Hindawi Publishing CorporationActive and Passive Electronic ComponentsVolume 2010, Article ID 362516, 5 pagesdoi:10.1155/2010/362516

Research Article

High-Input Impedance Voltage-Mode Multifunction Filter withFour Grounded Components and Only Two Plus-Type DDCCs

Hua-Pin Chen

Department of Electronic Engineering, Ming Chi University of Technology, Taishan 243, Taiwan

Correspondence should be addressed to Hua-Pin Chen, hpchen8888@xuite.net

Received 11 March 2010; Revised 10 May 2010; Accepted 20 May 2010

Academic Editor: Ali Umit Keskin

Copyright © 2010 Hua-Pin Chen. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This paper introduces a novel voltage-mode multifunction biquadratic filter with single input and four outputs using two plus-type differential difference current conveyors (DDCCs) and four grounded passive components. The filter can realize invertinghighpass, inverting bandpass, noninverting lowpass, and noninverting bandpass filter responses, simultaneously. It still maintainsthe following advantages: (i) using grounded capacitors attractive for integration and absorbing shunt parasitic capacitance, (ii)using grounded resistors at all X terminals of DDCCs suitable for the variations of filter parameters and absorbing series parasiticresistances at all X terminals of DDCCs, (iii) high-input impedance good for cascadability, (iv) no need to change the filtertopology, (v) no need to component-matching conditions, (vi) low active and passive sensitivity performances, and (vii) simplerconfiguration due to the use of plus-type DDCCs only. HSPICE and MATLAB simulations results are provided to demonstrate thetheoretical analysis.

1. Introduction

As a current-mode active device, the differential differencecurrent conveyor (DDCC) has the advantages of both thesecond-generation current conveyor (CCII) (such as largesignal bandwidth, great linearity, wide dynamic range) andthe differential difference amplifier (DDA) (such as high-input impedance and arithmetic operation capability) [1].This element is a versatile building block whose applicationsexist in the literature [1–7]. Voltage-mode active filterswith high-input impedance are of great interest becauseseveral cells of this kind can be directly connected forimplementing higher-order filters [3–11]. In 2003, Changand Chen proposed a universal voltage-mode filter with threeinputs and a single output [2]. The circuit can realize allfive different generic filtering responses but only highpassand bandpass responses have the advantage of high-inputimpedance. In 2004, Horng et al. proposed a multifunctionfilter with a single input and three outputs [3]. The circuitcan realize highpass, bandpass, and lowpass responses,simultaneously. However, it is based on two minus-typeDDCCs. In 2005, Ibrahim et al. proposed two single DDCC

biquads with high-input impedance and minimum numberof passive elements [4]. The highpass, bandpass, or lowpassfilter responses cannot be realized in the same configuration.In 2007, Chiu and Horng proposed a universal voltage-mode filter with three inputs and a single output [5]. Thecircuit has high-input and low-output impedance advantagesbut it uses three plus-type DDCCs. In the same year, Chenproposed a universal voltage-mode filter based on two plus-type DDCCs [6]. The proposed configuration suffers fromhigh-input impedance. Recently, Horng proposed anotheruniversal voltage-mode filter with three inputs and fiveoutputs [7]. However, it still uses three plus-type DDCCs.In this paper, a new voltage-mode multifunction biquadraticcircuit with single input and four outputs is presented.The proposed circuit employs only two plus-type DDCCs,two grounded capacitors, and two grounded resistors. Ithas the same advantages reported by Horng et al. [3],such as realization of highpass (HP), bandpass (BP), andlowpass (LP) filter responses from the same configura-tion, no requirements for component-matching conditions,the use of only grounded capacitors and resistors, high-input impedance, and low active and passive sensitivity

2 Active and Passive Electronic Components

Y1

Y2

Y3

DDCC

(2)

Z+

DDCC

(1)

X

Z+

X

Y1

Y2

Y3

Vin

Vo3

R1

C1

Vo1

Vo2

C2

Vo4

R2

Figure 1: The proposed high-input impedance voltage-modemultifunction biquad based on plus-type DDCCs.

performances. Moreover, the proposed circuit is simpler inconfiguration than the old circuit, since the use of only plus-type of DDCC is simpler than minus-type one like a CCII[11].

