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Engineering, 2010, 2, 179-183 doi:10.4236/eng.2010.23025 lished Online March 2010 (http://www.SciRP.org/journal/eng/) Copyright © 2010 SciRes. ENG Pub Tunable Bandwidth Third Order Switched-Capacitor with Multiple Feedbacks Filter for Different Center Frequencies Ganeshchandra N. Shinde1, Sanjay R. Bhagat2 1Indira Gandhi College Nanded, Maharashtra, India 2Dnyanasadhana College , Thane, Maharashtra, India Email: shindegn@yahoo.co.in, sanjaybhagat_14@yahoo.co.in Received October 6, 2009; revised November 8, 2009; accepted November 13, 2009 Abstract This paper proposes third order tunable bandwidth active Switched-Capacitor filter. The circuit consists of only op-amps and switched capacitors. The circuit is designed for circuit merit factor Q = 10. The proposed circuit implements three filter functions low pass, band pass and high pass simultaneously in single circuit. The filter circuit can be used for both narrow as well as for wide bandwidth. For various values of cut-off frequencies the behaviour of circuit is studied. The circuit works properly only for higher central frequencies, when f0 > 10 kHz. Keywords: Third Order Filter, Switched Capacitor, Pass Band Gain, Tunable Bandwidth, Circuit Merit Factor 1. Introduction Conventional analog circuits use the ratio of resistances to set the transfer function of filter circuits. The values of RC product determine the frequency responses of these circuits [1-4]. It is very difficult to make resistors and capacitors with the values and accuracy that are required in audio and instrumental applications. Resistors are ex- pensive and cannot be easily controlled [5]. The Switched-Capacitor concept can be used to realize a wide variety of universal filter that have the advantage of compactness and tunability [6]. In MOS integrated technology, it is relatively simple to achieve this objec- tive as compared to conventional techniques. It is due to high integration density, high precision and stability and ideal characteristics of MOSFET switches [7]. Switched capacitor techniques have been developed so that both digital and analog functions can be integrated on a single silicon chip. Switched capacitor filters are clocked sampled system. The input signal is sampled at a high rate and processed at a discrete time. Using these techniques resistors can be replaced by a capacitor and MOS switches that are rapidly turned on and off. Switched capacitor filters have the advantage of better accuracy in most of the cases [6-9]. Switched-Capacitor filters have the advantage of bet- ter accuracy in most cases. Typical center-frequency accuracies are normally on the order of about 0.2% for most Switched-Capacitor ICs, and worst-case numbers range from 0.4% to 1.5% (assuming, of course, that an accurate clock is provided). 2. Basic Switching Operation The essence of the Switched-Capacitor is the use of Ca- pacitors and analog Switches to perform the same func- tion as resistors. This replacement of resistor, analog with op. amp based integrator, then form an active filter [6]. Furthermore, the use of the Switched-Capacitor will be seen to give frequency tenability to active filters. Fil- ter using Switched-Capacitor technique overcome a ma- jor obstacle of filter on a chip fabrication—the imple- mentation of resistors by simulating resistors with high speed Switched-Capacitors using MOSFETs. The swit- ching function of the MOSFET produces a discrete resp- onse rather than a continuous response from the filter [6]. The operation of switched capacitor can be explained with the help of following circuit diagram: v 1 v 2 2 1 S 2 S 1 C S G. N. Shinde ET AL. 180 The circuit consists of two capacitors and two switc- hes controlled by two non-overlapping clocks, 1 and . When is high, S1 closes while S2 is open. When goes low, S1 closes. Then after a short delay 2 1 1 2 goes high, and S2 closes. This cycle repeats so that S1 and S2 close and open alternatively, but they are never closed at the same time. Each switching cycle transfers a charge q from the