analog filters design - bu shoubra/electrical... · to design an analog low-pass butterworth...
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Analog Filters Design
Different Filter Responses Approximation
Dr.Eng. Basem ElHalawany
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Analog Filters Design
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Frequency-Domain Filter Design
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Frequency-Domain Filter Design
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Frequency-Domain Filter Design
Zeros
Poles
Consider a frequency response function of a circuit in the rational form as a
function of jw
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We begin by defining tolerance regions on the power frequency response
design parameters that select the filter attenuation at the two
critical frequencies.
The filter functions :
ω
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The Butterworth Filter Approximation:
• Butterworth filters are also known as “maximally flat” filters
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The Butterworth Filter Approximation:
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that lie on a circle with radius
S = jω
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For stable Causal system, we only consider all poles in the left-half-
plane, which allows us to take the N poles only as the poles of the
filter H ( s ) ((From 1:N))
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Steps for Designing a Low-Pass Butterworth Filter Approximation:
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Example: Design a Butterworth low-pass filter to meet the power gain
specifications shown in Figure
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Example: Design a Butterworth low-pass filter to meet the power gain
specifications shown in Figure
The phase response is not linear, and
the phase shift (thus, time delay) of
signals passing through the filter
varies nonlinearly with frequency.
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Designing a Butterworth Filter using Matlab
To design an analog low-pass Butterworth filter using MATLAB:
• The ’s’ tells MATLAB to design an analog filter.
• The vectors a and b hold the coefficients of the denominator and the numerator
(respectively) of the filter’s transfer function.
bodemag used to plot the magnitude response
from 30 rad/s out to 3,000 rad/s.
bodemag used to plot the magnitude response
from 30 rad/s out to 3,000 rad/s.
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At 100 rad/s the response seems
to have decreased by about 3 dB
From 100 rad/s to 1,000 rad/s the
response seems to drop by about 80
dB. As this is a fourth order filter its
rolloff should be 4 × 20 dB/decade.
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The Chebyshev Filter Approximation:
• Filters with the Chebyshev response characteristic are useful when a rapid
roll-off is required because it provides a roll-off rate greater than -20
dB/decade/pole.
• This is a greater rate than that of the Butterworth, so filters can be
implemented with the Chebyshev response with fewer poles and less
complex circuitry for a given roll-off rate.
• This type of filter response is characterized by overshoot or ripples in the
pass-band or stop-band (depending on the number of poles
The Chebyshev filters allow these conditions:
ripple in the
stop-band.
ripple in the
Pass-band.
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The required filter order may be found as follows
So, The characteristic equation
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Take Cos of both sides, we Get:
which defines an ellipse of
The poles will lie on this ellipse
We can substitute by s now in the original equation of TN
& From characteristic equation : Compare
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As in the Butterworth design procedure, we select the left half-plane poles as the
poles of the filter frequency response.
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Steps for Designing a Low-Pass Chebyshev Type 1 Filter Approximation:
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The pole-zero plot for the Chebyshev Type 1
filter is shown in Fig.