# EEE 302 Electrical Networks II Dr. Keith E. Holbert Summer 2001

```EEE 302
Electrical Networks II
Dr. Keith E. Holbert
Summer 2001
Lecture 6
1
Maximum Average Power Transfer
• To obtain the maximum average power transfer to
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
2
Maximum Average Power Transfer
ZTh
Voc
+
-
ZL
ZL = ZTh*
• Note that ONLY the resistive component of the
Lecture 6
3
Max Power Xfer: Cases
Characteristic
Complex
ZL = ZTh* = RTh - j XTh
Purely Resistive Z  R = R 2 + X 2
L
L
Th
Th
(i.e., XL=0)
Further reduces to ZL= RL=RTh
for XTh=0 (old DC way)
Purely Reactive No Average power transfer to
(i.e., RL=0)
Lecture 6
4
Class Examples
• Extension Exercise E9.5
• Extension Exercise E9.6
Lecture 6
5
Effective or RMS Values
• Root-mean-square value (formula reads like the
name: rms)
I rms
1

T
t 0 T

2
i (t ) dt
and
t0
Vrms
1

T
t 0 T

v 2 (t ) dt
t0
• For a sinusoid: Irms = IM/2
– For example, AC household outlets are 120 Volts-rms
Lecture 6
6
Why RMS Values?
• The effective/rms current allows us to write
average power expressions like those used in dc
circuits (i.e., P=I&sup2;R), and that relation is really the
basis for defining the rms value
• The average power (P) is
1
Psource  VM I M cos v   i   Vrms I rms cos v   i 
2
2
Vrms
1
2
Presistor  VM I M  Vrms I rms 
 I rms R
2
R
Lecture 6
7
Class Examples
• Extension Exercise E9.7
• Extension Exercise E9.9
• Extension Exercise E9.10
Lecture 6
8
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