Engineering, 2010, 2, 179-183
doi:10.4236/eng.2010.23025 lished Online March 2010 (http://www.SciRP.org/journal/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
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.

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. = 2f0
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 033 nF 5·6 nF 100
5 1 82 nF 5·6 nF 100
10 22 33 nF 5·6 nF 100
20 33 01  F 4·7 nF 100
50 10
082  F 68 nF 82
70 10 22  F 022  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 12 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 36 14 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 31 3
5 99 55 11 10 89
10 87 10 3 20 17
20 74 21 10 31 21
50 58 55 30 70 40
70 52 67 60 90 30

G. N. Shinde ET AL. 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. Srinivasan, “Synthesis of transfer functions using the
operational amplifier pole,” International Journal of Elec-
tronics, Vol. 40,
[4] M. Ghausi, “Analog active filters,” IEEE Transactions on
Circuits and Systems, Vol. 31, pp. 13-31, 1984.
[5] G. N. Shinde, P. B. Patil, A. B. Kadam and P. R. Mirkute,
“Active-R biquadratic filter using positive feedforward
signal,” BRI’S JAST, Vol. 5(I and II), pp. 7-15, 2
[6] W. R. Grise, “Applications of switched capacitor circuits
in active filters and instrumental amplifiers,” Vol. 3, No.
pp. 1523-1526, 1999.
[7] U. Kumar, “Design and a nalytical study of strays-insen-
sisitive switched capaci
Electronic Components., Vol. 19, pp. 13-24, 1996.
[8] Z. X. Sun, “Active-R filter: A new biquadratic with four
terminal,” International Journal of Electronics, Vo
4, pp. 523-530, 1993.
[9] A. Kumar and S. K. Saha, “MOS switched capacitor
sample data filters,” Vol. 5
] M. A. Shah, M. R. Rathu and S. Z. Iqbal, “SITO elec-
tronically tunable high output impedance current mod
universal filter,” Analog-Integrated Circuit and Signal
Processing, Vol. 47, pp. 335-338, 2006.
[11] G. J. Yu, C. Y. Huang, J. J. Chen and B. D. Liu, “Design
of current mode square root domain ban
reduced voltage,” Analog-Integrated Circuit and Signal
Processing, Vol. 44, pp. 239-250, 2005.
[12] R. Senani and S. S. Gupta, “Low universal filter using
only current followers as active elemen
Journal of Electronics and Communication, Vol. 60, pp.
251-256, 2006.
[13] J. G. Jiang and Y. N. Wang, “Design of a tunable fre-
quency CMOS
filter,” Microelectronics Journal, Vol. 37, pp. 84-90, 2006.