Passive Filter

Topics: Low-pass filter, Butterworth filter, Filter Pages: 10 (1527 words) Published: October 31, 2013
Experiment: The frequency response characteristics of Passive Filter Networks.

Aim:
The main aim of this experiment is to investigate the response and the characteristics of different orders of Butterworth low pass filters and 5th order of Chebychev low pass filter.

Experimental Methods (including diagrams)

a) 3rd order of Butterworth low pass filter

b) 5th order of Butterworth low pass filter

c) 7th order of Butterworth low pass filter

d) 5th order of Chebychev low pass filter

1. The above figures show the circuit diagram of 3rd order of Butterworth low pass filter, 5th order of Butterworth low pass filter, 7th order of Butterworth low pass filter and 5th order of Chebychev low pass filter. 2. First, T-connecter is installed on the signal generator. One end of the T connector is connected to Channel 1 of the oscilloscope, while the other end is connected to the input of the 3rd order of Butterworth low pass filter (black test box). 3. The output of the 3rd order of Butterworth low pass filter (black test box) is connected to Channel 2 of the oscilloscope. 4. The signal generator is adjusted to give 1V peak-to-peak voltage and 1 kHz frequency. 5. The traces on Channel 1 and Channel 2 of the oscilloscope are tuned to give more accurate readings. 6. The output amplitude and the phase difference for 1 kHz frequency are measured and tabulated in Table 1. The phase difference can be computed using the formula in the figure below. 7. Step 2 to 6 is repeated by using different frequencies such as 3 kHz, 7 kHz, 10 kHz, 15 kHz, 20 kHz and 30 kHz. 8. Then, step 2 to 7 are repeated by replacing the 3rd order Butterworth low pass filter with 5th order Butterworth low pass filter, 7th order Butterworth low pass filter and 5th order Chebychev low pass filter. The readings for each low pass filter networks are tabulated in Table 2, Table 3 and Table 4 respectively.

Results
A) 3rd order of Butterworth low pass filter

Table 1
Frequency (kHz)

Phase difference (degrees)
Amplitude (mV)

1
3.000
7.20
212
-7.453
3
3.477
34.56
212
-7.453
7
3.845
85.68
188
-8.496
10
4.000
122.40
148
-10.574
15
4.176
178.20
68
-17.329
20
4.301
201.60
34
-23.350
30
4.477
237.60
14
-31.057

Formula:
=

Graph 1: Graph of |H(jω)| against log10f

B) 5th order of Butterworth low pass filter

Table 2
Frequency (kHz)

Phase difference (degrees)
Amplitude (mV)

1
3.000
14.40
212
-7.453
3
3.477
56.16
208
-7.618
7
3.845
141.12
188
-8.496
10
4.000
208.80
132
-11.568
15
4.176
302.40
36
-22.853
20
4.301
345.60
14
-31.057
30
4.477
367.20
10
-33.979

Graph 2: Graph of |H(jω)| against log10f

C) 7th order of Butterworth low pass filter

Table 3
Frequency (kHz)

Phase difference (degrees)
Amplitude (mV)

1
3.000
21.60
220
-7.131
3
3.477
82.08
216
-7.290
7
3.845
196.56
180
-8.874
10
4.000
316.08
96
-14.334
15
4.176
432.00
16
-29.897
20
4.301
-
10
-33.979
30
4.477
-
8
-35.918

Graph 3: Graph of |H(jω)| against log10f

D) 5th order of Chebychev low pass filter

Table 4
Frequency (kHz)

Phase difference (degrees)
Amplitude (mV)

1
3.000
21.60
220
-7.131
3
3.477
73.44
196
-8.134
7
3.845
176.40
188
-8.496
10
4.000
273.60
164
-9.683
15
4.176
405.00
16
-29.897
20
4.301
-
10
-33.979
30
4.477
-
8
-35.918

Graph 4: Graph of |H(jω)| against log10f

Discussions:
A) Theory and Background of Two Different Passive Filter Network A passive filter network can be realized by using passive components such as inductor, capacitor and resistor in the circuit design. It does not include any active components, such as transistor and operational amplifier in the circuit design. Butterworth filter and Chebychev filter can be constructed using the passive components and they are two different passive filter network. The circuit design is similar for both passive filter network but...

References: 1. http://www.dspguide.com/ch20/1.htm
2. http://en.wikipedia.org/wiki/Butterworth_filter
3. http://en.wikipedia.org/wiki/Chebyshev_filter
4. http://www.electronics-tutorials.ws/filter/filter_8.html
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