Download Experiment SIG1: Active Low-Pass Filter Design

FACULTY OF ENGINEERING
LAB SHEET
CIRCUITS AND SIGNALS
ECT 2036
TRIMESTER 1 (2011/2012)
SIG1-Active Low-Pass Filter Design
SIG2-Circuit analysis using ORCAD PSpice
ECT2036: Circuit and Signals
SIG1
Experiment SIG1: Active Low-Pass Filter Design
1.0 Objectives:
i) To demonstrate the active low-pass filter design techniques using Sallen Key
configuration.
ii) To demonstrate a sweep frequency measurement technique.
iii) To compare the differences between Butterworth and Chebyshev filters.
2.0 Apparatus:
 “Low Pass Filter Design” experiment board
 DC power supply
 Dual-trace oscilloscope
 Function generator
 Connecting wires
3.0 Introduction:
An electronics filter is a circuit that is used to pass signals which are within a selected
band or frequencies while attenuating all other signals which are beyond this band. Filter
networks can be classified as active or passive filters. Passive filter network contains only
passive components such as resistors, inductors and capacitors. Active filters, on the
other hand, provide amplification to the pass-band signals with the use of transistor or opamps together with a few frequency-selective passive components.
There are four basic type of filters, namely low-pass, high-pass, band-pass and band-stop
filters. A low pass-pass filter allows low-frequency signals to be passed forward to its
output terminals with little or no attenuation. Any signal above cutoff frequency will be
attenuated, and the attenuation increases with frequency, which is a measure of how
selective the filter is.
The basic 1st order low-pass filter section is shown in Figure 1, which is a passive RCfilter network coupled to a voltage follower.
Vo
Vi
Figure 1: 1st order low-pass filter network
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It can be shown that the transfer function is
V
1
o
V
sCR  1
i
The 2nd order Sallen Key low-pass filter configuration shown in Figure 2 is commonly
used in many practical electronic systems. It is sometimes known as a voltage-controlled
voltage source (VCVS) filter design.
RA
RB
Vo
Vi
Figure 2: Second-order low-pass filter network
It can be shown that the transfer function is
V
K
o 
2 2 2
V
i s C R  sCR(3  K )  1
where
R
K 1 B
R
A
1
cutoff frequency, f 
c 2CR
The roots of the denominator quadratic expression are called the poles of the transfer
function. These poles are usually complex numbers. They can be plotted on a graph in the
complex number plane. The locations of these poles on the complex plane determine the
pass-band frequency response of the filter. Notice that the poles of the Sallen Key lowpass filter can be set by selecting a suitable value of K. Hence, the filter response can be
optimized for different applications by varying the gain K of the amplifier. Normally a
standard value for C is chosen and the resulting value R is calculated for a given cutoff
frequency. The gain-setting resistors RA and RB are chosen to give either a Butterworth
(maximally flat) or Chebyshev (equal ripple) response. A Butterworth filter has a flat
response in the pass-band. A Chebyshev filter, on the other hand, sacrifices the flatness of
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the pass-band response to achieve a higher selectivity for the same filter order as the
Butterworth filter. Higher pass-band ripple can be traded for higher selectivity.
Higher-order filters may be constructed by cascading a combination of 1st and 2nd order
filter sections (stages).
The block diagrams in Figure 3 illustrate the schemes for higher-order low-pass filters.
Odd-order filters are obtained by cascading a 1st order section with one or more 2nd order
sections. For example, a 5th order low-pass filter can be built by cascading a 1st order
section with two 2nd order sections. For even-ordered filters, only 2nd order filter sections
are used.
1st order
2nd order
3rd Order Filter
2nd order
2nd order
4th Order Filter
1st order
2nd order
2nd order
5th Order Filter
Figure 3: Block diagram illustrating higher-order low-pass filters
The locations of the poles for each filter stage must be properly selected in order to obtain
the standard Butterworth or Chebyshev response. A 4th order filter cannot be simply
constructed by cascading two similar 2nd order filters. Instead, the cutoff frequency for
each filter stage must be slightly higher than the desired overall cutoff frequency fc.