in- put to the output at the switching frequency f. The charge q on a capacitor C is given by q = CV where V is the voltage across the capacitor. Therefore, when S1 is closed while S2 is open, the charge transferred from the source to is: S C 1 q = 1 CV When S2 is closed while S1 is open, the charge trans- ferred from to the load is: S C 2 q = 2 CV q = C1 (V2 V1) If this switching process is repeated N times in time t, then the amount of charge transferred per unit time is given by q t = C1 21 VV N t L.H.S. is current and number of cycles per unit time is switching frequency. i = C1 21 VV CLK f 21 VV i = 1 1 CLK Cf = R Thus the switched capacitor is equivalent a resistor. 3. Proposed Circuit Configuration The proposed circuit configuration for Switched-Ca- pacitor filter with multiple feedbacks is shown in Figure 1. The circuit consists of three op–amps ( A 741) with wide identical gain bandwidth product (GB) and three Capacitors with MOSFET, which form Switched-Ca- pacitor. Switched-Capacitor can replace resistors, which was proposed earlier [2]. The input sinusoidal voltage is applied to the non-in- verting terminal of the first op-amp through switched capacitor (SC). The non-inverting terminal is grounded. SC is used in the feedback circuit. The output of the first op-amp is supplied as non-inverting input of the second op-amp. The inverting terminal is grounded. SC is used as feedback. The output of the second op-amp is supplied as non-inverting input of the third op-amp. The inverting terminal is grounded. SC is used as feedback. Low pass function is observed at the output of the third op-amp. The output of the second op-amp gives Band pass func- tion. The High pass function is seen at the output of the first op-amp. Figure 1. Circuit diagram of universal third order Switched-Capacitor filter. Copyright © 2010 SciRes. ENG G. N. Shinde ET AL. 181 4. Circuit Analysis and Design Equations Op-amp A 741 is an internally compensated op-amp, which represented by “Single pole model”, C opyright © 2010 SciRes. ENG A(S) = 00 0 Aω Sω (1) where A0:- open loop D.C. gain of op-amp 0 ω: - open loop 3 dB bandwidth of the op-amp. = 2f0 A0:- GB = gain-bandwidth product of op-amp 0 ω for S>> 0 ω A(S) = 00 Aω S=GB S (2) This shows Op-amp as integrator. Transfer function of the proposed third order Swit- ched-Capacitor filter for low pass TLP(S), for band pass TBP(S) and for high pass THP(S) are given below. TLP(S) = 4123 32 123 CGBGBGB XSXSXS X 4 (3) TBP(S) = 412 32 123 CGBGBS XSXSXS X 4 (4) THP(S) = 2 41 32 123 CGBS XSXSXS X 4 (5) where X1 = C1 + C2 + C3 + C4 X2 = GB1C1 X3 = GB1GB2C2 X4 = GB1GB2 GB3C3 The circuit was designed using coefficient matching technique i.e. by comparing these transfer functions with general second order transfer functions [10]. The general second order transfer function is given by T(S) = 32 32 322 00 11 11 αSαSαα SωSωSω QQ S 10 + 3 0 (6) Table 1. Capacitor values for different Q. f0 kHz C1 F C2 C3 C4 F 1 22 033 nF 5·6 nF 100 5 1 82 nF 5·6 nF 100 10 22 33 nF 5·6 nF 100 20 33 01 F 4·7 nF 100 50 10 082 F 68 nF 82 70 10 22 F 022 F 82 Comparing Equations (3), (4) and (5) with Equation (6) 3 0 3 ω GB = GB1GB2 GB3C3 2 0 1 1ω Q = GB1GB2C2 0 1 1 ω Q = GB1C1 1 = C1 + C2 + C3 + C4 Using these equations, values of C1, C2 and C3 can be calculated for different values of central frequency f0. 5. Experimental Set Up The circuit consists of three op–amps. ( A 741 C) with wide identical gain bandwidth product (GB) and three Capacitors with MOSFET, which form Switched-Ca- pacitor. The circuit performance is studied for different values of Cut-off frequencies with circuit merit factor Q = 10. The general operating range of this filter is 10 Hz to 12 MHz. The value of GB (GB1 = GB2) is 652 rad/sec. 5 10 MOSFETs are driven by two non overlapping clocks. The input voltage of 5 mV is applied and the readings are taken at different terminals for different f0 (1k, 5k, 10k, 20k, 50k). 