SECOND-ORDER ACTIVE FILTER USING A SINGLE
CURRENT CONVEYOR
Doru E. Tiliute.
str. Mesteacanului No.2, Bl.24, Sc.A, Apt. 10, Suceava 5800, Romania,
Email: dtiliute@eed.usv.ro
ABSTRACT
In this paper the author presents a new second-order currentmode active filter. It uses a single minus type current conveyor
and the minimum number of passive components. Low-pass,
high-pass, band-pass and notch responses are provided by this
circuit without any modification.
1. INTRODUCTION
Since its introduction [1] the current conveyor becomes very
attractive in the active filter implementation due to the important
advantages that current-mode operation has over the
conventional voltage-mode operation [2]. In second-order active
filters simulation the RLC shunt circuit is a useful circuit
prototype. For the simulation of the shunt RLC circuit, various
methods are used. These methods simulate either the ideal
inductors by means of gyrators [3], or lossy inductors [4], or
shunt LC circuits [5], [6] and use at least two current conveyors
or a single current conveyor and an additional active device [7].
This letter presents a new current mode active filter based on the
non-ideal inductor simulation which uses a single inverting
current conveyor.
Z in =
sC 1 R1 R 2
=
1 + sC 1 ( R1 + R 2 )
sL eq
L
1 + s eq
R eq
(1)
R1 R 2
R1 + R 2
(2)
where Leq and Req have the expressions
L eq = C 1 R 1 R 2 , R eq =
If a shunt capacitor is connected between X terminal of the
current conveyor and the ground, as shown in figure 2, an
equivalent resonant RLC circuit is obtained.
2. CIRCUIT DESCRIPTION
Figure 2 Current mode active filter and its equivalent
circuit
It was demonstrated [8] that the circuit presented in fig.1 is
equivalent with a floating non-ideal inductor, whose parameters
are: Leq= C1R1R2 and Req= R1R2/(R1+R2).
The behaviour of noninverting second-generation current
conveyor is described by the equation 3.
 iY  0 0 0 vY 
v  = 1 0 0  i 
 X 
 X
 iZ  0 − 1 0 vZ 
(3)
Solving the circuit using the equation above, this leads to the next
expressions for the currents in circuit:
Figure 1 Non-ideal floating inductor simulation using a
single second generation current conveyor
If instead of consider the output node as being floating, we will
consider it as being grounded, the input impedance of the circuit
is found:
sC 1 R 1 R 2
Ii
s 2 C 1 C 2 R 1 R 2 + sC 1 ( R 1 + R 2 ) + 1
s 2 C 1 C 2 R1 R 2
Ii
= 2
s C 1 C 2 R 1 R 2 + sC 1 ( R 1 + R 2 ) + 1
I R1 =
(4)
IC2
(5)
that are the band-pass and high-pass responses of the circuit.
The angular frequency ωo and the quality factor Q are given by
the next expressions:
 C 2 R1 R 2
1
1

