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
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 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