Circuits and Systems, 2011, 2, 14-17
doi:10.4236/cs.2011.21003 Published Online January 2011 (http://www.SciRP.org/journal/cs)
A Novel Multifunction CFOA-Based Inverse Filter
Hung-Yu Wang1, Sheng-Hsiung Chang2, Tzu-Yi Yang1, Po-Yang Tsai1
1Department of Electronic Engineering, National Kaohsiung University of
Applied Scienc es, Ka o hsiu n g, Taiwan, China
2Department of Optoelectronic Engineering, Far East University, Hsin-Shih, Taiwan, China
Received October 7, 2010; revised November 3, 2010; accepted November 17, 2010
Abstract
We present a novel multifunction inverse biquad configuration based on current feedback operational ampli-
fiers (CFOAs) and grounded passive elements. The proposed scheme can be used to realize inverse lowpass,
inverse bandpass and inverse highpass filter functions. The relevant coefficients of the inverse filters are or-
thogonal adjustable by independent passive elements. All the passive elements in the proposed scheme are
grounded to benefit easier electronic tunability. With the high input impedance and low output impedance
properties, the scheme is input and output cascadable for voltage operation. The feasibility of the proposed
scheme is demonstrated by HSPICE simulations.
Keywords: Multifunction, Inverse Filter, CFOA
1. Introduction
In communication, control and instrumentation systems,
there are numerous situations in which an electrical sig-
nal is altered through a linear or nonlinear transformation
by a processing or a transmission system. So it is neces-
sary to recover the input signal from the available dis-
torted output signal resulted from the signal progress.
This can often be done by using a system that has an
inverse transfer characteristic of the original system [1].
For digital signal processing, several methods for ob-
taining digital inverse filters have been established [2].
Nevertheless, for analog signal processing, only a few
works are known for realizing continuous-time analog
inverse filters [1,3-6].
In [1], a general approach is presented for obtaining
the inverse transfer function for linear dynamic systems
and the inverse transfer characteristic for non-linear re-
sistive circuits. In [3], a procedure for deriving cur-
rent-mode, four-terminal floating nullor (FTFN)-based
inverse filter from the voltage-mode filter is given. It
uses the method in [1] and dual transformation [7] during
the procedure. Due to the use of dual transformation, this
approach can only be applied to planar circuit. By the use
of adjoint transformation, another easier procedure for
deriving current-mode FTFN-based inverse filter from
the voltage-mode filter is presented and it is applicable to
nonplanar circuits [4]. All the proposed approaches in
[1,3,4] are useful for obtaining single-input single-output
inverse filters. Additional various inverse current-mode
and voltage-mode filters are presented in [5] and [6],
respectively. However, each circuit proposed in [5,6] has
one inverse filter function. In this paper, we present a
novel inverse filter scheme based on CFOAs and
grounded passive elements. By slight modification of the
passive elements of the proposed scheme, various in-
verse filter functions can be realized. The presented
scheme possesses high input impedance and low output
impedance which enables the convenience of connecting
with the other stage in cascade. The workability of the
proposed scheme is verified by HSPICE simulations.
The simulated results confirm the theoretical prediction.
2. The Proposed Circuit
The current-feedback operational amplifier, such as
AD844 from Analog Devices Inc. [8], has gained the
acceptance of researchers as a building block in circuit
design. The advantages of CFOAs are their constant
bandwidths, independent closed-loop gains and high
slew-rate capabilities [9]. The CFOA can be described
using the following matrix-relations:
0100
0000
1000
0010
xx
yy
zz
ww
VI
I
V
I
V
VI





  

 


  

 




. (1)

H.-Y. WANG ET AL.
15
Considering the proposed scheme in Figure 1, three
CFOAs are used to construct the circuit functions. The
transfer functions can be expressed as:
13132
04
oo
in in
VV yyyy
VV yy

 4 (2)
21
4
o
in
Vy
Vy
 (3)
If the admittances are y0 = G0, y1 = sC1, y2 = sC2+G2, y3
= sC3 and y4 = G4, the functions of inverse lowpass filter
and inverse integrator can be realized at Vo1 and Vo2, re-
spectively. They are given by
2
131324 24
04
oo
in in
VV sCCsCGGG
VV GG

 (4)
21
4
o
in
V
s
C
VG
 (5)
From Equation (4), it is clear that the coefficients of the
s2, s1 and s0 terms in the numerator and the term in de-
nominator are tunable by the values of C1, C2, G2 and G0
respectively. So the system parameters, such as the corner
angular frequency

o and quality factor Q of the inverse
filter are tunable by independent passive elements.
In Equation (2), if the admittances are y0 = sC0, y1 =
sC1, y2 = sC2+G2, y3 = sC3 and y4 = G4, the functions of
inverse bandpass filter and inverse integrator can be re-
alized at Vo1 and Vo2, respectively. They can be given by
21
4
o
in
V
s
C
VG
 (6)
2
1 313 2424
04
oo
in in
VV sCCsCGGG
VV sCG

