This sheet describes the basics of electrical network analysis. The description focuses on the modeling of a circuit for static or dynamic analysis using nodal analysis. Calculation may be performed with a computer aid such as MATLAB.
A network of passive elements (such as resistance and/or reactance) can be analyzed on current and voltage in each circuit node as result of used component parameters, voltage- and current sources.
From this set of equations differential voltages and currents can be calculated:
Each passive may be described as resistance R, inductive reactance or capacitive reactance . Keep in mind that the components in the matrix are inverted so:
Conductance: or susceptance: . For dynamic analysis only the source of interest has to be described, other sources are short or open for voltage and current sources respectively.
Modeling matrix G by neglecting sources:
For passives; thus for example:
After establishing the description of the network in matrix notation, the sources can be added. Now we expand the equation by adding the voltage source descriptions , and current source: node current is sourced with and in node current is sourced with (thus sinked).
Vector may be calculated by:
or using the reduced row echelon form of matrix