Current Mode Multifunction Biquad Filter Using Two Iccııs With Grounded Resistors and Capacitors

©BEYKENT UNIVERSITY

CURRENT MODE MULTIFUNCTION BIQUAD

FILTER USING TWO ICCIIs WITH GROUNDED

RESISTORS AND CAPACITORS

This paper presents a cascadable current-mode (CM) multifunction biquadratic filter circuit. The proposed circuit realizes all five different transfer functions employing only two inverting-type second generation current conveyors (ICCIIs), and capacitors and resistors which all are grounded. Since the output of the proposed filter exhibits high output impedance, it can be directly cascaded to obtain higher order filters without any additional buffers. Moreover, the biquad filter offers low sensitivities and its natural frequency and Q-factor are insensitive to tracking errors of ICCIIs, but gain of the filter depends on the tracking errors. Finally, the theoretical results are verified with PSPICE simulations using CMOS realization of the ICCII.

Key words:Mmultifunction filters, Invertig-type second generation current

conveyor, Current-mode circuits, Continuous time filters, Sensitivity analysis.

TOPRAKLANMIŞ DİRENÇ VE

KAPASİTELERLE ICCII LAR KULLANILARAK

AKIM MODUNDA ÇOK FONKSİYONLU 2.

DERECEDEN SÜZGEÇLER

Bu makalede, kaskad bağlanabilir akım modlu (CM) çokfonksiyonlu ikinci dereceden bir süzgeç devresi sunulmuştur.Önerilen devre, yalnız iki eviren-tip ikinci kuşak akım taşıyıcı (ICCIIs), hepsi topraklı olan kapasite ve direçler kullanarak beş farklı transfer fonksiyonunun hepsini gerçekler. Süzgecin çıkış

Mahmut ÜN

Dept.of Elec. & Com. Eng., Beykent University umahmut@beykent.edu.tr

Fırat KAÇAR

Dept. of Elec. & Electronics Eng. İstanbul University fkacar@istanbul.edu.tr Received: 18 June 2007, Accepted: 26 December 2007

ABSTRACT

için ara tampon devreler kullanılmadan devre doğrudan kaskad bağlanabilir. Ayrıca ikinci dereceden süzgeç devresi küçük duyarlıklar önermekte ve süzgecin tabi frekansı ve iyilik faktörü akım taşıyıcının izleme hatalarına duyarsızdır, fakat filtre kazancı izleme hatalarına bağlıdır. En son olarak kuramsal sonuçlar, eviren ikinci kuşak akım taşıyıcıların C M O S gerçeklenmesi kullanılarak PSPICE benzetimleriyle doğrulanmıştır.

Anahtar sözcükler: Çokfonksiyonlu süzgeçler, Eviren-tip ikinci kuşak akım taşıyıcı,

Akım modlu devreler, Sürekli zaman filtreleri, Duyarlık analizleri

1. INTRODUCTION

Multifunction-type active filters are especially versatile, since the same topology can be used for different filter functions. In spite of the fact that numerous current-mode multifunction filters are reported in literature, most of them use at least three active elements, and only few can realize all types of current transfer functions using reduced order of active elements. Current-mode circuits have been receiving considerable attention due to their potential advantages such as inherently wide bandwith and low power consumption [1-4]. The active devices that have been used for the realization of current-mode circuits include current conveyor, current feedback operational amplifier, operational transconductance amplifier and four terminal floating nullor [1-2]. Of the various methods of multifunction filter design, those based upon current conveyors or their variants, have received recently more attention [5-8]. On the other hand, the well known KHN-biquad, which is the filter circuit consists of two integrators and a summer offers several advantages such as low passive and active sensitivities, low component spread and good stability [9].

