circuit theorems instructor: chia-ming tsai electronics engineering national chiao tung university...
TRANSCRIPT
![Page 1: Circuit Theorems Instructor: Chia-Ming Tsai Electronics Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C](https://reader030.vdocuments.us/reader030/viewer/2022033100/5697bff71a28abf838cbe724/html5/thumbnails/1.jpg)
Circuit Theorems
Instructor: Chia-Ming TsaiElectronics Engineering
National Chiao Tung UniversityHsinchu, Taiwan, R.O.C.
![Page 2: Circuit Theorems Instructor: Chia-Ming Tsai Electronics Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C](https://reader030.vdocuments.us/reader030/viewer/2022033100/5697bff71a28abf838cbe724/html5/thumbnails/2.jpg)
Contents• Introduction
• Linearity Property
• Superposition
• Source Transformation
• Thevenin’s Theorem
• Norton’s Theorem
• Maximum Power Transfer
• Summary
![Page 3: Circuit Theorems Instructor: Chia-Ming Tsai Electronics Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C](https://reader030.vdocuments.us/reader030/viewer/2022033100/5697bff71a28abf838cbe724/html5/thumbnails/3.jpg)
Introduction
• To develop analysis techniques applicable to linear circuits
• To simplify circuit analysis and help handling the complexity
![Page 4: Circuit Theorems Instructor: Chia-Ming Tsai Electronics Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C](https://reader030.vdocuments.us/reader030/viewer/2022033100/5697bff71a28abf838cbe724/html5/thumbnails/4.jpg)
Linearity Property
• Homogeneity (Scaling) + Additivity
• Homogeneity property:
• Additivity property:
• A linear circuit follows the relationship below
kiRkviRv
212121
2211 and
vvRiRiRiiv
RivRiv
InputConstantOutput
![Page 5: Circuit Theorems Instructor: Chia-Ming Tsai Electronics Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C](https://reader030.vdocuments.us/reader030/viewer/2022033100/5697bff71a28abf838cbe724/html5/thumbnails/5.jpg)
Superposition• Based on linearity property
• Statement– The voltage across (current through) an element
is the algebraic sum of the voltage across (current through) that element due to each independent source acting alone.
),...,0;0,...,0(...)0,...,;0,...,0(
)0,...,0;,...,0(...)0,...,0;0,...,(
),...,;,...,(
1
1
11
M
N
MN
IvIv
VvVv
IIVVv
![Page 6: Circuit Theorems Instructor: Chia-Ming Tsai Electronics Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C](https://reader030.vdocuments.us/reader030/viewer/2022033100/5697bff71a28abf838cbe724/html5/thumbnails/6.jpg)
Example 1
+
=
V 1082 11
vvv
![Page 7: Circuit Theorems Instructor: Chia-Ming Tsai Electronics Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C](https://reader030.vdocuments.us/reader030/viewer/2022033100/5697bff71a28abf838cbe724/html5/thumbnails/7.jpg)
Example 2
+=
"0
'00 iii
![Page 8: Circuit Theorems Instructor: Chia-Ming Tsai Electronics Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C](https://reader030.vdocuments.us/reader030/viewer/2022033100/5697bff71a28abf838cbe724/html5/thumbnails/8.jpg)
Example 3
321 iiii
![Page 9: Circuit Theorems Instructor: Chia-Ming Tsai Electronics Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C](https://reader030.vdocuments.us/reader030/viewer/2022033100/5697bff71a28abf838cbe724/html5/thumbnails/9.jpg)
Source Transformation
i1 i2
R
Vii
R
Vvi
abS
abS
2
1
RivR
vi
ii
SSS
S
or
Let 21
![Page 10: Circuit Theorems Instructor: Chia-Ming Tsai Electronics Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C](https://reader030.vdocuments.us/reader030/viewer/2022033100/5697bff71a28abf838cbe724/html5/thumbnails/10.jpg)
Applicable to Dependent Sources
RivR
vi SS
SS or
i1 i2
![Page 11: Circuit Theorems Instructor: Chia-Ming Tsai Electronics Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C](https://reader030.vdocuments.us/reader030/viewer/2022033100/5697bff71a28abf838cbe724/html5/thumbnails/11.jpg)
Example 1
![Page 12: Circuit Theorems Instructor: Chia-Ming Tsai Electronics Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C](https://reader030.vdocuments.us/reader030/viewer/2022033100/5697bff71a28abf838cbe724/html5/thumbnails/12.jpg)
