Symbols, Descriptions and Units

Symbol	Meaning	Metric Units
C	Capacitance	farad
Cij	Elastic stiffness constant	newton/meter2
C0	Shunt capacitance	farad
C1	Series capacitance	farad
dij	Piezoelectric strain constants	coulomb/newton
d33	Piezoelectric strain constant	x 10-12 Meter/Volt
d31	Piezoelectric strain constant	x 10-12 Meter/Volt
d15	Piezoelectric strain constant	x 10-12 Meter/Volt
E	Electric field	V/m
fa	Antiresonance frequency	cycles/second
fr	Resonance frequency	cycles/second
fn	Frequency of max. impedance	cycles/second
fm	Frequency of min. impedance	cycles/second
fp	Parallel resonance frequency	cycles/second
fs	Series resonance frequency	cycles/second
gij	Piezoelectric voltage constants	meter2/coulomb
g33	Piezoelectric voltage constant	X 10-3 voltmeter/newton
g31	Piezoelectric voltage constant	X 10-3 voltmeter/newton
g15	Piezoelectric voltage constant	X 10-3 voltmeter/newton
hij	Piezoelectric pressure constants	newton/coulomb
Kij	Electromechanical coupling constant
k31	Transverse coupling constant
k33	Longitudinal coupling constant
k15	Shear coupling constant
kt	Thickness coupling constant
kp	Planar coupling constant
KT	Free relative dielectric constant
KS	Clamped relative dielectric constant
P	Electric polarization	coulomb/meter2
QM	Mechanical quality factor
QE	Electrical quality factor
Sij	Elastic compliance constant	meter2/newton
|Y|	Admittance	mho
|Z|	Impedance	ohm

Curie Point:  The temperature at which the dielectric constant peaks and all polarization disappears.

Coupling Coefficient (k):  A dimensionless number related to the ratio of the energy stored in the mechanical and electrical portions of the material.  The first subscript indicates the direction of the electric field and the second indicates the direction of the mechanical strain, expressed in percent.

Density:  The ratio of mass to volume in the material, expressed in kg/m³.

Dielectric Constant:  The ratio of the permitivity of the material to the permitivity of free space.  The value specified is for the "free" condition (i.e., unclamped and well below the mechanical resonance of the part).

Dissipation Factor:  A measure of the dielectric losses in the material defined as the tangent of the loss angle or the ratio of parallel resistance to parallel reactance expressed in percent.

"d" Constant:  The piezoelectric constant relating mechanical strain and applied electric field - defined as the ratio of strain to field.  The first subscript indicates the direction of the field and the second the direction of the resulting strain, expressed in meters/volt.

Field:  The ratio of voltage developed to the distance between the electrodes.

Frequency Constant:  Defined as the resonant frequency (f_r) times the controlling dimension, expressed in KHz-m.

"g" Constant:  The piezoelectric constant relating open circuit voltage and mechanical stress - defined as the ratio of voltage to stress.  The first subscript indicates the direction of the generated voltage, and the second indicates the direction of the force, expressed in volt-meters/newton.

Mechanical Q (Q_M): The ratio of reactance to resistance in the equivalent electric series circuit representing the mechanical vibrating resonant system.  The shape of the part affects the value.

Strain:  The ratio of the change in length to the length.

Stress:  The ratio of applied force to the cross sectional area.

Young's Modulus (Y):  The mechanial stiffness property of a piezoelectric ceramic material and is expressed as the ratio or stress to strain the material, while vibrating at its resonant frequency, expressed in newtons/meter².