Lecture 6 1

EEE 302Electrical Networks II

Dr. Keith E. Holbert

Summer 2001

Lecture 6 2

Maximum Average Power Transfer

• To obtain the maximum average power transfer to a load, the load impedance (ZL) should be chosen equal to the complex conjugate of the Thevenin equivalent impedance representing the remainder of the network

ZL = RL + j XL = RTh - j XTh = ZTh*

Lecture 6 3

Maximum Average Power Transfer

Voc

+

-

ZTh

ZL

ZL = ZTh*

• Note that ONLY the resistive component of the load dissipates power

Lecture 6 4

Max Power Xfer: Cases

LoadCharacteristic

Load Equivalent

Complex ZL = ZTh* = RTh - j XTh

Purely Resistive(i.e., XL=0)

Further reduces to ZL= RL=RTh

for XTh=0 (old DC way)Purely Reactive(i.e., RL=0)

No Average power transfer toload; Not really a case

22ThThLL X+ R =RZ

Lecture 6 5

Class Examples

• Extension Exercise E9.5

• Extension Exercise E9.6

Lecture 6 6

Effective or RMS Values

• Root-mean-square value (formula reads like the name: rms)

• For a sinusoid: Irms = IM/2– For example, AC household outlets are 120 Volts-rms

Tt

t

rms

Tt

t

rms dttvT

VanddttiT

I0

0

0

0

)(1

)(1 22

Lecture 6 7

Why RMS Values?

• The effective/rms current allows us to write average power expressions like those used in dc circuits (i.e., P=I²R), and that relation is really the basis for defining the rms value

• The average power (P) is

RIR

VIVIVP

IVIVP

rmsrms

rmsrmsMMresistor

ivrmsrmsivMMsource

22

2

1

coscos2

1

Lecture 6 8

Class Examples

• Extension Exercise E9.7

• Extension Exercise E9.9

• Extension Exercise E9.10