KEEE 2276
EXPERIMENT TL2: FILTER (COMMUNICATION LAB)
MOHD FUAD BIN SARMAN (KEE 120026)
DEMONSTRATOR: MR. MD RAKIBAL
ABSTRACT
This experiment is about the study of the characteristics of some common filters. In
this experiment, there are three types of filter that had been looked on which are low-pass
filter, high-pass filter and band-pass filter. Here the frequency response of each of the
filters are being studied to understand the characteristics of their cut-off frequencies and
the insertion loss. All the values are being measured and recorded in the following
section.
INTRODUCTION
A filter is a circuit that passes a specific range of frequencies while rejecting other
frequencies. A passive filter consists of passive circuit elements, such as capacitors,
inductors, and resistors. The most common way to describe the frequency response of a
filter is to plot the filter voltage gain (Vo/Vin) in dB as a function of frequency (f). The
frequency at which the output power gain drops to 50% of the maximum value is called
the cutoff frequency (fc). When the output power gain drops 50%, the voltage gain drops
3 dB (0.707 of the maximum value). When the filter dB voltage gain is plotted as a
function of frequency on a semilog graph using straight lines to approximate the actual
frequency response, it is called a Bode plot. A Bode plot is an ideal plot of filter
frequency response because it assumes that the voltage gain remains constant until the
cutoff frequency is reached. The filter network voltage gain in dB is calculated from the
actual voltage gain (A) using the equation
AdB = 20 log10 A
where A = Vo/Vin
There are four basic types of filters, lo-pass filter, high-pass filter, band-pass filter,
and band-stop filter. A low-pass filter is designed to pass all frequencies below the cutoff
frequency and reject all frequencies above the cutoff frequency. A high-pass filter is
designed to pass all frequencies above the cutoff frequency and reject all frequencies
below the cutoff frequency. A band-pass filter passes all frequencies within a band of
frequencies and rejects all other frequencies outside the band. A band-stop filter rejects
all frequencies within a band of frequencies and passes all other frequencies outside the
band. A band-stop filter is often referred to as a notch filter. In this experiment, we will
study low-pass, high-pass and band-pass filters.
A low-pass R-C filter is shown in figure 1. At frequencies well below the cutoff
frequency, the capacitive reactance of capacitor C is much higher than the resistance of
resistor R, causing the output voltage to be practically equal to the input voltage (A = 1)
and constant with variations in frequency. At frequencies well above the cutoff frequency,
the capacitive reactance of capacitor C is much lower than the resistance of resistor R,
causing the output voltage to decrease 20 dB per decade increase in frequency. At the
cutoff frequency, the capacitive reactance of capacitor C is equal to the resistance of
resistor R, causing the output voltage to be 0.707 times the input voltage (-3 dB). The
expected cutoff frequency (fc) of the low-pass filter in figure 1, based on the circuit
component values, can be calculated from
XC = R
1
R
2πf C C
Solving for fc produces the equation
fC 
1
2RC
A high-pass R-C filter is shown in figure 2. At frequencies well above the cutoff
frequency, the capacitive reactance of capacitor C is much lower than the resistor R,
causing the output voltage to be practically equal to the input voltage (A = 1) ad constant
with variations in frequency. At frequencies well below the cutoff frequency, the
capacitive reactance of capacitor C is much higher than the resistance of resistor R,
causing the output voltage to decrease 20 dB per decade decrease in frequency. At the
cutoff frequency, the capacitive reactance of capacitor C is equal to the resistance of
resistor R, causing the output voltage to be 0.707 times the input voltage (-3 dB). The
expected cutoff frequency (fc) of the high-pass filter in figure 2, based on the circuit
component values, can also be calculated from
fC 
1
2RC
When the frequency at the input of low-pass filter increases above the cutoff
frequency, the filter output voltage drops at a constant rate. When the frequency at the
input of a high-pass filter decreases below the cutoff frequency, the filter output voltage
also drops at a constant rate. The constant drop in filter output voltage per decade
increase (×10) or decrease (÷10) in frequency is referred to as roll-off. An ideal low-pass
or high-pass filter would have an instantaneous drop at the cutoff frequency (fc), with full
signal level on one side of the cutoff frequency and no signal level on the other side of the
cutoff frequency. Although the ideal is not achievable, actual filters roll off at -20
dB/decade per pole (R-C circuit). A two-additional pole filter has two R-C circuits tuned
to the same cutoff frequency and rolls off at -40 dB/decade. Each additional pole (R-C
circuit) will cause the filter to roll off on additional -20 dB/decade. Therefore, an R-C
filter with more poles (R-C circuits) more closely approaches an ideal filter. In a one-pole
filter, as shown in figure 1 and 2, the phase difference between the input and the output
will change by 90 degrees over the frequency range and be 45 degrees at the cutoff
frequency. In a two-pole filter, the phase difference will change by 180 degrees over the
frequency range and be 90 degrees at the cutoff frequency.
