Linear Circuit Analysis

1. Introduction
2. Basic Concepts
3. Simple Circuits
4. Nodal and Mesh Analysis
5. Additional Analysis Techniques
6. AC Analysis
7. Magnetically Coupled Circuits
8. Polyphase Systems
9. Operational Amplifiers
10. Laplace Transforms
11. Time-Dependent Circuits
12. Two-Port Networks
Appendix

Superposition

Superposition is a technique used to analyze linear electric circuits with multiple independent sources. It is based on the principle that the voltages and currents in such a circuit can be found by algebraically summing the voltages and currents produced by each independent source acting alone, with all other independent sources replaced by their internal impedances.

Algorithm

Assume we have a circuit that contains at least two independent sources.

Step 1. Keep only one independent source and deactivate all other independent sources. Notice that if you circuit contains dependent sources you need to keep those in the circuit (in a way, they are treated like resistors).

Step 2. Calculate the potentials and currents in the circuit.

Step 3. Repeat the last two steps for each source in the circuit.

Step 4. Superimpose the values of potentials and currents obtained at Step 2; pay special attention to the direction of the voltage drops and current flows.

Miscellaneous
  • To deactivate a current source we remove it from the circuit (replace it with open-circuit or break); to deactivate a voltage source we replace it with a short-circuit (or wire).
  • Unlike mesh and nodal analysis that can be applied to both nonlinear and linear circuits, superposition can be applied only to linear circuits. Therefore, in general, we cannot use superposition to compute the potential and currents in a circuit containing diodes, transistors, or other nonlinear elements.
  • The superposition method can be applied to DC, AC and time-dependent circuits (as long as the circuit is linear).
  • Special attentian needs to be paid when computing the power using the method of superposition. If we need to compute the power generated or dissipated by a component, we need to compute the voltage across and the current flowing through the component, and then multiply them to obtain the power.
Examples of Solved Problems
See also
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Superposition theorem