TECHNIA
International Journal of Computing Science and Communication Technologies, VOL. 4, NO. 1, July 2011. (ISSN 0974-3375)
OFC based High Input Impedance First Order and
Multifunctional Biquadratic Filter Sections with
Grounded Components and Their Higher Order
Applications
T. Parveen
Electronics Engineering Department, A.M.U., Aligarh, India
tahiraparveen@rediffmail.com
Abstract
This paper presents new configurations for
realizing high input impedance first order, multifunctional
biquadratic filter (MBF) sections and their applications for
the realization of fifth order and eighth order filters using
cascade approach. The first order high input impedance
filter section is realized using single plus type OFC along
with two grounded admittances, which gives the realization
of low pass and high pass filters. The high input impedance
multifunctional biquadratic filter (MBF) is realized using
only two plus type low voltage OFCs along with four
grounded admittances, which enables easy cascadablity. The
MBF gives the realization of second order low pass, high pass
and band pass responses with appropriate selection of
admittances without any requirement for matching
conditions. The multifunctional biquadratic filter (MBF)
along with first order filter section is then used for the
realization of fifth order filter and the realization of eighth
order filter has been obtained by cascading the identical
sections of multifunctional biquadratic filter (MBF). The
filter has the advantages of low sensitivity, high input
impedance, independently tunable gain of the filters, and the
use of only grounded passive components. Simulation results
show excellent performance at low voltage operation of +
0.75 volts.
This paper presents new configurations for OFC
based high input impedance low output impedance voltage
mode first order and second order filters. The first order
filter section is realized using single plus type OFC along
with two grounded admittances, which gives the
realization of low pass and high pass filters. The
multifunctional biquadratic filter (MBF) is realized using
only two plus type low voltage OFCs along with four
grounded admittances, which gives the realization of
second order low pass, high pass and band pass responses
with appropriate selection of admittances without any
requirement for matching conditions. To show the
cascadablity, the multifunctional biquadratic filter (MBF)
along with first order filter section is then used for the
realization of fifth order filter and by cascading the
identical sections of multifunctional biquadratic filter
(MBF) for the realization of eighth order filter. The filters
has the advantages of low sensitivity, high input
impedance, independently tunable gain of the filters, and
the use of only grounded passive components. Simulation
results show excellent performance at low voltage
operation of + 0.75 volts.
Keywords: Operational Floating Conveyor, High input
impedance, first order filter, multifunctional biquadratic filter,
and higher order filters.
II. FIRST ORDER FILTER SECTIONS
I. INTRODUCTION
T The active filters with high input impedance [2, 3,
4], are of great importance because several blocks of this
kind can be directly connected in cascade to implement
higher order filters without any need to interpose active
separating stages voltage signal processing applications. In
[2] the Circuit for low pass, high pass and band pass filters
with high input impedance is proposed using only
grounded passive components and four plus type CCIIs. In
[3], the circuit is proposed to realize low pass, high pass
and band pass filters with high input impedance using
grounded passive components and three CCIIs. Recently
in [4] the two high input impedance circuits each with one
input and three outputs using three CCIIs along with four
grounded capacitors and three grounded resistors are
realized. However, the circuit has the advantage of high
input impedance, but employed large number of active and
passive devices.
710
First order low pass, high pass filter sections play an
important role in the realization of odd- order and higher
order filters. In addition these sections are also useful in
instrumentation
systems,
and
signal
processing circuits.
A. Low Pass Section
The first order high input impedance low pass filter
Section is shown in Fig.1. It is realized using single OFC
along with two grounded admittances. For the plus type
OFC, the v-i relations are defined by:
,
,
,
(1)
Routine analysis yields low pass transfer function
given by
y
TLP ( s )
Vo
Vi
1 / R1C 2
1
s
R2 C 2
(2)
TECHNIA
International Journal of Computing Science and Communication Technologies, VOL. 4, NO. 1, July 2011. (ISSN 0974-3375)
Vin
Y
OFC
X
W
Vin
Vo
Z
Y1
V2
Z1
OFC
R2
X1
C2
Y2
Y2
W1
V1
X2
Y4
W2
V3
Y1
R1
V4
Z2
OFC
Y3
Fig. 3: OFC Based Multifunctional Biquadratic Filter
Fig. 1: First Order OFC Based Low Pass Filter
The filter parameters pole frequency (
the low pass filter is given as
o
1
R2 C 2 ,
o)
and gain of
(3)
1
TLP ( s)
B. High Pass Section
The first order high pass filter section is shown in Fig.
