Transcript EEE 302 Electrical Networks II Dr. Keith E. Holbert Summer 2001 Lecture 20 Sinusoidal Frequency Analysis • The transfer function is composed of both magnitude and.

EEE 302
Electrical Networks II
Dr. Keith E. Holbert
Summer 2001
Lecture 20
1
Sinusoidal Frequency Analysis
• The transfer function is composed of both magnitude
and phase information as a function of frequency
H( j)  H ( j) e
j  ( )
where |H(jω)| is the magnitude and φ(ω) is the phase
angle
• Plots of the magnitude and phase characteristics are
used to fully describe the frequency response
Lecture 20
2
Bode Plots
• A Bode plot is a semilog plot of transfer function's
magnitude and phase as a function frequency
• The gain magnitude is many times expressed in terms
of decibels (dB)
dB = 20 log10 A
where A is the amplitude or gain
– a decade is defined as any 10-to-1 frequency range
– an octave is any 2-to-1 frequency range
20 dB/decade = 6 dB/octave
Lecture 20
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Bode Plots
• Straight-line approximations of the Bode plot may be
drawn quickly from knowing the poles and zeros
– response approaches a minimum near the zeros
– response approaches a maximum near the poles
• The overall effect of constant, zero and pole terms
Term
Magnitude
Break
Constant (K)
N/A
Zero
Pole
Asymptotic
Magnitude Slope
Asymptotic
Phase Shift
0
0
upward
+20 dB/decade
+ 90
downward
–20 dB/decade
– 90
Lecture 20
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Bode Plots
• Express the transfer function in standard form


K  j  (1  j1 ) 1  2 2 ( j 2 )  ( j 2 ) 2 
H( j ) 
(1  j a ) 1  2 b ( j b )  ( j b ) 2 
N


• There are four different factors:
1.
2.
3.
4.
Constant gain term, K
Poles or zeros at the origin, (j)±N
Poles or zeros of the form (1+ j)
Quadratic poles or zeros of the form 1+2(j)+(j)2
Lecture 20
5
Bode Plots
• We can combine the constant gain term and the
poles/zeros at the origin such that the magnitude
crosses 0dB at
K
Pole :
( j ) N
 0 dB  K 1 / N
Zero : K ( j ) N
 0 dB  (1 / K )1 / N
• Define the break frequency to be at ω=1/τ with
magnitude at ±3dB and phase at ±45°
Lecture 20
6
Bode Plots
Magnitude Behavior
Factor
Constant
Low
Freq
Break
Asymptotic
Phase Behavior
Low
Freq
Break
Asymptotic
20 log10(K) for all frequencies
0 for all frequencies
Poles or
zeros at origin
±20N dB/decade for all
frequencies with a crossover of
0 dB at ω=1
±90(N) for all frequencies
First order
(simple) poles
or zeros
0 dB
±3N dB
at ω=1/τ
±20N
dB/decade
0
±45(N) with
slope ±45
per decade
±90(N)
Quadratic
poles or zeros
0 dB
see ζ at
ω=1/τ
±40N
dB/decade
0
±90(N)
±180(N)
where N is the number of roots of value τ
Lecture 20
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Class Examples
• Extension Exercise E12.3
• Extension Exercise E12.4
• Extension Exercise E12.5
Lecture 20
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MATLAB Exercise
• Here we will use MATLAB to create Bode plots
for Extension Exercise E12.3
• Start MATLAB and open the file BodePlt.m from
the class webpage
Lecture 20
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