The 7th International Conference on Engineering and Technology
ICET-2015, Phuket, June 19-20, 2015
Prince of Songkla University, Faculty of Engineering
Hat Yai, Songkhla, Thailand 90112
Analysis of Active Filter Circuit Basic using
MATLAB-GUI for Electrical Engineering
Education
Sommart Khamkleang
Program of Industrial and Technology, Faculty of Industrial Technology, Songkhla Rajabhat University
160, Moo 4, Tambon Khoa-Roob-Chang, Muang District, Songkhla, Thailand 90000
E-mail: khamkleang@gmail.com
Abstract: This paper presents an analysis of active
filters circuit with graphical user interface developed for
electrical engineering studies. Four modules included in
the package are low-pass filter circuit, high-pass filter
circuit, band-pass filter circuit, and band-rejection filter
circuit. The design environment of this program is based
on the m-file of Matlab that provides the drawing
function and the graphical user interface development
environment, GUIDE. The simulated results obtained
through the presented methodology have shown close
agreement with experimental results thus validating the
performance of this software tool.
Key Words: MATLAB, graphical user interface, active
filter
1. INTRODUCTION
A comparison of passive filters and active filters as
follows: the advantages of each filter type, passive filter
are, no power supply required, can handle large currents
and high voltages, very reliable, least number of
components for given filter, noise arises from resistances
only, no bandwidth limitation, and active filter are, no
inductors, easier to design, high impedance input and
low impedance output for minimal loading, can produce
high gains, generally easier to tune, and small in size and
weight. The disadvantages of each filter type, passive
filter are, inductors large for lower frequencies, some
inductors (non-toroidal) may require shielding, limited
standard sizes, often requiring variable inductors and
therefore tuning, low tolerance inductors (1-2%) very
expensive, must be designed with consideration to input
and output loading, generally not amenable to
miniaturization, no power gain possible, no voltage gain,
and active filter are, power supply required, susceptible
to intermodulation, oscillations, susceptible to parasitic
from DC output offset voltage and input bias currents, op
amp gain bandwidth constrained, op amp slew rate
constrained, can require many components [1]. The
advantages and disadvantages mentioned above. It's as
difficult for students to understand. The solution Wythe
One popular use today is the implementation of
computer-aided analysis and design models.
Computer-aided circuit analysis has been a powerful
and widely used assistant tool of circuit analysis and
design accompanied with the development of modem
electrical technology and computer. MATLAB has
already been a powerful tool in developing circuit
analysis calculation software, which can process
scientific calculation, sign calculation and graphic
process. Meanwhile it can figure out some peculiar
problems which are out of the ability of Multisim. But
now, circuit analysis calculation of MATLAB mainly
aims at particular problems, not for all. From the trends
of software development, it is can be seen that friendly
user interface has been basic interactive portal. The
graphic user interface design tool of MATLAB GUIDE,
which supports GUI, can design easily-manipulated and
convenient interface with menus and controls [2-4].
Considerable research efforts are reported on
developed of MATLB-GUI in the electrical engineering,
highlighting the simplicity and friendly of this system [59]. Compared with C and Labview, Matlab is easier to
understand, convenient for image display and benefits
for system optimization, because of its strong numerical
calculation and various integrated image processing and
instrument control toolboxes [10]. Therefore, Matlab
provides an alternative approach to passive and active
filter design, which will be discussed of detail in the
section, so on.
2. BACKGROU CONCEPT OF THE PROGRAM
The developed software package includes four
modules. Theoretical background of each module is
briefly described below [11-13].
2.1 Low-Pass Filters
The transfer function of a single stage is:
Ai ( s) 
A0
.
1  ai s  bi s 2
(1)
For a first-order filter, the coefficient b is always zero
(b1=0), thus yielding:
A( s) 
A0
.
1  a1s
(2)
The first-order and second-order filter stages are the
building blocks for higher-order filters. Often the filters
operate at unity gain (A0=1) to lessen the stringent
demands on the op-amp’s open-loop gain.
Fig.1 shows the cascading of filter stages up to the
sixth order. A filter with an even order number consists
of second-order stages only, while filters with an odd
order number include an additional first-order stage at
the beginning.
With b=0 for all first-order filters, the transfer
function of a first-order filter simplifies to:
A( s ) 
A0
.
a
1 1
s
(5)
2.3 Band-Pass Filter
In Section 2.2, a high-pass response was generated
by replacing the term S in the low-pass transfer function
with the transformation 1/s. Likewise, a band-pass
characteristic is generated by replacing the S term with
the transformation:
1 
1
 s  .
 
s
(6)
In this case, the pass-band characteristic of a lowpass filter is transformed into the upper pass-band half of
a band-pass filters. The upper pass-band is then mirrored
at the mid frequency, f m (Ω=1), into the lower passband half (Fig.3).
Fig.1. Cascading filter stages for higher-order filters
2.2 High-Pass Filters
By replacing the resistors of a low-pass filter with
capacitors, and its capacitors with resistors, a high-pass
filter is created in show Fig.2.
Fig.3. Low-pass to Band-pass transition
The corner frequency of the low-pass filter
transforms to the lower and upper –3 dB frequencies of
the band-pass, Ω1 and Ω2. The difference between both
frequencies is defined as the normalized bandwidth ΔΩ:
  1   2 .
(6)
The normalized mid frequency, where Q = 1, is:
 m  1   21.
(7)
In analogy to the resonant circuits, the quality factor
(Q) is defined as the ratio of the mid frequency ( f m ) to
the bandwidth (B):
fm
fm
1


.
B
f 2  f1 2  1
1
Q
.