2. Circuit Description

The DDCC is a five-terminal analog building block and itsterminal relations are given by IY1 = IY2 = IY3 = 0,VX = VY1 − VY2 + VY3, and IZ = IX [1]. The proposedmultifunction biquadratic circuit comprises two plus-typeDDCCs, two grounded capacitors, and two grounded resis-tors, as shown in Figure 1. The use of grounded capacitorsmakes the circuit suitable for integration because groundedcapacitor circuit can compensate for the stay capacitancesat their nodes [12, 13]. Derived by each nodal equation ofthe proposed, the input-output relationship matrix form ofFigure 1 can be expressed as

⎡⎢⎢⎢⎣

sC1 0 −G1 0G2 sC2 0 01 −1 1 01 0 0 1

⎤⎥⎥⎥⎦

⎡⎢⎢⎢⎣

Vo1

Vo2

Vo3

Vo4

⎤⎥⎥⎥⎦ =

⎡⎢⎢⎢⎣

00

−Vin

0

⎤⎥⎥⎥⎦, (1)

where G1 = 1/R1 and G2 = 1/R2.To derive (1), all the Y1, Y2, and Y3 terminals of DDCC

are high-impedance terminals, since they are connected to

gates of MOS devices in actual implementation, whereas theport X is low-impedance terminal [1]. Similarly the portZ+ also exhibits high impedance since it is connected to theoutput stage of current mirror. From (1), the following fouroutput voltages can be derived as

Vo1

Vin= −sC2G1

s2C1C2 + sC2G1 +G1G2,

Vo2

Vin= G1G2

s2C1C2 + sC2G1 +G1G2,

Vo3

Vin= −s2C1C2

s2C1C2 + sC2G1 +G1G2,

Vo4

Vin= sC2G1

s2C1C2 + sC2G1 +G1G2.

(2)

Thus, we can obtain an inverting BP, a non-inverting LP,an inverting HP, and a non-inverting BP filter response at theoutput voltages; Vo1, Vo2, Vo3, and Vo4, respectively. In orderto realize allpass and bandstop filter functions, the unity gainvoltage difference amplifier is needed. Due to the fact thatinput voltage signal is connected directly to the Y2 port ofthe DDCC(1) and input current to the Y2 port is zero, thecircuit has the feature of high-input impedance. The employsof only plus-type DDCCs simplify the circuit configuration.

The resonance angular frequency ωo, quality factor Q,and bandwidth BW are given by

ωo= 1√R1R2C1C2

, Q=√R1C1

R2C2, BW= ωo

Q= 1R1C1

.

(3)

Equation (3), the parameters ωo, and BW can be orthogo-nally adjusted by resistor R1 while the orthogonal tuning ωoand Q can be achieved by simultaneous adjustment of R1

and R2 such that R1 = R2. It must be noted that the use ofgrounded resistors in the proposed circuit will benefit by aneasier electronic tunability. Thus, for the case of R1 = R2

can be solved by using two MOSFETs to replace R1 and R2

with its gate connected by the same voltage control [14, 15].Several realizations of tunable grounded resistors exist in theliterature [16, 17].

3. Effect of Nonidealities

Take into account the nonidealities of a DDCC, namely,VX = RXIX +βVY1−γVY2 +ηVY3 and IZ = αIX , where RX , α,β, η, and γ are the intrinsic resistance at the X terminal, theparasitic current gain at the X terminal to the Z terminal, theparasitic voltage gain at the Y1 terminal to theX terminal, theparasitic voltage gain at the Y2 terminal to the X terminal,and the parasitic voltage gain at the Y3 terminal to the Xterminal, respectively. These parasitic components limit the

Active and Passive Electronic Components 3

VDD

M3 M4M9 M10

M5 M6

M11 M12

Y1 M1M2 Y2 M7 M8 Y3 X ZZ

Vb1M13 M15 M17 M19

M14 M16 M18 M20Vb2

VSS

Figure 2: CMOS implementation of the plus-type DDCC.

high-frequency operation of the circuit and can be modeledwith the following first-order functions [18]:

α = αo1 + ταs

,

β = βo1 + τβs

,

γ = γo1 + τγs

,

η = ηo1 + τηs

.

(4)

In (4), the pole frequencies ωα = 1/τα, ωβ = 1/τβ, ωγ =1/τγ, and ωη = 1/τη depend on the technological parametersand ideally approach infinity. The operation frequency of thepresented filter can be defined as f � min{ωα,ωβ,ωγ,ωη}.In addition, the dc gain αo, βo, γo, and ηo are ideally equalto unity and can be expressed as αo = 1 − εα, βo = 1 − εβ,γo = 1 − εγ, and ηo = 1 − εη, where εβ, εγ, and εη are thevoltage tracking errors, and εα is the current tracking errorin addition to|εβ| � 1, |εγ| � 1, |εη| � 1, and |εα| � 1.Taking into account the nonidealities, the denominator of thetransfer functions of Figure 1 becomes

D(s) = s2C1C2 + αo1ηo1γo2sC2G′1 + αo1αo2βo1γo2G

′1G

′2. (5)

The nonideal resonance angular frequency ωo and qualityfactor Q are obtained by

ω0 =√αo1αo2βo1γo2G

′1G

′2

C1C2, Q = 1

ηo1

√√√αo2βo1C1G′2

αo1γo2C2G′1.