2 with high pass transfer function given by
Vo
Vi
sC1 / C 2
1
s
R2 C 2
The filter parameters pole frequency (
the high pass filter is given as
THP ( s)
o
1
H HP
R2 C 2
o)
and gain of
OFC
X
Vo
Z
W
R2
select
,
Y3
G3 ,
VLP
Vin
1
R1 R3 C 2 C 4
s2
s
1
R2 C 2
1
R4 C 4
1
R 2 R4 C 2 C 4
(7)
we
select
1
1
,
2
2
2
,
Y3
sC3 ,
, then this results in the following high pass
voltage transfer function, given by
C1
C2
Y
we
B. High Pass Filter
If
(4)
(5)
From equation (3) and (5) it can be seen that the
gain of low pass and high pass filter s can be tuned
independently through R1 and C1 respectively without
disturbing the pole frequency. The proposed filter has high
input impedance hence is inherently cascadable and is
suitable for realization of high order filters.
Vin
If
then this results in the following low pass
voltage transfer function, given by
2
LP
A. Low Pass Filter
C2
C1
THP ( s )
VHP
Vin
s2
s2
1
R2 C 2
s
C1C 3
C 2C4
1
R4 C 4
1
R2 R4 C 2 C 4
(8)
C. Band Pass Filter
If we select,
,
,
and
, then this results in the following
band pass voltage transfer function, given by
TBP ( s)
VBP
Vin
s
s2
s
1
R2 C 2
C1
R3 C 2 C 4
1
R4 C 4
1
R2 R 4 C 2 C 4
(9)
From equations (7), (8) and (9), it is seen that low
pass, high pass and band pass responses are realized
through appropriate selection of grounded admittances,
without any requirement for matching conditions. The
pole frequency o, band width and the quality factor Q of
the low pass, high pass and band pass filters are given by
the following equations,
o
1
R2 R4 C2 C4
Q
1 / R2 R4C2C4
1
R2C2
1
R4C4
(10)
The gain of the low pass, band pass and high pass
filters are given by
Fig. 2: First Order OFC Based High Pass Filter
III. MULTIFUNCTIONAL BIQUADRATIC FILTER
The proposed multifunctional biquadratic filter is
shown in Fig. 3. It consists of two plus type OFCs along
with four grounded admittances, which gives the
realization of second order low pass, high pass and band
pass responses with appropriate selection of admittances
without any requirement for matching conditions. The
analysis of the circuit of Fig.3 yields the following voltage
transfer functions
H LP
R 2 R4
H BP
R1 R3
R2 R4 C1
H
R3 ( R2 C2 R4 C 4 ) HP
C1C3
C2 C4
(11)
From eqns. (10) and (11) it can be seen that the gain
of LP, BP and HP filters can be tuned independently
through passive components R1/R3, R3/C1 and C1/C3
respectively. However the proposed circuit realizes low Q
filters; low Q filters are more or less insensitive to
component variations [5], which can be enhanced by
cascading identical stages.
IV. REALIZATIONS OF H IGHER ORDER FILTERS
The OFC based VM high order filters are designed
from high input impedance first order and multifunctional
(6)
711
TECHNIA
International Journal of Computing Science and Communication Technologies, VOL. 4, NO. 1, July 2011. (ISSN 0974-3375)
biquadratic filter (MBF) sections as depicted in sections 2
and 3. These filters are simple in design, are cascadable in
nature and suitable for IC implementation. Thus it is
possible to realize higher order filters by cascading
biquadratic filter sections for even n and biquadratic
sections along with an additional first order section for odd
values of n. With this cascade approach the realization of
higher order filter is reduced to a much simpler realization
of only second order filters. This section presents
examples for the realization of 5 th order and 8th order low
pass filters.
