Introduction#
Designers of analog electronic circuits often need to investigate or modify the small-signal static or dynamic behavior of circuits. Numerical circuit analysis is often performed with the aid of CAD programs. Although the obtained numeric results can be accurate, they do not provide design information. This is because the underlying mechanisms are not shown. Symbolic analysis of simplified circuits often does give a lot more design information, but it also often requires unpopular and cumbersome hand calculations.
Nowadays, many symbolic analysis tools are available to help designers with symbolic calculations. Adequate use of these programs requires proper formulation of the problem, which is often in the form of a matrix equation. One software tool for symbolic and numeric analysis of linear circuits is SLiCAP . It provides symbolic expressions for the circuit’s signal transfer. Aside from its symbolic analysis capabilities, it can perform parametric numeric analysis and generate frequency domain, time domain and complex frequency domain plots.
The theory behind the operation of SLICAP is summarized in this chapter. It starts with a summary of Nodal Analysis in section Nodal Analysis. Nodal Analysis (NA) can be used to solve network equations for networks with only voltage-controlled elements. Networks that also include elements whose behavior can only be described in a current-controlled form, such as voltage sources, can be transformed into networks with only voltage-controlled elements, by using the Norton transformation and Blakesley’s voltage shift theorem. Alternatively, the so-called Modified Nodal Analysis (MNA) can be used. MNA is implemented in SLICAP and in most SPICE-like simulators. It will be discussed in section Modified Nodal Analysis. An overview of MNA matrix stamps for commonly used network elements, as well as for Laplace transfer functions, will be given in section MNA stamps.
For more information on these topics, the reader is referred to Desoer Chua and Kuh [52].
Circuit designers often need to determine and/or manipulate the complex frequencies of poles and zeros. Techniques for numeric and symbolic determination of pole and zero frequencies will be presented in section Determination of poles and zeros. Symbolic approximation of pole and zero frequencies will be added to future versions of SLICAP.
In many engineering cases, it is convenient to model an electrical network as a two-port. In those cases, the port quantities (voltage and current) of one port are related to those of the other port and the electrical behavior of the two-port is described with the aid of a \(2\times2\) matrix. The conditions under which four-terminal networks can be modeled as two-ports, as well as two-port representation methods and properties, will be discussed in section Two-ports. Understanding of these conditions is important for correct application of the asymptotic gain feedback model discussed in Chapter Modeling of negative feedback circuits.