Circuits and Systems, 2011, 2, 237-241
doi:10.4236/cs.2011.23033 Published Online July 2011 (http://www.SciRP.org/journal/cs)
Electronically Tunable Minimum Component Biquadratic
Filters for Interface Circuits
Mehmet Sağbaş
Department of Electronics Engineering, Maltepe University, Istanbul, Turkey
Received November 23, 2010; revised May 24, 2011; accepted June 1, 2011
Abstract
In this paper, two new electronically tunable filter configurations are proposed. The proposed filters operate
current-mode (CM), voltage-mode (VM), transimpedance-mode (TIM) and transadmittance-mode (TAM).
The first configuration realizes second-order VM band-pass and TAM high-pass filter characteristics from
the same configuration. The second one realizes second-order TIM band-pass and CM low-pass filter char-
acteristics from the same configuration. They also use minimum number of electronic components (two ca-
pacitors and one active component namely; current controlled current difference transconductance amplifier).
The workability of the proposed structures has been demonstrated by simulation results.
Keywords: Second-Order Filters, CC-CDBA, Electronic Tunability, Current-Mode Circuits, Interface
Circuits
1. Introduction
It is well known that current-mode and voltage-mode are
still important integrated circuit (IC) operations [1-3].
Recently, there is a growing interest in transimpedance-
mode and transadmittance-mode operations. A current-
input voltage-output filter or voltage-input current-output
filter is described as an interface circuit connecting a
current-mode circuit to a voltage-mode circuit or a volt-
age-mode circuit to a current-mode circuit, respectively.
These interface circuits are needed in many applications
where VM and CM circuits are used together. In addition,
the other important application area of transadmittance-
mode filters are the receiver baseband blocks of modern
radio systems [4,5]. Also the outputs of the many digi-
tal/analog converters (DACs) are available as current
signals. Then the transimpedance-mode filters can be
used for conversion of the signals at the outputs of these
DACs, simultaneously. Therefore, several TAM- and
TIM-type filters are proposed using different-type active
components [6-12].
Simplicity, cost reduction, power consumption and
versatility are all important for the integrated circuit
manufacturers. Therefore, number of the components is
an important parameter. Therefore, numerous circuits are
proposed in literature that employing minimum number
of component [13-17]. However, these filters use at least
four electronic components. The proposed filter is com-
pared to the other filters reported in the literature by the
use of Table 1. According to Table 1, the proposed filter
has advantages over the proposed filters in Ref [13-14],
since it has electronically tunability property and no ex-
ternal resistors.
In this paper, two new second order filter configura-
tions using only single active component and two ca-
pacitors are presented. They realize CM, VM, TIM and
TAM second order filter characteristics from the same
configuration. Similar kinds of circuits in the literature
use more than three elements [13-16] (see Table 1).
The paper is organized as in the following sections: In
the next section, after a short introduction of CC-CDBA,
Table 1. Comparison of the cited references and the pro-
posed filter.
Ref. Active
Element
External
Capacitor
External
Resistor
Electronic
Tunability
[13] 1 CDBA2 2 No
[14] 1 CDBA2 2 No
[15] 1 CCII+ 2 2 No
[16] 1 CCCII2 1 Yes
Proposed
Filter 1 CC-CDBA2 0 Yes

238 M. SAĞBAŞ
two new filter configurations using CC-CDBA with two
capacitors are introduced. Sensitivities and simulation
results are discussed in Section 3.
2. Proposed Resistorless Circuit
Configurations and Their analysis
In order to accomplish electronic adjustability in CDBA,
Maheshwari and Khan have introduced current con-
trolled current controlled differencing buffered amplifier
(CC-CDBA) [17]. It has proven to be useful in many
voltage-mode and current-mode analog signal-processing
applications [17-21]. The circuit symbol of CC-CDBA is
shown in Figure 1 and its terminal equation can be writ-
ten as follow
,, ,
p
ppnnn zpnwz
VRiVRiiiivv (1)
Current controlled CDBA can easily be implemented
using bipolar junction transistor (BJT) technologies shown
in Figure 2 [17]. The parasitic input resistances Rp and
Rn using BJT implementation for Ip,n(t) 2Io can be
obtained as

