Transcript ECE 201 Exam #1 Review

Exam #1 Review
Dr. Holbert
February 15, 2006
ECE201 Exam #1 Review
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Circuit Analysis Techniques
•
•
•
•
While Obeying Passive Sign Convention
Ohm’s Law; KCL; KVL
Voltage and Current Division
Series/Parallel Impedance combinations
Z series  Z1  Z 2    Z N   Z j
1
1
1
1
1




Z par Z1 Z 2
ZM
Zi
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Sign Convention
• Passive sign convention : current should
enter the positive voltage terminal
I
+
Circuit Element
–
• Consequence for P = I V
– Positive (+) Power: element absorbs power
– Negative (-) Power: element supplies power
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Ohm’s Law
V=IZ
I
The
Rest of
the
Circuit
+
Z
ECE201 Exam #1 Review
V
–
4
KCL (Kirchhoff’s Current Law)
i1(t)
i5(t)
i2(t)
i4(t)
i3(t)
The sum of currents entering the node is zero:
n
 i (t )  0
j 1
j
Analogy: mass flow at pipe junction
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KVL (Kirchhoff’s Voltage Law)
+
v1(t)
+
–
v2(t)
–
+
v3(t)
–
• The sum of voltages around a loop is zero:
n
v
j 1
j
(t )  0
• Analogy: pressure drop thru pipe loop
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KVL Polarity
• A loop is any closed path through a circuit
in which no node is encountered more than
once
• Voltage Polarity Convention
– A voltage encountered + to - is positive
– A voltage encountered - to + is negative
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In General: Voltage Division
Consider N impedances in series:
Zi
VZi   VSk
Z j
Source voltage(s) are divided between the
elements in direct proportion to their
impedances
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In General: Current Division
Consider N impedances in parallel:
I Z j   I Sk
Z par
Zj
1
1
1
1
1




Z par Z1 Z 2
ZN
Zi
Special Case (2 impedances in parallel)
Z2
I Z1  I S
Z1  Z 2
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Equivalent Impedance
If we wish to replace the two parallel
impedances with a single impedance whose
voltage-current relationship is the same, the
equivalent impedance has a value of:
Z1 Z 2
Z eq 
Z1  Z 2
Parallel elements share the same 2 end nodes
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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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Complex Numbers
Polar: z   = A = x + jy : Rectangular
imaginary
axis
y
real
axis

• x is the real part
• y is the imaginary part
• z is the magnitude
•  is the phase angle
x
x  z cos 
z  x2  y2
y  z sin 
  tan
ECE201 Exam #1 Review
1
y
x
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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
• Impedance depends on frequency, 2f
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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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