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\title{Electronically Tunable Third-Order Switched-Capacitor Filter with Feedforward Signal to Minimize Overshoot}
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             \author[1]{Adnan Abdullah  Qasem}

             \author[2]{G. N.  Shinde}

             \affil[1]{  SRTM University}

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\date{\small \em Received: 7 December 2013 Accepted: 3 January 2014 Published: 15 January 2014}

\maketitle


\begin{abstract}
        


The study proposes an Electronically Tunable Third-Order Switched-Capacitor Filter with Feedforward Signal to minimize Overshoot Configuration. This circuit is designed for center frequency f0=15 KHz. The proposed circuit discusses a new configuration to realize third-order with three filter functions low-pass, band-pass, and high- pass simultaneously in single circuit. The circuit uses OP-AMP and MOSFET with Capacitor as Switched-Capacitor. The response of circuit is studied for different circuit merit factor Q and center frequency f0=15 KHz. The filter circuit can be used for both narrow as well as for wide bandwidth, Also, this circuit works for electronically tunable bandwidth. The gain roll-off for this circuit is close to the ideal value of 18 dB / octave (40dB/ decade) as for third order filters. This filter configuration shows better response for Q ? 0.4. Also, stabilization of gain for High- pass filter function can be achieved at 0dB for Q?0.4. In the proposed circuit configuration, the peak gain for overshoot is minimizing from 44dB to 5dB due to the feedforward input signal. The Low-pass filter function works practically only for higher merit factor Q. The circuit shows better response for Q ? 0.4 and f0 =15 kHz.

\end{abstract}


\keywords{electronically tunable, third-order switched-capacitor, pass band, merit factor q, cut-off frequency.}