(6)

A sensitivity study forms an important index of theperformance of any active network. The formal definitionof sensitivity is SFx = (x/F)(∂F/∂x), where F represents oneof ωo, Q and x represents any of the elements (G′1 − G′2,C1 − C2) or the active parameters (αi, βi, γi, ηi). Based onthe sensitivity expression, the active and passive sensitivitiesof the proposed circuit shown in Figure 1 are given as

Sωoαo1,αo2,βo1,γo2= SωoG′1,G′2

= −SωoC1,C2= 1

2,

SQαo2,βo1= SQC1,G′2

= −SQαo1,γo2= −SQC2,G′1

= 12

,

SQηo1= −1.

(7)

Hence, the filter parameter sensitivities are low and not largerthan unity in absolute value.

4. Simulation Results

The device model parameters used for the HSPICE simula-tions are TSMC 0.35 μm CMOS 2P4M process and MATLABfor the theoretical part to compare the results. The CMOSimplementation of the differential difference voltage currentconveyor is shown in Figure 2 [4]. The NMOS and PMOStransistor aspect ratios are given by W/L = 2.5μm/0.5 μmand W/L = 10μm/0.5 μm, respectively. The supply voltagesare VDD = −VSS = 1.65 V, and the biasing voltages of Vb1

and Vb2 are –0.1 V and –0.8 V, respectively. The proposedcircuit was designed for fo = 1 MHz and Q = 1 by choosingR1 = R2 = 50 kΩ and C1 = C2 = 3.18 pF. Figure 3 showsthe simulated results amplitudes for HP, LP, and two BP filterresponses of Figure 1. The total power dissipation is foundto be 0.52 mW. As can be seen, there is a close agreementbetween theory and simulation.

The noise behavior of the filter was simulated using theINOISE and ONOISE statements of frequency responses ofthe BP response at Vo4 output terminal. Figure 4 shows thesimulated amplitude-frequency responses for the BP filterwith INOISE- and ONOISE-designed R1 = R2 = 31.8 kΩand C1 = C2 = 5 pF. The total equivalent input and outputnoise voltages are 13.8 mV and 0.48 mV, respectively.

To test the input dynamic range of the filter, thesimulation has been repeated for a sinusoidal input signal atfo = 1 MHZ . Figure 5 shows the input dynamic range of theinverting BP response atVo1 output terminal with R1 = R2 =50 kΩ andC1 = C2 = 3.18 pF, which extends up to amplitudeof 0.7 V (peak to peak) without signification distortion. Thedependence of the output harmonic distortion of BP filteron input voltage amplitude is illustrated in Figure 6. FromFigure 6, we can see that the harmonic distortion rapidlyincreases if the input signal is increased beyond 0.7 V for thechosen DDCC implementation.

5. Conclusion

In this paper, the author also proposes a new high-inputimpedance voltage-mode multifunction biquadratic filter.

4 Active and Passive Electronic Components

−90

−80

−70

−60

−50

−40

−30

−20

−10

0

10

Mag

nit

ude

(dB

)

104 105 106 107 108

Frequency (Hz)fo = 1 MHz

BP1 simulation (Vo1)BP1 theoreticalLP simulation (Vo2)LP theoretical

HP simulation (Vo3)HP theoreticalBP2 simulation (Vo4)BP2 theoretical

Figure 3: Simulated frequency responses of highpass, bandpass,and lowpass of Figure 1 at fo = 1 MHz and Q = 1.

1 f

10 f

100 f

1p

10p

100p

1n

10n

Noi

se(l

og)

10k 100k 1x 10x 100x

Frequency (log) (Hz)

InputOutput

Figure 4: Equivalent output and input noise of the bandpass filterversus frequency.

This circuit offers several advantages, such as no require-ments for component-matching conditions, the use of onlygrounded passive components, high-input impedance, andlow active and passive sensitivity performances. The pro-posed circuit has the same advantages reported by [3] whichis using two minus-type DDCCs, two grounded capacitors,and two grounded resistors. Moreover, the proposed circuitis simpler in configuration than the old circuit, since theuse of only plus-type of DDCCs is simpler than the useof the minus-type of DDCCs. In addition to inverting

−500−450−400−350−300−250−200−150−100−50

050

100150200250300350400450500

Vol

tage

s(l

in)

(m)

118μ 118.5μ 119μ 119.5μ 120μ

Time (lin) (TIME)

InputOutput (Vo1)

Figure 5: The input and output waveforms of inverting BP responsefor a 1 MHz sinusoidal input of 0.7 V (peak to peak).