Figure 1 Basic configuration of low-pass filter.
Figure 2 Basic configuration of high-pass filter.
Figure 3 Basic configuration of band-pass filter.
Figure 3 shows band-pass filter circuit. By connecting or “cascading” together a
single Low Pass Filter circuit with a High Pass Filter circuit, we can produce another type
of passive RC filter that passes a selected range or “band” of frequencies that can be
either narrow or wide while attenuating all those outside of this range. This new type of
passive filter arrangement produces a frequency selective filter known commonly as a
Band Pass Filter or BPF for short.
Unlike a low pass filter that only pass signals of a low frequency range or a high pass
filter which pass signals of a higher frequency range, a Band Pass Filters passes signals
within a certain “band” or “spread” of frequencies without distorting the input signal or
introducing extra noise. This band of frequencies can be any width and is commonly
known as the filters Bandwidth.
Bandwidth is commonly defined as the frequency range that exists between two
specified frequency cut-off points ( ƒc ), that are 3dB below the maximum centre or
resonant peak while attenuating or weakening the others outside of these two points.
Then for widely spread frequencies, we can simply define the term “bandwidth”, BW
as being the difference between the lower cut-off frequency ( ƒc
cut-off frequency ( ƒc
HIGHER
LOWER
) and the higher
) points. In other words, BW = ƒH – ƒL. Clearly for a pass
band filter to function correctly, the cut-off frequency of the low pass filter must be
higher than the cut-off frequency for the high pass filter.
OBJECTIVE
To measure the response of a low pass filter, a high pass filter, and a band pass filter and
study an application.
RESULT AND DISCUSSION
TEST 1: LOW-PASS FILTER
Given Rg = RL
= 600 Ω.
Set V0 = 20 V.
Hence
V1 =
10 V.
Design capacitance and inductance values:
C1 = C3 =
Insertion loss
9.9 nF and L2 = 2.45 mH.
= 20 log10 (10/V2) dB
Measure values for low-pass filter:
C1 =
12.2 nF
C3 =
18.9 nF
L2 = 2.4 mH
F (kHz)
10
20
30
40
50
60
70
80
90
100
120
140
160
180
200
V2 (V)
9.200
8.800
9.000
9.000
6.200
3.680
2.080
1.280
1.040
0.800
0.352
0.216
0.188
0.148
0.120
Insertion loss (dB)
0.724
1.110
0.915
0.915
4.152
8.683
13.639
17.856
19.659
21.938
29.069
33.311
34.517
36.595
38.416
Table 1 Tabulation of V2 and insertion loss with respective frequencies of low-pass filter.
Frequency, f (Hz)
0
0
50
100
150
200
250
5
Insertion loss (dB)
10
15
20
25
30
35
40
45
Graph 1 Graph of insertion loss versus frequency for low-pass filter.
The 3 dB frequency (cutoff frequency) is 47.2 kHz.
The dB difference at 80 and 160 kHz is obtained;
34.517 – 17.856 = 16.661 dB/octave.
For low-pass filter, only the input signal with frequencies below the cut off frequency
can pass through the circuit. Bode plot shows that for low frequency, H () is high
and vice versa. There are not much insertion loss for the low input frequencies.
