A Novel Multifunction CFOA-Based Inverse Filter

doi:10.4236/cs.2011.21003

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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

E-mail: [email protected]

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













































. (1)

H.-Y. WANG ET AL.

Considering the proposed scheme in Figure 1, three

CFOAs are used to construct the circuit functions. The

transfer functions can be expressed as:

13132

in in

VV yyyy

VV yy



 4

(2)

 (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

131324 24

in in

VV sCCsCGGG

VV GG



 (4)

 (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

 (6)

1 313 2424

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.

13 24421

in in

VV sCCsCGGG

VV sCC



 3

(8)

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.

Table 1. All the inverse filter functions using six passive elements.

Case Function at Vo1

Function at Vo2

1 Inverse lowpass Differential G0

sC1

sC2+G2

sC3

2 Inverse lowpass Inverse lowpass G0

sC1+G1

sC3

3 Inverse lowpass Differential G0

sC1

sC3+G3

4 Inverse bandpass Differential sC0

sC1

sC2+G2

sC3

5 Inverse bandpass Inverse lowpass sC0

sC1+G1

sC3

6 Inverse bandpass Differential sC0

sC1

sC3+G3

7 Inverse bandpass Integration G0

sC2+G2

sC4

8 Inverse bandpass Integration G0

sC2

sC3+G3

sC4

9 Inverse bandpass Inverse highpass G0

sC1+G1

sC2

sC4

10 Inverse highpass Integration sC0

sC2

sC3+G3

sC4

11 Inverse highpass Inverse highpass sC0

sC1+G1

sC2

sC4

12 Inverse highpass Integration sC0

sC2+G2

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.

realizations for inverse filter functions. The feasibility of

the proposed circuit is verified by simulation results.

5. References

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