, Q =
ω0 =
1/ 2
( C 1C 2 R1 R 2 )
(R1 + R 2 )  C1



1/ 2
(6)
Since high-pass gain is equal to one, the gain of the band-pass
response, at the angular frequency (ω = ωo) depends on the
resistor ratio:
R2
<1
R1 + R 2
(7)
In order to obtain higher outputs impedance for the currents of
interest, additional current followers or current conveyors may be
used. The circuit sensitivities are small:
S Rω1o = S Rω 2o = S Cω1o = S Cω o2 = −
S RQ2 = − S RQ1 =
1,
1
S CQ 2 = − S CQ1 = ,
2
2
R1 − R 2
2 ( R1 + R 2 )
The magnitudes of the last two sensitivities are smaller than 0.5.
If we consider the non-ideal current conveyor, its current and
voltage gain are not exactly equal to one, as they were assumed
to be in equation 3. In this case, the function of the device is
described by the hybrid equation 8
 iY   0 0 0 vY 
v  = β 0 0 i 
 X
 X 
 iZ   0 ± α 0 vZ 
(8)
sβ C 1 R1 R 2
Ii
β s 2 C 1 C 2 R 1 R 2 + sC 1 ( R 1 + R 2 ) + α
(9)
IC2 =
Figure 3 Frequency response of the circuit from fig.2
- High-pass response (IC2)
- Band-pass response (IR1)
The results from figure 3 show a good match with the theoretical
prediction.
4. CONCLUSIONS
Certainly the transfer functions change
I R1 =
GAIN
H BP (ω o ) =
and the resonance gain, for the band-pass output, is HBP(fo)=
HBP0= 0.9.
β s 2 C 1 C 2 R1 R 2
Ii
β s C 1 C 2 R1 R 2 + sC 1 ( R 1 + R 2 ) + α
A new current-mode active filter is presented. It is very simple
and contains a minimum number of components required to
achieve a second-order transfer function. Two types of transfer
functions are available at once, without any circuit modification.
However, due to the circuit simplicity, fo, Q and HBP0 are not
independently adjustable.
(10)
2
REFERENCES
and the new expressions for the angular frequency and Q are
 βC 2 R1 R 2
1
α

, Q=
ω0 =
1/ 2
(R
R
)
C1
+
( βC1C 2 R1 R 2 )
1
2 



1/ 2
The sensitivities of ωo and Q to the device’s gains are small too.
1
Sαωo = −S βωo = − S βQ = , SαQ = 0
2
Unlike the circuit in figure 1 where the output currents, IR1, IC2,
are floating, in the proposed circuit they flow towards the ground.
In this way it is easier to extract them and is possible to directly
drive other current-mode circuits, as Gilbert cells, in order to
process these signals. In addition, because the simulated inductor
is a lossy one, only a single current conveyor is necessary to
achieve the filter. No additional shunt resistor across C2 is
required to control the Q factor; the equivalent shunt resistance is
a function of R1 and R2 which are used to bias the current
conveyor.
3. SIMULATED RESULTS
To verify the theoretical results, SPICE simulations were
performed. The high-pass, low-pass and band-pass responses of
the circuit are displayed in figure 3. The components’ values are
R1= 5K, R2= 45K, C1=1n, C2= 100n; the current conveyor is of
high performance type and uses an AD844 operational amplifier
and simple Wilson current mirrors. In these conditions the
resonance frequency is fo=1.06KHz, the quality factor is Q = 3
[1]. Smith K. C. and Sedra A., ‘The current conveyor: a new
circuit building block’, Proc. IEEE, Vol. 56, Aug. 1968,
pp.1368-1369.
[2]. Barrie Gilbert, ‘Current Mode Circuits from a Transliniar
Viewpoint’, Analogue IC Design The Current Mode Approach,
C. Toumazou, F.J.Lidgey (editors), Peter Pelegrinus 1990,
pp.127-178
[3]. Sedra A. S. and Smith K. C. ‘A second- generation current
conveyor and its application’, IEEE Trans. Circuit Theory, 1970,
17, pp. 132-134
[4]. S. Ozoguz and C. Acar ‘Universal current-mode filter with
reduced number of active and passive components’ Electronics
Letters, 22nd May 1997, Vol.33, No.11. pp 948-949
[5]. C. M. Chang ‘Universal active filter with single input and
three outputs using CCIIs’ Electronics Letters, 28th October
1993, Vol. 29, No.22, pp 1932-1933
[6]. C. M. Chang ‘Current-mode lowpass, bandpass and highpass
biquads using two CCIIs’ Electronics Letters, 11th November
1993, Vol. 29, No.23, pp 2020-2021
[7]. D.-S. Who, Y.-S. Hwang and al. “New multifunction filter
using an inverting CCII and a voltage follower’ Electronics
Letters, 31st March 1994, Vol. 30 No.7, pp 551-552.
[8]. R. Senani, ‘Novel higher-order active filter design using
current conveyors’ Electronics Letters 24th October 1985,
Vol.21 No.22