AIR UNIVERSITY
DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
EXPERIMENT NO 3
Lab Title: 2ND ORDER ACTIVE AND PASSIVE BAND PASS FILTERS.
Student Name: SALMAN ALI Reg. No: 200176
Objective: To design and construct Active & Passive Band-pass Butterworth filters using
operational amplifiers.
LAB ASSESSMENT:
Excellent Good Average Satisfactory Unsatisfactory
Attributes (5) (4) (3) (2) (1)
Ability to Conduct
Experiment
Ability to assimilate the
results
Effective use of lab
equipment and follows
the lab safety rules
Total Marks: ________________________ Obtained Marks: _______________________
LAB REPORT ASSESSMENT:
Excellent Good Average Satisfactory Unsatisfactory
Attributes (5) (4) (3) (2) (1)
Data presentation
Experimental results
Conclusion
Total Marks: ________________________ Obtained Marks: _______________________
Date: ______________________________ark Signature: _______________________
Objective:
To design and construct active and passive Band-pass Butterworth filters using
operational amplifiers.
Equipment required:
Oscilloscope
Function Generator
Trainer
Operational Amplifier (LM-741)
Resistors
Capacitors
Introduction:
We can say that a Band pass filter is a combination of both low pass filter and high pass filter.
The name of the filter itself indicates that it allows only a certain band of frequencies and blocks
all the remaining frequencies.
In audio applications, sometimes it is necessary to pass only a certain range of frequencies, this
frequency range do not start at 0Hz or doesn’t end at very high frequency but these frequencies
are within a certain range, either wide or narrow. These bands of frequencies are commonly
termed as Bandwidth.
Passive Band Pass filter:
Band pass filter is obtained by cascading passive low pass and passive high pass filters. This
arrangement will provide a selective filter which passes only certain frequencies. This new RC
filter circuit can able to pass either a narrow range of frequencies or wide range of frequencies.
This passage range of frequencies that is either narrow or wide range will depend upon the way
the passive low pass and high pass filter cascade. The upper and lower cut-off frequencies
depend on filter design. This band pass filter is simply appearing like a frequency selective filter.
The input given is a sinusoidal signal. The properties of low pass and high pass combinations
give us Band pass filter. By arranging one set of RC elements in series and another set of RC
elements in parallel the circuit behaves like a band pass filter.
This gives us a second order filter because the circuit has two reactive components. One
capacitor belongs to low pass filter and another capacitor belongs to high pass filter. Without any
variations in the input signal this band pass filter will pass a certain range of frequencies. This
filter does not produce any extra noise in the signal.
Frequency Response of Passive band pass filter:
Active Band Pass Filter:
Depending on the quality factor the band pass filter is classified into Wide band pass filter and
Narrow band pass filter. The quality factor is also referred as ‘figure of merit’. By cascading
High Pass Filter and Low Pass Filter with an amplifying component we obtain band pass filter.
The amplifier circuit between these high pass and low pass filter will provide isolation and gives
over all voltage gain of the circuit. The values of the cut-off frequencies of both the filters must
be maintained with minimum difference.
If the value of quality factor is less than ten, then the pass band is wide, which gives us the larger
bandwidth. This band pass filter is called Wide Band Pass Filter.
Frequency response of Active band pass Filter:
Butterworth Filter
For a particular desired specification of a digital filter the order of Butterworth filter will be
higher than chebyshev filter.
Butterworth filter has no ripples either in passband or stopband.
A Butterworth filter is a type of signal processing filter designed to have a frequency
response as flat as possible in the passband. Hence the Butterworth filter is also known as
“maximally flat magnitude filter”.
The frequency response of the Butterworth filter is flat in the passband (i.e. a band pass
filter) and roll-offs towards zero in the stopband. The rate of roll-off response depends on
the order of the filter. The number of reactive elements used in the filter circuit will decide
the order of the filter.
All poles lie on a circle having a radius of the cut-off frequency.
The applications of a Butterworth filter are listed below:
Because of the maximal flat frequency response in the passband, it is used as an
anti-aliasing filter in data converter applications.
The Butterworth filter is used in the audio processing application. An efficient audio
noise reduction tool can be developed using a Butterworth filter.
Chebyshev Filter
For a particular desired specification of a digital filter the order of chebyshev filter will be
lower as compared to Butterworth filter.
Chebyshev filter will have ripples either in stop band or passband.
The order of the Chebyshev filter is less compared to the Butterworth filter for the same
desired specifications.
It requires less hardware. All poles lie on ellipse having major axis R, ξ, minor axis r.
The cutoff frequency of this filter is equal to the passband frequency.
CALCULATIONS:
TASK 1:
Let us assume that the band pass filter will allow the frequencies from 1 kHz to 30 kHz and it
contains 10 kΩ resistor. By considering these values, we can calculate the capacitance of the
capacitor.
We already know that the cut off frequency value of the low pass filter must be higher than
the high pass filter. So the cut off frequency of the high pass filter is 1 kHz and cut off
frequency of the low pass filter is 30 kHz.
BW=Fh-Fl/2
F0=Fh-Fl/2 +Fl
F0=30kHz-1kHz/2+1KHz
F0=15.5kHz
At High pass filter stage:
fL = 1 kHz
Resistance R = 10 kΩ
C = 1/(2πfLR) = 1/(2*π*1000*1000) = 15.8 nF=16nF
At Low pass filter stage:
fH = 30 kHz
Resistance R = 10 kΩ
C = 1/(2πfHR) = 1/(2*π*30000*10000) = 510 pF
From the above calculations the capacitor value required for the high pass filter is 16 nF and
the low pass filter capacitor value is 510 pF.
CALCULATIONS:
TASK 2:
ACTIVE BAND PASS FILTER:
C1=C2=C=0.01uF
Fh=15KHz , Fl=3KHz
BW=Fh-Fl/2
BW=15kHz-3kHz/2
BW=6KHz
F0=Fh-Fl/2 +Fl
F0=15kHz-3kHz/2+3KHz
F0=9kHz
As R1R3=1/C^2*Wo^2
Wo=2*pi*F0
Wo=56520
And
R1R3=3130k ohm
As we put R1=1K ohm
R3=3130K /1K
R3=3130
R3=3.130K ohm
Applications of Band Pass Filters:
These are used to optimize the signal to noise ratio of the receiver.
These are used in optical communication area like LIDARS.
They are used in some of the techniques of color filtering.
These are also used in medical field instruments like EEG.
In telephonic applications, at DSL to split phone and broad band signals.
CONCLUSION:
To understand the band, pass active and passive filters that allows the high and low frequency
passes means which is passes than fc Cut-off frequency. In this filter circuit, the quality factor Q
is more sensitive to component tolerances and it also provides the wide band pass region of active
and passive filters.
