King Saud University
College of Engineering
Electrical Engineering Department
EE-205 Electrical Circuit Lab
Experiment No. 4
Thevenin’s and Maximum Power Transfer Theorems
In ac Circuits
Objectives
-
To verify experimentally Thevenin’s and maximum power transfer theorems
as applied to ac circuits.
Material Required
Resistors:
Inductors:
Capacitors:
Equipment:
100 Ω ,1 k Ω , 3.3 k Ω , 10 k Ω , one decade resistance box.
17.5 mH inductor with iron core.
Two 0.1 µ F, 0.47 µ F, 1 µ F, 4.7 µ F, 22 µ F.
Multimeter, signal generator.
Background
I. Thevenin’s Theorem
Thevenin’s theorem can be applied to ac circuits in the same manner as has been
applied to dc circuits. To find the variable of interest, isolate the related branch from
the circuit, short out all the independent voltage sources and open all the
independent current sources (this can be done only in theory, not in practice) and
calculate ZTH across the terminals in question. Then replace all sources and calculate
ETH, which is the voltage across the terminals of question. Draw the Thevenin’s
equivalent and replace the branch that has been isolated and find using basic rules
the desired variable (voltage, or current etc.). See Fig.1
a
Zth
Active
AC Circuit
ZL
Eth
a
+
-
ZL
b
b
where
a
Active
AC Circuit
Eth = Vab
b
a
+
-
&
Zth
Passive
AC Circuit
b
Fig. 1: Thevenin's Theorem.
1
II. Maximum Power Transfer Theorem
Maximum power transfer theorem in ac circuits states that the max power will be
transferred to a load when the load impedance is the conjugate of the Thevenin’s
impedance across the load terminals. See Fig.2
a
Active
AC Circuit
ZL
*
( for maximum power transfer ) = Z th
b
a
Passive
AC Circuit
Zth
b
Fig. 2 Maximum power transfer theorem.
2
Procedure I:
١. Wire the circuit shown in Fig. 6a, and measure VR and IR.
٢. Isolate the (10 KΩ) resistor from the circuit and measure the voltage across
the terminals (a-b). This voltage is ETH.
٣. Calculate ZTH by shorting the supply.
٤. Reconstruct the Thevenin’s equivalent circuit for the circuit of Fig.6-a by
inserting the ETH and ZTH as shown in Fig.6-b and measure IR. and VR.
Compare this with step (1).
96 mH
1 KΩ
a
( With Iron Core )
+
+
5V
1 KHz
3.3 KΩ
VR
-
10 KΩ
a
Zth
IR
+
Eth
VR
-
-
b
IR
10 KΩ
b
(b)
(a)
Fig. 6: Circuits for procedure I.
Procedure II :
١. Construct the circuit of Fig.7. Set Rpot = R + RL
100 Ω
a
17.5 mH
V
Potentiometer
5V
1 KHz
b
C
ZL
Fig. 7: Circuit for procedure II.
٢. Replace different capacitor combinations as shown in Table 1 and measure for
each combination the V(a-b).
٣. Calculate ZTH for the circuit of Fig. 7 and record it in the rectangular form.
٤. Calculate ZL for each combination of capacitor and list the data in Table 1.
٥. Calculate the power transferred to the load using.
P = V 2 ( a −b ) / R pot
Repeat this for all combinations of capacitors and list this data in Table 1.
3
٦. On a graph, plot P vs X C and locate the maximum power transfer on the
graph what can you conclude about the maximum power transfer?
Table 1
Combination of
capacitors
V(a-b)
(V)
Xc
(Ω)
ZL
(Ω)
P
(mW)
0.1 µF
0.47 µF
0.57 µF
1 µF
1.1 µF
1.2 µF
1.47 µF
4.7 µF
22 µF
4