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Minimum Components Universal Filters
Chun-Ming Chang and Hua-Pin Chen
Dept. of Electrical Engineering, Chung Yuan Christian University,
Chung-Li, Taiwan 32023, R. O. China
Abstract: Two new universal biquads based on the recently introduced fully differential current
conveyor (FDCCII) are presented. The universal biquads employ a single FDCCII, two grounded
resistors and two grounded capacitors, which are the minimum components, necessary to
simultaneously realize five 2nd-order generic filtering responses (low-pass, high-pass, band-pass,
notch, and all-pass) unlike the biquads reported in [1] employing more active and passive components,
and [2] without voltage-mode all-pass output signals or employing an extended 12-terminal FDCCII
for the current-mode realization. Simulation results validate the theoretical analysis.
Key-Words: Analogue circuit design, active filters, current conveyors, voltage-mode circuits, currentmode circuits.
1 Introduction
current-mode signals. This paper describes two
In 2000, a new active element called the fully
new minimum components filter biquads. The
differential current conveyor (FDCCII) has been
voltage-mode one has all-pass signals in
proposed [1] to improve the dynamic range in
addition to four other generic filtering (low-pass,
mixed-mode
fully
band-pass, high-pass, and notch) signals, and the
differential signal processing is required. The
current-mode one employs a 9-terminal FDCCII
application of FDCCII in filter design was also
smaller in size than the 12-terminal FDCCII
demonstrated in [1], where three filter biquads
used in [2].
applications
where
were described. Each biquad employs three
FDCCIIs, two grounded capacitors and three
2 Circuit Descriptions
resistors, which have been implemented using
Two minimum components universal biquads,
MOS transistors. From the wealth of knowledge
one of which is a voltage mode one, and the
on RC active filters, it is known that it is
other of which is a current mode one, are
possible to design filter biquads using a single
proposed as follows.
active element, two resistors and two capacitors.
Such filters are known as minimum components
2.1 Voltage-Mode Universal Filter
count circuits and were realized recently [2].
The proposed voltage-mode universal biquad is
However, in [2], the voltage-mode all-pass
shown in Fig.1. It is based on one FDCCII, two
signal cannot be realized and the 8-terminal
grounded resistors, and two grounded capacitors.
FDCCII is expanded to be a 12-terminal
The matrix input-output relationship of the
FDCCII for realizing five generic biquadratic
eight-terminal FDCCII [1] is shown as follows.
1
0 1 1
0 1 1
0 0 0
1 0 0
V X   0
V  0
 X   
 I Z   1

 
 I Z   0
1
0
0
0
I X  
0  I X  
1  VY 1 


0 VY 2 

0 VY 3 


VY 4 
Vo 5 Vo3  Vo 4

Vin
Vin
s 2 C C  sC 2 G2  G1G2
 2 1 2
s C1C 2  sC 2 G2  G1G2
(0)
(9)
Note that no component matching conditions are
Circuit analysis yields the following voltage-
required in the design.
mode filter transfer functions:
Vo1 
Vi1 sC1G1   Vi 3 G1G2   
V  sC G  G G 

1 1
1 2
 i2

s 2 C1C 2  sC 2 G2  G1G2

Vo 2
On the other hand, the specializations of the
numerator in Eq. (3) result in the following filter
(1)

Vi1 sC1G1  s 2 C1C 2  


Vi 2  sC1G1  

Vi 3 G1G2  sC 2 G2  

 2
s C1C 2  sC 2 G 2  G1G2
functions:
(i)
low-pass: Vi1 = Vi3 = 0, and Vi2= Vin;
(ii)
band-pass: Vi1 = Vi2 = 0, and Vi3 = Vin;
(iii) high-pass: Vi2 = Vi3 = 0, and Vi1 = Vin;
(iv) notch: Vi3 = 0, and Vi1 = Vi2 = Vin;
(2)
(v)
capacitor C2 be floating, and insert the voltage
Vo 3 

input signal Vi3 into the floating terminal of the

Vi1 s C1C 2  Vi 2 G1G2   Vi 3 sC 2 G2 
s 2 C1C 2  sC 2 G2  G1G2
2
Vo 4 
If we make the resistor R2 be grounded, the
Vi1 sC 2 G2  G1G2  

