Basic Element Stamps
In the context of nodal analysis in electrical circuit theory, a "network stamp" refers to a numerical value associated with a particular circuit element that represents its contribution to the nodal equations. Nodal analysis is a method used to analyze electrical circuits by determining the voltages at various nodes within the circuit.
When formulating nodal equations, each circuit element (resistor, capacitor, inductor, etc.) contributes to the system of linear equations through its corresponding network stamp. The network stamp is based on the behavior of the circuit element and is used to populate the entries of the nodal admittance matrix.
Fisrst the resistor stamp will be introduced. The res stamp adds the admittance 1/R to Yjj and -1/R to Yij in the Y-matrix.
Second will be the capacitor. The cap stamp adds the capacitive admittance s*C to Yjj and -s*C to Yij in the Y-matrix, where s=jω.
Let’s create the Y-matrix of the circuit to the left directly in Python. We can use the addRES function from before and create a new one addCAP that adds the capacitor C1.
Last of the basic passive components is the inductor. The inductor stamp adds the inductive admittance 1/(s*L) to Yjj and -1/(s*L) to Yij in the Y-matrix.
Let’s create the Y-matrix of the RLC circuit to the left. Using the previous stamps as template it is easy to make the function that adds an inductor to the Y-matrix - addIND.
With the three available stamps it is possible to create the Y-matrix of any passive circuit regardless of its complexity.