6. Result and Discussion Following observations are noticed for low pass, band pass and high pass at corresponding terminals. A) Low pass response: The Figure 2 shows the low pass response for different 101001k10k 100k 1M 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 2fQ10 F1k F5k F10k F20k F50k f70k Gain (dB) Frequency (Hz) Figure 2. Low pass response for Q=10. G. N. Shinde ET AL. 182 T. Gain Roll-off/octave able 2. Data sheet for low pass response in stop band F0 Max. Pass F0L ( F0 F0L dB/octave rting at band gain (dB) kHz) (kHz) Octave sta (kHz) 1 165 7 6 19 3 5 123 20 15 19 10 10 105 22 12 18 20 20 86 52 32 20 40 50 62 100 50 18 100 70 53 130 60 20 100 alues of f0. Theoretically it is predicted to give high pass ilter for different values of f0 nd pass response: nd pass response for dif- fe realization of tunable bandwidth third order active pass function cannot be achieved. v band gain 165 dB for f0 = 1 kHz which is expected to decrease to 105 dB f0 = 10 kHz. Experimental result shows high pass band gain (86 dB) for 20 kHz and de- creases with increase in value of f0. Gain roll-off values varies between 18 to 20dB/octave, which are close to the ideal value of 18 dB/octave for third order filter. The response shows overshoot of about 17 dB. B) High pass response: High pass response of the f is shown in Figure 3. Gain roll-off values varies be- tween 13 to 14 dB/octave which is less than the ideal value of 18 dB/octave for third order filter. The value of overshoot decreases from 72 dB to 33 dB with increase in the value of central frequency. The overshoot appears in the leading edge of curve & trailing edge is stabilized after saturation at 0 dB, so it works for high pass re- sponse. C) Ba The Figure 4 shows the ba rent values of f0. The expected maximum passband gain is 127 dB for F0 = 1 kHz and 99 dB for F0 = 5 kHz. The experimental result shows maximum pass band gain of 87 dB for F0 = 10 kHz decreases with increase in cen- tral frequency. The bandwidth is increases with f0 but reduces for f0 = 70 kHz. It is also observed that the pass band distribution of frequency is almost symmetric for both sides. The gain roll-off/octave in leading and trail- ing part of the response is different. 7. Conclusions A Switched-Capacitor filter has been proposed. The three filter function, low pass, high pass and band pass at dif- ferent terminals works with satisfied results. The filter circuit can be used for both narrow as well as for wide bandwidth. Low pass function works practically only for higher central frequencies. Stabilization of gain for High 101001k10k 100k1M -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 fQ F1k F5k F10k F20k F50k F70k Gain (dB) Frequency (Hz) Figure 3. High pass response for Q = 10. T and able 3. Data sheet for high pass response. Gain Roll-off / octave in stop b F0 (kHz) (kHz)(kHz) dB/octave Octave starting at F0H F0 F0L 1 07 03 14 600 5 36 14 13 2 k 10 7 3 13 4 k 20 15 5 13 10k 50 40 10 13 20k 70 60 10 13 40k 101001k10k100k1M -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 F1k F5k F10k F20k F50k F70k Gain (dB) Frequency (Hz) Figure 4. Band pass response for Q=10. T. F0 (kHz) Hz) able 4. Data sheet for band pass response Max. Pass ban gain (dB) F0B (kHz) f1 (kHz) f2 (kHz) BW (k 1 127 1 0.1 31 3 5 99 55 11 10 89 10 87 10 3 20 17 20 74 21 10 31 21 50 58 55 30 70 40 70 52 67 60 90 30 Copyright © 2010 SciRes. ENG G. N. Shinde ET AL. Copyright © 2010 SciRes. ENG 183 use of tSwitchedpacitor to ace resisto in active filter circuit will suitedee aajor ob and P. B. Patil, “Study of active-R second ing feedback of non-inverting terminal,” Bulletin of Pure and Applied Sciences, Vol. 21 D, No. 1, Physics, Vol. 82, No. 10, pp. 1329-1337, No. 1, pp. 5-13, 1976. 002. tor filter,” Active and Passive l. 54, 5, No. 4, pp. 631-637, 1983. e dpass filter with ts,” International fully differential fourth order chebyshev The he -Careplr 3, to ov rcom m stacle to filter on chip fabrication. 8. References [1] G. N. Shinde order filter us No. [10 pp. 23-30, 2002. [2] G. N. Shinde and S. R. Bhagat, “Universal second order active switched-capacitor filter for different Q values,” Indian Journal of 2008. [3] S. 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