Circuit_analysis

Circuit analysis normally refers to finding all node voltages and all branch currents for an electrical circuit.

The term circuit analysis is often used to mean linear circuit analysis. However non-linear circuits may also be analyzed. Resistive networks normally consisting of a single independent source and resistors may also be analyzed using simpler techniques, however the term resistive network analysis should be used for this. Unfortunately, some have taken to using the term circuit analysis to describe resistive network analysis, which is misleading at best.

Linear DC circuits include independent voltage and current sources, dependent current and voltage sources, and linear resistors. Linear AC circuits also include at least one linear differential component (capacitors and inductors) along with at least one AC source. If a circuit does not include capacitors and inductors DC circuit analysis may be used. If a circuit includes one or more linear differential component and an AC source AC circuit analysis must be used.

DC linear circuit analysis techniques

There are several methods of linear DC circuit analysis.

(1) Nodal analysis ("node") (2) Mesh analysis ("mesh") - Does not work for complex 3D cases (3) Superposition - normally done in conjunction with node or mesh if the circuit has dependent sources (4) Source transformations - a limited technique (5) Equivalent circuits - normally done in conjunction with node or mesh

AC linear circuit analysis techniques

The methods for AC circuit analysis are generally the same as for DC circuit analysis. However the inclusion of capacitors and inductors (linear differential elements) means that complex math, or phasor must be used.

The effective resistance, or impedance, for such components are

$Z(C)\; =\; \backslash frac\{1\}\{j\; \backslash omega\; C\}$ and $Z(L)\; =\; j\; \backslash omega\; L\; \backslash ,$,

where $j\; =\; \backslash sqrt\{-1\}$, $\backslash omega\; =\; 2\; \backslash pi\; f$, $f$ = the frequency of the AC source, C = the capacitance, and L = the inductance. In short the introduction of $j$ means that the math is much, much more onerous.

Non-linear circuit analysis

The general procedure for non-linear circuit analysis is to:

1. Guess the operating mode (on, off, active, etc.) for all non-linear components, substituting the correct linear component for the non-linear part.
2. Apply linear circuit analysis to the resulting circuit.
3. Verify that all guesses were correct. Repeat with a new guess if not all guesses were correct.

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