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\let\tabcellsep& 	 	 		 
\section[{Introduction}]{Introduction}\par
onventional 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 \hyperref[b0]{[1]}\hyperref[b1]{[2]}. A switchedcapacitor can replace a resistor \hyperref[b1]{[2]}. MOSFET technology can be used for designing switchedcapacitor circuits \hyperref[b2]{[3]}. The filter circuits using Switched-Capacitor allow very sophisticated, accurate and tunable analog circuits to be manufactured. Many of the circuits proposed the working of only one type of operation \hyperref[b4]{[5]}\hyperref[b5]{[6]}\hyperref[b6]{[7]}\hyperref[b7]{[8]}\hyperref[b8]{[9]}\hyperref[b9]{[10]}. The Switched-Capacitor concept can be used to realize wide variety of universal filter that have the advantage of compactness and tenability \hyperref[b4]{[5]}. Switched capacitor techniques have been developed so that both digital and analog functions can be integrated on a single silicon chip. Switched-Capacitor filters have the advantage of better accuracy in most cases. Typical center frequency accuracies are normally on the order of Author ?: School of Physics, SRTM University, Nanded, Maharashtra, India. e-mail: almogammer80@gmail.com Author ?: Principal, Indira Gandhi (SR) College, CIDCO, Nanded, Maharashtra, India. e-mail: shindegn@yahoo.co.in about 0.2\% foremost Switched-Capacitor ICs, and worst-case numbers range from 0.4\% to 1.5\% (assuming, of Course, that an accurate clock is provided) \hyperref[b5]{[6]}. This Paper of Electronically Tunable Third-Order Switched-Capacitor Filter with Feedforward Signal to minimize Overshoot has been studied for different values of circuit merit factor Q and f 0 =15 KHz . 
\section[{II.}]{II.} 
\section[{Basic Switching Operation}]{Basic Switching Operation}\par
The essence of the Switched-Capacitor is the use of Capacitors and analog Switches to perform the same function as resistors. This replacement of resistor, analog with op. amp based integrator, and then forms an active filter. Furthermore, the use of the Switched-Capacitor will be seen to give frequency tenability to active filters. Filter using Switched-Capacitor technique overcome a major obstacle of filter on a chip fabrication?the implementation of resistors by simulating resistors with high speed Switched-Capacitors using MOSFETs. The switching function of the MOSFET produces a discrete response rather than a continuous response from the filter \hyperref[b13]{[14]}. The operation of switched-capacitor can be explained with the help of following circuit diagram. Therefore, when S 2 closes with S 1 open, then S 1 closes with S 2 open a charge q is transferred fromV 2 to V 1 with ??? = ?? (?? ? ?? )\par
If this switching process is repeated N times in time (t), then the amount of charge transferred per unit time is given by  
\section[{??? ???}]{??? ???}\par
= ?? 1 (?? 2 ? ?? 1 ) ?? ??? L.H.S. is current and number of cycles per unit time is switching frequency.? ?? = ?? 1 (?? 2 ? ?? 1 ) ð??"ð??" ?????? ? (?? 2 ? ?? 1 ) ?? = 1 ?? 1 ð??"ð??" ?????? = ??\par
Thus the switched-capacitor is equivalent a resistor. 
\section[{III.}]{III.} 
\section[{Proposed Circuit Configuration}]{Proposed Circuit Configuration}\par
The proposed circuit configuration for Electronically Tunable Third-Order Switched-Capacitor Filter with Feedforward Signal to minimize Overshoot is shown in Figure 2. The circuit consists of three op-amps (µA 741) with wide identical gain bandwidth product Switched-Capacitor. Switched-Capacitor can replace resistors, which was proposed earlier \hyperref[b1]{[2]}. The input sinusoidal voltage is applied to the inverting 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 feedforward input signal is given to the inverting terminal of the second op-amp. SC is used as feedback. The output of the second op-amp is supplied as noninverting 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 function. The High-pass function is seen at the inverting input of the first op-amp.  
\section[{Circuit Analysis and Design Equations}]{Circuit Analysis and Design Equations}\par
Op-amp (µA 741) is an internally compensated op-amp, which represented by "Single pole model", ( ) ( )0 0 0 / A s A S ? ? = +\textbf{(1)}\par
Where, ( )0 0 / / , A s A S GB S ? = =\textbf{(2)}\par
Where,0 S ? >> ?? ???? = ? ???? 1 ???? 2 ???? 3 ?? 4 ?? 1 ?? 3 +?? 2 ?? 2 +?? 3 ??+?? 4\par
The voltage transfer function for band-pass filter:?? ???? = ? ?????? 1 ???? 2 ?? 4 ?? 1 ?? 3 +?? 2 ?? 2 +?? 3 ??+?? 4\par
The voltage transfer function for high-pass filter:?? ???? = ?? 3 ?? 4 ?? 1 ?? 3 +?? 2 ?? 2 +?? 3 ??+?? 4\par
Where?? 1 = ?? 1 + ?? 2 + ?? 3 + ?? 4 ?? 2 = ???? 1 ?? 1 + ???? 2 ?? 2 ?? 3 = ???? 1 ???? 2 ?? 2 + ???? 2 ???? 3 ?? 3 ?? 4 = ???? 1 ???? 2 ???? 3 ?? 3\par
The circuit was designed using coefficient matching technique i.e. by comparing these transfer functions with General Third-order transfer functions \hyperref[b9]{[10]}. The general Third-order transfer function is given byT(S) = 3 0 2 0 2 0 3 0 1 2 2 3 3 S Q 1 1 S Q 1 1 S S S S ? + ? ? ? ? ? ? ? ? + ? + ? ? ? ? ? ? ? ? + ? + ? + ? + ? + ? (6)\par
By comparing (3), (4), and (  {\ref 5}) with (6), we get the design equation as This shows that the op-amplifier is an "integrator", Thus Electronically Tunable Third-Order Switched-Capacitor Filter transfer function at three different terminals are given below. The voltage transfer function for low-pass filter:\par
(3) (4) \hyperref[b4]{(5)} Electronically Tunable Third-Order Switched-Capacitor Filter with Feedforward Signal to minimize Overshoot (GB) and four Capacitors with MOSFET, which form  V.?? 1 + ?? 2 + ?? 3 + ?? 4 = 1 ???? 1 ?? 1 + ???? 2 ?? 2 =W \{1+1 /Q\} (8) ???? 1 ???? 2 ?? 2 + ???? 2 ???? 3 ?? 3 =W \{1+1/Q (9)\textbf{(7)} 
\section[{Sensitivity}]{Sensitivity}\par
The sensitivities of 0 ? and Q in this Electronically Tunable third-order Switched-capacitor Filter are as follows.?? C 1 ?? 0 = ? 1 3 C 1 ?? C 2 ?? 0 = ? 1 3 C 2 ?? C 3 ?? 0 = ? 1 3 \{C 3 ? 1\} ?? C 4 ?? 0 ? 1 3 C 4 ?? ???? 1 ?? 0 = ?? ???? 2 ?? 0 = ?? ???? 3 ?? 0 = 1 3 S C 1 Q = ? 1 3 (1 + ??)C 1 S C 2 Q = ?(1 + ??)C 2 ? 1 (?? 2 + ?? 3 ) ? 1 3 ? ?? C 3 ?? = ?(1 + ??) ? 1 (?? 2 + ?? 3 ) ? 1 3 ? 2 3?? 3 ? ?? C 4 ?? = ? 1 3 (1 + ??) C 4 ?? GB 1 ?? = ?(1 + ??) ? ?? 2 ?? 2 + ?? 3 ? 2 3 ? ?? GB 2 ?? = ? 1 3 (1 + ??) ?? GB 3 ?? = ?(1 + ??) ? ?? 3 ?? 2 + ?? 3 ? 2 3 ? VI. 
\section[{Experimental Set Up}]{Experimental Set Up}\par
The circuit consists of three op-amps (µA 741) with wide identical gain bandwidth product (GB) and different Values of circuit merit factor Q with center frequency f 0 =15 KHz. The general operating range of this filter is 10 Hz to 1.2 MHz The value of GB (GB 1 =GB 2 =GB 3 ) is ( 2?? × (5.6) × 10 5 rad/sec). The table1 shows the capacitor values for different circuit merit factor Q. MOSFETs are driven by two nonoverlapping clocks. The input voltage of 0.5mV is applied. The table1 shows the capacitor values for different circuit merit factor Q. 
\section[{VII.}]{VII.} 
\section[{Result and Discussion}]{Result and Discussion}\par
Following observations are noticed for Lowpass, Band-pass and High-pass at corresponding terminals. 
\section[{a) Low-Pass Response}]{a) Low-Pass Response}\par
The figure 3 shows the low pass response for different values of circuit merit factor Q.  The maximum pass-band gain varies between 91.3dB to 94dB and the gain roll-off per octave varies between 17 to 18dB/octave. But in previous reported configuration maximum pass-band gain varies between 82dB to 87dB. Also, the gain roll-off per octave in stopband varies between 14 to 19dB/octave \hyperref[b13]{[14]}. The maximum pass-band gain increase with increase in Global Journal of Researches in Engineering ( )F Volume XIV Issue VII Version I ???? 1 ???? 2 ???? 3 ?? 3 =W\textbf{(10) 0 3}\par
four Capacitors with MOSFET, which form Switched -Capacitor. The circuit performance is studied for values of circuit merit factor Q but after Q?4 this value gets stabilized at the maximum pass-band gain. The 18dB/octave for third order switched-capacitor filter. The response shows no overshoot for all the values of circuit merit factor Q where as the previous reported configuration shows overshoot with increase in Q (for Q=10, the overshoot is 14 dB) \hyperref[b13]{[14]}. 
\section[{b) High-pass response}]{b) High-pass response}\par
The figure 4 shows the High pass response for different values of circuit merit factor Q.  The Gain roll-off in stop-band varies between 17.4dB to 18dB/octave which is close to the ideal value of 18 dB /octave for third order Switched-Capacitor filter .Also, the gain is stabilized for all values of circuit merit factor Q ? 0.4 . But in previous reported Configuration, the Gain roll-off in stop-band varies between 11 to 12dB/octave. Also, the gain can't be stabilized at 0dB for all values of circuit merit factor Q \hyperref[b13]{[14]}. The peak gain for overshoot is minimizing from 44dB to 5dB due to the feedforward input signal that's given to the second Op-amp in the proposed circuit configuration. The gain gets stabilized almost at 0 dB for all values of Q ? 0.4. The response shows overshoot for all the values of Q ? 4. The analysis for the responses are summarizes in the table 3. c) Band-pass response\par
The figure 5 shows the Band-pass response for different values of circuit merit factor Q.  The maximum pass-band gain varies between 39dB to 62.5dB. Also, the bandwidth varies between 43.2 KHz to 59.2 KHz and Gain roll-off in trailing part varies between 11.6 to 12dB/octave. But in previous reported configuration the maximum pass-band gain varies between 33dB to 73dB.Also, the bandwidth varies between 59.4 KHz to 22 KHz and Gain roll-off in trailing part varies between 8dB/octave to 13dB/octave \hyperref[b13]{[14]}. The maximum pass-band gain increases with increase in circuit merit factor Q. The bandwidth decreases with increasing in values of circuit merit factor Q but after Q?4 this value gets stabilized at 43.2 KHz. For lower values of circuit merit factor Q, this filter can be used for wide bandwidth and for higher values of circuit merit factor Q it can be used for narrow bandwidth. There is no shift in the central frequency. It is also observed that the pass band distribution of frequency is symmetric for both sides. The gain roll-off/octave in leading and trailing part of the response is same. The circuit works better band pass response for Q ?0.4. 
\section[{VIII.}]{VIII.} 
\section[{Conclusions}]{Conclusions}\par
A realization of Electronically Tunable Third-Order Switched-Capacitor Filter with Feedforward Signal to minimize Overshoot has been proposed. The filter circuit can be used for both narrow as well as for wide bandwidth, so this circuit works for electronically tunable bandwidth. The gain roll-off for this circuit is close to the ideal value. The gain gets stabilized almost at 0 dB for all values of Q ? 0.4.The Low pass filter function works practically only for higher merit factor Q. The circuit the proposed circuit configuration, the peak gain for overshoot is minimizing from 44dB to 5dB due to the feedforward input signal.\begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-2.png}
\caption{\label{fig_0}Figure 1 :}\end{figure}
       \begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{P{0.07244318181818181\textwidth}P{0.18352272727272728\textwidth}P{0.2028409090909091\textwidth}P{0.1786931818181818\textwidth}P{0.2125\textwidth}}
\tabcellsep \tabcellsep values of Q\tabcellsep \tabcellsep \\
Q\tabcellsep ?? 1 (µf)\tabcellsep ?? 2 (µf)\tabcellsep ?? 3 (nf)\tabcellsep ?? 4 (µf)\\
0.1\tabcellsep 286.8\tabcellsep 7.9\tabcellsep 19.2\tabcellsep 705.3\\
0.4\tabcellsep 91.3\tabcellsep 2.5\tabcellsep 19.2\tabcellsep 906.2\\
0.8\tabcellsep 58.7\tabcellsep 1.6\tabcellsep 19.2\tabcellsep 939.7\\
1\tabcellsep 52.2\tabcellsep 1.4\tabcellsep 19.2\tabcellsep 946.4\\
4\tabcellsep 32.6\tabcellsep 0.9\tabcellsep 19.2\tabcellsep 966.5\\
8\tabcellsep 29.3\tabcellsep 0.8\tabcellsep 19.2\tabcellsep 909.8\\
10\tabcellsep 28.7\tabcellsep 0.77\tabcellsep 19.2\tabcellsep 970.5\end{longtable} \par
 
