International Journal of Scientific & Engineering Research, Volume 5, Issue 4, April-2014 1598

ISSN 2229-5518

IMPLEMENTATION OF A SIXTH ORDER ACTIVE BAND-PASS R-FILTER.

1Igwue, G. A. 2Amah, A. N. and 3Atsuwe B.A.

1Department of Electrical/Electronic Engineering, University of Agriculture

Makurdi-Nigeria.

2Department of Physics, University of Agriculture, Makurdi-Nigeria.

3Department of Science Education, University of Agriculture, Makurdi-Nigeria.

Correspondence: Atsuwe Bernard Aondofa.

E-mail: ella4mneuter@yahoo.com

ABSTRACT

In this paper, an active band-pass R- filter output response at different values of center frequency using MAPLE programming is carried out. A sixth order active band pass R-filter are constructed at center frequencies of 10 kHz and 100 kHz and quality factors of 2, 5, 7, 8 and 10 and roll off rate of 20dB/decade. The architecture used is the multiple feedbacks. The filter parameters and values for the passive components were calculated, the gain and phase response were then simulated with MAPLE programming. The simulation shows that at high Quality factors, the bandwidth of the filter response reduces considerably while its frequency selectivity increases without a shift in its center frequency. This is an indication that the filter will function well at high frequencies and perform poorly at lower frequencies. This result also shows that the R-filter is most selective at a quality factor of Q=8 and centre frequency of fo = 100KHz Keywords: R-filter, Quality factor, Band pass, MAPLE.

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INTRODUCTION

A filter is defined as a network which passes a certain portion of a frequency spectrum and blocks the remaining portion of the spectrum. (Igwue, 2007).The term “blocking” means that
the magnitude response

H ( jω)

of the filter is approximately zero for that frequency range. In
other words, a filter is a frequency –selective device or system. The active filter without the capacitor is called an active-R filter; and has received much attention due to its potential advantages in terms of miniaturization, ease of design and high frequency performance (Srinivasan 1992; Kadam & Mahajan 1995; Shinde & Mirkute 2003). It has been also pointed out in the literature that active-R networks offer substantially low sensitivity characteristics as compared to R-C active structures (Soderstand & Mitra 1971). Although several papers have been published on evaluation of the second order active-R filter, we have not come across any reported circuit regarding direct coupled circuit for realizing third-order active-R filters with feedforward input signals. This gives greater stop-band attenuation and sharper cut-off at the edge of the passband. The band-pass response is characterised by a frequency band between the lower cut off frequency, fL and upper cut off frequency, fH such that input signals with frequencies(f) within the band fL (i-e fL <f<fH ) less than f and f itself is less than fH (fL < f<fH ) emerge unchanged while those signals with frequencies outside the band are attenuated. The difference (fH - fL ) is called the bandwidth of the filter, and the point of frequency spectrum at which the band is centered is called the centre frequency fo (Sergio,F, 1988).
Filters are usually classified according to filtering range, frequency response in pass band, and circuit component. Classified by filtering range, there are four types of filters: low- pass, high-pass, band-pass, and band-reject filters. According to frequency response in pass band, there are two types: Butterworth and Chebyshev filters. According to circuit component, they are active and passive filters.
Passive filters are circuits that contain only passive components (resistors, inductors and capacitors) connected in such a way that they will pass certain frequencies while rejecting others. Active filters, which are the only type covered in this paper, employ active
components (transistors or operational amplifiers) plus resistors, inductors and capacitors. Active filters are widely used in modern communication systems, because they have the following advantages:

1. Because the transfer function with inductive characteristic can be achieved by particular circuit design, resistors can be used instead of inductors.

2. The high input impedance and low output impedance of the operational amplifier means that the filter circuit is excellent in isolation characteristic and suitable for cascade.

3. Because active components provide amplification, therefore active filters have gain.

METHODOLOGY

The circuit configuration for the sixth –order active R- Band pass filter was gotten from the work of Prabhat, U. and Pal, L. (2006) which is on the second order active Band pass filter as
shown in Fig 1. The resistor values were calculated using equation 1 and 2.

