CIRCUIT ANALYSIS TYPE BASIC INFORMATION

Circuit Reduction Techniques.
When a circuit analyst wishes to find the current through or the voltage across one of the elements that make up a circuit, as opposed to a complete analysis, it is often desirable to systematically replace elements in a way that leaves the target elements unchanged, but simplifies the remainder in a variety of ways.

The most common techniques include series/parallel combinations, wye/delta (or tee/pi) combinations, and the Thevenin-Norton theorem.

Series Elements.
Two or more electrical elements that carry the same current are defined as being in series.

Parallel Elements.
Two or more electrical elements that are connected across the same voltage are defined as being in parallel.

Wye-Delta Connections.
A set of three elements may be connected either as a wye, shown in or a delta. These are also called tee and pi connections, respectively. The equations give equivalents, in terms of resistors, for converting between these connection forms.

Thevenin-Norton Theorem.
The Thevenin theorem and its dual, the Norton theorem, provide the engineer with a convenient way of characterizing a network at a terminal pair. The method is most useful when one is considering various loads connected to a pair of output terminals. The equivalent can be determined analytically, and in some cases, experimentally.

Thevenin Theorem.
This theorem states that at a terminal pair, any linear network can be replaced by a voltage source in series with a resistance (or impedance). It is possible to show that the voltage is equal to the voltage at the terminal pair when the external load is removed (open circuited), and that the resistance is equal to the resistance calculated or measured at the terminal pair with all independent sources de-energized.

De-energization of an independent source means that the source voltage or current is set to zero but that the source resistance (impedance) is unchanged. Controlled (or dependent) sources are not changed or de-energized.

Norton Theorem.
This theorem states that at a terminal pair, any linear network can be replaced by a current source in parallel with a resistance (or impedance). It is possible to show that the current is equal to the current that flows through the short-circuited, terminal pair when the external load is short circuited, and that the resistance is equal to the resistance calculated or measured at the terminal pair with all independent sources de-energized.

De-energization of an independent source means that the source voltage or current is set to zero but that the source resistance (impedance) is unchanged. Controlled (or dependent) sources are not changed or de-energized.