\caption{\label{tab_0}Table 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2} \par 
\begin{longtable}{P{0.056666666666666664\textwidth}P{0.17\textwidth}P{0.14355555555555555\textwidth}P{0.10955555555555554\textwidth}P{0.31355555555555553\textwidth}P{0.056666666666666664\textwidth}}
\tabcellsep \tabcellsep \multicolumn{3}{l}{Graph (Fig. 3)}\tabcellsep \\
Q\tabcellsep Max. Passband Gain (dB)\tabcellsep f 0L (kHz)\tabcellsep f 0L (kHz) f 0 ?\tabcellsep \multicolumn{2}{l}{Gain Roll-off in stop band dB/Octave Octave (kHz) starting at (kHz)}\\
0?1\tabcellsep 91.3\tabcellsep 20\tabcellsep 5\tabcellsep 17\tabcellsep 215\\
0?4\tabcellsep 93.4\tabcellsep 38\tabcellsep 23\tabcellsep 17.7\tabcellsep 90\\
0.8\tabcellsep 93.6\tabcellsep 43\tabcellsep 28\tabcellsep 18\tabcellsep 60\\
1\tabcellsep 93.8\tabcellsep 43\tabcellsep 28\tabcellsep 18\tabcellsep 60\\
4\tabcellsep 94\tabcellsep 44\tabcellsep 29\tabcellsep 18\tabcellsep 60\\
8\tabcellsep 94\tabcellsep 44\tabcellsep 29\tabcellsep 18\tabcellsep 60\\
10\tabcellsep 94\tabcellsep 44\tabcellsep 29\tabcellsep 18\tabcellsep 60\end{longtable} \par
 
