**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.

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