Download Minimum Components Universal Filters

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
count circuits. This paper describes two new
the recently introduced fully differential current
minimum components filter biquads based on
conveyor (FDCCII) are presented. The biquads
the recently introduced FDCCII. Filters using
employ a single FDCCII, two grounded resistors
single active element have the advantages of
and two grounded capacitors, which are the
lower cost and power consumption.
minimum components, necessary to realize a
2nd-order filtering response (low-pass, high-pass,
II. CIRCUIT DESCRIPTIONS
band-pass, notch, and all-pass) unlike the
biquads reported in [1] employing more active
Two minimum components universal biquads,
and passive components. Simulation results
one of which is a voltage mode one, and the
validate the theoretical analysis.
other of which is a current mode one, are
Keywords: Analogue circuit design, Active
proposed as follows.
filters, Current conveyors
Circuit I
I. INTRODUCTION
The proposed voltage-mode universal biquad is
Recently, a new active element called the fully
shown in Fig.1. It is based on one FDCCII, two
differential current conveyor (FDCCII) has been
grounded
proposed [1] to improve the dynamic range in
capacitors. The matrix input-output relationship
mixed-mode
of the eight-terminal FDCCII [1] is shown as
applications
where
fully
differential signal processing is required. The
resistors,
and
two
grounded
follows.
application of FDCCII in filter design was also
demonstrated in [1], where three filter biquads
were described. Each biquad employs three
V X   0
V  0
 X   
 I Z   1

 
 I Z   0
FDCCII, two grounded capacitors and three
resistors, which have been implemented using
MOS transistors. From the wealth of knowledge
on RC active filters, it is known that it is
possible to design filter biquads using a single
0 1 1
0 1 1
0 0 0
1 0 0
1
0
0
0
I X  
0  I X  
1  VY 1 


0 VY 2 

0 VY 3 


VY 4 
(0)
active element, two resistors and two capacitors.
Such filters are known as minimum components
Circuit analysis yields the following voltage-
1
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

On the other hand, the specializations of the
(1)
(2)
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;
(v)

Vi1 s C1C 2  Vi 2 G1G2   Vi 3 sC 2 G2 
s 2 C1C 2  sC 2 G2  G1G2
2
Vo 4 
(i)
(iv) notch: Vi3 = 0, and Vi1 = Vi2 = Vin;
Vo 3 

numerator in Eq. (3) result in the following filter
functions:

Vi1 sC1G1  s 2 C1C 2  


Vi 2  sC1G1  

Vi 3 G1G2  sC 2 G2  

 2
s C1C 2  sC 2 G 2  G1G2
Vo 2
required in the design.
Vi1 sC 2 G2  G1G2  

V  G G   V  sC G 
1 2
i3
2 2 
 i2
s C1C 2  sC 2 G2  G1G2
2
If we make the resistor R2 be grounded, the
capacitor C2 be floating, and insert the voltage
(3)
input signal Vi3 into the floating terminal of the
capacitor C2, then
Vo 3 


Vi1 s 2 C1C 2  Vi 2 G1G2   Vi 3  sC 2 G2  (10)
s 2 C1C 2  sC 2 G2  G1G2
(4)
If Vi1=Vi2=Vin, and Vi3=0, then
The all-pass signal can be obtained from the
Vo1
 G1G2
 2
Vin s C1C 2  sC 2 G2  G1G2
output terminal Vo3 provided Vi1=Vi2=Vi3=Vin.
(5)
The resonance angular frequency ωo and the
quality factor Q are given by
2
Vo 2
s C1C 2
 2
Vin s C1C 2  sC 2 G2  G1G2
(6)
o 
Vo3
s 2 C1C 2  G1G2

Vin s 2 C1C 2  sC 2 G2  G1G2
(7)
Q
Vo 4
sC 2 G2
 2
Vin s C1C2  sC 2 G2  G1G2
(8)
G1G2
C1C 2
C1G1
C 2 G2
(11)
(12)
This shows that the biquad o and Q can not be
tuned orthogonally. This is not a limitation
associated with just the proposed biquad since it
Vo 5 Vo3  Vo 4

Vin
Vin

s C1C 2  sC 2 G2  G1G2
s 2 C1C 2  sC 2 G2  G1G2
2
is known that active RC filters based on a single
active element have non-independent o and Q
(9)
tunability [2]. It is possible for the biquad of
Fig.1 to provide non-interactive tunability if
more FDCCIIs are added to the circuit.
Note that no component matching conditions are
However, this is in conflict with the motivation
2
of the presented work, which is the design of
MOS transistors, in an FDCCII is needed for
filter biquads using a single FDCCII.
producing an extra output current Io2. The
resonance angular frequency ωo and the quality
factor Q are shown in Eqs. (11) and (12) by the
Circuit II
replacement of G1 with G2 and vise versa.
On the other hand, the proposed current-mode
universal biquad is shown in Fig.2. It is also
III. SIMULATION RESULTS
based on one FDCCII, two grounded resistors,
and two grounded capacitors. Routine analysis
To validate the theory predict of the proposed
yields the following current transfer functions:
minimum components universal biquads shown
I o1 I i1 sC 2 G2   I i 2  G1G2 
 2
I in
s C1C2  sC 2 G1  G1G2
I o2

