Applications of network synthesis and zero-pole analysis in transducer modeling
Daniel Max Warren · Proceedings of meetings on acoustics · 2013
When a transducer is an immutable component of a larger system being simulated, it is sufficient that the transducer model correctly reproduce behavior only at the available ports of the transducer.The behavior of two-port electroacoustic transducer should be completely characterized by three transfer functions related to the electrical and acoustic termination impedance and the transfer impedance.To the extent that the transducer could be represented as a analog circuit of passive linear elements, the same circuit could be exactly represented by rational polynomials of the Laplace s, embodied as a set of poles and zeros of the transfer functions.This invites the reverse process of identifying poles and zeros by nonlinear curve fit of rational polynomials to measured transfer data, perhaps even synthesizing a circuit directly from the identified poles and zeros.Measured transducer transfer data have been fit demonstrating both the utility and the pitfalls of this method.Curve fit transfer functions can be a compact and faithful representation of complex data over frequency, but have no predictive value outside the given data.Judicious selection of the number of poles and zeros, initial values, proper constraints, and some physical insight are necessary for stable curve fits.