PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Direct Current and Transient Analysis 119

currents or voltages produced independently by each source (current or voltage).

The concept of independence means that only one source is considered active,

whereas all the other sources (voltage or current) are set to zero.

Recall that when a voltage source is set to zero, the source can be replaced by a

short circuit, and similarly, when a current source is set to zero, the source can be

replaced by an open circuit.

The superposition theorem states then that in an n source electrical network, the

current through or the voltage drop across any arbitrary network element can be

obtained by solving n single source networks (where the single source network

refers to the original network with only one source at the time whereas all the

remaining sources are set to zero) for the variable of interest, which can be a cur-

rent or a voltage. The solution is the algebraic sum of the partial solutions (of the

single source networks).

Note that the voltage and current polarities (directions) are important when

solving each single source network, since the solution is the algebraic sum of the

(solutions) contribution of each source.

R.2.79 Thevenin’s theorem states that any two-terminal linear DC network across a load

RL can be replaced by two elements: a voltage source called the Thevenin volt-

age VTH and a resistor placed in series called the Thevenin resistance RTH. The

Thevenin resistance RTH is calculated by setting all the sources to zero, removing

the arbitrary load RL (replace it by an open), labeling its terminals aa’, a n d e i t h e r

calculating or measuring the resistance looking into the terminals (aa’).

The Thevenin voltage VTH is the open-circuit voltage across terminals aa’, a f t e r

having removed the arbitrary load RL from the original circuit, while preserving

all the sources.

R.2.80 Norton’s theorem states that any two-terminal linear DC network can be replaced

by two elements, a current source in parallel with a resistor, where the current

source is the Norton short-circuit current denoted by IN, and the resistance is the

Thevenin resistance RTH.

FIGURE 2.10

Equivalent circuits obtained by source transformation.

Rs

I = V/Rs

Arbitrary network

Arbitrary network

V

Rs

FIGURE 2.11

Equivalent source transformation circuits as seen through terminals A and B.

Rs = 5 Ω

Rs = 5 Ω

I = V/Rs = 10/5 = 2 A

V = 10 V

A

B

A

B