Download EEE 302 Lecture 1 - Arizona State University

EEE 302
Electrical Networks II
Dr. Keith E. Holbert
Summer 2001
Lecture 1
1
Electrical Analogies (Physical)
Electrical
Hydraulic
Base
Charge (q)
Mass (m)
Flow
Current (I)
Fluid flow (G)
Potential
Voltage (V)
Pressure (p)
Power
P=IV
P=Gp
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Phasors
• A phasor is a complex number that
represents the magnitude and phase of a
sinusoidal voltage or current:
X M cost   
X  X M 
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Class Examples
• Extension Exercise 8.3
• Extension Exercise 8.4
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Complex Numbers
Polar: z   = A = x + jy : Rectangular
imaginary
axis
• x is the real part
• y is the imaginary part
• z is the magnitude
•  is the phase
y
real
axis

x
z  x2  y2
x  z cos
y  z sin 
  tan
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1
y
x
5
Complex Number
Addition and Subtraction
• Addition is most easily performed in rectangular
coordinates:
A = x + jy
B = z + jw
A + B = (x + z) + j(y + w)
• Subtraction is also most easily performed in
rectangular coordinates:
A - B = (x - z) + j(y - w)
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Complex Number
Multiplication and Division
• Multiplication is most easily performed in polar
coordinates:
A = AM  
B = BM  f
A  B = (AM  BM)  (  f)
• Division is also most easily performed in polar
coordinates:
A / B = (AM / BM)  (  f)
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Circuit Element Phasor Relations
(ELI and ICE man)
Element V/I Relation Phasor Relation
Phase
Capacitor I = C dV/dt I = j ω C V
I leads V
= ωCV 90° by 90º
Inductor V = L dI/dt V = j ω L I
V leads I
by 90º
= ωLI 90°
Resistor V = I R
V=RI
In-phase
= R I 0°
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Class Examples
• Extension Exercise 8.5
• Extension Exercise 8.6
• Extension Exercise 8.7
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Impedance
• AC steady-state analysis using phasors
allows us to express the relationship
between current and voltage using a
formula that looks likes Ohm’s law:
V=IZ
• Z is called impedance (units of ohms, W)
• Impedance is (often) a complex number, but
is not a phasor
• Impedance depends on frequency 
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Impedance Summary
Element
Impedance
Capacitor
ZC = 1 / jC = -1/C  90
Inductor
ZL = jL = L  90
Resistor
ZR = R = R  0
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Series Impedance
Z1
Z2
Zeq
Z3
Zeq = Z1 + Z2 + Z3
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Parallel Impedance
Z1
Z2
Z3
Zeq
1/Zeq = 1/Z1 + 1/Z2 + 1/Z3
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Class Examples
• Extension Exercise E8.10
• Extension Exercise E8.8
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