\caption{\label{tab_1}Table 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3} \par 
\begin{longtable}{P{0.07548262548262548\textwidth}P{0.0722007722007722\textwidth}P{0.07548262548262548\textwidth}P{0.13455598455598455\textwidth}P{0.1640926640926641\textwidth}P{0.029536679536679537\textwidth}P{0.21003861003861005\textwidth}P{0.06563706563706563\textwidth}P{0.022972972972972974\textwidth}}
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{3}{l}{Graph (Fig. 4)}\tabcellsep \\
\tabcellsep \tabcellsep \tabcellsep \multicolumn{3}{l}{Gain Roll-off in}\tabcellsep \tabcellsep Gain\\
Q\tabcellsep f 0H (kHz)\tabcellsep f 0 ? f 0H (kHz)\tabcellsep dB/Octave\tabcellsep \multicolumn{2}{l}{stop band Octave Starting at ( kHz )}\tabcellsep \multicolumn{3}{l}{Stabilization Peak Gain of overshoot (dB) f (dB) S (kHz)}\\
\multicolumn{3}{l}{0.1 158 143}\tabcellsep \multicolumn{2}{l}{17.4}\tabcellsep 2\tabcellsep -3\tabcellsep 460\tabcellsep 0\\
0.4\tabcellsep 37\tabcellsep 22\tabcellsep \multicolumn{2}{l}{18}\tabcellsep 3.5\tabcellsep 0\tabcellsep 170\tabcellsep 0\\
0.8\tabcellsep 19\tabcellsep 4\tabcellsep \multicolumn{2}{l}{18}\tabcellsep 5\tabcellsep 0\tabcellsep 46\tabcellsep 0\\
1\tabcellsep 13\tabcellsep 2\tabcellsep \multicolumn{2}{l}{18}\tabcellsep 5\tabcellsep 0\tabcellsep 46\tabcellsep 0\\
4\tabcellsep 13\tabcellsep 2\tabcellsep \multicolumn{2}{l}{18}\tabcellsep 5\tabcellsep 0\tabcellsep 40\tabcellsep 3\\
8\tabcellsep 13\tabcellsep 2\tabcellsep \multicolumn{2}{l}{18}\tabcellsep 5\tabcellsep 0\tabcellsep 40\tabcellsep 5\\
10\tabcellsep 13\tabcellsep 2\tabcellsep \multicolumn{2}{l}{18}\tabcellsep 5\tabcellsep 0\tabcellsep 40\tabcellsep 5\end{longtable} \par
 