Q
Fig.2. Low-pass to High-pass transition through
components exchange
The general transfer function of a high-pass filter is
then:
A( s ) 
A
.
a
b
 (1  1  12 )
i
s s
(3)
With A∞ being the passband gain.
Since Equation (3) represents a cascade of secondorder high-pass filters, the transfer function of a single
stage is:
Ai ( s ) 
A
.
a b
(1  1  12 )
s s
(4)
(8)
The simplest design of a band-pass filter is the
connection of a high-pass filter and a low-pass filter in
series, which is commonly done in wide-band filter
applications. Thus, a first order high-pass and a firstorder low-pass provide a second-order band-pass, while
a second-order high-pass and a second-order low-pass
result in a fourth-order band-pass response.
2.4 Band-Rejection Filter
A band-rejection filter is used to suppress a certain
frequency rather than a range of frequencies.
Two of the most popular band-rejection filters are
the active twin-T and the active Wien-Robinson circuit,
both of which are second-order filters.
To generate the transfer function of a second-order
band-rejection filter, replace the S term of a first-order
low-pass response with the transformation in (9):

1
s
s
(9)
be expressed as an existent circuit selected of the active
filter circuits under study, after providing data input, the
user can select one of the four modules in the program
and performs studies.
Start
Which gives:
A0 (1  s 2 )
As  
.
1    s  s 2
Input
(10)
Thus the pass-band characteristic of the low-pass
filter is transformed into the lower pass-band of the
band-rejection filter. The lower pass-band is then
mirrored at the mid frequency, f m (Ω=1), into the upper
pass-band half (Fig.4).
Module Option
Low-pass
Band-pass
High-pass
Band-reject
Fig. 5. Flowchart of the construction of the developed
software.
4. EXECUTION DISPLAY OF THE DEVELOPED
PROGRAM
Fig.4. Low-pass to Band-rejection transition
The corner frequency of the low-pass transforms to
the lower and upper –3dB frequencies of the bandrejection filter Ω1 and Ω2. The difference between both
frequencies is the normalized bandwidth ΔΩ:
   max   min .
(11)
Identical to the selectivity of a band-pass filter, the
quality of the filter rejection is defined as:
Q
fm
1

.
B 
Fig. 6 shows the main display for execution control
of the program. When the main display is brought up, the
user must select the input data format. The data
contained in the input file includes the low-pass filter,
high-pass filter, band-pass filter and band-rejection filter.
(12)
Therefore, replacing ΔΩ in Equation (10) with 1/Q
yields:
As  
A0 (1  s 2 )
.
1
2
1  s  s
Q
(13)
3. FLOWCHARAT AND GUI OF THE
DEVELOPED PROGRAM
The proposed active filter circuit analysis program is
developed under Matlab environment, where the merits
of universal and effective computation capabilities of
MATLAB, user-friendly GUIDE, and the convenient
drawing function provided by m-file are adopted in the
development. The purpose of this program is to facilitate
the user’s understanding of active filters circuit studies.
Peculiar features and prominent functions of this
program include
1. Simple displays.
2. Flexible input data format.
3. Output results are easily understood.
Fig. 5 depicts the flowchart of the developed
program. As the user accesses the main screen, the input
data format must be determined first. The input data can
Fig. 6. Main display for execution control of the
program.
To have a better understanding for users about the
developed program, a band-pass filter test is
demonstrated in the applications (Fig.7). When the user
chooses to band-pass filter analysis, this program will
open a set of value in GUI (Value of circuit element) as
follows; V (t )  10 sin( 2f  0 ), R1  R2  47  , and
C1  1F , f1  10 H Z , f 2  100 H Z , and can be
calculated, R  1591 .55, C2  0.1F ,
f m  31.62 H Z , bandwidth = 90 HZ and Q = 0.351 as
shown in Fig. 8.
5. CONCLUSION
This paper presents a User-friendly educationoriented active filter circuit simulation tool developed
under Matlab/ m-file and GUI environments. At present,
main modules of the software package include low-pass
filter, high-pass filter, band-pass filter, and bandrejection filter. This package can be used in the
classroom or by practicing engineers. The simulation
results are in accordance with theory.
Fig.7. Band-pass filters circuit at test.
Fig.8. The design parameters of f 0  f m , bandwidth and
quality factor (Q) using program.
Fig.8. Response of the band-pass filters circuit of the
program.
The analysis of the circuit of Fig. 9 shows that the
response of the output voltage ( VO ( j ) ) at the cut-off
frequency ( f1 , f 2 ) = 7.07 V. Considering of bode plot,
the size of the cut-off frequency response ( f1 , f 2 ) = -3.0
dB, the angle response the range -92 to -268 degrees,
when considering the middle frequency ( f m ) with an
angle of -180 degrees, and the frequency ( f1 ) is equal to
the angle of -141 degrees and the frequency ( f 2 ) is
equal to the angle of -219 degrees.
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