# Norton and Thevenin Equivalent

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Given the one-port network. The output port of the one-port is defined by terminals A and B.

a) Find the Thevenin and Norton Equivalent circuits.

b) Plot the current voltage characteristic of the one-port.

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##### Solution Summary

The solution finds the Thevenin and Norton equivalent circuits. The current voltage characteristics of the one-port is graphed.

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Solution:

Thevenin equivalent circuit

As per Thevenin's theorem, the equivalent circuit at the given terminals will comprise of a voltage source in series with an equivalent impedance. The voltage of the voltage source and the equivalent impedance are to be determined as follows :

i) to determine the voltage of the voltage source, we open the terminals and determine the open circuit voltage across the terminals.

ii) to determine the equivalent impedance, we short the voltage sources and open the current sources in the circuit and determine the impedance looking into the terminals.

The terminals A and B are already open. We determine the voltage appearing across terminals A and B using Kirchhoff's laws as follows:

I1 = 0.8 mA

I1

Loop 1 R3 = 10kΩ

1 2

A

I2 I3

R2 = 20kΩ R1 = 10kΩ R4 = 10kΩ

+

V1 = 20V

B

Loop 2 Loop 3

Let the loop currents be as shown in the fig.. We write Kirchhoff's loop equations as follows:

Loop 1: (I1 - I3) R3 = V12

=> 10000(I1 - I3) = V12 ...(1)

Loop 2: I2R2 - 20 + (I2 - I3)R1 = 0

=> (R2+R1)I2 - R1I3 = 20

=> 30000I2 - 10000I3 = 20 ...(2)

Loop 3: (I3 - I2)R1 + 20 + I3R4 + V21 = 0

=> - R1I2 + 20 + I3(R4 + R1)+ V21 = 0 ...

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