22
T
pn
OO
V kT q
RR
I
I
 (2)
where, k is the Boltzman’s constant, T is the temperature
in Calvin and q is the electron charge; VT = kT/q is the
thermal voltage. Hence, Rp and Rn can be controlled by
varying the bias current Io. In addition to this, the quality
factor Q and the undamped natural frequency ωo depend
on Rp and Rn, which makes them electronically adjustable.
Taking the non-idealities of CDBA into account, the
above terminal equations can be rewritten as
,, ,
p
ppnnn zppnnwz
VRiVRiiiiV V




  (3)
where αp, αn and β are the current and voltage gains, re-
spectively, and can be expressed as αp = 1 − εp, αn = 1 −
εn, αβ = 1 − εv, with 1
p
 , 1
n
 , 1
v
 . εp and
εn denote the current tracking errors and εv denotes volt-
age tracking error.
The proposed voltage-mode second-order band-pass
filter circuit is shown in Figure 3(a). Routine analysis
yields the voltage transfer function as follows:
Figure 1. Block diagram of CC-CDBA.
I
1
I
2
I
0
Figure 2. Schematic implementation for CC-CDBA using BJT technology.

M. SAĞBAŞ
239

1
2
1212 1
out n
in pnp n
VsCR
VsCCRRs CRCR
 (4)
The proposed filter in shown Figure 3(a) also gives
minimum component transimpedance-mode high-pass
filter response. Therefore, the current output response of
the proposed circuit is

2
12
2
1212 1
out n
in pnp n
IsCCR
VsCCRRs CRCR

(5)
The proposed current-mode second-order band-pass
filter circuit is shown in Figure 3(b). Routine analysis
yields the voltage transfer function as follows:

2
2
1212 1
out n
in pnp n
IsCR
IsCCRRs CRCR

(6)
It also gives minimum component TIM low-pass filter
response. Therefore, the voltage output response of the
proposed circuit is

2
1212 1
out n
in pnp n
VR
IsCCRRs CRCR
 (7)
The undamped natural frequency and the quality factor
of the proposed circuit are obtained from the denomina-
tor of the transfer function as follows:
12
12
12
1,
p
n
o
p
n
pn
CC RR
ωQCRC R
CC RR

 (8)
Taking the non-idealities of CC-CDBA given in Equa-
tion (3) into account, the denominator polynomial of the
transfer function for the proposed filters becomes
 
2
121 2
p
nnpn
DssCCRR sβαCRC Rβα
n
 (9)
Using Equation (9), non-ideal the undamped natural
frequency and the quality factor becomes
,n12 pn
n
o
12 pnn1 p2n
βα CC RR
βα
ω=Q=
CC RRβα CR +CR (10)
From Equation (10), the quality factor Q and the un-
damped natural frequency ωo depend on Rp and Rn which
can be controlled by varying the bias current Io. There-
fore, they can be adjusted electronically.
3. Sensitivity Consideration and Simulation
Results
The ideal sensitivities of the natural frequency and the
quality factor with respect to passive components are
calculated as follows
0.5,
oooo
pn12
ωωωω
RRCC
====
SSSS (11)
11
0.5
p
QQ
R
C
CR k
SS
p (12)
22
0.5
n
QQ
R
C
CRk
SS
n (13)
where,


12
1
p
n
kCRCR
.
If the passive component values are chosen appropri-
ately, the ideal sensitivities will be smaller than 1.
Using Equation (10), the non-ideal sensitivities can be
found as
0.5, 0
oo o
n
ωω ω
β α
=
SS S
p
α