\caption{\label{tab_2}Table 3 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{4} \par 
\begin{longtable}{P{0.51\textwidth}P{0.3\textwidth}P{0.04\textwidth}}
\tabcellsep Overshoot observed in dB\tabcellsep \\
\multicolumn{3}{l}{Q Previous Reported circuit Proposed circuit}\\
0.1\tabcellsep 0\tabcellsep 0\\
1\tabcellsep 0\tabcellsep 0\\
5\tabcellsep 38\tabcellsep 3\\
10\tabcellsep 44\tabcellsep 5\end{longtable} \par
 
\caption{\label{tab_3}Table 4 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{5} \par 
\begin{longtable}{P{0.16451612903225807\textwidth}P{0.12444168734491315\textwidth}P{0.06538461538461539\textwidth}P{0.12022332506203474\textwidth}P{0.02109181141439206\textwidth}P{0.016873449131513646\textwidth}P{0.2889578163771712\textwidth}P{0.012655086848635236\textwidth}P{0.016873449131513646\textwidth}P{0.01898263027295285\textwidth}}
\tabcellsep \multicolumn{5}{l}{Gain roll-off values are close to ideal value of}\tabcellsep \\
XIV Issue VII Version I\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
( ) F Volume\tabcellsep \tabcellsep \tabcellsep \tabcellsep r\tabcellsep \tabcellsep \\
Global Journal of Researches in Engineering\tabcellsep Q\tabcellsep Max. Passband gain (dB)\tabcellsep f 1 (kHz)\tabcellsep f 2 (kHz)\tabcellsep BW (kHz)\tabcellsep \multicolumn{2}{l}{dB/ octave Gain Roll-off / octave in stop Octave starting at (kHz) dB/ octave Octave starting at (kHz) band Leading Part Trailing Part}\\
\tabcellsep 0?1\tabcellsep 39\tabcellsep \multicolumn{4}{l}{0.4 55 54.6 5.8}\tabcellsep 0.6\tabcellsep 12\tabcellsep 206\\
\tabcellsep 0?4\tabcellsep 52\tabcellsep \multicolumn{3}{l}{0.8 60 59.2}\tabcellsep 6\tabcellsep 3\tabcellsep 12\tabcellsep 61\\
\tabcellsep 0.8\tabcellsep 57\tabcellsep \multicolumn{3}{l}{1.2 52 51.8}\tabcellsep 6\tabcellsep 3\tabcellsep 12\tabcellsep 40\\
\tabcellsep 1\tabcellsep 58\tabcellsep \multicolumn{3}{l}{1.3 51 50.7}\tabcellsep 6\tabcellsep 3\tabcellsep 12\tabcellsep 41\end{longtable} \par
 
\caption{\label{tab_4}Table 5 :}\end{figure}
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\end{document}