A. Fifth Order Low Pass Filter
The odd order functions can be realized by cascading
biquadratic sections of 3 along with an additional first
order filter of section 2. Consider the realization of 5 th
order low pass filter as an example of odd order function.
Fig.4 shows the block diagram representation of 5 th order
low pass filter.
sections 3. For C2 = C4 = C and R1 = R2 = R3 = R4 = R,
transfer function of 8th order low pass filter is given by
(16)
V. DESIGN AND SIMULATION
To demonstrate the performance of fifth order and
eight order voltage mode low pass filters presented in
section 4, the circuit is simulated using level 3 P-SPICE
Parameter in 0.5 µm CMOS process with supply voltages
VDD = - VSS = 0.75V using OFC model [6]. The circuit is
designed for centre frequency of 2.5MHz. For the C 2 = C4
= 6.3PF, design values obtained from equations (13) and
(14) are R1 = R2 = R3 = R4 = 10K. The simulated fifth
order LP response is shown in Fig.6 with a centre
frequency of 2.51 MHz shows good agreement with the
theory. It may be noted that pole Q increases as the order
of the filter increases.
Fig. 4: OFC Based Fifth Order Voltage Mode Low Pass Filter
The transfer function for nth order LP filter is
given as
n
TLP ( s)
s
n
a1 s
Ko
a2 s n
n 1
2
.......... a n
(12)
where
frequency of the nth order filter is given by
(13)
Fifth order low pass filter can be obtained by coupling
two identical biquadratic LP filter of sections 3 and first
order LP filter of section 2. For C2 = C4 = C and R1 = R2 =
R3 = R4 = R, transfer function of 5 th order low pass filter is
given by
5
LP
LP
4
5
i
5
3
2
2
2
3
3
4
4
5
5
(14)
B. Eighth order Low Pass Filter
Fig. 6: Frequency Response of Fifth Order Low Pass Filter
The simulated eighth order LP response is shown in
Fig.7 also shows close conformity with the theory.
From Fig.7, It is evident as order n increases the pole
Q of the filter increases. The theoretical value of Q8
obtained from equation (14) is equal to 1.66. The resulting
plot is shown in Fig. 7, gives a simulated value of Q8
=1.48, shows good agreement with the theory.
To present an example for the realization of even
order filter function, consider the realization of 8 th order
low pass filter using identical blocks of section 3. Fig.5
shows the block diagram representation of 8 th order low
pass filter.
in
SECOND
ORDER LP
SECTION
O1
SECOND
ORDER LP
SECTION
O2
SECOND
ORDER LP
SECTION
O3
SECOND
ORDER LP
SECTION
O
Fig. 5: OFC Based Eighth Order Voltage Mode Low Pass Filter
The pole Q of n identical cascaded second order
filters (Qn) is related by pole Q of individual biquad (Qo)
[1] by
Qn
Qo
2
1/ n
1
1/ n
(15)
Eight order low pass filter can be obtained by
coupling 4 identical second order low pass functions of
712
Fig. 7: Frequency Response of Eighth Order Low Pass Filter
VI. CONCLUSION
The proposed first order and multifunctional
biquadratic filter are cascadable in nature. The
TECHNIA
International Journal of Computing Science and Communication Technologies, VOL. 4, NO. 1, July 2011. (ISSN 0974-3375)
multifunctional biquadratic filter (MBF) along with first
order filter section are used for the realization of fifth
order filter and by cascading the identical sections of
multifunctional biquadratic filter (MBF) for the realization
of eighth order filter. Any type of high order filter i.e.,
either even order or an odd order functions can be realized
by cascading second order filter of section 4 and first order
filter of section 3. With this cascade approach the
realization of higher order filter is reduced to a much
simpler realization of only second order filters or first
order filters. The resulting filters consist of grounded
passive components; hence can be easily implemented in
IC-form. The proposed circuit also has low sensitivity,
simplicity, and high performance at low supply voltage of
0.75V, with a low power consumption of 3.2mW,
which shows a good overall performance.
713
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