DOI 10.4010/2016.757
ISSN 2321 3361 © 2016 IJESC
Research Article
Volume 6 Issue No. 4
Active and Passive Filters: Wave Shapes of Magnitude and Phase
Angle
M. N. H. Khan1, M. M. Alam2, M. T. Anowar 3, M. D. Hossen4, K. A. Jamil5, M. S. Zahan6
Department of Electrical and Electronic Engineering
Uttara University, House-4 & 6, Road-15, Sector-6, Uttara Model Town, Uttara, Dhaka-12301, 2, 3, 4, 6
International Islamic University Malaysia, P.O. Box 10, 50728 Kuala Lumpur 5
Abstract:
To operate the maximum electronic based circuits need filters which is part and parcel in different sectors such as mechanical,
electrical, computer and so on. These filters can be either active or passive which actually constructed through amplifiers,
resistance, capacitance, inductance, transformers and so on. However, passive filters which are non linear shows more complex
such as transmission lines. Active and passive filters both are four individual kinds such as Low Pass Filter (LPF), High Pass
Filter (HPF), Band Pass Filter (BPF) and Band Reject Filter (BRF). In this paper will be shown the characteristic of these filters
with appropriate circuit diagrams as well as simulated result for both magnitude and phase angle.
Keywords: Low Pass Filter (LPF), High Pass Filter (HPF), Band Pass Filter (BPF), Band Reject Filter (BRF), Magnitude and
Phase angle.
I.
INTRODUCTION
Filters are importance for different purposes especially in
circuit design [1-2] and achieving good output signal [3-5]. In
instance, Finite Impulse Response (FIR) filters which can be
design easily to match a particular frequency for response
requirement [6]. To synthesize the desired filter
characteristics, an active filter uses amplifying elements,
especially an operational amplifier (op-amp) whose output is
connected to its input through passive components, usually
resistors and capacitors. To build filters with imaginary poles
using resistors and capacitors alone, feedback of the output to
the input is required. With any arbitrary gain active filters
have high input impedance and low output impedance. Most
important attribute of active filters is to eliminate inductors
thereby reducing the value of the filter's capacitors [7]. A filter
that uses no active components and amplifying elements (such
as, operational amplifiers, transistors etc.) and made up of
passive components (such as, resistors, capacitors and
inductors) is referred to as passive filter. It is the easiest
instrumentation of a given transfer function because of its
limited number of necessary components. Passive filters
generate slight noise and they can provide service well at very
high frequencies [7].
High Pass Filter:
The filter which uses amplifying elements, especially an
operational amplifier (op-amp) whose output is connected to
its input through passive components, usually RC (ResistorCapacitor) components and only allows high frequency signals
from its cut-off frequency is well known as Passive High Pass
Filter (PHPF) that shown in figure 1(b). In this case, op-amp
provides amplification and gain control.
II. CIRCUIT DIAGRAM OF FILTERS
1. Active Filters
Low Pass Filter:
Generally, the filter which only allows low frequency signals
from 0Hz to its cut-off frequency and usually constructed
using amplifying elements, especially an operational amplifier
(op-amp) whose output is connected to its input through
passive components, such as, RC (Resistor-Capacitor)
networks is referred to as Active Low Pass Filter (ALPF)
shown in figure 1(a).
Band Pass Filter
Usually, the filter which permits signals falling within a
certain frequency band setup between two points to pass
through while preventing both the lower and higher
frequencies either side of this frequency band and which is
constructed using amplifying elements, especially an
operational amplifier (op-amp) whose output is connected to
its input through passive components, such as, RC (ResistorCapacitor) networks is familiar as Active Band Pass Filter
(ABPF) (figure 1(c)).
International Journal of Engineering Science and Computing, April 2016
Fig 1(a): Circuit Diagram ALPF
Fig 1(b): Circuit Diagram AHPF
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Figure 2(c): Circuit Diagram PBPF
Fig 1(c): Circuit Diagram ABPF
Band Reject Filter:
The filter which uses amplifying elements, especially an
operational amplifier (op-amp) whose output is connected to
its input through passive components and which rejects signals
falling within a certain frequency band setup between two
points while permitting both the lower and higher frequencies
is known as Active Band Reject Filter (ABRF) (figure 1(d)).
