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Lecture 4 Overview • More circuit analysis – Thevenin’s Theorem – Norton’s Theorem

Lecture 4 Overview More circuit analysis –Thevenin’s Theorem –Norton’s Theorem

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Page 1: Lecture 4 Overview More circuit analysis –Thevenin’s Theorem –Norton’s Theorem

Lecture 4 Overview

• More circuit analysis– Thevenin’s Theorem– Norton’s Theorem

Page 2: Lecture 4 Overview More circuit analysis –Thevenin’s Theorem –Norton’s Theorem

Announcements

• Assignment 0 due Thursday

• Lab reports due today and tomorrow

• Physics Colloquium 4pm tommorrow

Page 3: Lecture 4 Overview More circuit analysis –Thevenin’s Theorem –Norton’s Theorem

Method 3: Thevenin and Norton Equivalent Circuits

vTH= open circuit voltage at terminal (a.k.a. port)

RTH= Resistance of the network as seen from port(Vm’s, In’s set to zero)

Léon Charles Thévenin1857-1926

Page 4: Lecture 4 Overview More circuit analysis –Thevenin’s Theorem –Norton’s Theorem

Method 3: Thevenin and Norton Equivalent Circuits

vTH= open circuit voltage at terminal (a.k.a. port)

RTH= Resistance of the network as seen from port(Vm’s, In’s set to zero)

Any network of sources and resistors will appear to the circuit connected to it as a voltage source and a series resistance

Page 5: Lecture 4 Overview More circuit analysis –Thevenin’s Theorem –Norton’s Theorem

Norton Equivalent Circuit

Any network of sources and resistors will appear to the circuit connected to it as a current source and a parallel resistance

Ed Norton – Bell Labs, 1898-1983

Page 6: Lecture 4 Overview More circuit analysis –Thevenin’s Theorem –Norton’s Theorem

Calculation of RT and RN

• RT=RN ; same calculation (voltage and current sources set to zero)

• Remove the load.• Set all sources to zero (‘kill’ the sources)

– Short voltage sources (replace with a wire)– Open current sources (replace with a break)

Page 7: Lecture 4 Overview More circuit analysis –Thevenin’s Theorem –Norton’s Theorem

Calculation of RT and RN continued

• Calculate equivalent resistance seen by the load

Page 8: Lecture 4 Overview More circuit analysis –Thevenin’s Theorem –Norton’s Theorem

Calculation of VT

• Remove the load and calculate the open circuit voltage

SROC VRR

RVV

21

22

(Voltage Divider)

Page 9: Lecture 4 Overview More circuit analysis –Thevenin’s Theorem –Norton’s Theorem

Example

• Use Thevenin’s theorem to calculate the current through Resistor R6. – (solution RTH=6.67Ω, VTH=12V, I=0.95A)

Page 10: Lecture 4 Overview More circuit analysis –Thevenin’s Theorem –Norton’s Theorem

Exercise: Draw the Thevenin Equivalent

• To find RTH remove the load, kill the sources (short voltage sources, break current sources) and find the equivalent resistance.

• To find VTH Remove the load and calculate the open circuit voltage

Page 11: Lecture 4 Overview More circuit analysis –Thevenin’s Theorem –Norton’s Theorem

Exercise: Draw the Thevenin Equivalent

• To find RTH kill the sources (short voltage sources, break current sources) and find the equivalent resistance.

• To find VTH Remove the load and calculate the open circuit voltage

Page 12: Lecture 4 Overview More circuit analysis –Thevenin’s Theorem –Norton’s Theorem

Exercise: Draw the Thevenin Equivalent

• To find RTH kill the sources (short voltage sources, break current sources) and find the equivalent resistance.

• To find VTH Remove the load and calculate the open circuit voltage

VAB = 20 - (20Ω x 0.33amps) = 13.33V

Page 13: Lecture 4 Overview More circuit analysis –Thevenin’s Theorem –Norton’s Theorem

Exercise: Draw the Thevenin Equivalent

• To find RTH kill the sources (short voltage sources, break current sources) and find the equivalent resistance.

