Transcript AC Circuit Analysis Techniques (8-3)

AC Circuit Analysis
Techniques
Dr. Holbert
April 7, 2008
Lect18
EEE 202
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Introduction
• Today, we continue to perform AC
analyses using phasors and impedances
• We utilize all our circuit analysis tools to
accomplish this
– KCL, KVL, Ohm’s Law
– Voltage and current division
– Superposition, source transformation
– Nodal and loop/mesh analyses
– Thevenin’s and Norton’s theorems
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Series Impedance
Z1
Z2
Zeq
Z3
Z series  Z1  Z 2    Z N   Z j
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Parallel Impedance
Z1
Z2
Z3
Zeq
1
1
1
1
1




Z par Z1 Z 2
ZM
Zi
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Leading and Lagging Phase
x1 (t )  X M1 cost  q 
x2 (t )  X M 2 cost   
x1(t) leads x2(t) by q-
x2(t) lags x1(t) by q-
On the following plot, which signals lead
and which signals lag?
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Phase
Green leads
blue and red
Red lags blue
and green
8
6
4
2
0
-2 0
0.01
0.02
0.03
0.04
0.05
-4
-6
-8
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Circuit Element Phasor Relations
(ELI and ICE man)
Element
V/I Relation Phasor Relation
Capacitor I = C dV/dt I = j ω C V
= ω C V 90°
Inductor V = L dI/dt V = j ω L I
= ω L I 90°
Resistor V = I R
V=RI
= R I 0°
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Phase
I leads V
by 90°
V leads I
by 90°
V and I are
in-phase
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Class Examples
• Drill Problems P8-6, P8-9, P8-8
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