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Novel mixed-mode universal biquad configuration

Article  in  IEICE Electronics Express · November 2005

DOI: 10.1587/elex.2.548

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 IEICE Electronics Express, Vol.2, No.22, 548–553

Novel mixed-mode universal

biquad configuration
V. K. Singh1 , A. K. Singh2 , D. R. Bhaskar3 , and R. Senani4a)
1
Department of Electronics Engineering, Institute of Engineering and Technology,
Sitapur Road, Aliganj, Lucknow (UP), 226021, India
2
Electronics and Communication Engineering Department, Inderprastha Engineer-
ing College, Surya Nagar Flyover Road, Sahibabad, Ghaziabad (UP), 201010, India
3
Department of Electronics and Communication Engineering, Faculty of Engineer-
ing and Technology, Jamia Millia Islamia, New Delhi, 110025, India
4
Division of Electronics and Communication Engineering, Netaji Subhas Institute of
Technology (formerly, Delhi Institute of Technology), Sector-3, Dwarka, New Delhi,
110075, India
a) senani@nsit.ac.in, dr senani@yahoo.com

Abstract: Although a variety of CFOA-based biquads have been

known in the literature, any CFOA-based circuit capable of realising
universal biquad filters in all the four possible modes i.e. voltage-mode,
current-mode, trans-admittance-mode and trans-impedance-mode, has
not been reported in the literature so far. In this paper, a novel con-
figuration has been presented, which realises all the five generic filter
functions (namely, low-pass, band-pass, high-pass, notch and all-pass)
from the same circuit in all the four possible modes, employing only
four-Current feedback operational amplifiers (CFOA) along with two
grounded-capacitors as desirable for Integrated Circuit implementa-
tion. The workability of the circuit has been confirmed by hardware
implementation based on AD844 type CFOAs.
Keywords: current-feedback operational amplifiers, biquad filters,
current-mode circuits, circuit theory and design, mixed-mode filters
Classification: Integrated circuits

References

[1] A. K. Singh and R. Senani, “CFOA-based state variable biquad and its
high frequency compensation,” IEICE Electron. Express, vol. 2, no. 7,
pp. 232–238, April 2005.
[2] R. Senani, “Realization of a class of analog signal processing/signal gen-
eration circuits: Novel configurations using current feedback op-amps,”
Frequenz: J. Telecommunications, vol. 52, pp. 196–206, Sept.–Oct. 1998.
[3] R. Senani and S. S. Gupta, “Universal voltage-mode/Current Mode bi-
quad filter realised with current feedback op-amps,” Frequenz: J. Telecom-
munications, vol. 51, no. 7–8, pp. 201–208, 1997.
[4] M. T. Abuelma’atti, A. B. Bentrcia, and S. M. Al-Shahrani, “A novel
mixed-mode current-conveyor based filter,” Int. J. Electron., vol. 91, no. 3,


c IEICE 2005 pp. 191–197, March 2004.
DOI: 10.1587/elex.2.548
Received August 28, 2005
Accepted October 18, 2005
Published November 25, 2005

548
 IEICE Electronics Express, Vol.2, No.22, 548–553

1 Introduction
A current feedback op-amp (CFOA)-based state variable (SV) biquad filter
was recently presented in [1] which possesses the following advantageous fea-
tures: (i) simultaneous realisability of LP, HP and BP filters from the same
circuit (ii) availability of low-output impedance outputs in all the cases (iii)
use of both grounded-capacitors as desirable from Integrated Circuit imple-
mentation viewpoint (iv) independent control of various filter parameters (v)
low sensitivities, and (vi) employment of a reasonable number (only four) of
the CFOAs.
A limitation of the four-CFOA circuit of [1] was that it realised only three
(LP, HP, BP) of the five generic filter functions (namely, LP, HP, BP, Notch
and all-pass).
In this paper, we introduce a new four-CFOA-configuration which, by
contrast to the circuit of [1], not only realises all the five generic filter func-
tions in voltage mode but also realises all the five functions in current-mode,
trans-admittance-mode and trans-impedance-mode (hence, the name ‘mixed-
mode’) while providing all of the advantageous features mentioned above. To
the best knowledge of the authors, any ‘mixed-mode’ universal biquad em-
ploying only four CFOAs has not been reported in the literature earlier.
The workability of the proposed circuit has been confirmed by hardware
implementation based upon AD844 type CFOAs.