• To find VTH Remove the load and calculate the open circuit voltage

VAB = 20 - (20Ω x 0.33amps) = 13.33V

Page 14: Lecture 4 Overview More circuit analysis –Thevenin’s Theorem –Norton’s Theorem

Exercise: Draw the Thevenin Equivalent

• To find RTH kill the sources (short voltage sources, break current sources) and find the equivalent resistance.

• To find VTH Remove the load and calculate the open circuit voltage

Page 15: Lecture 4 Overview More circuit analysis –Thevenin’s Theorem –Norton’s Theorem

Calculation of IN

• Short the load and calculate the short circuit current

(R1+R2)i1 - R2iSC = vs

-R2i1 + (R2+R3)iSC = 0

(KCL at v)

(mesh analysis)

RN=RTH

Page 16: Lecture 4 Overview More circuit analysis –Thevenin’s Theorem –Norton’s Theorem

Source Transformation

Summary: Thevenin’s Theorem• Any two-terminal linear circuit can be replaced with a voltage source

and a series resistor which will produce the same effects at the terminals

• VTH is the open-circuit voltage VOC between the two terminals of the circuit that the Thevenin generator is replacing

• RTH is the ratio of VOC to the short-circuit current ISC; In linear circuits this is equivalent to “killing” the sources and evaluating the resistance between the terminals. Voltage sources are killed by shorting them, current sources are killed by opening them.

Page 17: Lecture 4 Overview More circuit analysis –Thevenin’s Theorem –Norton’s Theorem

Summary: Norton’s Theorem• Any two-terminal linear circuit can be replaced with a current source

and a parallel resistor which will produce the same effects at the terminals

• IN is the short-circuit current ISC of the circuit that the Norton generator is replacing

• Again, RN is the ratio of VOC to the short-circuit current ISC; In linear circuits this is equivalent to “killing” the sources and evaluating the resistance between the terminals. Voltage sources are killed by shorting them, current sources are killed by opening them.

• For a given circuit, RN=RTH

Page 18: Lecture 4 Overview More circuit analysis –Thevenin’s Theorem –Norton’s Theorem

Maximum Power Transfer

• Why use Thevenin and Norton equivalents?– Very easy to calculate load related

quantities

– E.g. Maximum power transfer to the load

• It is often important to design circuits that transfer power from a source to a load. There are two basic types of power transfer– Efficient power transfer: least power loss.

Power is usually large (e.g. power utility)

– Maximum power transfer (e.g. communications circuits)

• Want to transfer an electrical signal (data, information etc.) from the source to a destination with the most power reaching the destination. Power is usually small so efficiency is not a concern.

Page 19: Lecture 4 Overview More circuit analysis –Thevenin’s Theorem –Norton’s Theorem

Maximum Power Transfer: Impedance matching

LLT

TL R

RR

vRip

2

2

4

2

4

22

4

22

)(

)(2

)(

)(

0)(

)(2)(

LT

LTTL

LT

LTT

LT

LTLLTT

L

RR

RRvR

RR

RRv

RR

RRRRRv

dR

dp

LT RR L

T

R

vp

4

2

max so maximum power transfer occurs when and

Differentiate w.r.t. RL using quotient rule:

Set to zero to find maximum:

2vdxdv

udxdu

v

vu

dx

d

http://circuitscan.homestead.com/files/ancircp/maxpower1.htm

http://circuitscan.homestead.com/files/ancircp/maxpower1.htm
Page 20: Lecture 4 Overview More circuit analysis –Thevenin’s Theorem –Norton’s Theorem

Maximum Power Transfer: Impedance matching

LLT

TL R

RR

vRip

2

2

4

2

4

22

4

22

)(

)(2

)(

)(

0)(

)(2)(

LT

LTTL

LT

LTT

LT

LTLLTT

L

RR

RRvR

RR

RRv

RR

RRRRRv

dR

dp

LT RR L

T

R

vp

4

2

max so maximum power transfer occurs when and

Differentiate w.r.t. RL using quotient rule:

Set to zero to find maximum:

2vdxdv

udxdu

v

vu

dx

d

http://circuitscan.homestead.com/files/ancircp/maxpower1.htm

http://circuitscan.homestead.com/files/ancircp/maxpower1.htm

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