THEVENIN THEOREM

SARIATI DALIB

POLITEKNIK MERLIMAU, MELAKA

Thevenin’s Theorem

Any circuit with sources (dependent and/or

independent) and resistors can be replaced by

an equivalent circuit containing a single voltage

source and a single resistor.

Thevenin’s theorem implies that we can

replace arbitrarily complicated networks with

simple networks for purposes of analysis.

Thevenin Equivalent Cct

Vth +

–

Zth

Thevenin equivalent circuit

Circuit with

independent

sources

A

B

Any two-terminal linear ac circuit can be reduced to

an equivalent circuit that consists of an ac voltage

source in series with equivalent impedance.

Vth and Zth

Thevenin’s equivalent voltage (Vth) is the open-circuit

voltage between two specified terminals in a circuit

Thevenin’s equivalent impedance (Zth) is the total

impedance appearing between two specified terminals in

a given circuit with all sources replaced by their internal

impedances.

Steps for applying Thevenin theorem

1. Open the two terminals between which you want to

find the Thevenin circuit. This is done by removing the

component from which the circuit is to be viewed.

2. Determine the voltage across the two open terminals. -

Vth = Vo/c.

3. Determine the impedance viewed from the two open

terminals with ideal voltage sources replaced with

shorts and ideal current sources replaced with opens

(Zth).

4. Draw the Thevenin equivalent circuit by connecting Vth

and Zth in series.

Example 1

Q: Find the Thévenin equivalent circuit for the network external to ZL in

the circuit below

Solution;

Step 1: Open the two terminals between which you

want to find the Thevenin circuit

Step 2: Determine the voltage across the two open terminals. -Vth = Vo/c

𝑉4Ω = 𝑉𝑇𝐻

Use current divider

𝐼4Ω = 𝐼𝑠 𝑥 −𝑗5

−𝑗5 + 4 + 𝑗3

= (30 < 0)−𝑗5

−𝑗5 + 4 + 𝑗3

= 33.54 < −63.43°

Thus 𝑉𝑇𝐻= 𝑉4Ω = 𝐼4Ω x 4 =(33.54∠-63.43°)(4)=134.164∠-63.43°V

Step 3: Open current sources and find Zth

𝑍𝑡ℎ = 4 𝑥 (𝑗3−𝑗5)

4+𝑗3 −𝑗5 = 1.79∠-63.43°Ω

Step 4: Draw the Thevenin equivalent

circuit by connecting Vth and Zth in series.

Example 2

Q: Find Zth , Vth for the Thevenin Equivalents of the circuit external to the

load impedance ZL in the circuit shown above.

Find Vth

Find Zth . (set Vs to zero )

Zth = [ 10//j20] + -j5

𝑍𝑡ℎ =10 𝑥 𝑗20

10 + 𝑗20− j5

= 8.94 < 26.57 − j5 = 8.06Ω < −7.13° = 8 − 𝑗1

Zth = 8 - j1

Vth = 89.44V <26.57

Thevenin Equivalent Circuit

Exercise 1

Q: Find the Thevenin equivalent at terminals a-b of the circuit

below.

Answer :

𝒁𝑻𝑯 = 𝟏𝟐. 𝟒 − 𝒋𝟑. 𝟐Ω 𝒐𝒓 𝟏𝟐. 𝟖𝟏 < −𝟏𝟒. 𝟒𝟕° 𝑽𝒕𝒉 = 𝟏𝟖. 𝟗𝟕𝑽∠ − 𝟓𝟏. 𝟓𝟕°