Based on active element used in the integrator and summer circuits, several KHN-biquads have been presented in literature [10-14].Some of them employ current conveyors, which do not suffer from the limited gain-bandwidth products of the op-amps.Considering the advantages of the current mode (CM) circuits such as relevant wider bandwidth, greater linearity, low power consumption and wider dynamic range [15], some CM KHN-biquads have been presented.However the inverting second-generation current conveyor has also been receiving attention for the current-mode filter design since it was proposed by Awad and Soliman in 1999 [7-10]

In this paper , ICCII-based current-mode multifunction biquadratic filter circuits are presented. Then all five different transfer functions are derived for the same circuit topology proposed assuming that ICCIIs used in the circuit are not ideal. Furthermore, sensitivity analysis are applied to the transfer function

of biquadratic filter. Finally, PSPICE simulations are performed for the frequency response analysis of the biquadratic filter circuits.

2. PROPOSED MULTIFUNCTION BIQUAD FILTER

CIRCUIT

The ICCII, whose circuit symbol is shown in Figure.1, is characterized by the following port relations

I

Y

= 0,v

x

=-pV

Y

, I

z

= ±aI

₍₁₎ Where the positive sign indicates the ICCII+ and the negative sign indicates the ICCII-.In Eq. (1), P=1-ev is the voltage gain, and a=1-Ci is the current gain

of the ICCII, where ev denotes the voltage tracking error between the X and Y

terminals and ei denotes the current tracking error between the Z and X terminals, absolute values of the voltage and current gains being much less than unit value.Current and voltage gains become unity for an ideal ICCII.

I Y

Figure-l.Symbol of the ICCII

The current transfer function of the circuit in Figure.2 using two ICCII elements has the following form in the case that the ICCII are ideal.

-o Io

Figure-2. ICCII-based current mode multifunction biquad circuit

H = h = a a M l l A . ( 2 )

I YY

1i i 3

Where Yi are positive real admittance functions of passive two terminal elements. One of their terminals is grounded. Based upon this configuration, Figure.2 displays the proposed current-mode, ICCII-based multifunction filter. If the passive component admittances are selected as Yi=Gi+ sCi , which is parallel equivalent admittance of Ri and Ci and Y3=G3+ sC3 , which is

parallel equivalent admittance of R3 and C3 , transfer function (2) becomes

H ( s)

ag

2

ßß

2

(Y

2

YJ C A )

2

, 1 1

s

1

(3)

s + ( + ) s +

-R1C1 R3C3 R1R3C1C3

Here Gi = 1/Ri and Ci are respectively conductance and capacitance, where resistance Ri is the inverse of conductance.The natural angular frequency wo

and the pole Q-factor of this filter are

= ( R 1 R 3 C 1 C 3 ) "1 / 2 (4)

q _ ( R1R3C1C3) 1 / 2 (5)

R1C1 + R3C3

It is apparent that pole frequency wo and Q-factor are independent of tracking

errors of the ICCIIs and only depend on the component values of the admittances Yi and Y3.But filter gain is affected by tracking error of the

ICCIIs in the circuit.

Note that the circuit is a low-pass (LP) filter if Y2 = G2 and Y4 = G4 ;

aq

2

ßß

2

(G

2

GJ C A )

L p y s )

2 / 1 1 \ 1 (6)

s + ( + )s +

-HLP(s)= R1C1 R3C3 R1R3C1C3 (6)

It becomes a high-pass (HP) filter in the case that Y2 = C2s and Y4 = C4s

H ( s ) *aM(C2C4/C1C3)s2

H ^ 2 / 1

1

\

1

(7)

s + ( + ) s +

R1C1 R3C3 R1R3C1C3

H

bp

(s) =

axa2ßxß2(C 2 GJ C O s

s

2

+ (—— + —-—)s + -

1 . 1 ^ . -

(8)

R1C1 R 3 C 3 R1R3C1C3

Other filter types can be obtained as a combination of these three type filters mentioned above.

3. SENSITIVITY ANALYSIS

From Eq. (3) and (4) notice that both natural frequency and Q-factor of this filter are not influenced by tracking errors of the ICCIIs.Therefore, they are insensitive to tracking errors.Other wo and Q-factor sensitivities are

S « WO = S„2 ^ = SA Wo = S ^ W =0 (9) SR w = SR w = SC W o = S rw' =-1/2 (10) n - ^ 2 i - - " C 2 Sa =S a2 = Sß 1 = Sß2 =0 ( 1 1 ) S rÖ = S c ° = —

—

+ (12) R1 C1 2 R1C1 + R3C3 ' } S RQ = S CQ =

—

1 + (13) R3 C3 2 R1C1 + R3C3

Here, for filters with complex or real poles, Q-factor sensitivities (11-13) can be minimized by proper selection of component values.All absolute wo and

Q-component sensitivities at these above given Q-component values are les than or equal to unity.

