Lecture 06
30
Lecture 6 Thévenin Equivalent Circuits ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
description
lecture
Transcript of Lecture 06
Lecture 6
Thévenin Equivalent Circuitsq
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Thévenin Equivalent CircuitsThévenin Equivalent Circuits
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Thévenin Equivalent CircuitsThévenin Equivalent Circuits
oct vV =ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
oct
Thévenin Equivalent CircuitsThévenin Equivalent Circuits
Vtsc R
Vi =
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
tR
Thévenin EquivalentThévenin Equivalent Circuits
voc
ivRt =
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
sci
Find the Thevenin Equivalent Circuit
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Find the Thevenin Equivalent Circuit
Use voltage divider formed by R1 and R2 to find voc:
VVvRR
Rv soc 51550100
50
21
2 =+
=+
=
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
21
Find the Thevenin Equivalent Circuit
Vv 15 AVRv
i ssc 15.0
10015
1=
Ω==
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Find the Thevenin Equivalent Circuit
5VvΩ=== 3.33
15.05
AV
iv
Rsc
oct
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
sc
Find the Thevenin Equivalent Circuit
VAvoc 50)10)(5( =Ω=
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Find the Thevenin Equivalent Circuit
isc
sci
sc
sc
Use current divider to find isc:
=+
=+
=
50
154010
10521
1
Vv
AAARR
Risc
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Ω=== 501
50AV
iv
Rsc
oct
Find the Thevenin Equivalent Circuit
Rt = 50Ω
Vt= 50V
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Finding the Thévenin Resistance DirectlyResistance Directly
We can find the Thévenin resistance byWe can find the Thévenin resistance by zeroing the sources in the original network and then computing the resistance betweenand then computing the resistance between the terminals.
When zeroing a voltage source, it becomes a short circuit. When zeroing a current source, it becomes an open circuit.
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Find the Thevenin Equivalent
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Find the Thevenin Equivalent
Ω==+
== 425
10021
RRRRRR teq + 2521 RRq
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Find the Thevenin Equivalent
Vi
2002 =
AAAAii
AVi
6242
4520
1 =Ω
=
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
AAAAiisc 62421 =+=+=
Find the Thevenin Equivalent
VAiRV sctt 24)6)(4( =Ω==
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Find the Thevenin Resistance
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Find the Thevenin Resistance
Zero the voltageZero the voltage source
Ω++ 14410)20)(5(10RELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Ω=+=+
+= 14410205
))((10tR
Find the Thevenin Resistance
Zero the currentZero the current source
Ω=+= 302010RELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Ω=+= 302010tR
Find the Thevenin Resistance
Zero the current and voltage sources
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Find the Thevenin Resistance
4Ω
10Ω
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
5Ω
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Thevenin Equivalent with a Dependent Source
v
Vvvvv
i
iv
iiNodeatKCL
ocococ
xoc
xx
57810
310
310
2:1
=→=−
→−
=
==+
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Vvi ocx 57.8105
35
→→
Thevenin Equivalent with a Dependent Source
==+10
32V
iiii scxxx
Ω
=→=Ω
=
43157.8
625
10
VVR
AiAVi
t
scx
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Ω=== 43.16Ai
Rsc
tt
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
iI = scn iI =
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Step-by-step Thévenin/Norton EquivalentThévenin/Norton-Equivalent-
Circuit Analysisy1. Perform two of these:
D t i th i it lt Va. Determine the open-circuit voltage Vt = voc.
b Determine the short-circuit current I = ib. Determine the short circuit current In = isc.
c. Zero the sources and find the Thévenin resistance Rt looking back into the terminals.
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
2. Use the equation Vt = Rt In to compute the remaining value.
3. The Thévenin equivalent consists of a voltage source Vt in series with Rt .
4. The Norton equivalent consists of a current source In in parallel with Rt .
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
