Electronically Tunable ECCII-Based Current-Mode Biquadratic Filters
Worapong TANGSRIRAT
E-mail: ktwrrapo@kmitl.ac.th,
Wanlop SURAKAMPONTORN
E-mail: kswatilop@kniiti.ac.th
Kiattisak KUMWATCHARA
E-mail: kiatti@mvlsi.eng.kmiti.ac.th
Faculty of Engineering and The Research Center for Communication and information Technology
(ReCCIT),King Mongkut's Institute of Technology Ladkrabang, Bangkok 10520, THAILAND
Treerasilapa DUMAWIPATA
Faculty of Engineering, King Mongkut's Institute of Technology North-Bangkok,
Bangkok 10800, THAILAND
Abstract
An electronically tunable current mode filter, using a CMOS-based
electronically tunable second generation current conveyor (ECCII), is presented and
analyzed. The proposed filter can be realized highpass bandpass and lowpass current
transfer functions simultaneously and both ωo and Q-factor can be separated
electronically tuned. PSPICE simulation results are given to verify the theoretical
expectation.
1. Introduction
Since the second generation current conveyor (CCII) was introduced by Sedra
and Smith in 1970, its applications and advantages in the realization of various active
filter transfer functions have received considerable attention [1-2]. At present, some
techniques to realize current-mode biquadratic filters using current conveyors and
discrete components is now becoming popular and have been published [3-6].
Although the selectivity of the filters considered in references [3-6] was quite
satisfactory, it requires a large number of CCIIs and passive components, needs
component matching conditions and can riot electronically tunable. Thus, these
1
configurations are not flexible and suitable for some a applications in the frequency
selective systems which requires such filter tunability. Recently, further research has
been specially focused on current conveyor which provide a variable current gain [7].
This configuration seem to be flexible and suitable for design and implementation of
tunable filters. Consequently, the tunable filter circuit, whose the natural frequency
ωo and the quality factor Q can be electronically tuned, are remarkably attractive for
the filter realizations.
Therefore, this paper addresses an alternative technique of constructing
electronically tunable current mode biquadratic filters by using a CMOS-based
electronically tunable second generation current conveyor (ECCII) with variable
current gain. The proposed circuit consist of three ECCII, three grounded resistors and
three grounded capacitors. Particularly, the use of grounded capacitors is importance
for an integrated circuit implementation. The circuit provide three types of current
transfers, highpass bandpass and lowpass, which is achieved simultaneously, and its
quality factor Q can be electronically adjusted and separated from the tuning of the
natural frequency ωo . Because of the circuit operation is in current mode, then its
expected to be useful in high frequency analogue signal processing applications [8].
Finally, simulation results using PSPICE is used to confirm the theoretical analysis of
the proposed circuit.
Figure 1: Proposed schematic diagram
2 Circuit description
The proposed biquad filtering network based on the electronically tunable
second-generation current conveyors (ECCIIs) is depicted in Fig.1 The circuit scheme
is based on the use of the CMOS-based ECCII which proposed by
2
Figure 2 : Circuit diagram of CMOS – based ECCII
Surakampontom and Kumwatchara [7], shown in Fig.2. By using Surakarnpontom's
ECCII notation, the port characteristics of the ECCII can be described by the
following set of equations :
iY = 0 , vX = vY and iZ = ± h32 iX
(1)
where X and Y are input ports, Z is the output port the plus and minus signs denote
positive and negative current conveyors, respectively, and h32 is the current transfer
ratio which can be accurately controlled by the ratio of the bias currents and can be
characterized by
Ai = h32 = Q, %
(2)
, $
where IA,IB are the bias current of the conveyor and n is the device dimension ratio
which related by the dimension of (M4 and M5) and (M/4 and ), Where (W/L)M5 /
(W/L)M4 = (W/L) M/5 /(W/L) M/4 = n. If all the transistors of the ECCII Circuit are the
Same dimension, then the dimension ratio n = 1
From a routine circuit analysis of the current model configuration shown in
Fig. 1, the current transfer functions are given by the following equations
3
HHP (s) =
HLP(s) =
, +3
=
, LQ
, /3
, LQ
and
HBP(s) =
, %3
, LQ
V
$ $ $   $ $ 
V + V   +  
 5&   (5& ) 
(3)
 $ $ 


 (5& ) 
=
$ $ $   $ $ 
V + V   +  
 5&   (5& ) 
 $ 
V 
 5& 
=
$ $ $   $ $ 
V + V   +  
 5&   (5& ) 
(4)
(5)
Where HHP HLP and HBP can realize the highpass, lowpass and bandpass filtering
functions, respectively. It is clearly seen that the three current transfer function are
simultaneously available in the same configuration. From the above equations, if we
set .A1 = A2 = A, then the natural frequency ωo and the quality factor Q of this
universal current-mode filter are given by
ωo =
and
Q=
$
5&
(6)
$$
(7)
Note that ωo can be electronically varied by tuning current ratio A and Q-factor can
be electronically tuned by varying current ratio A3. It is important to note that the ωo
and Q- factor can be independently controlled by electronic means.