An application of the Low pass filter
Figure 4 Application of low-pass filter
For a square wave input signal, frequency f = 10, 20, 30 and 40 kHz, the output
waveforms (CRO2) are as followed.
Figure 5 Frequency = 10kHz.
Figure 6 For frequency = 20kHz.
Figure 7 For frequency = 30kHz.
Figure 8 For frequency = 40kHz.
From the graphs obtained, it can be seen that a low-pass filter will only allow signal with
frequencies lower than the cut -off frequency to pass through.
A low-pass filter is a circuit that can be designed to reshape, modify or reject all
unwanted frequencies of an electrical signal. It also accepts only those signals wanted by
the circuit's designer. There are two basic types of circuits capable of achieving this
objective: the inductive low-pass filter in and the capacitive low-pass filter.
Graph 1 shows how the low frequency wave is allowed to pass while the higher one
is rejected from achieving any gain which result in attenuation of higher frequency. From
the scope obtained above in experimenting the function of low-pass filter, observation
stated that the lower the frequency, the higher the gain in which it is exceeding the
limited amplitude being set, thus producing a square wave. However, once the frequency
is increasing, the amplitude of the wave is getting smaller means an attenuation is
occurred. Thus, this prove the concept of low-pass filter.
The input signal is a square wave which by definition consists of an infinite number
of odd harmonic sine waves. So when filtering such a square wave, some of these sines
waves contained in the square wave are filtering out. Therefore, it is very natural to see
the ringing effect for a lower frequency in which in this test, we can observed it when
applying 10kHz and 20kHz frequencies.
In the Fourier analysis, we can shows that the periodic waveform such as a square
wave input signal consists of harmonic component which frequency is doubling or
multiplied of the input signal. At here, the low pass filter act as a filter to filter out all the
components that frequency is higher than 50 kHz. For those components that frequency is
lower than 50 kHz will pass through the circuit.
In this experiment, by using a 10 kHz input signal, the harmonic component with the
frequency of 10 kHz, 20 kHz, 30 kHz, 40 kHz and 50 kHz will pass through the circuit.
Also, if we are using a 20 kHz input signal, the harmonic component with 20 kHz and 40
kHz will pass through the circuit. Because the cases above allow two, or more than two
harmonic component to pass through the circuit, therefore the superposition of the
harmonic component caused the waveform that we are detected in the output is not a
purely sinusoidal waveform.
However, for the 30 kHz and 40 kHz input signal, the circuit only allow one
harmonic component to pass through the circuit, so we can detect a purely sinusoidal
waveform from the output.
TEST 2: HIGH-PASS FILTER
Given Rg = RL = 600 Ω.
Set V0 = 20 V.
Design capacitance and inductance values:
C1 =
C3 = 2.85 nF and L2 =
1.5 mH.
Measured values of high-pass filter:
C1 =
12.2 nF
C3 =
18.9 nF
L2 = 2.4 mH.
F (kHz)
10
20
30
40
50
60
80
100
120
150
200
V2 (V)
0.037
0.248
1.000
2.640
5.840
8.320
8.800
8.600
8.600
8.600
8.600
Insertion loss (dB)
48.636
32.111
20.000
11.568
4.672
1.598
1.110
1.310
1.310
1.310
1.310
Table 2 Tabulation of V2 and insertion loss with respective frequencies of high-pass
filter.
Frequency, f (kHz)
0
0
50
100
150
200
250
Insertion loss (dB)
10
20
30
40
50
60
Graph 2 Graph of insertion loss versus frequency for high-pass filter.
The 3dB frequency is 53.2 kHz.
The dB difference at 10 and 20 kHz is obtained; 48.636 - 32.111 = 16.525 dB/octave.
Graph 2 shows the properties of high-pass filter in which only allows high frequency
to pass through while the lower one is attenuated. From the graph above, once passing
from the cut-off frequency, the insertion loss is almost zero in which all the frequencies
after that is accepted in the range after the cutoff frequency. Thus, this prove the
characteristics of the high-pass filter. Basically, the properties of the high-pass filter is not
much differ instead of both of them are opposite of each other.
