Electronically Tunable Minimum Component Biquadratic Filters for Interface Circuits

doi:10.4236/cs.2011.23033

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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

E-mail: [email protected]

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

,, ,

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



kT q

 (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

,, ,

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



, 1



, 1



. 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.

Figure 2. Schematic implementation for CC-CDBA using BJT technology.

M. SAĞBAŞ

239



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



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:



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



1212 1

out n

in pnp n

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:

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



121 2

nnpn

DssCCRR sβαCRC Rβα

 (9)

Using Equation (9), non-ideal the undamped natural

frequency and the quality factor becomes

,n12 pn

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)

0.5

CR k

p

(12)

0.5

CRk

n

(13)

where,





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

ωω ω

SS S



 (14)

0.5

αn1p

== βα CRk

SS  (15)

where,





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-

ce of the center

nstrate workability of the other output

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

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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