Symbolic-numeric circuit analysis or symbolic circuit analysis with online approximations

This paper describes a method for obtaining simplified symbolic expressions for the transfer functions of analog electronic circuits and, in particular, analog transistor circuits. The circuits are modeled as linear lumped RLC electrical networks with dependent sources. Both the frequency and the values of the components appear as symbols in the transfer functions. The simplification is done by symbolic computation with approximations taking place during the computation. The method has three essential parts of the method. (1) The user partitions the network to modules satisfying mismatch conditions (to the first approximation). The transfer functions of each module are evaluated and the results are combined to form the transfer functions of the network. (2) A nominal value is associated with each component; R1≫R2 if and only if the absolute nominal value of R1 is “much larger” than the absolute nominal value of R2; When R1+R2 is evaluated, R1 is returned if R1≫R2. The relation ≫ is defined between functions of the frequency as well as between values. (3) Whenever possible, polynomials are represented as a product of lower order polynomials. When the lower order polynomials are of order one or two, poles or zeros are available in symbolic form. This paper presents transistor circuit examples computed by the SCHEME program which implements the method