Band Reject Filter
The filter which made from passive components (such as,
resistors, capacitors and inductors) and have no signal gain
and which rejects signals falling within a certain frequency
band setup between two points while permitting both the
lower and higher frequencies is familiar as Passive Band
Reject Filter (PBRF) (figure 2(d)).
Fig 2(d): Circuit Diagram PBRF
Fig 1(d): Circuit Diagram ABRF
2. Passive Filters
Low Pass Filter:
Usually, the filter which only allows low frequency signals
from 0Hz to its cut-off frequency and usually constructed
using simple RC (Resistor-Capacitor) networks is referred to
as Passive Low Pass Filter (PLPF) (figure 2(a)).
III. MAGNITUDE AND PHASE ANGLE
1.
Active Filters
Low Pass Filter:
In figure 3(a) is showing the magnitude of the low pass filter
which is simulated by using AC mode and Figure 3(b) is the
Phase Angle of ALPF.
20
18
SEL>>
16
DB(V(U1:OUT))
10.0V
7.5V
5.0V
100Hz
V(U1:OUT)
300Hz
1.0KHz
3.0KHz
10KHz
30KHz
100KHz
Frequency
Fig 3(a): Magnitude of ALPF.
0d
Fig 2(a): Circuit Diagram PLPF
High Pass Filter:
The filter which made from RC (Resistor-Capacitor)
components shown in figure 2(b) and only allows high
frequency signals from its cut-off frequency is known as
Passive High Pass Filter (PHPF).
Fig 2(b): Circuit Diagram PHPF
Band Pass Filter:
Generally, the filter which permits signals falling within a
certain frequency band setup between two points to pass
through while preventing both the lower and higher
frequencies either side of this frequency band and which is
constructed using passive components (such as, resistors,
capacitors and inductors) that shows in figure 2(c) and have no
signal gain is referred to as Passive Band Pass Filter (PBPF).
-50d
SEL>>
-100d
P(V(U1:OUT))
10.0V
7.5V
5.0V
100Hz
V(U1:OUT)
300Hz
1.0KHz
3.0KHz
10KHz
30KHz
100KHz
Frequency
Fig 3(b): Phase Angle of ALPF.
High Pass Filter:
To simulate the circuit diagram for showing up the magnitude
in figure 4(a) and phase angle in figure 4(b) done by AC
signal where used 50hz frequency.
200
0
SEL>>
-200
DB(V(U1:OUT))
4.0V
2.0V
0V
100Hz
V(U1:OUT)
300Hz
1.0KHz
3.0KHz
10KHz
30KHz
100KHz
Frequency
Fig 4(a): Magnitude of AHPF.
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2.
Passive Filters
Low Pass Filter:
In figure 7(a) is showing the magnitude of the low pass filter
which is simulated by using AC mode and Figure 7(b) is the
Phase Angle of PLPF.
160d
120d
P(V(U1:OUT))
4.0V
2.0V
20
SEL>>
0V
100Hz
V(U1:OUT)
300Hz
1.0KHz
3.0KHz
10KHz
30KHz
100KHz
Frequency
10
Fig 4(b): Phase Angle of AHPF.
Band Pass Filter:
In figure 5(a) is showing the magnitude of the Band pass filter
in the active mode condition where in figure 5(b) shows the
phase angle of ABPF.
0
0
DB(V2(C1))
10V
5V
SEL>>
0V
100Hz
V(C1:2)
300Hz
1.0KHz
3.0KHz
10KHz
30KHz
100KHz
Frequency
Fig 7(a): Magnitude of PLPF.
-100
0d
-200
DB(V(U2:OUT))
100uV
-50d
0V
SEL>>
-100d
P(V2(C1))
SEL>>
-100uV
0s
10V
1us
2us
3us
4us
5us
6us
7us
8us
9us
10us
V(U2:OUT)
Time
5V
Fig 5(a): Magnitude of ABPF.
0V
100Hz
V(C1:2)
1.0ud
300Hz
1.0KHz
3.0KHz
10KHz
30KHz
100KHz
Frequency
Fig 7(b): Phase Angle of PLPF.
