Lecture 1 
RIE 
4 wi . 
jZ TAN jZ> TANS 
av 
-jZo/sin 
Fig. 1.1. Equivalent electrical circuit 
of a piezoelectric bar. 
p= _ daw = transformation ratio 
E 
si 
Zo = wt yo/sit 
= 1/ Yost 
Bal 
Co= = LZ capacity of the clamped crystal 
< 
where / is the length, w is the width, t is the thickness, d3, is the piezoelectric 
constant, s¥, is the compliance at constant electric field, p is the density, and «33 
is the dielectric constant at constant strain. 
More complex acoustic oscillators can be analyzed by adding the appropriate 
acoustic components to the terminals F; and F. In the immediate neighborhood 
of resonance, a considerably simplified circuit, Fig. 1.2, can be used. Cy) and R 
are the clamped capacity and resistance; and K, N, S;, and Sp are the motional 
capacity, inductance, internal loss resistance, and radiation resistance, respec- 
Fig. 1.2. Simple lumped equivalent 
electrical circuit of a piezoelectric 
transducer. SR 
