Generation of the Transfer Functions for MIMO Systems

The main aim of the symbolic analysis is the generation of the symbolic expressions of the circuit functions and computation of their sensitivities, in order to evaluate the circuit characteristics and their variation in respect of the parameter values. Other important information for circuit designer is about the location of poles and zeros in the complex frequency plane, or about the eigenvalues of the state matrix, necessary to develop a qualitative analysis of the circuit. For multiple inputs (multiple excitations) and multiple outputs it is of interest to obtain the transfer functions involving the inputoutput variables. In this case, the concepts of controllability and observability are of importance.

In this chapter two approaches for transfer function generation both in Single-Input- Single-Output (SISO) and in Multiple-Input-Multiple-Output (MIMO) systems are presented: one approach is based on the state equations and the other one on the semistate equations of the circuit. Two variants for the first approach and three variants for the second one are developed and compared on illustrative examples, pointing out the advantages.

Keywords: Symbolic analysis, transfer functions, matrix transfer functions, MIMO systems, design of analog circuits, state variables, state equations, normal tree, nodal analysis, modified nodal equations, frequency domain analysis, time-domain analysis.