I in
in Fig. 1 with Vi1=Vi2=Vin, and Vi3=0, and Fig.
2, we use level-49 H-Spice with 0.5 μm process
(13)
to
the
simulation.
The
CMOS
implementation of the fully differential second-
I i1  sC 2 G1  G1G2   I i 2  sC1G1 
s 2 C1C 2  sC 2 G1  G1G2
generation current conveyor is shown in [1]. The
(14)
simulation
circuits
are
built
with
R1=R2=15.9kΩ, and C1=C2=10pF with the
supply voltages: VDD = -Vss = 5V (for voltage
I o3

I in
mode) and 3.5V (for current mode), Vbp = -Vbn =
 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

do
1V, and the bias currents: IB = ISB = 1.65mA (for

voltage mode) and IB = 0.6mA, and ISB = 1mA
(for
current
mode).
The
voltage-mode
amplitude-frequency response with fo = 1MHz is
shown in Fig. 3. As can be seen, they agree very
The specializations of the numerators in Eqs.
well with theory. So do the current-mode
(13) to (15) result in the following filter transfer
amplitude and voltage and current-mode phase
functions:
(all-pass only)-frequency responses.
(i) low-pass: Ii2=Iin, Ii1=0, and Io1= Iout;
IV. DISCUSSION AND CONCLUSIONS
(ii) band-pass: Ii2=Iin, Ii1=0, and Io2=Iout; or Ii1=Iin ,
Ii2=0, and Io1=Iout;
This paper has presented two new filter biquads
(iii) high-pass: Ii1=Iin, Ii2=0, and Io3=Iout;
that employ the minimum number of active
(iv) notch: Ii2=Iin, Ii1=0, C1=C2, and Io3=Iout;
elements (i.e. one
(v) all-pass: Ii2=Iin, Ii1=0, C1=C2, and Io3+ Io2=Iout.
components
(i.e.
FDCCII)
two
and
resistors,
passive
and
two
capacitors). It is useful to give insight into how
To realize the above all-pass output signal, one
biquad filters based on a single FDCCII
more output terminal Z+, which can be easily
compare with other alternatives. For example, if
realized by using a current mirror [3] with four
we are to compare the proposed voltage-mode
3
biquad (Fig.1) with an op-amp based filter, a
very good example is the Sallen-Key circuit.
Both filter configurations employ the same
Y1
number of active elements (i.e. one) and passive
Y2
components (i.e. four). However, the Sallen-Key
Vi1
Y3
filter requires additional passive and active
R2
Z+
FDCCII
circuitry if notch or all-pass is required [2],
Vo1
Z-
Y4 X+
Vi3
Vo2
X-
C2
Vo4 - V + V
o5
o3
which is not the case with the proposed biquad
C1
R1
since it is capable of achieving filter functions
(LP, HP, BP, NH and AP) using the circuit
Vi2
shown in Fig.1. It is not possible to do a
comparison similar to the above between the
Fig. 1 Proposed voltage-mode universal biquad.
proposed universal biquad (Fig.2) and a currentmode single current conveyor-based universal
biquad because the recently published current
conveyor-based universal biquad uses “two”
Y4 Y3 Y2 Y1
current conveyors in addition to two capacitors
Ii1
and two resistors [6].
R2
Ii2
X+ FDCCII X-
References
1.
R1
Z+
C1
EL-ADAWY, A. A., SOLIMAN, A. M., and
Ii3
ELWAN, H. O.: “A novel fully differential
VLSI”, IEEE Trans Circuits Syst. II, 2000, 47,
C2
Io2
Io3
current conveyor and applications for analog
Z-
Io1
Fig. 2 Proposed current-mode universal biquad
(4), pp. 306-313.
2.
SEDRA, A. S., and BRACKETT, P. O., Filter
Theory and Design: Active and Passive (Chapter
9, p. 481): Matrix Publishers, Inc., 1978.
3.
CHANG, C. M., and PAI, S. K.: “Universal
current-mode OTA-C biquad with the minimum
components”, IEEE Trans. Circuits Syst. I,
2000, 47, (8), pp. 1235-1238.
4.
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., 2002, 89,
(12), pp. 897-903.
Fig. 3 Amplitude-frequency responses of the
proposed voltage-mode universal biquad
4