V  G G   V  sC G 
1 2
i3
2 2 
 i2
s 2 C1C 2  sC 2 G2  G1G2
capacitor C2, then
(3)
Vo 3 


Vi1 s 2 C1C 2  Vi 2 G1G2   Vi 3  sC 2 G2  (10)
s 2 C1C 2  sC 2 G2  G1G2
The all-pass signal can be obtained from the
(4)
output terminal Vo3 provided Vi1=Vi2=Vi3=Vin.
The resonance angular frequency ωo and the
If Vi1=Vi2=Vin, and Vi3=0, then
quality factor Q are given by
Vo1
 G1G2
 2
Vin s C1C 2  sC 2 G2  G1G2
(5)
o 
Vo 2
s 2 C1C 2
 2
Vin s C1C 2  sC 2 G2  G1G2
(6)
Q
Vo3
s 2 C1C 2  G1G2

Vin s 2 C1C 2  sC 2 G2  G1G2
Vo 4
sC 2 G2
 2
Vin s C1C2  sC 2 G2  G1G2
G1G2
C1C 2
C1G1
C 2 G2
(11)
(12)
This shows that the biquad o and Q can not be
(7)
tuned orthogonally. This is not a limitation
associated with just the proposed biquad since it
(8)
is known that active RC filters based on a single
2
active element have non-independent o and Q
To realize the above all-pass output signal, one
tunability [3]. It is possible for the biquad of
more output terminal Z+, which can be easily
Fig.1 to provide non-interactive tunability if
realized by using a current mirror [4] with four
more FDCCIIs are added to the circuit. However,
MOS transistors, in an FDCCII is needed for
this is in conflict with the motivation of the
producing an extra output current Io2. The
presented work, which is the design of filter
resonance angular frequency ωo and the quality
biquads using a single FDCCII.
factor Q are shown in Eqs. (11) and (12) by the
replacement of G1 with G2 and vise versa.
2.2 Current-Mode Universal Filter
On the other hand, the proposed current-mode
3. Simulation Results
universal biquad is shown in Fig.2. It is also
To validate the theory predict of the proposed
based on one FDCCII, two grounded resistors,
minimum components universal biquads shown
and two grounded capacitors. Routine analysis
in Fig. 1 with Vi1=Vi2=Vin, and Vi3=0, and Fig. 2,
yields the following current transfer functions:
we use level-49 H-Spice with 0.5 μm process to
I o1 I i1 sC 2 G2   I i 2  G1G2 
 2
I in
s C1C2  sC 2 G1  G1G2
I o2

I in
do the simulation. The CMOS implementation
of the fully differential second-generation
(13)
current conveyor is shown in [1]. The simulation
circuits are built with R1=R2=15.9k, C1=C2=
I i1  sC 2 G1  G1G2   I i 2  sC1G1 
s 2 C1C 2  sC 2 G1  G1G2
10pF (for voltage mode), and R1=R2=3.18k,
(14)
C1=C2=50pF (for current mode),
with the
supply voltages: VDD = -Vss = 5V (for voltage
mode) and 3.5V (for current mode), Vbp = -Vbn =
I o3

I in
1V, and the bias currents: IB = ISB = 1.65mA (for
 I i1  sC 2 G1  G1G2   I i 2  sC1G1    (15)


2
 I i 3 s C1C 2  sC 2 G1  G1G2

2
s C1C 2  sC 2 G1  G1G2
voltage mode) and IB = ISB = 1.2mA (for current
The specializations of the numerators in Eqs.
be seen, they agree very well with theory. So do
(13) to (15) result in the following filter transfer
the voltage-mode and current-mode phase (all-
functions:
pass only)-frequency responses, shown in Figs.