 (14)
0.5
n
QQ
β αn1p
== βα CRk
SS  (15)
where,


12
1np n kβα CRC R.
Again, if passive component values are chosen appro-
priately, the sensitivities due to non-ideal effects will
also be small than 1.
The performance of the filter topology given in Figure
3(a) is verified using PSpice. Each CC-CDBA is realized
by its BJT implementation shown in Figure 2 with the
transistor model of PR100N (PNP) and NR100N (NPN)
of the bipolar arrays ALA400 from AT & T [22]. In all
of the simulations, the voltage supplies of CC-CDBA are
taken as Vcc = 2.5 V and Vee = –2.5 V.
To confirm the obtained results with the theoretical
results and demonstrate tunability property of the pro-
posed configuration, the gain characteristics obtained by
PSPICE for two cases are plotted in Figure 4 together. In
these simulations, bias currents of CC-CDBA are Io = 10
μA and Io = 20 μA, for simulation 1 and 2, respectively.
(a) (b)
Figure 3. Circuit diagram of the proposed filters. (a) VM and TAM filter; (b) CM and TIM filter.

M. SAĞBAŞ
240
or these sim
cted by this figure, it is con-
cl
ce of the center
fr
nstrate workability of the other output
re
components
this paper, an electronically tunable VM band-pass, CM
Fulations, the passive components are taken 10 μA (Rp = Rn = 1.3 kΩ) and the passive
as C1 = C2 = 1 nF. These parameters correspond to a BP
filter with the with the center frequency fo = 124.34 kHz
and fo = 248.68 kHz, quality factor Q = 0.5, which are
found by using Equation (2) (with VT = 25.5 mV thermal
voltage at 25˚C) to find Rp and Rn, and then Equation (8).
The simulation results for the voltage-mode band-pass
filter shown in Figure 4.
From the results predi
uded that the simulation results are in good agreement
with the theoretical ones over a wide range of frequen-
cies. Although, the two characteristics well coincide over
a wide range of frequency, the numerical data reveal the
following differences; The maximum peak attenuations
for simulation I are −6.41 dB and −6.02 dB, the maxi-
mum peak attenuations for simulation II are 6.76 dB and
−6.02 dB, the center frequencies for simulation I are
117.34 kHz and 124.34 kHz, the center frequencies for
simulation II are 224.78 kHz and 248.68 kHz for simula-
tion and theoretical results, respectively.
Figure 4 also shows that the dependen
equency on the bias current of CC-CDBA is as predicted
theoretically; namely when the bias current increases two
times its tuning effect appears increasing the center fre-
quency two times.
In order to demo
sponses, the simulations are also done. For these simu-
lation, the bias currents of CC-CDBA are taken as Io =
are taken as C1 = C2 = 1 nF. The magnitude characteris-
tics of the filters which are shown in Figures 3(a) and
3(b) are given in Figure 5.
. Conclusions 4
In
band-pass, TAM high-pass and TIM low-pass filters using
current controlled CDBA are proposed. The proposed
circuit offers the following advantageous features: 1) use
of minimum number of electronic active and passive ele-
Figure 4. Simulation results for the proposed filter.
(a) (b)
(c)
Figure 5. (a) The transadmittance grain for the proposed circin Figure 3(a); (b) The current gain for the proposed circuit
in Figure 3(b); (c) The transimpedance gain for the proposed circuit in Figure 3(b).
uit

M. SAĞBAŞ
241
ecent Developments in Current Conve
de Circuits,” IEE Proceedings of Circuits
ments, namely; two grounded capacitors and one CC-
DBA; 2) the quality factor and natural frequencies can C
be adjusted electronically without changing the values of
the passive components; 3) single active component,
which means less power consumption; 4) having one or
more advantages over the proposed configurations in the
literature [13-16]; 5) low sensitivities; 6) TIM and TAM
outputs, this eliminates the need for current to voltage or
voltage to current conversions in DAC and ADC applica-
tions; The above properties most of which are well veri-
fied by the PSpice simulation make the proposed filter
attractive for circuit designers and engineers.
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