TEST 3: BAND-PASS FILTER
For Vo = 20 volts and frequencies 47 to 55 kHz, V2 is measured and the insertion loss is
calculated in dB.
F (kHz)
47.0
48.0
49.0
49.5
50.0
50.5
51.0
51.5
52.0
52.5
53.0
53.5
54.0
55.0
V2 (V)
0.272
1.400
2.420
2.560
2.580
2.460
1.980
1.460
0.940
0.560
0.440
0.320
0.220
0.134
Insertion loss (dB)
31.309
17.077
12.324
11.835
11.768
12.181
14.067
16.713
20.537
25.036
27.131
29.897
33.152
37.458
Table 3 Tabulation of V2 and insertion loss with respective frequencies of high-pass
filter.
Frequency, f (kHz)
0
42
44
46
48
50
52
54
Insertion Loss (dB)
5
10
15
20
25
30
35
40
Graph 3 Graph of insertion loss versus frequency for band-pass filter.
56
The cut-off frequencies are 48.3 kHz and 51.15 kHz.
The center frequency is:
Center frequency
=
f1 f 2
=
(48.3)(51.15)
= 49.70kHz
The 40 dB frequencies are 46.4 kHz and 55.90 kHz.
Graph 3 shows the characteristics of band-pass filter in which allows frequencies to
pass through a band while the rest while lie outside the and will be attenuated. The graph
above has an allowed band of 2.8 kHz in which out of this range of band, the frequency
will be eliminated.
A Bandpass filter Application - Frequency Multiplier
Figure 9 Application of bandpass filter.
A frequency multiplier is a device for multiplying by an integer the frequency of a
circuit. It is an electronic circuit that generates an output signal of which the output
frequency is a multiple (or harmonic) of the input frequency. Frequency multipliers
consist of a nonlinear circuit which distorts the input signal and generates multiples of the
input signal. A band-pass filter selects the desired harmonic frequency and removes the
unwanted fundamental as well as other harmonics from the output.
The main mechanism for a frequency multiplier is called non-linear signal transfer.
When a frequency generator output is viewed on a spectrum analyzer, there is a single
vertical line with a top end aligned with the amplitude of the signal. The level can be 1
volt (V). The horizontal axis indicates the frequency of this signal. For instance, the
frequency of a 500 million hertz (Hz) or 500 megahertz (MHz) signal will be indicated on
the horizontal axis of the spectrum analyzer.
When the reference frequency is fed into a non-linear device such as a class C
amplifier or a diode detector, the result is a frequency spectrum with harmonics, or
multiples, of the original frequency. Using a band-pass filter with a capability to pass
only the desired outputs, the result is the desired harmonic.
The frequency multiplier approach is used in special cases where there is only one
output frequency required, due to the various combinations of bandpass filters needed to
produce clean sinusoidal signals. For instance, a 10 billion cycles per second or
10-gigahertz (GHz) signal may not be possible to generate directly. It may be possible to
use a 5 GHz oscillator, or frequency generator, followed by a multiplier and a bandpass
filter tuned to 10 GHz.
Due to the limitations of the device used during this experiment, the experimental
results are unattainable. Thus, no experimental results to be compared with the theoretical
one.
CONCLUSION
From this experiment, we are proving the theory of the characteristics of filters.
Low-pass filter allows frequencies lower than the cut-off frequency while high-pass filter
allows frequencies higher than the cut-off frequencies. Band-pass filter allows
frequencies in the bandwidth. These filter also have advantages which beneficial in
industries. Some of the applications are studied in this experiment.
REFERENCES
1.
Simon Haykin, An Introduction To Analog And Digital Communications, John Wiley & Sons,
1989.
2.
Richard C. Jaeger, Microelectronic Circuit Design, McGraw-Hill Companies, Inc., 1997
3.
James W. Nilsson, Susan A. Riedel, Electric Circuits, 5th Edition, Addison-Wesley Publishing
Company, 1996.