 (7)
Similarly, if the admittances are y0 = sC0, y1 = G1, y2 =
sC2+G2, y
3 = G 3 and y4 = sC4, the functions of inverse
highpass filter and inverse differentiator can be realized
at Vo1 and Vo2, respectively. They can be expressed by
Figure 1. The proposed inverse filter scheme.
2
13 24421
2
04
oo
in in
VV sCCsCGGG
VV sCC

 3
(8)
21
4
o
in
VG
VsC
 (9)
The output of Vo3 has the same function as Vo1, it pro-
vides the additional output which makes the filter appli-
cation more flexible.
From (2) and (3), after the restricting ourselves only to
the using of six passive elements, we can derive all the
filter functions as shown in Tab le 1. It can be found that
the coefficients of all terms in the numerator and de-
nominator of the transfer functions are adjustable by in-
dependent passive elements. Furthermore, for the pre-
sented scheme in Figure 1, it can be observed that all
the employed passive elements are grounded. The use
of grounded passive elements conduces to easier elec-
tronic tunability and integrated-circuit implementation
[10]. A number of realizations of tunable grounded pas-
sive elements can be found in the literature [10-13]. The
passive sensitivities of corner angular frequency are
equal to 0.5 for the inverse filter realizations in Tab le 1,
so they can be classified as insensitive. In addition, the
proposed configuration in Figure 1 possesses the char-
acteristics of input and output cascadability due to its
high input impedance and low output impedance. So it is
convenient to connecting other stages at both input and
output terminals for signal processing. It must be noted
that the proposed inverse lowpass and inverse bandpass
filters in [6] are included in the filter realizations of Ta -
ble 1. The presented scheme in Figure 1 provides more
flexible functions and different realization with identical
configuration.
3. Simulation Results
To verify the potentialities of the proposed scheme, cir-
cuit simulations of the presented multi-function inverse
filters have been carried out. The commercial current
feedback amplifiers AD844 macromodel with ± 12 V
voltage supply is used to realize the CFOA in Figure 1
[12]. Using an AD844 IC to realize the CFOA, its
equivalent model can be shown in Figure 2. It is impor-
tant to understand that the low input impedance at x ter-
Vo3
Vin
Vo2
Vo1
Figure 2. The realization of CFOA with an AD844 IC.

H.-Y. WANG ET AL.
16
Table 1. All the inverse filter functions using six passive elements.
Case Function at Vo1 Function at Vo2 y0 y
1
y
2
y
3
y
4
1 Inverse lowpass Differential G0 sC1 sC2+G2 sC3 G
4
2 Inverse lowpass Inverse lowpass G0 sC1+G1 G
2
sC3 G
4
3 Inverse lowpass Differential G0 sC1 G
2
sC3+G3 G
4
4 Inverse bandpass Differential sC0 sC1 sC2+G2 sC3 G
4
5 Inverse bandpass Inverse lowpass sC0 sC1+G1 G
2
sC3 G
4
6 Inverse bandpass Differential sC0 sC1 G
2
sC3+G3 G
4
7 Inverse bandpass Integration G0 G
1
sC2+G2 G
3
sC4
8 Inverse bandpass Integration G0 G
1
sC2 sC3+G3 sC4
9 Inverse bandpass Inverse highpass G0 sC1+G1 sC2 G
3
sC4
10 Inverse highpass Integration sC0 G
1
sC2 sC3+G3 sC4
11 Inverse highpass Inverse highpass sC0
sC1+G1 sC2 G
3
sC4
12 Inverse highpass Integration sC0
G
1
sC2+G2 G
3
sC4
minl is locally generated and does not depend on feed-
back. This is very different from the “virtual ground” of
a conventional operational amplifier used in the current
summing mode which is essentially an open circuit until
the loop settles [8]. In the simulation, the values of all
resistors and all capacitors are 40 kΩ and 1 nF, respec-
tively.
It is found that the workability of all the inverse biqu-
ids in Table 1 is in good agreement with our theoretical
prediction. The typical frequency responses of inverse
lowpass (the case 1 of Table 1), inverse bandpass (the
case 4 of Table 1) and inverse highpass (the case 12 of
Table 1) are shown in Figure 3. The deviation to theo-
retical response is due to the parasitic impedance of
nonideal CFOA [14].
(b)
4. Conclusions
We have proposed a novel scheme for the realization of
an input and output cascadable voltage-mode multifunc-
(c)
Figure 3. Typical frequency responses of inverse filters: (a)
inverse lowpass; (b) inverse bandpass; (c ) inver se highpass.
tion inverse filter. It consists of CFOAs and grounded-
passive elements. Many various inverse filter functions
are realized by slight modification of the passive ele-
ments of the proposed scheme. It offers more convenient (a)

H.-Y. WANG ET AL.
17
realizations for inverse filter functions. The feasibility of
the proposed circuit is verified by simulation results.
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