, a
thicker element has a lower resonance frequency than a thinner
element of the same shape.
As the cycling frequency is further increased, impedance
increases to a maximum (minimum admittance). The maximum
impedance frequency, f_{n} , approximates the parallel
resonance frequency, f_{p} , the frequency at which
parallel resistance in the equivalent electrical circuit is
infinite if resistance caused by mechanical losses is ignored.
The maximum impedance frequency also is the antiresonance
frequency, f_{a}. Maximum response from the
element will be at a point between f_{m} and f_{n}.
Values for minimum impedance frequency, f_{m} , and
maximum impedance frequency, f_{n} , can be determined
by measurement. Figure 1.10 shows a system designed to
ascertain these values, and summarizes the procedure.
Figure 1.8. Impedance as a Function of Cycling Frequency
A ceramic element's oscillations first approach the minimum
impedance frequency (f_{m} ) / resonance frequency (f_{r}
), at which the element vibrates most readily, and most
efficiently converts electrical energy into mechanical energy.
As cycling frequency is further increased, impedance increases
to the maximum impedance frequency (f_{n} ) /
antiresonance frequency (f_{a} ).
Figure 1.10. System for Determining Minimum Impedance
(Resonance Frequency) and Maximum Impedance (AntiResonance
Frequency) of a Piezoelectric Ceramic Element
Procedure:
 Set the switch to A.
 Place the ceramic element into
position.
 Adjust the frequency generator
to give a maximum voltage value on the voltmeter. This value
is the resonance frequency.
 Set the switch to B.
 Adjust R4 to give a voltage
value on the voltmeter equal to the value in step 3. This
value is the impedance resonance (Zr).
 Set the switch to A.
 Adjust the frequency generator
to give a minimum voltage value on the voltmeter. This value
is the antiresonance frequency.
f_{m} and f_{n} can be used to calculate the
electromechanical coupling factor, k. k depends on the mode of
vibration and the shape of the ceramic element. The
relationships between k and f_{m} and f_{n} for
a ceramic plate, a disc (surface dimensions large, relative to
thickness), or a rod are:
Coupling Factor for Plates / k_{31}*
* electric field
parallel to direction of polarization,
induced strain
perpendicular to direction of polarization
Coupling Factor for Discs / k_{p}**
** electric field
parallel to direction of polarization,
induced strain in same direction
Coupling Factor for Rods / k_{33}***
*** electric field
parallel to direction of polarization,
induced strain in same direction