Example 2
V 5.7
A 5.4
013
01853
x
x
x
v
i
vi
vi
![Page 13: Circuit Theorems Instructor: Chia-Ming Tsai Electronics Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C](https://reader030.vdocuments.us/reader030/viewer/2022033100/5697bff71a28abf838cbe724/html5/thumbnails/13.jpg)
Thevenin’s TheoremA variableelement
Thevenin equivalent circuit
![Page 14: Circuit Theorems Instructor: Chia-Ming Tsai Electronics Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C](https://reader030.vdocuments.us/reader030/viewer/2022033100/5697bff71a28abf838cbe724/html5/thumbnails/14.jpg)
Continued
ThLTh
LLLL
LTh
ThL
VRR
RIRV
RR
VI
A simple voltage divider
=
![Page 15: Circuit Theorems Instructor: Chia-Ming Tsai Electronics Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C](https://reader030.vdocuments.us/reader030/viewer/2022033100/5697bff71a28abf838cbe724/html5/thumbnails/15.jpg)
Proof of Thevenin’s Theorem
+
=
=
All indep.sources on
All indep.sources off
1v+_
+_
2v
2111 )0,...,0;0,...,0;(),...,;,...,;0( vvivIIVVvv MN
![Page 16: Circuit Theorems Instructor: Chia-Ming Tsai Electronics Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C](https://reader030.vdocuments.us/reader030/viewer/2022033100/5697bff71a28abf838cbe724/html5/thumbnails/16.jpg)
Finding VTh and RTh
• If no dependent sources included
![Page 17: Circuit Theorems Instructor: Chia-Ming Tsai Electronics Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C](https://reader030.vdocuments.us/reader030/viewer/2022033100/5697bff71a28abf838cbe724/html5/thumbnails/17.jpg)
Continued• If dependent sources inclu
ded, two methods can be applied to determine RTh
– External voltage source method
– External current source method
![Page 18: Circuit Theorems Instructor: Chia-Ming Tsai Electronics Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C](https://reader030.vdocuments.us/reader030/viewer/2022033100/5697bff71a28abf838cbe724/html5/thumbnails/18.jpg)
Example 1
=RTh
VTh
![Page 19: Circuit Theorems Instructor: Chia-Ming Tsai Electronics Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C](https://reader030.vdocuments.us/reader030/viewer/2022033100/5697bff71a28abf838cbe724/html5/thumbnails/19.jpg)
Example 2
=RTh
voc
1
0iRTh
![Page 20: Circuit Theorems Instructor: Chia-Ming Tsai Electronics Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C](https://reader030.vdocuments.us/reader030/viewer/2022033100/5697bff71a28abf838cbe724/html5/thumbnails/20.jpg)
Norton’s Theorem
Norton equivalent circuit inTh RRRN
![Page 21: Circuit Theorems Instructor: Chia-Ming Tsai Electronics Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C](https://reader030.vdocuments.us/reader030/viewer/2022033100/5697bff71a28abf838cbe724/html5/thumbnails/21.jpg)
Proof of Norton’s Theorem
+
=
=
All indep.sources on
All indep.sources off
1211 ),...,;,...,;0()0,...,0;0,...,0;( iiIIVViVii MN
![Page 22: Circuit Theorems Instructor: Chia-Ming Tsai Electronics Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C](https://reader030.vdocuments.us/reader030/viewer/2022033100/5697bff71a28abf838cbe724/html5/thumbnails/22.jpg)
Example
= RNIN
![Page 23: Circuit Theorems Instructor: Chia-Ming Tsai Electronics Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C](https://reader030.vdocuments.us/reader030/viewer/2022033100/5697bff71a28abf838cbe724/html5/thumbnails/23.jpg)
Maximum Power Transfer
Th
Th
ThL
LTh
LThTh
LTh
LThLLThTh
L
LLTh
ThL
R
Vp
RR
RR
RRV
RR
RRRRRV
dR
dp
RRR
VRip
4
0
2
sfer,power tran maximum achieve To
2
max
3
2
4
22
2
2
A linear circuit
![Page 24: Circuit Theorems Instructor: Chia-Ming Tsai Electronics Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C](https://reader030.vdocuments.us/reader030/viewer/2022033100/5697bff71a28abf838cbe724/html5/thumbnails/24.jpg)
Applications: Source Modeling
sLs
LL v
RR
Rv
s
Ls
LL v
RR
Rv
sLs
LL v
RR
Rv
Voltage source
Current source
sLs
LL v
RR
Rv
sLp
pL i
RR
Ri
0sR
pR