Table 1 summarizes the required design parameters for some of the commonly used
filters.
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Table 1: Higher-order low-pass filter parameters.
1st stage
2nd stage
3rd stage
RB/RA
f`
RB/RA
f` RB/RA
f`
Order
Butterworth
3
4
5
6
1dB Chebyshev
3
4
5
6
2dB Chebyshev
3
4
5
6
0.152
0.068
1.000
1.235
0.382
0.586
1
1
1
1
1.382
1.482
1
1
6.0
8.2
10.3
12.5
1.504
1.719
1.286
1.545
0.911
0.943
0.714
0.733
1.820
1.875
0.961
0.977
8.0
13.4
16.2
21.8
0.322 1.608
0.913
0.466 1.782
0.946
0.223 1.437
0.624
0.321 1.637
0.727
Note: Normalized cutoff frequency, f` = 1/[2RC  fc]
1.862
1.901
0.964
0.976
8.3
14.6
16.9
23.2
0.725
0.686
1
1
1
1
Overall passband gain (dB)
0.452
0.502
0.280
0.347
0.924
0.879
Industrial function generators usually have a voltage controlled frequency (VCF)
input. The frequency of the sine wave output can be electronically adjusted by
applying an external voltage to this input. If a saw-tooth waveform is connected, as
shown in Figure 4, the output sine-wave frequency can be linearly swept from a lowfrequency value to a high-frequency value. This frequency sweep signal can be
connected to the filter under test to evaluate the frequency response. The AC-DC
converter is essentially a peak-detector circuit which converts the alternating
amplitude of the signal into an equivalent DC level. With the saw-tooth waveform
also connected to the oscilloscope as the trigger source, the frequency response can be
displayed on the CRT screen.
P7
Function generator
Filter under test
VCF
P1
P3
CH1
Oscilloscope
CH2
P5
AC-to-DC
converter
Figure 4: Experimental setup to test the frequency response of a filter
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PRECAUTIONARY STEPS:
1) There are 2 types of DC power supply in the laboratory, the M10-380D-303-A and
the GPR-3030. If you’re using the M10-380D-303-A power supply:
i) make sure that you use only one part of the power supply i.e. either master or
slave, and
ii) select the “indep” button
2) Connect all the wires accordingly as per instructed, directly between the supply and
the experiment board.
3) Do not increase the power supply’s voltage abruptly, and ensure that the supply’s
value is within the stated limit (e.g. 24V for the voltage), as otherwise, you might
burn the IC chip.
4) Make sure that the current supply is set at a low level when you are about to connect
the power supply to the experiment board.
5) Connect the oscilloscope probe to the “cal” point, and make sure that you can see a
square waveform of the appropriate amplitude and period in order to ensure that the
oscilloscope is properly calibrated.
4.0 Procedure:
1. Set both CH1 and CH2 of the oscilloscope to DC coupling.
2. Set the function generator for a 15kHz sine wave. Check the waveform using the
oscilloscope, and adjust the amplitude so that it will be a 2V peak-to-peak
amplitude.
3. Set the DC power supply to 24V, connect the positive terminal to V+, the
negative terminal to V-, and the ground terminal to GND on the experiment
board.
4. Examine the output at terminal P1 (The output should be a saw-tooth waveform).
Check the waveform to confirm that the amplitude is about 12V peak-to-peak and
the waveform period is about 50ms (or 100ms). (Adjusting the potentiometer
VR1 and VR2 will adjust the amplitude and frequency of this saw-tooth signal
respectively.)
5. Connect the saw-tooth waveform to the VCF input of the function generator. The
sinewave output of the function generator will sweep from about 5kHz to 25kHz.
6. Connect the same saw-tooth waveform to CH1 of the oscilloscope.
7. Set “Vert mode” of the oscilloscope to “CH2”.
8. Connect terminal P5 to CH2 of the oscilloscope.
9. Now, the filter response can be tested by connecting the function generator output
to the input terminal of the filter P7, and the output of the filter to terminal P3.
