Article : Andy Collinson
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Two powerful circuit analysis techniques are Thevenin's theorem and Norton's theorem. Both theories convert a complex circuit to a simpler series or parallel equivalent circuit for easier analysis. Analysis involves removing part of the circuit across two terminals to aid calculation, later combining the circuit with the Thevenin or Norton equivalent circuit. There are plenty of books on this subject, so this is just a quick look.

Thevenin
The top left diagram represents the circuit for analysis at terminals A and B. The top right hand circuit is the Thevenin equivalent circuit, a voltage source Vth with a series resistance, Rth. The bottom left diagram is the same circuit driving a load. The load is NOT included in the thevenin equivalent circuit and must be separated, this is why the terminals are marked A and B.
Value of Vth and Rth
To find the equivalent Thevenin resistance of the circuit. Rth the load is first removed and any circuit voltages are short circuited. The resistance is then calculated. The Thevenin voltage is found by first removing the circuit load and then working out the voltage across point A and B in the circuit.

An Example
A demonstration of the thevenin technique to find I1 in the diagram below:

The circuit to the right of points A and B is converted to a Thevenin source and resistance. With the 30v battery and left hand 10ohm resistor omitted, the Thevenin voltage becomes:

Vth = 40 * 10/30 = 400/30

Rth = 10||20 = 200/30  (10 ohm parallel with 20 ohm voltage source s/c )

I1 then becomes  30 - Vth / ( 10 + Rth )

I1 = 30 - 400/30 / 10 + 200/30 = 900/30 - 400/30 / ( 300/30 + 200/30)

   =  500/30 / 500/30 = 1 amp

The above is a messy numerical example, but this can also be solved using kirchoff or a simulator program. The early results are sometimes best kept as fractions to make the division easier.

Norton
The Norton theorem converts an ordinary circuit to an equivalent parallel circuit which is a current source in parallel with a resistor. The technique is similar to the thevenin theorem and two points in a circuit must be defined, this is where the analysis will take place.

As with Thevenin, the equivaent circuit is a current generator In and norton equivalent resistance, Rn. These must be worked out to use the Norton theorem. The analysis points using Norton are short circuited, whereas using the Thevenin Method they are open circuit.

Value of Vth and Rth
The value of Vth is found by either measuring (if you don't know what's in the circuit) or be using circuit analysis. To find Rth ( with load removed) short circuit voltage supplies, open current sources and calculate the equivalent resistance.

An Example
Norton's theorem is demonstrated to find the current I1 in the diagram below :

The points A and B is where the Norton conversion takes place, the right 50 ohm resistor is removed, A and B are short circuited, see below:

First the total current is calculated; 100 / ( 50 + 100 || 50 ) = 1.2 amp. Using the current division rule,
In is worked out:   1.2 * 100 / (50+100) =0.8 amp

Rn is 50 + 100 || 50 =83.3333 ohm

The Norton equivalent circuit can now be completed with the right hand 50 ohm resistor included:

The currentI can now be found using the current division rule :

I = 0.8 * (83.3333 / ( 50 + 83.3333) = 0.5 amp

This can be verified using the Thevenin method or a simulation program.