The passive sensitivities of ωo and Q-factor for this biquad filter are obtained
as :
6 5ω R = 6 &ω R = −
(8)
6 4$ = 6 4$ = −
(9)
we can see that all the passive sensitivities are independent of the Q-factor and their
values are quite small.
4
By taking into consideration the non-idealities of the ECCIIs, namely, the
characteristics of the non-ideal ECCIIs can be expressed as
vX = βvY and iZ =
±α AiX
(10)
where β = (1 - εv) and εv (εv << 1) denotes the input voltage-tracking error and
α = (1 - εi) and εi (εi << 1) represents the current-tracking error of an ECCII.
A detailed analysis for the current transfer function of Fig. 1, the ωo and Q-factor can
be rewritten as
ωo =
and
Q=
$ αα α β β (11)
5&
(12)
$$α β αα β β where αi and βi are the voltage tracking error and current tracking error, respectively,
of the conveyor ECCIIj.
The active and passive sensitivities of this case can be represented by
(13)
6 5ωR& = 6 $4 $ α β = −
6αωRα β β = − 6α4 α β β =
(14)
and
(15)
All of the magnitude of the active and passive sensitivities are equal or less than unity.
6 ω$ R = 3 Simulation Results
The characteristics of the proposed circuit of Fig. 1 were studied by using the
PSPICE analogue simulatidn program [9] with the typical values for passive
components R = 1 kΩ and C = 1 nF, this choice leads to fO = ωO/2π =- 159 kHz. In
PSPICE simulation, transistor SPICE level 2 models were used and the aspect ratios
of the transistors were W/L = 50/10 for all the MOS devices. Bias currents IB and IC
were set to IB = 500 µA and IC = 400 µA.
5
The simulated current responses of the lowpass, highpass and bandpass
filtering are shown in Fig.3 with the bias current ratio of the conveyor were set to
A = A1 = A2 = A3 = 1 . The following setting was selected to obtain the filtering
responses with unity gain at the natural frequency fO ≅ 159 kHz and Q = 1.
Figure 3: Simulated results of LPF, HPF and BPF
characteristics of the proposed biquad filter
when A = A1 = A2 =A3 = 1
Figure 4: Bandpass filter responses when Q = 1 fixed
and A1 = A2 = A were varied.
Fig.4 shows the resultant characteristics of the bandpass output when the
circuit was tested for Q = 1 by adjusting the current gain A = Al = A2 , i.e. , A = 0.5, 1
and 1.5. From the obtained characteristics, we obtain fO about at 79.85 kHz, 158.91
kHz and 239.50 kHz, respectively.
6
To demonstrate the feasibility of the Q-factor by varying the current gain
A3 while the current gain A1 and A2 are both kept to be constant at unity. The obtained
responses of the bandpass output when A3 was varied, i.e., A3 = 2, 1 and 0.5 , are
shown in Fig.5.
Figure 5: Bandpass filter responses when
A1 = A2 = 1 fixed and Q-factor were varied.
As shown, all the simulated values were found to be in good agreement with
the theoretical ones deduced from eqns. (6) and (7). The simulated responses with
PSPICE have been quite good over a wide frequency range.
4 Conclusions
In summary, we have presented an electronically tunable current mode
universal biquad filters using only three ECCIIs, three grounded capacitors and three
grounded resistors. The proposed network can be realized highpass, lowpass and
bandpass filtering functions simultaneously from the same configuration and both ωo
and Q-factor can be separated electronically tunable. The circuit has been found to be
insensitive to the passive components which its used and the non-idealities of the
conveyors. PSPICE simulation results using Surakarnpontom's ECCII were very close
to the theoretical analysis.
Acknowledgments
The support of this work by the Japan International Cooperation Agency
(JICA) is gratefully acknowledge.
7
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