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CC

R1

V1

R2

VSS

R3

R4

VSS

R3

R2

VCC

Fig 1: Circuit diagram of a second order active R-band pass filter
The architecture that has been used to implement both the sixth order active R-band-pass filter is the multiple feed-back topology which can be realized through cascading of the second order filter stages. The circuit diagram in Fig. 2 shows the implemented circuit composed of triply
cascaded second order active R-band pass filter.

Analysis

R 4 =

k1 × R3

(1)

(1 − k1 )

R 2 =

k2 × R1

(2)

(1 − k2 )

Since k1 and k2 are attenuators, their values are given as

1

k1 =

Q

(3)

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k2 =

2 × π × f

Ao

T

(4)

The value of Ao
is taken as

6.2 × 10 6

which is the gain bandwidth product of the amplifier.
The gain of the filter can be determined according to Prabhat and Pal (2006) as;

Gain =

Ao K 2

(1 + sT )

= Ao

T

(5)

V

The voltage transfer function Tf = o of the circuit is given by( Prabhat and Pal, 2006) as;

Vi

Vo =

sT

Ao k2 1

s T +

sTK1 + 1

2 2

i 2 2

o 2

Ao k2

(6)
Where K is the attenuator given by equations 3 and 4 above.
Thus the role of attenuator K 2 is that it controls the open loop gain of operational amplifiers used in the circuit. Thus adjustment of K2 results in control of centre frequency of the band pass filter. The resistances R2 ’s can be varied using Field Effect Transistor (FET) replaced resistances, thus giving single control of two attenuators K 2 . The quality factor Q is independently adjusted using element K1 , which is adjustable through resistance R4 . The sixth order active R-band pass filter is obtained by cascading of the second order active R-band pass filter of Fig. 1 and is represented in Fig. 2. Since filter orders determine the gain and selectivity of the filter, there have been attempts to improve on the filter orders hence the need to cascade filters. Fig 1 shows the simplest form of a filter which is called the Second order. If a better functionality of the filter in terms of selectivity is needed, then there will be the need to put two of the second orders together to make the fourth order. Again if a much higher gain is needed, then we increase the order. Consequently the higher the filter order, the higher the gain and the filter selectivity. (Wayne, S, 2011).Furthermore, there has been no known literature for the sixth order Band pass filter, so it was selected. The circuit performance was
studied with different values of quality factor (Q = 2, 5, 7, 8 and 10) with constant fo =10 kHz.

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12V

12V

V1 3

120 Vrms 2

60 Hz

U1

7 1 5

6

R1

0Ω

VSS R2

0Ω

U3

7 1 5

3

6

2

R7

0Ω

VSS R8

0Ω

0° 4

-12V R5

0Ω

R6

0Ω

R3741

VS0SΩ

6

5 1

4

7

12V

-12V

U2

2

3

741

VCC

VCC

R4

0Ω

12V

4

-12V R11

0Ω

R12

0Ω

R9741

VS0SΩ

6

5 1

4

7

12V

-12V

U4

2

3

741

VCC

R10

0Ω

U5

7 1 5

3

6

2

R13

0Ω

VSS

6th -order Active Bandpass filter multiple FeedBack

R14

4 R15

0VΩSS

741

-12V

U8

4

0Ω

R16

0Ω

-12V R17

0Ω

R18

0Ω

6

5 1 7

12V

2

3

741

VCC

Fig 2: Circuit Diagram of Sixth Order Active-R Band Pass Filter

RESULT

For a centre frequency fo =10kHz, the value of R1 was chosen to be 100kΩ. After the substitution in the same equation 2,R 2 was calculated to be 1.0k Ω .The results for the maximum pass band gain and the bandwidth for the filter at fo=10kHz and fo=100kHz are presented in Tables 1 and 2 respectively,while their respective

magnitude responses are shown in Figures 3 and 4.

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Table 1. Maximum PassBand Gain and Bandwidth of the Sixth-Order Active R- BandPass

Filter at f0 = 10kHz

Table 2. Maximum PassBand Gain and Bandwidth of the Sixth-Order Active R- BandPass

Filter at f0 = 100kHz

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Results for f o = 1.0*10^5 rad/sec

Fig.3: Sixth order active R-band pass filter at centre frequency fo = 10 kHz and Q= 2, 5, 7, 8, 10 respectively.

