ArticlePDF Available

Abstract and Figures

This paper presents a high order filter for the Butterworth filters up to 8 th and 9 th order. The higher order filters are formed by using the combination of second and third order filters. While designing the Band-Pass Butterworth filter, four parameters need to be specified such as Ap (dB attenuation in the pass band), As (dB attenuation in the stop band), fp (frequency at which Ap occurs) and fs (frequency at which As occurs). The design procedure involves two steps, the first step is to find the required order of the filter and the second step is to find the scale factor that must be applied to the normalized parameter values. The Band-Pass Butterworth filler is a combination between low pass and high pass For the low pass Butterworth filter, the value of a resistor that has been used are 100KΩ and the value of the capacitor is found by scaled inversely with the frequency and the selected resistor value. While for the high pass Butterworth filter, the value of a capacitor that has been used is 0.05µF and the resistor value is found by scaled inversely with the frequency and the selected resistor value. The Butterworth Band-Pass filler required to bypass certain band of interest while suppressing the frequency below and above than pass band. Two configurations design circuit was tested by using LTspice software.
Content may be subject to copyright.
Design of Butterworth Band-Pass Filter
32
Politeknik & Kolej Komuniti Journal of Engineering and Technology, Vol.1, 2016
eISSN 0128-2883
Design of Butterworth Band-Pass Filter
Siti Farah Binti Hussin
Electrical Engineering Department
Polytechnic Tuanku Sultanah Bahiyah, Kulim, Kedah
E-mail: farah@ptsb.edu.my
Gauri a/p Birasamy
Electrical Engineering Department
Polytechnic Tuanku Sultanah Bahiyah, Kulim, Kedah
E-mail: b.gauri @ptsb.edu.my
Zunainah Binti Hamid
Electrical Engineering Department
Polytechnic Tuanku Sultanah Bahiyah, Kulim, Kedah
E-mail: zunainah @ptsb.edu.my
Abstract
This paper presents a high order filter for the Butterworth filters up to 8th and 9th order.
The higher order filters are formed by using the combination of second and third order
filters. While designing the Band-Pass Butterworth filter, four parameters need to be
specified such as Ap (dB attenuation in the pass band), As (dB attenuation in the stop
band), fp (frequency at which Ap occurs) and fs (frequency at which As occurs). The
design procedure involves two steps, the first step is to find the required order of the
filter and the second step is to find the scale factor that must be applied to the
normalized parameter values. The Band-Pass Butterworth filler is a combination
between low pass and high pass For the low pass Butterworth filter, the value of a
resistor that has been used are 100KΩ and the value of the capacitor is found by scaled
inversely with the frequency and the selected resistor value. While for the high pass
Butterworth filter, the value of a capacitor that has been used is 0.05µF and the resistor
value is found by scaled inversely with the frequency and the selected resistor value.
The Butterworth Band-Pass filler required to bypass certain band of interest while
suppressing the frequency below and above than pass band. Two configurations design
circuit was tested by using LTspice software.
Keywords: Ap, As, LTspice.
1. Introduction
A filter is a system that processes a signal in some desired fashion. A
continuous-time signal or continuous signal of x(t) is a function of the
continuous variable t. A continuous-time signal is often called an analog
signal. A discrete-time signal or discrete signal x(kT) is defined only at
discrete instances t=kT, where k is an integer and T is the uniform
spacing or period between samples. There are two broad categories of
filters which are an analog filter process continuous-time signals and a
digital filter process discrete-time signals. The analog or digital filters can
be subdivided into four categories, low pass filters, high pass filters, band
stop filter and bandpass filters.There are a number of ways to build
filters and of these passive and active filters are the most commonly used
Design of Butterworth Band-Pass Filter
33
Politeknik & Kolej Komuniti Journal of Engineering and Technology, Vol.1, 2016
eISSN 0128-2883
in voice and data communications[1]. The passive filters use resistors,
capacitors, and inductors (RLC networks). To minimize distortion in the
filter characteristic, it is desirable to use inductors with high quality
factors (remember the model of a practical inductor includes a series
resistance), however, these are difficult to implement at frequencies below
1 kHz due to the particularly non-ideal (lossy) as well as bulky and
expensive. The active filters overcome these drawbacks and are realized
using resistors, capacitors, and active devices (usually op-amps)[2]. The
function of filters is to eliminate background noise, radio tuning to a
specific frequency, direct particular frequencies to different speakers,
modify digital images and remove specific frequencies in data analysis.
The approximations to the ideal filter are the Butterworth
filter,Chebyshev filter and Bessel filter. The Butterworth filter is a type
of signal processing filter designed to have as flat a frequency response as
possible in the passband. It is also referred to as a maximally flat
magnitude filter. The frequency response of the Butterworth filter is
maximally flat (has no ripples) in the passband and rolls off towards zero
in the stopband.When viewed on a logarithmic Bode plot the response
slopes off linearly towards negative infinity. A first-order filter's response
rolls off at −6 dB per octave (−20 dB per decade) (all first-order lowpass
filters have the same normalized frequency response). A second-order
filter decreases at −12 dB per octave, a third-order at −18 dB and so on.
Butterworth filters have a monotonically changing magnitude function
with ω, unlike other filter types that have non-monotonic ripple in the
passband and/or the stopband. Compared with a Chebyshev Type I/Type
II filter or an elliptic filter, the Butterworth filter has a slower roll-off, and
thus will require a higher order to implement a
particular stopband specification, but Butterworth filters have a more
linear phase response in the pass-band than Chebyshev Type I/Type II
and elliptic filters can achieve.
2. Literature Review
Analog filters can be found in almost every electronic circuit. It used as
for pre-amplification, equalization and tone control in audio systems. In
communication systems, filters are used for tuning in specific frequencies
and eliminating others. Digital signal processing systems use filters to
prevent the aliasing of out-of-band noise and interference[3]. The data
acquisition system signal chain that includes an analog filter is shown in
Figure 1.
Figure 1. The data acquisition system signal chain can utilize analog or
digital filtering techniques or combination of both
Bandpass filters play a significant role in wireless communication
systems. Transmitted and received signals have to be filtered at a certain
center frequency with a specific bandwidth. Figure 2 shows the Band-
Pass filter specifications and frequency response.
Design of Butterworth Band-Pass Filter
34
Politeknik & Kolej Komuniti Journal of Engineering and Technology, Vol.1, 2016
eISSN 0128-2883
Figure 2. Band-Pass filter specifications and frequency response
The Butterworth filter is one type of signal processing filter design. It is
designed to have a frequency response which is as flat as mathematically
possible in the pass band. Butterworth solved the equations for two and
four pole filters and showed how the latter could be cascaded when
separated by vacuum tube amplifiers [3]. This made possible the
construction of higher order filters in spite of inductor losses.
Butterworth discovered that it was possible to adjust the component
values of the filter to compensate for the winding resistance of the
inductors. Figure 3 show the Frequency Response of the Butterworth
filter.
Figure 3. Frequency Response of the Butterworth filter
3. Methodology
This section of this paper will presented about the order and
configuration of Butterworth band-pass filter by using LTSpice as the
tools for the simulation and make a comparison between the
mathematical theory and the simulation. A Butterworth filter must
design according to specifications, to require being at 8th and 9th order
order and fulfill the Ap (dB attenuation in the pass band), As (dB
attenuation in the stop band), fp (passband frequency) and fs (stop band
frequency).
Design of Butterworth Band-Pass Filter
35
Politeknik & Kolej Komuniti Journal of Engineering and Technology, Vol.1, 2016
eISSN 0128-2883
Bandpass Butterworth filter need to design in this paper must have the
characteristic as shown in figure 4.
Figure 4: Gain versus Frequency
There were two different designs have been done that were Low Pass
Filter and High Pass Filter. And then combine this design to build
Butterworth Band Pass Filter. For the first design LPF, the calculations
showed in appendix 1 and 2 and HPF shown in appendix 3 and 4.
So, the LPF circuit was designed as figure 5 below.
Figure 5. 9th order LPF Circuit Design using LT spiceIV
So, the HPF circuit was designed as figure 6 for 8th order by using 2nd
order + 2nd order + 2nd order + 2nd order.
Design of Butterworth Band-Pass Filter
36
Politeknik & Kolej Komuniti Journal of Engineering and Technology, Vol.1, 2016
eISSN 0128-2883
Figure 6. 8th order HPF Circuit Design using LTspice
Now combine this design, LPF and HPF is built Butterworth band-pass
filter (BPF) circuit. So the figure of BPF is shown as figure 6. BPF is
combining of LPF HPF order as shown in figure 8.
Figure 7. The order of combination of LPF and HPF
Figure 8. First Design of BPF Circuit combination of LPF-HPF
For the second design of LPF, the arrangement was as follows is by using
3rd order + 2nd order + 2nd order + 2nd order. The capacitance value is
same but changes the orders in the circuit diagram. The circuit of second
design is described in figure 9.
LPF
HPF
Vin
Vout
Design of Butterworth Band-Pass Filter
37
Politeknik & Kolej Komuniti Journal of Engineering and Technology, Vol.1, 2016
eISSN 0128-2883
Figure 9. 8rd order LPF Circuit Design using LTspice
For HPF just do one design only because the order four stages of second
order only, so if change the arrangement in circuit diagram it’s remained
same. Let’s change the arrangement of BPF using this design as figure 10
and figure 11 show that circuit diagram of BPF with this combination.
Figure 10. The order of combination of LPF and HPF
Figure 11. Second design of BPF Circuit combination of HPF-LPF
4. Results
In this section, the result of LPF, HPF and BPF circuit for both designs
were represented using bode plot. The output of LPF at -3dB and -43dB
are presented in figure 11. At -2.977dB get around 22.821kHz, by the
way at -43dB fall at 43.9kHz.
HPF
LPF
Vin
Vout
Design of Butterworth Band-Pass Filter
38
Politeknik & Kolej Komuniti Journal of Engineering and Technology, Vol.1, 2016
eISSN 0128-2883
Figure 11. First Design of LPF Circuit at -3dB and -43dB
Figure 12 shows the design for HPF at -3db and -43dB. The output of
HPF at -3dB and -43dB is 2kHz and 1.077kHz.
Figure 12. The Design of HPF Circuit at -3dB and -43dB
The combination of plotting the LPF and HPF will form the BPF. Figure
13a and 13b, shows the first design for BPF at -3dB. The combination of
the LPF and HPF will form the BPF. Figure 14a and 14b, shows the first
design for BPF at -43dB.
(a)
Design of Butterworth Band-Pass Filter
39
Politeknik & Kolej Komuniti Journal of Engineering and Technology, Vol.1, 2016
eISSN 0128-2883
(b)
Figure 13. Design of BPF Circuit at -3dB (a) for LPF and (b) for HPF
(a)
(b)
Figure 14. Design of BPF Circuit at -43dB (a) for HPF and (b) for LPF.
Figure 15 and 16 shows the second design for LPF at -3dB and -43dB.
For -3dB, frequency is 22.821kHz and 44.301kHz at -43dB.
Figure 15. Second Design of LPF Circuit at -3dB
Design of Butterworth Band-Pass Filter
40
Politeknik & Kolej Komuniti Journal of Engineering and Technology, Vol.1, 2016
eISSN 0128-2883
Figure 16. Second Design of LPF Circuit at -43dB
The combination of plotting the LPF and HPF will form the BPF. Figure
17a and 17b, shows the second design for BPF at -3dB combination of
LPF and HPF.
(a)
(b)
Figure 17. Second Design of BPF Circuit at -3dB for combination of HPF
and LPF
Design of Butterworth Band-Pass Filter
41
Politeknik & Kolej Komuniti Journal of Engineering and Technology, Vol.1, 2016
eISSN 0128-2883
The combination of plotting the LPF and HPF will form the BPF. Figure
18a and 18b, shows the second design for BPF at -43dB
(a)
(b)
Figure 18: Second Design of BPF Circuit at -3dB for combination of HPF
and LPF
5. Discussion
Procedure of designing LPF and HPF is divided into two parts, the first
part is finding the required order of the filter and the second part is
finding the scale factor that must be applied to the normalized parameter
value. After that, can design the LPF and HPF, to combine this two filter
to build BPF. As a result, LPF can be designed in two combination of
stage that is 2-2-2-3 and 3-2-2-2, its result at -3d and -43dB are almost
same. From this can be concluded that the stage not influence the result.
Anyhow, for HPF only has one design, combination of 2nd order only.
Other than that, in this paper also discuss about the combination of the
LPF and HPF to perform BPF. Therefore, there are two combination also
in designing BPF where, LPF-HPF and HPF-LPF. The aim of this
combination to get know is there have an influence on the performance of
BPF. After the simulation is clearly shown that there is no difference
between this combination orders. The performance of BPF is same for
both combination stages.
6. Conclusion
Band-pass filter design using a Butterworth filter is presented in this
paper. These circuits are composed using 8th and 9th order and two types
of configuration which are 2-2-2-3 and 3-2-2-2 for 9th order and 2-2-2-2
for 8th order. Moreover the combination between LPF and HPF to form a
BPF is design. There was two configuration have make to analysis the
Design of Butterworth Band-Pass Filter
42
Politeknik & Kolej Komuniti Journal of Engineering and Technology, Vol.1, 2016
eISSN 0128-2883
performance and influence in designing BPF. That is, LPF-HPF far first
combination and HPF-LPF for second combination. As a conclusion, can
be say that, there was no different with this combination, the results are
almost same for both configuration. The BPF design in this paper have
fulfill the characteristic given.
References
R. C. Dorf , J. A. Svoboda, Introduction to electric circuits: John Wiley &
Sons, 2010.
C. Bowick, RF circuit design: Newnes, 2011.
M. T. Kyu, Z. M. Aung, Z. M. Naing, "Design and implementation of active
filter for data acquisition system," ICIME'09. International Conference on,
Information Management and Engineering, pp. 406-410,2009.
E. Deptt , S. BMIET, "Performance evaluation of Butterworth Filter for
Signal Denoising."
M. Z. M. M. Myo, Z. M. Aung, and Z. M. Naing, "Design and
Implementation of Active Band-Pass Filter for Low Frequency RFID
(Radio Frequency Identification) System," in Proceedings of the
International MultiConference of Engineers and Computer, 2009.
Design of Butterworth Band-Pass Filter
43
Politeknik & Kolej Komuniti Journal of Engineering and Technology, Vol.1, 2016
eISSN 0128-2883
Appendix 1
i. Low-pass filter (LPF):
Where
1
)110(
)110(
1
31.0
1
1.0
1
X
Ap
3.141
)110(
)110(
2
431.0
2
1.0
2
X
As
Calculate the number of orders:
So therefore choose 𝑛𝐵= 9 order
According to the calculation need to choose the 9th order, and then
calculate the value of capacitors needs to for LPF design. A Butterworth
coefficients table is used as a reference to calculate the value of
capacitors and the stages also refer to the table which shown as table 1.
The first design 9th order by using 2nd order + 2nd order + 2nd order + 3rd
order.
Table 1. Butterworth Coefficient Table
Order,
n
C1 / C
or
R/R1
C2 / C
or R /
R2
C3/C or
R/R3
9
1.455
1.305
2.000
5.758
1.327
0.7661
0.5000
0.1736
0.5170
927.8
)
25
45
log(
)
13.141
log(
k
k
B
Design of Butterworth Band-Pass Filter
44
Politeknik & Kolej Komuniti Journal of Engineering and Technology, Vol.1, 2016
eISSN 0128-2883
Appendix 2
The scaling factor, C is found in a choice of R = 100k Ω
C is scaling capacitance:
pFC
KkHz
C
Rf
C
P
662.63
)100)(25(2 1
21
The values of the capacitor for stage 1, 2, 3 and 4 can be obtained from
table 1, as follows.
Stage 1: C1 = 5.758 x 63.662 X 10-12 = 366.55 X 10-12 F
C2 = 0.1736 x 63.662 X 10-12 = 11.05 X 10-12 F
Stage 2: C3 = 2 x 63.662 X 10-12 = 127.32 X 1012 F
C4 = 0.5 x 63.662 X 10-12 = 31.83 X 10-12 F
Stage 3: C5 = 1.305 x 63.662 X 10-12 = 83.07 X 10-12 F
C6 = 0.7661 x 63.662 X 10-12 = 48.77 X 10-12 F
And, stage 4
C8 = 1.455 x 63.662 X 10-12 = 92.67X 10-12 F
C7 = 1.327 x 63.662 X 10-12 = 84.48 X 10-12 F
C9 = 0.517 x 63.662 X 10-12 = 33.91 X 10-12 F
Design of Butterworth Band-Pass Filter
45
Politeknik & Kolej Komuniti Journal of Engineering and Technology, Vol.1, 2016
eISSN 0128-2883
Appendix 3
For high-pass filter (HPF):
Where,
1
)110(
)110(
1
31.0
1
1.0
1
X
Ap
3.141
)110(
)110(
2
431.0
2
1.0
2
X
As
Calculate the number of orders:
𝑛𝐵= log(Ɛ2 / Ɛ1 )
log(𝑓
𝑠 /𝑓
𝑝 )
814.7
)
2
1
log(
)
13.141
log(
kHz
kHz
B
So therefore
8
B
choose order
For HPF, need to calculate the value of the resistors and the capacitor
value are fixed to 0.05uF to find the scaling resistor. By referring to the
Butterworth coefficients table which shown as table 2 for 8th order.
Table 2 Butterworth Coefficients Tables
Order, n
C1 / C
or
R/R1
C2 / C or
R / R2
C3/C
or
R/R3
8
1.020
1.202
1.800
5.125
0.9809
0.8313
0.5557
0.1950
Choose C = 0.05µF,
Design of Butterworth Band-Pass Filter
46
Politeknik & Kolej Komuniti Journal of Engineering and Technology, Vol.1, 2016
eISSN 0128-2883
Appendix 4
So the scaling factor R is:
5.1591
)05.0)(2(2 1
21
R
uFkHz
R
Cf
R
P
Stage 1:
5.310
125.5 5.1591
2
R
5.8161
1950.0 5.1591
1
R
Stage 2:
2.884
800.1 5.1591
3
R
0.2864
5557.0 5.1591
4
R
Stage 3:
0.1324
202.1 5.1591
5
R
5.1914
8313.0 5.1591
6
R
Stage 4:
3.1560
020.1 5.1591
7
R
5.1622
9809.0 5.1591
8
R
... The Network Analyzer was used to measure the insertion loss of the optimized filter [11]. In [2016], a Butterworth filter up to 8 th and 9 th order was designed using the combination of 2 nd and 3 rd order [12]. In [2017], a dualband passband filter was designed for the GSM application. ...
... Butterworth filters are maximally flat in the passband, but their out-of-band attenuation slopes are unsuitable [13]. These filters are designed to process signals with flat frequency response in the passband (no ripple) and zero roll-off in the stopband [12]. A steep attenuation transmission from passband to stopband requires Butterworth filters to have more components and provide monotonic attenuation for the low pass filters, as shown in Fig 1. [18]. ...
Conference Paper
Continuous monitoring of blood oxygen saturation level (SpO2) during the second triage in the high casualty event and determining the hemostability of a patient/victim until arrival to a medical facility, is essential in emergency situations. Using a SmartPatch device attached to a victim’s chest that contains a Photoplethysmogram Waveforms (PPG) sensor, one can obtain the SpO2 parameter. Our interest in the process of the SmartPatch prototype development is to investigate the monitoring of a blood oxygen saturation level by using the embedded PPG sensor. We explore acquiring the SpO2 by extracting the set of features from the PPG signal utilizing two Python toolkits, HeartPy and Neurokit, in order to model the Machine learning predictors, using multiple regressors. The PPG signal is preprocessed by various filtering techniques to remove low/high frequency noise. The model was trained and tested using the clinical data collected from 52 subjects with SpO2 levels varying from 83 - 100%. The best experimental results - MAE (1.45), MSE (3.85), RMSE (1.96) and RMSLE (0.02) scores are achieved with the Random Forest regressor in the experiment with 7 features extracted from the both toolkits.
Design and implementation of active filter for data acquisition system
  • M T Kyu
  • Z M Aung
  • Z M Naing
M. T. Kyu, Z. M. Aung, Z. M. Naing, "Design and implementation of active filter for data acquisition system," ICIME'09. International Conference on, Information Management and Engineering, pp. 406-410,2009.
Performance evaluation of Butterworth Filter for Signal Denoising
  • E Deptt
  • S Bmiet
E. Deptt, S. BMIET, "Performance evaluation of Butterworth Filter for Signal Denoising."
Design and Implementation of Active Band-Pass Filter for Low Frequency RFID (Radio Frequency Identification) System
  • M Z M M Myo
  • Z M Aung
  • Z M Naing
M. Z. M. M. Myo, Z. M. Aung, and Z. M. Naing, "Design and Implementation of Active Band-Pass Filter for Low Frequency RFID (Radio Frequency Identification) System," in Proceedings of the International MultiConference of Engineers and Computer, 2009.