KLMmodel.m

Implements KLM model for piezoelectric transducers. Includes loss and up to 3 matching layers

% KLMmodel.m
% Code for the piezoelectric transducer lumped element model proposed by
% Leedom, D. A., Krimholtz, R., and Matthaei.
% The method used here sequentially propagates impedance and voltage
% through the network. (a more elegant, but slower method is to use T
% matrices)

% The basic model is extended here to allow for up to 3 matching layers,
% with loss in each layer. (if only one layer is desired, enter 0 for
% thickness of other layers)

% The voltage variables represent force. Pressure can be obtained by
% dividing by transducer area. The current variables represent
% velocity.

% Leedom, D. A., Krimholtz, R., and Matthaei, G. L. "New Equivalent Circuits For Elementary
% Piezoelectric Transducers." Electronics Letters vol. 6 no. 13 (1970).
% Selfridge, A. Gehlback,S. "KLM TRANSDUCER MODEL IMPLEMENTATION USING TRANSFER MATRICES"
% ULTRASONICS SYMPOSIUM p875 (1985)
% "Equivalent circuits for transducers having arbitrary even- or odd-symmetry piezoelectric
% excitation." IEEE Trans. Sonics Ultrason. SU-25, 1 15-125 (1978).
% Kino, G. S. (1987). Acoustic Waves: Devices, Imaging, and Analog Signal Processing. Prentice-
% Hall, Englewood Cliffs, NJ.
% Leedom, D. A., Krimholtz, R., and Matthaei, G. L. (1978). Equivalent circuits for transducers
% having arbitrary even- or odd-symmetry piezoelectric excitation. IEEE Trans. Sonics Ultrason.
% SU-25, 1 15-125.

% Optimal values for facing layer impedance can be found in J. Souquet, P.Defranould, J. Desbois,
% "design of low loss wide band ultrasonic transducers for noninvasive medical application"
% IEEE Trans.Son. Ultrason., vol SU-26, p75-81 (1979)