Transcript Review for Final Exam

Final Exam Review
Dr. Holbert
April 28, 2008
LectRF
EEE 202
1
Don’t Forget the Essentials
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Verify voltage polarity and current direction
Obey the passive sign convention
The Fundamentals: Ohm’s Law; KCL; KVL
Series/Parallel Impedance combinations
Z series  Z1  Z 2    Z N   Z j
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1
1
1
1




Z par Z1 Z 2
ZM
Zi
LectRF
EEE 202
2
Circuit Analysis Techniques
• All these circuit analysis techniques have
wide applicability: DC, AC, and Transient
• Voltage and Current Division
• Nodal and Loop/Mesh Analyses
• Source Transformation
• Superposition
• Thevenin’s and Norton’s Theorems
LectRF
EEE 202
3
AC Steady-State Analysis
• AC steady-state analysis using phasors allows
us to express the relationship between current
and voltage using an Ohm’s law-like formula:
V=IZ
• A phasor is a complex number that represents
the magnitude and phase of a sinusoidal voltage
or current
x(t) = XM cos(ωt+θ) ↔ X = XM θ
Time domain
LectRF
Frequency Domain
EEE 202
4
Impedance Summary
Element
Resistor
Impedance
ZR = R = R  0
Inductor
ZL = sL = jωL = ωL  90
Capacitor ZC = 1/(sC) = 1/(jωC) = –1/(ωC)  90
• Z is called impedance (units of ohms, Ω)
• Impedance is (often) a complex number, but is
not technically a phasor
• Impedance depends on frequency, ω
LectRF
EEE 202
5
Complex Numbers
Polar: z  q = A = x + jy : Rectangular
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imaginary
axis
y
real
axis
q
z  x2  y2
x
y  z sin q
LectRF
x is the real part
y is the imaginary part
z is the magnitude
q is the phase angle
x  z cos q
EEE 202
q  tan
1
y
x
6
Transfer Function
• Recall that the transfer function, H(s), is
Y ( s) Output
H (s) 

X( s )
Input
• The transfer function in a block diagram form is
X(j) ejt = X(s) est
Y(j) ejt = Y(s) est
H(j) = H(s)
• The transfer function can be separated into
magnitude and phase angle information (s=jω)
H(j) = |H(j)| H(j)
LectRF
EEE 202
7
Bode Plots
• Place system function in standard form
– The terms should appear as: (1 + s)
• Magnitude and phase behavior of terms
– Constant gain term (K):
• with poles/zeros at the origin: find ω0dB
• without poles/zeros at origin: use 20 log10(K) dB
– Poles and zeros of the form (1 + j)
• Sketching the magnitude and phase plots
• Reverse: Bode plot to transfer function
LectRF
EEE 202
8
Bode Plot Sketch Summary
Gain
ωp
0 dB
–20 dB
ω
Phase
One
Decade
0°
Plot
Gain
(magnitude)
Pole (–) or Zero (+)
Rolloff at
ωbreak=1/; slope of
±20 dB/decade
Phase
Asymptotic shift of
±90° with ±45°/dec
slope and ±45°
cross-over at ωbreak
–45°
–90°
ω
Pole at
ωbreak=1/
LectRF
EEE 202
9
Low Pass
Gain
Gain
Bode Plots of Common Filters
Frequency
High Pass
Frequency
Gain
Gain
Band Pass
Frequency
LectRF
Band Reject
Frequency
EEE 202
10
Some Terminology & Quantities
Our vocabulary has
expanded further with
several new terms,
including:
• Resonant frequency
• Quality factor (Q)
• Decibels (dB) and
decade
• Active vs. passive
filter
LectRF
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Phase shift lead/lag
RMS current/voltage
Bandwidth
Break freq., corner
freq., cutoff freq., halfpower frequency
• Notch filter
• Butterworth filter
• FFT
EEE 202
11
Course Summary
• Bottom line for the semester—can you perform a
comprehensive analysis of a given electrical
network by determining (as appropriate):
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the dc and/or ac output of the circuit
the system response to a step or impulse input
the network transfer function(s)
the system characteristics such as the poles and
zeros, and the type of damping exhibited
– the frequency response by sketching a Bode plot
(magnitude and phase) of the system function
– the type of filtering the circuit performs, if any
LectRF
EEE 202
12