Circuit Theorems – Notes – 1

Electrical Engineering » Notes » Circuit Theorems

1. In the node method one node is designated as a reference or ground node, and all other node voltages are measured with respect to that node. Only the KCL equations and the constituent relations need be written.

2. In the loop method currents are defined to flow in loops. Loop currents are defined until all branches are traversed by at least one current. Only KVL equations need be written.

3. Superposition means that if the circuit is linear, multisource networks can be solved for one source at a time by setting all other independent sources to zero. Setting a voltage source to zero means replacing it with a short circuit; a current source set to zero is an open circuit. The complete response is the sum of the responses to each individual source. For circuits with dependent sources, a practical solution is to leave all the dependent sources in the circuit. The network can then be solved for one independent source at a time by setting all other independent sources to zero, and summing the individual responses.

4. The Thévenin equivalent circuit for any linear network at a given pair of terminals consists of a voltage source in series with a resistor. The element value for the Thévenin equivalent voltage source can be found by calculating or measuring at the designated terminal pair on the original network the open-circuit voltage. The equivalent resistance can be calculated or measured as the resistance of the network seen from the designated terminal pair with all independent sources internal to the network set to zero.

5. The Norton equivalent circuit contains a current source in parallel with a resistor. The element value for the Norton equivalent current source can be found by calculating or measuring at the designated terminal pair on the original network the short circuit current. As with the Thévenin equivalent resistance, the Norton equivalent resistance can be calculated or measured as the resistance of the network seen from the designated terminal pair with all independent sources internal to the network set to zero. Note that the value of the equivalent resistance is the same for the Thévenin and Norton equivalent circuits, that is, R_TH=R_N.

6. Since the Thévenin equivalent voltage v_TH, the Norton equivalent current i_N, and the equivalent resistance R_TH=R_N are related as

v_TH=i_NRTH,

the element values for these equivalents can be found by calculating or measuring any two of the open-circuit voltage, the short-circuit current, or the resistance.

7. Circuit analysis is often simplified by applying superposition or finding Thévenin or Norton equivalents, because complicated circuits are reduced to simpler circuits, for which the solution may already be known.

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