0d
SEL>>
-1.0ud
P(V(U2:OUT))
100uV
0V
-100uV
0s
1us
2us
3us
4us
5us
6us
7us
8us
9us
10us
V(U2:OUT)
High Pass Filter:
To simulate the circuit diagram for showing up the magnitude
in figure 8(a) and phase angle in figure 8(b) done by AC
signal where used 50hz frequency.
Time
Fig 5(b): Phase Angle of ABPF.
40
Band Reject Filter:
Below in figure 6(a) shows the magnitude of the Band reject
filter and the simulated figure is time response.
0
-40
DB(V1(R1))
10V
5V
0
SEL>>
0V
100Hz
V(R1:1)
-25
300Hz
1.0KHz
3.0KHz
10KHz
30KHz
100KHz
Frequency
Fig 8(a): Magnitude of PHPF.
SEL>>
-50
DB(V(U2:OUT))
12.8924uV
100d
12.8922uV
50d
12.8920uV
18ms
19ms
V(R5:2)
20ms
21ms
22ms
23ms
24ms
25ms
26ms
27ms
28ms
29ms
30ms
31ms
32ms
Time
SEL>>
0d
Fig 6(a): Magnitude of ABSF.
P(V2(C1))
10V
1.0ud
5V
0d
0V
100Hz
V(R1:1)
-1.0ud
P(V(U2:OUT))
300Hz
1.0KHz
3.0KHz
10KHz
30KHz
100KHz
Frequency
12.8924uV
Fig 8(b): Phase Angle of PHPF.
12.8922uV
SEL>>
12.8920uV
18ms
19ms
V(R5:2)
20ms
21ms
22ms
23ms
24ms
25ms
26ms
27ms
28ms
29ms
30ms
31ms
32ms
Time
Fig 6(b): Phase Angle of ABSF.
Band Pass Filter:
In figure 9(a) is showing the magnitude of the Band pass filter
in the active mode condition where in figure 9(b) shows the
phase angle of PBPF.
Above figure 6(b) is showing the Phase angle form of the
Band stop filter.
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40
0
SEL>>
-40
DB(V2(R1))
10V
5V
0V
100Hz
V(C1:2)
300Hz
1.0KHz
3.0KHz
10KHz
30KHz
100KHz
Frequency
Fig 9(a): Magnitude of PBPF.
100d
0d
SEL>>
-100d
P(V2(R1))
10V
5V
0V
100Hz
V(C1:2)
300Hz
1.0KHz
3.0KHz
10KHz
30KHz
100KHz
Frequency
Fig 9(b): Phase Angle of PBPF.
Band Reject Filter:
Below in figure 10(a) shows the magnitude of the Band reject
filter and the simulated figure is time response.
20
0
-20
DB(V(L1:1))
10V
5V
SEL>>
0V
100Hz
V(L1:1)
300Hz
1.0KHz
3.0KHz
10KHz
30KHz
100KHz
Frequency
Fig 10(a): Magnitude of PBSF.
0d
acquisition systems subsume filters that will influence signals
in a manner described by the transfer function of the system.
Any analog or digital filter that could be applied in real time
during data acquisition would essentially introduce some
frequency-dependent phase shifts, which become large near
the filter’s passband borders. ‘Group delay’ is another
important term in frequency response (magnitude and phase
shift). It is an essential measure of delay eventually when the
phase response is non-linear. The phase shift at a known
frequency can be transferred into a time delay for a pure
sinusoid at that frequency. Time shift will decreases as the
frequency increases, if the phase shifts are constant across
frequencies. On the other hand, the phase response would be a
linear function of frequency, with the magnitude of the slope
reflecting the magnitude of the delay, if the phase shifts of a
system are the result of a pure time delay of the signal. The
negative derivative of the phase with respect to frequency, is
referred to as ‘group delay’ [8]. Four basic types of ideal
filters (Low Pass, High Pass, Band Pass and Band Reject)
have different magnitude functions [9]. Amplitude Modulation
(AM) and Phase Modulation (PM) is essential to gain a deep
insight to the origins and quantitative evaluations of every
important inter-harmonic effects, such as the behavior of the
power electronic devices [10]. In practical case, the phase
response is generally of lesser interest than the amplitude
response of the filter. So what, the phase response of the filter
is important in some applications. For example, a filter is an
element of a process control loop. Where, the total phase shift
is of concern, since it may influenced the loop stability [11].