0

2

4

6

8

10

12

14

16

18

20

TH

D(%

)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Input voltage (peak to peak) (V)

Figure 6: THD variations of the BP filter versus amplitudes of theapplied sinusoidal voltages at 1 MHz.

highpass, inverting bandpass, and non-inverting lowpassfilter responses, the proposed circuit can also realize non-inverting bandpass filter response.

Acknowledgments

The author would like to thank National Chip Implemen-tation Center (CIC) for technical support. The work wassponsored by NSC-98-2221-E-131-027.

References

[1] W. Chiu, S. I. Liu, H. W. Tsao, and J. J. Chen, “CMOS differen-tial difference current conveyors and their applications,” IEE

Active and Passive Electronic Components 5

Proceeding—Circuits Devices and Systems, vol. 143, no. 2, pp.91–96, 1996.

[2] C.-M. Chang and H.-P. Chen, “Universal capacitor-groundedvoltage-mode filter with three inputs and a single output,”International Journal of Electronics, vol. 90, no. 6, pp. 401–406,2003.

[3] J.-W. Horng, W.-Y. Chiu, and H.-Y. Wei, “Voltage-modehighpass, bandpass and lowpass filters using two DDCCs,”International Journal of Electronics, vol. 91, no. 8, pp. 461–464,2004.

[4] M. A. Ibrahim, H. Kuntman, and O. Cicekoglu, “Single DDCCbiquads with high input impedance and minimum numberof passive elements,” Analog Integrated Circuits and SignalProcessing, vol. 43, no. 1, pp. 71–79, 2005.

[5] W. Y. Chiu and J.-W. Horng, “High-input impedance voltage-mode universal biquadratic filter using three plus-type CCIIs,”IEEE Transactions on Circuits and Systems II, vol. 54, no. 8, pp.649–652, 2007.

[6] H.-P. Chen, “Universal voltage-mode filter using only plus-type DDCCs,” Analog Integrated Circuits and Signal Processing,vol. 50, no. 2, pp. 137–139, 2007.

[7] J.-W. Horng, “High input impedance voltage-mode universalbiquadratic filter with three inputs using DDCCs,” Circuits,Systems, and Signal Processing, vol. 27, no. 4, pp. 553–562,2008.

[8] J.-W. Horng, J.-R. Lay, C.-W. Chang, and M.-H. Lee, “Highinput impedance voltage-mode multifunction filters usingplus-type CCIIs,” Electronics Letters, vol. 33, no. 6, pp. 472–473, 1997.

[9] J.-W. Horng, “High-input impedance voltage-mode universalbiquadratic filter using three plus-type CCIIs,” IEEE Transac-tions on Circuits and Systems II, vol. 48, no. 10, pp. 996–997,2001.

[10] J.-W. Horng, “High input impedance voltage-mode universalbiquadratic filter using two OTAs and one CCII,” InternationalJournal of Electronics, vol. 90, no. 3, pp. 185–191, 2003.

[11] J.-W. Horng, “High input impedance voltage-mode universalbiquadratic filters with three inputs using plus-type CCIIs,”International Journal of Electronics, vol. 91, no. 8, pp. 465–475,2004.

[12] M. Bhushan and R. W. Newcomb, “Grounding of capacitorsin the integrated circuits,” Electronics Letters, vol. 3, no. 4, pp.148–149, 1967.

[13] R. Senani, “New universal current mode biquad employing allgrounded passive components but only two DOCCs,” Journalof Active and Passive Electronic Devices, vol. 1, no. 3-4, pp. 281–288, 2006.

[14] G. Moon, M. E. Zaghloul, and R. W. Newcomb, “Anenhancement-mode MOS voltage-controlled linear resistorwith large dynamic range,” IEEE Transactions on Circuits andSystems, vol. 37, no. 10, pp. 1284–1288, 1990.

[15] Z. Wang, “2-MOSFET transresistor with extremely low distor-tion for output reaching supply voltages,” Electronics Letters,vol. 26, no. 13, pp. 951–952, 1990.

[16] M. A. Ibrahim, S. Minaei, and H. Kuntman, “A 22.5 MHzcurrent-mode KHN-biquad using differential voltage currentconveyor and grounded passive elements,” International Jour-nal of Electronics and Communications, vol. 59, no. 5, pp. 311–318, 2005.

[17] S. Minaei and M. A. Ibrahim, “A mixed-mode KHN-biquadusing DVCC and grounded passive elements suitable fordirect cascading,” International Journal of Circuit Theory andApplications, vol. 37, no. 7, pp. 793–810, 2009.

[18] A. Fabre, O. Saaid, and H. Barthelemy, “On the frequencylimitations of the circuits based on second generation currentconveyors,” Analog Integrated Circuits and Signal Processing,vol. 7, no. 2, pp. 113–129, 1995.

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