FILTERS

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CHAPTER 7

• FILTERS

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Chapter 7FILTERS - DEFINATION

• WHAT IS FILTER ?
• It can be classified as Analog or Digital.
• Digital filters are implemented using a digital
  computer or special purpose digital hardware.
• Analog filters may be classified as either
  passive or active and are usually implemented
  with R, L, and components and operational
  amplifiers.

It is a circuit that is designed to pass
signals with desired frequencies and reject or
attenuate others.
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Chapter 7 FILTERS- Classification of Filters

• An active filter is one that, along with R, L,
  and C components, also contains an energy source,
  such as that derived from an operational
  amplifier.
• A passive filter is one that contains only R, L,
  and C components. It is not necessary that all
  three be present. L is often omitted (on
  purpose) from passive filter design because of
  the size and cost of inductors and they also
  carry along an R that must be included in the
  design.

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Chapter 7 FILTERS Types of Filters

• In this course we will be concerned with Passive
  Filters.
• There are 4 types of passive filter as shown
  below
• H(?) IDEAL
• REALISTIC
• ?c
• A Lowpass Filter passes low frequencies and stop
  high frequencies

Lowpass Filter
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Chapter 7 FILTERS Types of Filters
Highpass Ideal

• H(?)
• IDEAL
• REALISTIC
• 
  
• 
  ?c
• A Highpass Filter passes high frequencies and
  rejects
• low frequencies
• 
  IDEAL
• 
  
  
• H(?)
  REALISTIC
• ?1
  ?2

Bandpass Ideal
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Chapter 7 FILTERS Types of Filters
Bandstop Ideal

• H(?)
• IDEAL
• REALISTIC
• 
  
• 
  ?1 ?2
• A Bandstop Filter passes frequencies outside
  frequency
• band and blocks or attenuates frequencies within
  the
• band

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Chapter 7FILTERS Application

• The lowpass filter circuit is formed when the
  output of an RC circuit taken off capacitance as
  shown below
• ? Pass frequencies from dc up to cut-off
  frequency

Low Pass Filter Circuit
R
?c 1/RC

VO
VI
C
_
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Chapter 7 FILTERS Application

• Bode Plot of Lowpass Filter
• Linear Plot of Lowpass Filter

0 dB
.
-3 dB
?
1/RC
x
0.707
1/RC
?
0
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Chapter 7 FILTERS Application

• The highpass filter is formed when the output of
  an RC circuit is taken off the resistor as shown
  below

High Pass Filter
?Pass all frequencies above its cut-off frequency

?c 1/RC
C
VO
R
Vi
_
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Chapter 7 FILTERS Application

• Bode plot of Highpass Filter
• Linear plot of highpass filter
• 0.707

-3 dB
1/RC
?
0 dB
0
?
1/RC
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Chapter 7 FILTERS Application

• The bandpass filter is formed of RLC circuit
  where the output is taken off the resistor as
  shown below
• Designed to pass all frequencies within a
  band of frequencies, ?1 lt ? lt ?2

BandPass Filter
?0 1/
L
C
R
VO
Vi
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Chapter 7 FILTERS Application

• Bode plot of Bandpass Filter
• dB
• ?lo
  ?
• Linear plot of bandpass filter
• 1
• 0.707

?hi
0
?lo
?hi
?
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Chapter 7 FILTERS Application

• Suppose we use the previous series RLC
  circuit with output across R to design a bandpass
  filter. We will place poles at 200 rad/sec and
  2000 rad/sec hoping that our 3 dB points will
  be located there and hence have a bandwidth of
  1800 rad/sec. To match the RLC circuit form we
  use

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Chapter 7 FILTERS Application

• MATLAB Program for Bandpass Filter
• N 10 10th order butterworth analog
  
• ZB, PB, KB buttap(N)
• numzb poly(ZB)
• denpb poly(PB) 
• wo 600 bw 200 wo is the
  center fre
• 
  bw is the bandwidth
• numbbs,denbbs lp2bs(numzb,denpb,wo,bw)
  
• w 111200
• Hbbs freqs(numbbs,denbbs,w)
• Hb abs(Hbbs)
• plot(w,Hb)
• grid
• xlabel('Amplitude')
• ylabel('frequency (rad/sec)')
• title('10th order Butterworth filter')
•  

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Chapter 7 FILTERS Application

• Bandpass Filter plot by MATLAB

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Chapter 7 FILTERS Application

• The bandstop filter is formed of RLC circuit
  where the output is taken off the LC combination
  as shown in figure 14.37 in the textbook.
• Design to stop or eliminate all frequencies
  within a band of frequencies, ?1 lt ? lt ?2
• H(?) Vo / Vin j(?L 1/?C) / R j(?L
  1/?C)

BandStop Filter
?0 1/
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Chapter 7 FILTERS Application

• RLC Bandstop Filter

R
L
C
The transfer function for VO/Vi can be expressed
as follows
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Chapter 7 FILTERS Application

• Design a band stop filter with a center frequency
  of 632.5 rad/sec and having poles at 100 rad/sec
  and 3000 rad/sec.
• MATLAB program for Bandstop filter

num 1 0 300000 den 1 3100 300000 w
1 5 10000 Bode(num,den,w)
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Chapter 7 FILTERS Application

• BODE PLOT VS MATLAB FOR BANDSTOP FILTER

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Chapter 7 Filters Application

• EXERCISE 1 (Exercise Problem 14.48)
• Find the transfer function Vo / Vs of the
  circuit shown below. Show that the circuit is
  lowpass filter.

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Chapter 7 Filters Application

• SOLUTION TO EXERCISE 1
• 1. Obtain the transfer function,
• 2. Simplify the transfer function,
• 3. the circuit is a lowpass filter.

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Chapter 7 Filters Application

• Active Lowpass Filter
• Active Highpass Filter

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Basic Active Filters
Chapter 7 Filters Application

• Active Highpass Filter

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Chapter 7 Filters Application

• Aktif Bandpass Filter

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Chapter 7 Filters Application

• Active Bandstop filter

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