V. CONCLUSION
The importance of filters is dramatically improved. Filter
actually used in different purposes especially in computer,
mechanical, electrical sector to do the design and simulation.
In above shows the importance of using active and passive
filters. Shows the simulation result in both magnitude and
phase angle of LPF, HPL, BPL and BRF through AC mode.
-100d
SEL>>
-200d
[1]
P(V(L1:2))
10V
5V
0V
100Hz
V(L1:1)
300Hz
1.0KHz
3.0KHz
10KHz
30KHz
100KHz
VI. REFERENCE
Zheng, Y., & He, J. (2013, October). A new
representation method based on mapping functions for
analog circuit automatic design. In Advanced
Computational Intelligence (ICACI), 2013 Sixth
International Conference on(pp. 171-176). IEEE.
Frequency
Fig 10(b): Phase Angle of PBSF.
[2]
Ohe, K., Konishi, M., & Imai, J. (2008, August). Design
support classifier of filter circuit structure. In SICE
Annual Conference, 2008 (pp. 2695-2699). IEEE.
[3]
Khan, H., Noman, M., Khan, S., Gunawan, T. S., &
Shahid, Z. (2013, November). Wave shaping with
reduced leakage current in transformer-less inverter.
In Smart
Instrumentation,
Measurement
and
Applications (ICSIMA), 2013 IEEE International
Conference on (pp. 1-5). IEEE.
[4]
Khan, M. N. H., Gunawan, T. S., Rahman, M. T., &
Khan, S. (2014, September). Evaluation of Various
Leakage Current Paths with Different Switching
Conditions.
In Computer
and
Communication
Engineering (ICCCE), 2014 International Conference
on (pp. 269-272). IEEE.
Above figure 6(b) is showing the Phase angle form of the
Band stop filter.
IV. DISCUSSION
The Low Pass, High Pass, Band Pass and Band Reject filters
are characterized by their frequency response. Frequency
response is most important feature of filters that indicates how
near-ideal their filter operation actually is. Filters of different
specifications are realized as mostly 2nd order active filters
utilizing amplifying components (op-amps). Their frequency
response is identified and the cut-off frequencies are
calculated. Generally, the frequency response is divided into
two parts. The first one is magnitude (amplitude) and another
one is phase parts. How closely the operable circuit imitates
the ideal filter characteristics, it can be indicated by the
magnitude (amplitude) curve of a filter. Physiological data
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[5]
Khan, M. N. H., Ahmad, K. J., Khan, S., &
Hasanuzzaman, M. (2015). Leakage Current Paths in
PV Transformer-Less Single-Phase Inverter Topology
and
Its
Mitigation
through
PWM
for
Switching. International Journal of Power Electronics
and Drive Systems, 6(1), 148-159.
[6]
Koilpillai, R. D., & Vaidyanathan, P. P. (1992). Cosinemodulated FIR filter banks satisfying perfect
reconstruction. Signal Processing, IEEE Transactions
on, 40(4), 770-783.
[7]
Kerry Lacanette, “A Basic Introduction to FiltersActive, Passive and Switched-Capacitor”- National
Semiconductor Application Note 779- April 1991.
[8]
M.J. Nelson et al, “Review of signal distortion through
metal microelectrode recording circuits and filters”Journal of Neuroscience Methods 169 (2008) 141–157.
[9]
R.C. Drof, Z. Wan, “Transfer Functions of Filters”- The
Electrical Engineering Handbook- Ed. Richard C. DorfBoca Raton: CRC Press LLC, 2000.
[10] R. Langella, A. Testa, “Amplitude and Phase
Modulation Effects of Waveform Distortion in Power
Systems”- Electrical Power Quality and Utilization,
Journal Vol. XIII, No. 1, 2007.
[11] H. Zumbahlen, “Phase Relations in Active Filters”Analog Dialogue 41-10, October 2007.
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