EEL2186: Circuit and Signals SIG1


FACULTY OF ENGINEERING

LAB SHEET

CIRCUITS AND SIGNALS

EEL 2186

TRIMESTER 1 (2015/2016)

SIG1-Active Low-Pass Filter Design

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 op-amps 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 RC-filter network coupled to a voltage follower.

Figure 1: 1st order low-pass filter network

It can be shown that the transfer function is

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.

Figure 2: Second-order low-pass filter network

It can be shown that the transfer function is

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 low-pass 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 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.

3rd Order Filter

4th Order Filter

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.

Table 1: Higher-order low-pass filter parameters.

Order / 1st stage
RB/RA f` / 2nd stage
RB/RA f` / 3rd stage
RB/RA f` / Overall pass-band gain (dB)
Butterworth
3
4
5
6 / - 1
0.152  1
- 1
0.068 1 / 1.000 1
1.235  1
0.382  1
0.586 1 / - -
- -
1.382  1
1.482 1 / 6.0
8.2
10.3
12.5
1dB Chebyshev
3
4
5
6 / - 0.452
0.725 0.502
- 0.280
0.686 0.347 / 1.504 0.911
1.719 0.943
1.286 0.714
1.545 0.733 / - -
- -
1.820 0.961
1.875 0.977 / 8.0
13.4
16.2
21.8
2dB Chebyshev
3
4
5
6 / - 0.322
0.924 0.466
- 0.223
0.879 0.321 / 1.608 0.913
1.782 0.946
1.437 0.624
1.637 0.727 / - -
- -
1.862 0.964
1.901 0.976 / 8.3
14.6
16.9
23.2

Note: Normalized cutoff frequency, f` = 1/[2pRC ´ fc]

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 low-frequency 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.

Figure 4: Experimental setup to test the frequency response of a filter

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 are 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)  Establish the connections 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)  Please 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 to generate a 15kHz sine wave with 2V (peak-to-peak). Check the waveform using the oscilloscope.

3.  Set the DC power supply value to 24V and connect the supply terminals to the experiment board.

4.  Examine the output waveform 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 sine wave output of the function generator will sweep from about 5kHz to 25kHz.)

6.  Connect a probe from CH1 of the oscilloscope to the saw-tooth waveform.

7.  Set “Vert mode” of the oscilloscope to “CH2”.

8.  Connect a probe from CH2 of the oscilloscope to terminal P5.

9.  Check the filter response by connecting the function generator output to the input terminal of the filter P7, and the output of the filter to terminal P3.

10.  Construct the connection shown in Figure 4.

11.  Design the filters as per the following sections:

4.1. Third order Butterworth filter

Design a third order Butterworth low-pass filter with a cutoff frequency of 19.4kHz. Set C = 0.01mF for all the calculations.

The selected resistance value should be 820W for all 1st and 2nd stages of filters (Refer Table 1).

Construct the third order low-pass filter. Disconnect the saw-tooth waveform from the VCF input of the function generator in order to measure the overall pass-band gain. 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. Sketch the response curve on page 9 of the lab sheet.

4.2. Fifth order Butterworth filter

Design a fifth order Butterworth low-pass filter with a cutoff frequency of 19.4kHz.

Set C = 0.01mF for all the calculations.

Determine all the suitable resistance values (Refer Table 1).

Construct the fifth order low-pass filter. Disconnect the saw-tooth waveform from the VCF input of the function generator to measure the overall pass-band gain. 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. Sketch the response curve on page 9 of the lab sheet.

4.3. Third order Chebyshev filter

Design a third order 2dB Chebyshev low-pass filter with a cutoff frequency of 21.4kHz. Set C = 0.01mF for all the calculations.

The first stage of the resistance value can be calculated as follows:

Determine suitable resistance values for the rest of the resistors (Refer Table 1).

Construct the third order low-pass filter. Disconnect the saw-tooth waveform from the VCF input of the function generator to measure the overall pass-band gain. 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. Sketch the response curve on page 9 of the lab sheet.

4.4. Fifth order Chebyshev filter

Design a fifth order 2dB Chebyshev low-pass filter with a cutoff frequency of 20.1kHz. Set C = 0.01mF for all the calculations.

The first stage of the resistance value can be calculated as follows:

Determine suitable resistance values for the rest of the resistors (Refer Table 1).

Construct the fifth order low-pass filter. Disconnect the saw-tooth waveform from the VCF input of the function generator to measure the overall pass-band gain. 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. Sketch the response curve on page 9 of the lab sheet.

Important:

·  Your report must contain:-

i.  Introduction

ii. Results

iii.  Analysis/discussion

iv.  Conclusion

·  For the discussion, describe the characteristics, advantages and disadvantages of each filter by analysing their responses.

·  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 and use your own findings and results.

·  You MUST use the FOE lab report cover template. The template can be downloaded at http://foe.mmu.edu.my/v3/lab/form/student_lab-report_cover-1%202010.doc

·  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 entertained.

·  This lab report carries 5% of the total course marks.

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