Follow the connections as given in Figure 4.
10. Design the filters as per the following sections:
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4.1. Third order Butterworth filter
Design a third order Butterworth low-pass filter with a cutoff frequency of 19.4kHz.
Set C = 0.01F for all the calculations.
By referring to Table 1, we can determine that the selected resistance value should be
820 for all 1st and 2nd stages of filters.
R
1
 820
2π  0.01μ  19.4k
Construct the third order low-pass filter. In order to measure the overall pass-band
gain, disconnect the saw-tooth waveform from the VCF input of the function
generator. Measure the signal amplitude at the filter input and output. (Make sure the
output waveform is not clipped. Reduce the input amplitude if necessary.)
Test the frequency response using the measurement setup as shown in Figure 4. Draw
the response curve.
4.2. Fifth order Butterworth filter
Design a fifth order Butterworth low-pass filter with a cutoff frequency of 19.4kHz.
Set C = 0.01F for all the calculations.
By referring to Table 1, determine all the suitable resistance values.
Construct the fifth order low-pass filter. In order to measure the overall pass-band
gain, disconnect the saw-tooth waveform from the VCF input of the function
generator. Measure the signal amplitude at the filter input and output. (Make sure the
output waveform is not clipped. Reduce the input amplitude if necessary.)
Test the frequency response using the measurement setup as shown in Figure 4. Draw
the response curve.
4.3. Third order Chebyshev filter
Design a third order 2dB Chebyshev low-pass filter with a cutoff frequency of
21.4kHz. Set C = 0.01F for all the calculations.
The first stage of the resistance value can be calculated as follows:
R
1
 2310  2200
2 π  0.01μ  21.4k  0.322
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By referring to Table 1, determine suitable resistance values for the rest of the
resistors.
Construct the third order low-pass filter. In order to measure the overall pass-band
gain, disconnect the saw-tooth waveform from the VCF input of the function
generator. Measure the signal amplitude at the filter input and output. (Make sure the
output waveform is not clipped. Reduce the input amplitude if necessary.)
Test the frequency response using the measurement setup as shown in Figure 4. Draw
the response curve.
4.4. Fifth order Chebyshev filter
Design a fifth order 2dB Chebyshev low-pass filter with a cutoff frequency of
20.1kHz. Set C = 0.01F for all the calculations.
The first stage of the resistance value can be calculated as follows:
R
1
 3551  3600
2π  0.01μ  20.1k  0.223
By referring to Table 1, determine suitable resistance values for the rest of the
resistors.
Construct the fifth order low-pass filter. In order to measure the overall pass-band
gain, disconnect the saw-tooth waveform from the VCF input of the function
generator. Measure the signal amplitude at the filter input and output. (Make sure the
output waveform is not clipped. Reduce the input amplitude if necessary.)
Test the frequency response using the measurement setup as shown in Figure 4. Draw
the response curve.
Important:
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You are given one week to prepare and submit your lab report to the lab staff.
Reports can be handwritten or typed. Neatness and carefulness will be taken into
account in the marking of your report.
You MUST use the FOE lab report cover template. The template can be downloaded
at http://foe.mmu.edu.my/lab/Docs/Student_Lab-Report_cover-1.doc
Prepare your own lab report and use your own findings and results
Please be instructed that plagiarism is an academic offence and if similar reports are
found, you should be required to give an explanation for the similarities and no
marks will be given for both the original and the copied ones.
Late submission of your lab report will not be usually entertained unless if there is
any emergency cases and strong proof for late submission. Otherwise, automatically
awarded 0 (zero) mark for the late submission.
This lab report carries 5% of the total course marks.
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Student Name: _______________________________
ID: _____________________
Experiment Date: __________________
Third order Butterworth filter
Volts/Div
CH1:
Fifth order Butterworth filter
CH2:
Volts/Div
Third order Chebyshev filter
Volts/Div
CH1:
CH1:
CH2:
Fifth order Chebyshev filter
CH2:
Volts/Div
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CH1:
CH2: