Research Article Volume 6 Issue No. 4

DOI 10.4010/2016.1088 ISSN 2321 3361 © 2016 IJESC Research Article Volume 6 Issue No. 4 Design and Analysis of Active High Pass, Low Pass & Band Pa...
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DOI 10.4010/2016.1088 ISSN 2321 3361 © 2016 IJESC

Research Article

Volume 6 Issue No. 4

Design and Analysis of Active High Pass, Low Pass & Band Pass Butterworth Filters Using LM741 S.Vigneshwaran1, A.Santhoshkumar2, S.Srikanth3 Assistant Professor 1, 2, 3 Department of Electronics & Communication Engineering SNS College of Technology, India [email protected], [email protected], [email protected] Abstract: Active filter plays an important role in today’s world of communication. A popular application uses an op-amp to build active filter circuits.A filter circuit can be constructed using passive components: resistors and capacitors. An active filter additionally uses an amplifier to provide voltage amplification and buffering. A filter that provides a constant output from dc upto cutoff frequency fOH And passes no signal above that frequency is called ideal low pass filter. A filter that provides or passes a signal above the cutoff frequency is called ideal high pass filter. When a filter circuit passes signals that are above one ideal cutoff of frequency and below a second cutoff frequency is called a bandpass filter all this filters play a vital role from the day 1 of communication. The butterwort technique is used to idealize the practical responses for proper communication because noise occurs in channel. For removing noise or cancellation of noise we use various type o f Butterworth filter. In this paper, Active Butterworth filters is designed using LM741. The output of the filter design by MATLAB & MULTISIM simulation. The performance of the three active filter is designed in both first order and second order and analyzed. Keywords: LPF, HPF, BPF,Butterworth,Op-Amp, Frequency Response. 1. Introduction 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. It was first described in 1930 by the British engineer and physicist Stephen Butterworth in his paper entitled "On the Theory of Filter Amplifiers" Butterworth had a reputation for solving "impossible" mathematical problems. At the time, filter design required a considerable amount of designer experience due to limitations of the theory then in use. The filter was not in common use for over 30 years after its publication. Butterworth stated that "An ideal electrical filter should not only completely reject the unwanted frequencies but should also have uniform sensitivity for the wanted frequencies". Butterworth also showed that his basic low-pass filter could be modified to give low- pass, high-pass, band-pass and band-stop functionality.

orders 1 through 5, with cutoff frequency . Note that the slope is 20n dB/decade where n is the filter order. Like all filters, the typical prototype is the low-pass filter, which can be modified into a high-pass filter, or placed in series with others to form band-pass and band-stop filters, and higher order versions of these. 2.

HPF Design

Fig.1: Circuit for HPF Av= 1+RF/R1 (i) To calculate the cutoff frequency of a second order high pass filter for R1=R2=2.1KΩ,C1=C2=0.05uF and RG=10KΩ,RF=50KΩ. The Gain Av is Av=1+RF/RG=1+50KΩ/10KΩ=6 The Cutoff frequency FOL is then

FOL=1/2πR1C1 =1/2π(2.1*103)*(0.05*10-6) =1.5KHz

Fig.2: Plot of the gain of Butterworth low-pass filters of

International Journal of Engineering Science and Computing, April 2016

3. LPF Design

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FOH=1/2πR1C1 =1/2π(10*103)*(0.002*106 ) =7.69KHz 4. Frequency Response

Fig.3:Circuit for LPF To calculate the cutoff frequency of a first order low pass filter for R1= 1.2KΩ,C1=0.02uF and RG=10KΩ,RF=50KΩ. The Gain Av is Av=1+RF/RG=1+50KΩ/10KΩ=6 The Cutoff frequency FOL is then

FOL=1/2πR1C1 =1/2π(1.2*103)*(0.02*10-6) =6.63KHz

4. BPF Design

Frequency response is the quantitative measure of the output spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system. It is a measure of magnitude and phase of the output as a function of frequency, in comparison to the input. In simplest terms, if a sine wave is injected into a system at a given frequency, a linear system will respond at that same frequency with a certain magnitude and a certain phase angle relative to the input. Also for a linear system, doubling the amplitude of the input, will double the amplitude of the output. In addition, if the system is time-invariant (so LTI), then the frequency response also will not vary with time. Thus for LTI systems, the frequency response can be seen as applying the system's transfer function to a purely imaginary number argument representing the frequency of the sinusoidal excitation Properties of the Butterworth filter are  Monotonic amplitude response in both passband And stopband  Quick roll-off around the cutoff frequency, which Improves with increasing order  Considerable overshoot and ringing in step Response, which worsens with increasing order  Slightly non-linear phase response Group delay Largely frequency-dependent

Fig4: Circuit for BPF To calculate the cutoff frequency of a first order band pass filter for R1=R2=10KΩ,C1,C2=0.1uF,0.02uF The Gain Av is Av=1+RF/RG=1+50KΩ/10KΩ=6

The Cutoff frequency FOL is then

FOL=1/2πR1C1 =1/2π(10*103)*(0.1*10-6) =159.15KHz The Cutoff frequency FOH is then

International Journal of Engineering Science and Computing, April 2016

Fig.5: Image showing the gain of a discrete-time Butterworth filter next to other common filter types. All of these filters are fifth-order. 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. It was first described in 1930 by the British engineer and physicist Stephen Butterworth in his paper entitled "On the Theory of Filter Amplifiers"There are several different filter topologies available to implement a linear analogue filter. The most often used topology for a passive realisation is Cauer topology and the most often used topology for an active realisation is Sallen–Key topology.The Cauer topology uses passive components (shunt capacitors and series inductors) to implement a linear analog filter.[1] 4784

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5. Simulation Output

Fig.6: High Pass Filter magnitude response simulated in MULTISIM.

Fig.7: High Pass Filter phase response simulated in MULTISIM.

Fig.8: Low Pass Filter magnitude response simulated in MULTISIM.

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Fig.9: Low Pass Filter phase response simulated in MULTISIM.

Fig.10: Band Pass Filter magnitude response simulated in MULTISIM.

Fig.11: Band Pass Filter phase response simulated in MULTISIM.

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The Fig. 6 to 11 show the realization of the High pass, Low pass & Band pass Butterworth filter using MULTISIM. The Bode plotter tool has been used for obtaining the desired filter magnitude and phase results has been used as the designing method. The different responses of the Active filter using the two different windows are shown which are Magnitude and Phase response for the frequency spectrum. Adding capacitors to filter provide external setting of cutoff frequency 3. Graphed view

7. Comparisons Filters/Parameter s V

HPF

LPF

BPF

-11.1V -4.16V V(p-p) 22.2V 18.9V V(rms) 9.66V 6.68V V(dc) 3.52mV 514μV I -185 μA -4.16pA I(p-p) 371 μA 18.9pA I(rms) 161 μA 6.68pA I(dc) 70.4nA 0 Freq 1.50kHz 563Hz Table 1:Comparisions of HPF,LPF & BPF

-7.63V 22.2V 10.3V 234 μV -127 μA 371 μA 172 μA 15.6nA 1kHz

The table 1 shows the comparison various parameters such as voltage,peak to peak voltage,rms voltage,current,peak to peak current,dc current & frequency for different active filters we designed in this paper in which the second order shows the flat response compared to other type of filters

Fig.12: HPF Magnitude and phase responses

6. Conclusion The LM741,resistors and capacitors are used in the design of High pass,Low pass and Band pass Butterworth filters to compare the performances of the designed filter based on several electrical parameters. Looking at the response curves plotted for the two windows used in the design of our Butterworth filters, the magnitude responses of second order high pass filter with first order low pass and band pass filters shows that higher order filters roll-off rate than the first order. For a low pass filter, a lower roll- off is easier to handle than the higher roll-off. Also looking at the simulation results, it is evident that Butterworth filters has better filtering effect to produce flat-flat responses. References [1] https://www.ni.com/multisim [2] https://en.wikipedia.org/wiki/Active_filter [3] R o b e r t L.Boylestad Louis Nashelsky, Electronic Devices and Circuit theory,Tenth Edition

Fig.13: LPF Magnitude and phase responses [4] Theodore F.Bogart Jr.Jeffrey S.Beasley Guillermo Rico, Electronic Devices and Circuit, Sixth Edition [5] http://www.arc.id.au/FilterDesign.html [6] J.B.Gupta, Engineering

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[7] https://en.wikipedia.org/wiki/Digital_filter. [8] Matthaei, George L.; Young, Leo and Jones, E. M. T., Microwave Filters, Impedance- Matching Networks, and Coupling Structures, McGraw-Hill, 1964 LCCN 64-7937 Fig.14: BPF Magnitude and phase responses

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