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Results for fo = 1.0*10^6 rad/sec

Fig. 4: Sixth order active R- band pass filter at centre frequency fo = 100 kHz and Q= 2, 5, 7, 8, 10

respectively

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DISCUSSION

Table 1 presents results for f0 = 10kHz, the pass band gain increases from a value of 6.71dB at Q=2 to 19.00 dB at Q=10. The bandwidth decreases from a value of

3629.24Hz to 1694.22Hz at Q=8 and Q=10. This implies good behavior of the filter at this centre frequency. Also the filter works and it has high selectivity which is in line with literature. Theory specifies that “increase in Q, leads to increase in the gain (G)” and “increase in Q yields a decrease in the bandwidth”. Also the increase in fo gives a decrease in the bandwidth. Furthermore, at a constant fo =100kHz, as presented in table 2,the pass band Gain is 6.73dB at Q=2 and increases to

16.18dB at Q=10, while the Bandwidth decreases from 40,107.05 Hz at Q=2 to

25,886.24 Hz at Q=10. This implies consistent behavior of the filter at this centre frequency. Also the filter really works and it has high selectivity which is in line with literature. In summary, the active R-band pass filter is characterized by high gain and narrow bandwidth at both f o= 10kHz and 100kHz.

CONCLUSION

It can be concluded from the above results that even though the constructed filter does not have same values as the simulated results, it still maintains the filter behaviour or characteristics. Therefore the filter

performs well at f0 = 10kHz and f0 = 100kHz up to a quality factor of Q=8. It is

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believed that there can be further improvement in the characteristics if more precise values of resistors and better operational amplifiers were used. This filter can also be used as a narrow band device because the selectivity is high, as well as to obtain high gains.

REFERENCES

Carter, B(2001): Filter Design in thirty seconds. Texas Instrument Inc. Dallas.USA. Hashemi, K (2004): Filter design guide.

http/www.opamp,htm.Operational Amplifier Basics (01/11/2008).

Huelsman, L. P(1971): Equal Valued Capacitor Active-RC Network Realization of third Order Lowpass Butterworth Characteristic. Electron Lett.7: 291 – 293.

Hyong, K.K. and RA, J.B(1977): An Active Biguadratic Building Block without

External capacitors, IEEE Transactions on circuit and system, Vol. CAS-

24,No12.

Igwue, G. A(2007): Basic circuit theory and Industrial Electronics for Physicists.

Aboki Publishers, Makurdi. Nigeria.

Mesami, H(1992): Active–R Realisation of Current Mode Highpass

Filter.Int.J.Electronices,63: p. 335 -338.

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Prabhat, U. and Pal, K(2006): An Active Bandpass realization using Amplifier, Old city publishing inc.vol.1, p. 241 -245

Sergio, F(1998): Design with Operational Amplifiers and Analog Integrated Circuit, McGraw-Hill. New York, USA.

Shinde, G. N; Kadam, A. B; Kurumbatte, S. B and Patil, P.B(2002): Study of Active – R Second Order filter using feedback at Non-inverting terminal. Bulletin of pure and applied sciences vol.21D (1), p. 23 -31.

Shinde, G. N; Patil, P. B and Mirkute, P.R (2003): A third order active –R filter with feed forward input signal. Sadhana vol.28 (6) 1019 -1026.

Stark, P. A (2004): Band pass filters and Resonance.

Soderstand, M. A(1976): Design of Active –R Filter using only Resistance and

Operational Amplifier.Int.J.Electronics, Vol.(N0:8): p. 417 -437.

Soderstand, M. A and Mitra, S.K(1971): Sensitivity Analysis of Third Order –Filter

Int.J.Electron.30; p. 265 -273.

Srinivasan, S(1992): Synthesis of transfer function using the operation amplifier pole. Int. J. Electron.73; p. 1279–1283.

Wayne, S(2011): Active Band pass Filter, Electronics-Tutorials.ws. P.7-8

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