mode). The voltage-mode and current-mode
amplitude-frequency responses with fo = 1MHz
are shown in Figs. 3 and 5, respectively. As can
4 and 6, respectively.
(i) low-pass: Ii2=Iin, Ii1=0, and Io1= Iout;
(ii) band-pass: Ii2=Iin, Ii1=0, and Io2=Iout; or Ii1=Iin ,
4. Discussion and Conclusions
Ii2=0, and Io1=Iout;
This paper has presented two new filter
biquads that employ the minimum number
of active elements (i.e. one FDCCII) and
passive components (i.e. two resistors, and
two capacitors). It is useful to give insight
(iii) high-pass: Ii1=Iin, Ii2=0, and Io3=Iout;
(iv) notch: Ii2=Iin, Ii1=0, C1=C2, and Io3=Iout;
(v) all-pass: Ii2=Iin, Ii1=0, C1=C2, and Io3+ Io2=Iout.
3
into how biquad filters based on a single
(Chapter 9, p. 481): Matrix Publishers, Inc.,
FDCCII compare with other alternatives.
1.
For example, if we are to compare the
proposed voltage-mode biquad (Fig.1) with
an op-amp based filter, a very good example
is the Sallen-Key circuit. Both filter
2.
configurations employ the same number of
active elements (i.e. one) and passive
components (i.e. four). However, the SallenKey filter requires additional passive and
active circuitry if notch or all-pass is
1978.
[4] CHANG, C. M., and PAI, S. K.: “Universal
current-mode OTA-C biquad with the minimum
components”, IEEE Trans. Circuits Syst. I, Vol.
47, No. 8, 2000, pp. 1235-1238.
[5] TU, S. H., CHANG, C. M., and LIAO, K. P.:
“Novel versatile insensitive universal currentmode biquad employing two second-generation
current conveyors”, Int. J. Electron., Vol. 89, No.
12, 2002, pp. 897-903.
required [3], which is not the case with the
proposed biquad since it is capable of
achieving all filter functions (LP, HP, BP,
NH and AP) using the circuit shown in Fig.1.
Fig. 1 is also better than the recently
reported single-FDCCII-based voltage-mode
biquad filter [2] without the all-pass
function. Similarly, the proposed currentmode universal biquad (Fig.2) is simpler
than the current conveyor-based universal
R2
Y1
Y2
Vi1
Y3
Z+
FDCCII
Vo1
Z-
Y4 X+
Vi3
Vo2
X-
C2
Vo4 - V + V
o5
o3
C1
filter [5] and the recently reported one [2]
employing a 12-terminal FDCCII in
addition to two capacitors and two resistors.
R1
Vi2
Fig. 1 Proposed voltage-mode universal biquad.
References
[1] EL-ADAWY, A. A., SOLIMAN, A. M., and
ELWAN, H. O.: “A novel fully differential
Y4 Y3 Y2 Y1
current conveyor and applications for analog
R1
Ii1
VLSI”, IEEE Trans Circuits Syst. II, Vol. 47, No.
R2
Ii2
X+ FDCCII X-
4, 2000, pp. 306-313.
[2] CHANG, C. M., AL-HASHIMI, B. M.,
Z+
C1
WANG, C. L., and HUNG, C. W.: “Single fully
Ii3
differential current conveyor biquad filters” IEE
Z-
C2
Io2
Io3
Io1
Proc.-Circuits Devices Syst., Vol. 150, No. 5,
2003, pp.394-398
Fig. 2 Proposed current-mode universal biquad
[3] SEDRA, A. S., and BRACKETT, P. O.,
Filter Theory and Design: Active and Passive
4
Fig. 3 Amplitude-frequency responses of the
Fig. 5 Amplitude-frequency responses of the
proposed voltage-mode universal biquad
proposed current-mode universal biquad
Fig. 4 Phase-frequency response of the proposed
Fig. 6 Phase-frequency response of the proposed
voltage-mode all-pass biquad
current-mode all-pass biquad
5