Circuits Lecture 9: Thevenin and Norton Theorem (2) 李宏毅 Hung-yi Lee

Circuits Lecture 9: Thevenin and

Norton Theorem (2)李宏毅 Hung-yi Lee

Review - Thevenin and Norton Theorem

TwoTerminalNetwork

Thevenin Theorem

Norton Theorem

tRsci

t

ocv

Risc

tocv Risc

TwoTerminalNetwork

ocv

v

V10V10

TwoTerminalNetwork

v

V10ocv

ocvV10

=


The same concept is applied on isc.


TwoTerminalNetwork

suppress

tv

ti

tv

ti t

tt i

vR

TwoTerminalNetwork

suppress

tv

ti

TwoTerminalNetwork

suppress

tvti

?Rt

tt i

v ?R

t

tt i

v


TwoTerminalNetwork

v

V10Two

TerminalNetwork

Ai 10

1Ri

vt Is it correct?

Find voc Find isc

Outline

• Maximum Power Transfer• Chapter 3.1• Application of Thevenin Theorem

Review: Power

• Consumed Power

• Suppied Power

ivp A Bv

i

+ -

reference current should flow from “+” to “-”

ivp A Bv

i

+ -

reference current should flow from “-” to “+”

Negative Communed Power = Supplied Power

Ideal Sources

sv

i-v curse

si

i-v curse

v

v

i

i

Larger power

Larger power

Ideal sources can supply unlimited power.

Real Source

• Real voltage sources cannot supply unlimited power

Real voltage source =Ideal voltage source + resistor

sv

i

v

i-v characters for real voltage source

Real Source

• Real current sources cannot supply unlimited power

Real current source =Ideal current source || resistor

i-v characters for real current source

Maximum power transfer

Real source

Device (Load)

power

Rs is fixed, increase RL

Power consumed by Rs

Power consumed by RL

sRR L

L

s

R

v

4

2



s

s

R

vP

4

2

max

Maximum power transfer to (consumed by) a load resistance requires RL = Rs:

(Only 25%)


2

3

2

4

2

2

s

Ls

Ls

s

Ls

LLsLs

L

L

vRR

RR

vRR

RRRRR

dR

dP

)(

)()()()(

)(

)(2

''

xg

xgxfxfxg

xg

xf

dx

d

When dPL/dRL=0,PL is maximum

Ls

s

RR

vi

RL is a variableFind RL which maximizes PL

viL P sLs

L vRR

Rv

2

2 s

Ls

LL v

RR

RP

dPL/dRL=0, when Rs=RL

Power-transfer efficiency

sL

L

PP

P

Eff

Eff=50%


s

s

R

vP

4

2

max

When RL = Rs

When RL = Rs

4

2

maxssiR

P


Audio Amplifier

Signals fromSound Card

http://ming-shian.blogspot.tw/2013/05/radio-tear-down.html

Find a speaker that can gain sufficient power


http://angelfire.com/ab3/mjramp/index.html

Audio Amplifier

Input audio signal

Difficult to compute the power

Thevenin Theorem


(speaker)Sound Card + Audio Amplifier


Application of Thevenin

• Which value of R can absorb maximum power? Find the power.

+- +- +-V15 V5 V85

A220 20

10 105

R

RRfRiv RR RfiR

RRfvip RRR 2

pR is maximum when dpR/dR=0


• Which value of R can absorb maximum power? Find the power.

+- +- +-V15 V5 V85

A220 20

10 105

R

R

tRR

5||101020||20 tR

s

oc

R

vP

4

2

max Have to find voc


• Find voc

+- +- +-V15 V5 V85

A220 20

10 105

voc

+

-


+- +- +-V15 V5 V85

A220 20

10 105

201020||20 tR+- +-V15 V5

20 2010

ocv

+

-Vvoc 10

• Use Thevenin Theorem several times

Application of Thevenin• Use Thevenin Theorem several times

+-+-

V10

V85

A2

20 105

R

301020 tRocv

+

-Vvoc 50+-V10

1020

A2


+-+-

V50V85

305

R

5||30tR

Vvoc 80

+-+-

V50V85

305

ocv

+

-


+-V80

5||30

R

5||30 tRR

5||304

80

4

22

max s

oc

R

vP

Remind – Exercise 3.3

• What value of RL should be used to obtain the maximum available power?

4tR

40ocV

5i

4

20v

W100PL W100Ps W180

W20

Homework

• 1ST ORDER DIFFERENTIABLE EQUATIONS

• https://www.youtube.com/watch?v=2s9z1zLOAJY

• 2ND ORDER DIFFERENTIABLE EQUATIONS

• https://www.khanacademy.org/math/differential-equations/second-order-differential-equations/linear-homogeneous-2nd-order/v/2nd-order-linear-homogeneous-differential-equations-1

tftBydt

tdyA

tftCydt

tdyB

dt

tyd

2

2

A

https://www.youtube.com/watch?v=2s9z1zLOAJY



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

Documents

Circuits Lecture 9: Thevenin and Norton Theorem (2) 李宏毅 Hung-yi Lee