2 The proposed mixed-mode universal biquad structure

The proposed circuit which is devised using two inverting integrators and
two specially devised summers, each realised by a single CFOA, is shown in
Fig. 1. The universal biquad filters, in the four possible modes, are realisable
from the configuration of Fig. 1 as follows:

Fig. 1. The proposed CFOA-based mixed-mode universal

biquad configuration

(i) Voltage-mode universal biquad filter: Assuming ideal CFOAs, char-

acterized by iy = 0, iz = ix , vx = vy , and vw = vz , the five voltage-mode
transfer functions realized by this circuit are given by


r2 r3
V01 H0 ω02 − r1 r2 R1 C1 R2 C2
= = 2 1 r3 (1)


c IEICE 2005 Vin D(s) s + R1 C1 s + r2 R1 C1 R2 C2
DOI: 10.1587/elex.2.548
Received August 28, 2005
Accepted October 18, 2005
Published November 25, 2005

549
 IEICE Electronics Express, Vol.2, No.22, 548–553



ω0 r3 1
V02 H0 Q0 s r1 R1 C1 s
= = 1 r3 (2)
Vin D(s) s2 + R1 C1 s + r2 R1 C1 R2 C2


r3
V03 H0 s2 − r1 s2
= = 2 1 r3 (3)
Vin D(s) s + R1 C1 s + r2 R1 C1 R2 C2



  r3 r3
V04 H0 s2 + ω02 r1 s2 + r2 R1 C1 R2 C2
= = 2 (4)
Vin D(s) s + 1
R1 C1 s + r2 R1 Cr31 R2 C2

with the switch at BS position and choosing r2 = r3 ; r4 = r6 = r7

 


ω0 r3 1 r3
V04 H0 s2 − Q0
s + ω02 r1 s2 − R1 C1 s + r2 R1 C1 R2 C2
and = = 1 r3
Vin D(s) s2 + R1 C1 s + r2 R1 C1 R2 C2
(5)

with the switch at AP position and choosing r2 = r3 ; r4 = r5 = r6 = r7

Thus, the circuit realises a LP response at V01 , BP response at V02 , a HP
response at V03 , and notch and all pass responses at V04 under appropriate
conditions.
It is interesting to note that in all the five filters, all the three parameters
of interest can be tuned through separate resistors as follows. After adjusting
the bandwidth by R1 , the desired ω0 can be adjusted by R2 and finally, the
gain H0 of the filters (in all the five responses) is tunable by r1 .
We now show how the same circuit, with simple modifications, can also
realise universal biquad filters in the remaining three modes.
(ii) Current-mode universal biquad filter: With r1 and r7 deleted, the
circuit can be converted into an universal current-mode biquad with ideally
zero input impedance and ideally infinite output impedance. With an input
current Iin injected into input terminal ‘m’ and output current Iout taken
out from the node ‘n’, the circuit can realise all the five filter functions
in current mode. The general transfer function for this single-input-single-
output universal current-mode filter is given by-
 2

 
Iout r3 sr6 − C1 R11 r5 s + C1 C2 R11 R2 r4
=   (6)
Iin r3
s2 + s C11R1 + C1 C2 R 1 R2 r2

The circuit realises a LPF with r5 and r6 open circuited; a bandpass with
r6 and r4 open circuited; a high pass with r5 and r4 open circuited; a notch
with r5 open circuited (along with r2 = r4 = r6 = r0 (say) thereby yielding
H0 = r3 /r0 ) and finally, an all pass with r2 = r3 = r4 = r5 = r6 yielding
H0 = 1. The gains for LP, BP and HP responses are r3 /r4 , r3 /r5 and r3 /r6
respectively.
In the CM biquad, LP and HP filters have only H0 controllable (through
r4 and r6 respectively); in notch and AP, H0 is not tunable, however, BW
and ω0 can be independently adjusted (through R1 and R2 ) respectively and
finally, in BP realisation, BW, ω0 and H0 , all are independently tunable


c IEICE 2005
DOI: 10.1587/elex.2.548 (through R1 , R2 and r5 respectively).
Received August 28, 2005
Accepted October 18, 2005
Published November 25, 2005

550
 IEICE Electronics Express, Vol.2, No.22, 548–553

(iii) Trans-admittance universal biquad filter: In this case, we retain

the input resistor r1 but take the output Iout from z-terminal of the fourth
CFOA. The various functions realised and their features are similar to those
of case (ii).
(iv) Trans-impedance universal biquad filter: In this case, with r1
deleted the input will be a current Iin , however, the output voltages will be
V01 , V02 , V03 and V04 . The realisability conditions, parameters of filters and
their features are similar to those of case (i).
Thus, the proposed circuit is an universal mixed-mode biquad.

