Circuits
Lecture 9: Thevenin and
Norton Theorem (2)
李宏毅 Hung-yi Lee
Review - Thevenin and Norton
Theorem
voc  i sc R t
Thevenin
Theorem
Two
Terminal
Network
i sc
voc
i sc 
Rt
Rt
Norton
Theorem
Review - Thevenin and Norton
Theorem

 10V
voc

Two
Terminal
Network

v  10V

=
voc
 10V

voc

Two
Terminal
Network
The same concept is applied on isc.

v  10V

Review - Thevenin and Norton
Theorem
suppress
it
vt
suppress
Two
Terminal
Network
it
vt
it
Two
Terminal
Network
vt
R t  ? suppress
it
Two
Terminal
Network
vt
Rt 
it
vt
it
vt
Rt  ?
it
vt
Review - Thevenin and Norton
Theorem
Find voc
Two
Terminal
Network
Find isc

v  10V

v
R t   1
i
Two
Terminal
Network
Is it correct?
i  10 A
Outline
• Maximum Power Transfer
• Chapter 3.1
• Application of Thevenin Theorem
Review: Power
Negative Communed Power
= Supplied Power
• Consumed Power
p  v i
A +
v
- B
i
reference current should flow from “+” to “-”
• Suppied Power
p  v i
A +
v
- B
i
reference current should flow from “-” to “+”
Ideal Sources
Larger power
i

i-v curse
v
vs

Ideal sources can
supply unlimited
power.
i

is
v

i-v curse
Larger power
Real Source
• Real voltage sources cannot supply unlimited
power
i
vs
v
i-v characters
for real voltage source
Real voltage source =
Ideal voltage source +
resistor
Real Source
• Real current sources cannot supply unlimited
power
i-v characters
for real current source
Real current source =
Ideal current source ||
resistor
Maximum power transfer
power
Device
(Load)
Power consumed
by Rs
vs2
4 RL
RL  Rs
Real source
Power consumed
by RL
Rs is fixed, increase RL
Maximum power transfer
Maximum power transfer to (consumed
by) a load resistance requires RL = Rs:
Pmax
2
s
v

4 Rs
(Only 25%)
Power consumed
by RL
d  f ( x)  g ( x) f ' ( x)  f ( x) g ' ( x)

dx  g ( x) 
g ( x)2
Maximum power transfer
RL is a variable
Find RL which maximizes PL
PL  vi
vs
i
Rs  RL 
RL
v
vs
Rs  RL
RL
2
PL 
 vs
2
Rs  RL 
dPL Rs  RL   2Rs  RL RL 2

 vs
4
dRL
Rs  RL 
2
Rs  RL
2


v
s
3
Rs  RL 
When dPL/dRL=0,
PL is maximum
dPL/dRL=0,
when Rs=RL
Power-transfer efficiency
Eff=50%
PL
Eff 
PL  Ps
Maximum power transfer
When RL = Rs
Pmax
2
s
v

4 Rs
When RL = Rs
Pmax
Rs is2

4
Maximum power transfer
Audio
Amplifier
Signals from
Sound Card
Find a speaker that can
gain sufficient power
http://ming-shian.blogspot.tw/2013/05/radiotear-down.html
Maximum power transfer
Difficult to compute
the power
Input
audio
signal
Audio Amplifier
http://angelfire.com/ab3/mjramp/index.html
Thevenin Theorem
Maximum power transfer
Sound Card +
Audio Amplifier
(speaker)
Power consumed
by RL
Application of Thevenin
• Which value of R can absorb maximum power? Find the
power.
20
20
10
10
5
2A
15V +-
R
5V +-
iR  f  R 
85V +-
v R  iR  R  f  R   R
p R  iR  v R  f  R   R
2
pR is maximum when dpR/dR=0
Application of Thevenin
• Which value of R can absorb maximum power? Find the
power.
20
20
10
10
5
2A
15V +-
R
5V +-
85V +-
R  Rt
R
Rt  20 || 20   10  10  || 5
Pmax
voc2

4 Rs
Have to find voc
Application of Thevenin
• Find voc
20
20
10
10
2A
15V +-
5V +-
85V +-
+
5
voc
-
Application of Thevenin
• Use Thevenin Theorem several times
20
20
10
10
5
2A
15V +-
5V +-
85V +-
Rt  20 || 20   10  20
voc  10V
20
15V +-
20
5V +-
10
+
voc
-
Application of Thevenin
• Use Thevenin Theorem several times
20
10V +-
10
5
2A
Rt  20  10  30
voc  50V
R
85V +-
20
10V +-
2A
10
+
voc
-
Application of Thevenin
• Use Thevenin Theorem several times
30
50V +-
Rt  30 || 5
voc  80V
5
R
85V +-
30
50V +-
85V +-
5
+
voc
-
Application of Thevenin
• Use Thevenin Theorem several times
30 || 5
80V +-
R
R  Rt  30 || 5
Pmax
2
voc
80 2


4 Rs
430 || 5
Remind – Exercise 3.3
• What value of RL should be used to obtain the
maximum available power?
Rt  4
Voc  40
180 W
4
i  5 v  20
20 W
PL  100 W Ps  100 W
Homework
• 1ST ORDER DIFFERENTIABLE EQUATIONS
dy t 
A
 By t   f t 
dt
• https://www.youtube.com/watch?v=2s9z1zLOAJY
• 2ND ORDER DIFFERENTIABLE EQUATIONS
d 2 y t 
dy t 
A
B
 Cy t   f t 
2
dt
dt
• https://www.khanacademy.org/math/differentialequations/second-order-differential-equations/linearhomogeneous-2nd-order/v/2nd-order-linearhomogeneous-differential-equations-1
Thank you!
Appendix –
Non-linear Elements
Non-linear Elements
(http://www-inst.eecs.berkeley.edu/~ee42/sp03/LectNotes/42_05_6.pdf)
Non-linear Elements
Non-linear Elements
Which operating regions?
Non-linear Elements