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Symbolic circuit analysis : ウィキペディア英語版
Symbolic circuit analysis
Symbolic circuit analysis is a formal technique of circuit analysis to calculate the behaviour or characteristic of an electric/electronic circuit with the independent variables (time or frequency), the dependent variables (voltages and currents), and (some or all of) the circuit elements represented by symbols.〔G. Gielen and W. Sansen, Symbolic Analysis for Automated Design of Analog Integrated Circuits. Boston: Kluwer Academic Publishers, 1991.〕〔Labrèche P., (presentation: Linear Electrical Circuits:Symbolic Network Analysis ), 1977〕
When analysing electric/electronic circuits, we may ask two types of questions: What is the value of certain circuit variable (voltage, current, resistance, gain, etc.) or what is the relationship between some circuit variables or between a circuit variable and circuit components and frequency (or time). Such relationship may take the form of a graph, where numerical values of a circuit variable are plotted versus frequency or component value (the most common example would be a plot of the magnitude of a transfer function vs. frequency).
Symbolic circuit analysis is concerned with obtaining those relationships in symbolic form, i.e., in the form of analytical expression, where the complex frequency (or time) and some or all of the circuit components are represented by symbols.
==Frequency domain expressions==

In the frequency domain the most common task of symbolic circuit analysis is to obtain the relationship between input and output variables in the form of a rational function in the complex frequency \mathit\, and symbolic variables \mathbf:
T(s,\mathbf)=\frac

The above relationship is often called the network function. For physical systems, N(s,\mathbf) and D(s,\mathbf) are polynomials in \mathit\, with real coefficients:
T(s,\mathbf)=\frac) s^i}) s^i}=K\frac))}))}

where z_i(\mathbf) are the zeroes and p_i(\mathbf) are the poles of the network function; m \geqslant n.
While there are several methods for generating coefficients a_i(\mathbf) and b_i(\mathbf), no technique exists to obtain exact symbolic expressions for poles and zeroes for polynomials of order higher than 5.

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