Norton's Theorem

Named after E,L. Norton, a scientist with bell telephone Laboratories Norton’s theorem is used for simplifying a network in terms of current instead of voltages. In many cases, analyzing the division of currents may be easier than voltage analysis. For current analysis, therefore, Norton’s theorem can be used to reduce a network to a simple parallel circuit, with a current source. The idea of a current source is that it supplies a total line current to be divided among parallel branches, corresponding to voltage source applying a total voltage to be divided among series components. This comparison is illustrated in Fig.10-7.

EXAMPLE OF A CURRENT SOURCE

A source of electric energy supplying voltage is often shown with a series resistance which represents the internal resistance of the source, as in Fig.10-7a. This method corresponds to showing an actual voltage source, such as a battery for dc circuits. However, the source may be represented also as a current with a parallel resistance, as in Fig.10-7b. Just as a voltage source is rated at, say, 10V , a current source may be rated at 2 A . For the purpose of analyzing parallel branches, the concept of a current source may be more convenient than a voltage source.
If the current I in Fig. 10-7is a 2-A source, it supplies 2A no matter what is connected across the output terminals A and B. Without anything connected across A and B, all 2 A flows through the shunt R. When a load resistance R/L is connected across A and B, then the 2-A I divides according to the current division rules for parallel branches.
Remember the parallel current divide inversely to branch resistance but directly with conductance. For this reason it may be preferable to consider the current source shunted by the conductance G, as shown in Fig. 10-7c. we can always convert between resistance and conductance, because 1/R in ohms is equal to G in siemens.
The symbol for a current source is a circle with an arrow inside, as shown inFig.10-7b and c, to shown the direction of current . This direction must be the same as the current produced by the polarity of the corresponding voltage source.
Remember that a source produce electron flow out from the negative terminal.
An important difference between voltage and current sources is that a current source is killed by making it open, compared with short-circuiting a voltage source. Opening a current source kills its ability to supply current without affecting any parallel branches. A voltage source is short-circuited to kill its ability to supply voltage without affecting any series components.