3 Sensitivity
From the various expressions of the filter parameters featuring in the expres-
sions (1)-(6) of the previous section, it can be easily deduced that all the
sensitivity coefficients of ω0 , Q0 , BW and H0 are given by

0 ≤ SxF ≤ 1 (7)

where F represents any of ω0 , Q0 , BW and H0 and x represents any of

the resistors and capacitors with respect to which the sensitivities are to be
evaluated. Thus, the circuit enjoys very low sensitivities in all the four modes
of operation.

4 Consideration of CFOA parasitics

To keep the influence of Cz and x-port resistance rx small, the external resis-
tors need to be chosen such that all the resistors are smaller than (1/ωCz ) and
larger than rx [1, 2, 3, 4]. On the other hand, since the circuit employs both
grounded capacitors (GC), it facilitates easy incorporation of z-pin parasitic
capacitances of the CFOAs and is also desirable from the integrated circuit
(IC) implementation view point. Thus, z-pin parasitic capacitance (Cz ) of
the CFOAs configured as integrators can be easily absorbed in capacitors C1
and C2 .

5 Hardware implementation results

The proposed circuit was implemented in hardware using IC AD844 type
CFOAs. In Fig. 2 (a)-(c) we present experimentally observed responses of
LP, BP, HP, notch and AP filers realised from the proposed VM biquad
with CFOAs biased with ±12 V DC. The circuit was designed for Q0 =
0.707, f0 = 112.5 kHz and H0 = 1; the components values were taken as
R1 = 1 kΩ, R2 = 2 kΩ, ri = 1 kΩ, i = 1-7, C1 = 1 nF and C2 = 1 nF. The
practically obtained responses of LP/HP filters are shown in Fig. 2 (a); those
for BP/notch are shown in Fig. 2 (b) and the magnitude response of AP filter
is shown in Fig. 2 (c). For obtaining correct AP response, the resistors r4 , r5
and r6 were required to be adjusted to the following values: r4 = 0.993 kΩ,


r5 = 0.689 kΩ and r6 = 0.797 kΩ.
c IEICE 2005
DOI: 10.1587/elex.2.548
Received August 28, 2005
Accepted October 18, 2005
Published November 25, 2005

551
 IEICE Electronics Express, Vol.2, No.22, 548–553

(a) (b)

(c)
Fig. 2. Experimentally determined frequency responses
for the CM LP/BP/HP/ Notch and AP filters re-
alised from the biquad of Fig. 1

In all the cases, the practically observed behavior of the circuit was found
to be in conformation to the theoretical results. The experimental results
thus, establish the workability of the proposed configuration.

6 Comparison with previously known mixed-mode biquads

A comparison with previously known mixed mode biquads [2, 3, 4] is now in
order. In this context, we note that whereas the circuits of [2, 3, 4] employ
seven to ten CFOAs or Current Conveyors, the new circuit employs a much
reduced number (only four!) of CFOAs. Furthermore, whereas the earlier
circuits [2, 3, 4] realise only VM and CM biquads, the present one realises,
in addition, trans-impedance and trans-admittance mode biquads also and
hence, is a true mixed-mode universal biquad.

7 Concluding remarks
A novel configuration has been presented which realises all the five generic
filter functions (namely, low-pass, band-pass, high-pass, notch and all-pass)
from the same circuit in all the four possible modes namely, voltage-mode,
current-mode, trans-admittance-mode and trans-impedance-mode and hence,
is a true mixed-mode biquad, employing only four-Current feedback opera-


c IEICE 2005 tional amplifiers (CFOA) along with two grounded-capacitors as desirable for
DOI: 10.1587/elex.2.548
Received August 28, 2005 Integrated Circuit implementation. The circuit allows tunabilityof the three
Accepted October 18, 2005
Published November 25, 2005

552
 IEICE Electronics Express, Vol.2, No.22, 548–553

filter parameters, namely, BW, ω0 and H0 through separate resistors in all

the five responses and enjoys low sensitivity properties. The workability of
the proposed circuit has been confirmed by hardware implementation results
based on AD844 type CFOAs. To the best knowledge of the authors, the pro-
posed circuit is the only one which is capable of realising universal biquads in
all the four modes using only four CFOAs and any other CFOA-based circuit
having these properties with only four CFOAs has never been reported in the
literature earlier.

Acknowledgment
This work was performed at the Analog Signal Processing Research Lab. at
NSIT.

c IEICE 2005
DOI: 10.1587/elex.2.548
Received August 28, 2005
Accepted October 18, 2005
Published November 25, 2005

553

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