4. CIRCUIT SIMULATIONS

In order to demonstrate the feasibility of the proposed multifunction biquad, PSPICE circuit simulations were performed for the circuit given in Figure.1 using a CMOS realization of ICCII [16]. Additionally, the circuit shown in Figure.2 was simulated with PSPICE. The component values employed in the simulations are given below:.

a) For LPF; R2=1 kQ, R4=10 k O

b) For HPF; C2=10 nF, R4=10 kQ

c) For BPF; C2=10 nF, C4=20 nF

demonsrate the performance of the higher order which is made up more than one cascaded biquad filter sections, cascaded two and three LP and BP sections having the same component values given above for the LP and BP filters are simulated with PSPICE and simulation resuls are given in Figure.4 and Figure.5. Simulation results of the proposed biquad filter are in good agreement with the predicted theory. Actually, the parasitic resistances and capacitances and non-idealities of the ICCCs cause small deviations in the frequency responses of the filter from the theoretical values.

Frequency

Figure-3. PSPICE simulation results of the proposed multifunction biquad

Frequency

Figure-5. PSPICE simulation results for the cascaded BP biquad filter sections

5. CONCLUSION

A cascadable current-mode multifunction biquadratic filter circuit has been presented. The proposed circuit realizes all five different transfer function employing only two ICCIIs, capacitors and resistors which all are grounded while previously reported (CM) multifunction filters require more active elements and also not use all grounded passive elements for the same number of filter transfer function realizations. All the passive elements are grounded, which is important in integrated circuit implementation. Since the output of the filter exhibits high impedance the synthesized current-mode biquadratic filters can be cascaded without additional buffers.Also higher order quadratic filter can be realized by cascading the proposed biquadratic filter sections.Furhermore,the proposed biquad offers low sensitivities and its natural frequency and Q-factor are insensitive to tracking errors of ICCIIs. But gain of the biquadratic filter depends on the tracking errors of ICCIIs. In order to compare the theoretical results with the experimental data, PSPICE simulations were performed by using CMOS realization of the ICCII. PSPICE simulation results of the frequency responses of the proposed circuits are in good agreement with the predicted theory.

REFERENCES

[1] Toumazou, C., Lidjey, F. J., Haigh D., Analog IC Design: The Current-Mode Approach, Peter Peregrinus, UK, (1990).

[2] Palmisano G., Palumbo G., Pennisi S., CMOS Current Amplifiers, Kluwer Academic Publishers, (1999).

[3] Mucha I.,Current operational amplifiers: Basic architectures, properties, exploitation and future, Analog Integrated Circuits and Signal Processing, Vol.24, (1995), pp.243-255.

[4] Schauman, R., Valkenburg, M. E., Design of analog filters. Oxford University Press, New York, (2001).

[5] Elwan HO, Soliman AM, A novel CMOS current conveyor realization with an electronically tunable current mode filter suitable for VLSI, IEEE Transaction on Circuits and Systems-II: Analog Digital Signal Process 1996, 43, 663-70. [6] Chang CM, Lee MJ, Voltage-mode multifunction filter with single input and

three outputs using two compound current conveyors, IEEE Trans Circuits Syst I: Fundamental Theory Appl 1999, 46, 1364-5.

[7] Cicekoglu O, Current-mode biquad with a minimum number of passive elements, IEEE Trans Circuits SYST II: Analog Digital Signal Process 2001, 48, 221-2.

[8] Wang HY, Lee CT, Versatile insensitive current-mode universal biquad implementation using current conveyors, IEEE Trans Circuits Syst II:Analog Digital Signal Process 2001, 48, 409-13.

[9] Kerwin W, Huelsman L, Newcomb R, State variable synthesis for insensitive integrated circuit transfer functions, IEEE J Solid-State Circuits 1967, SC-2, 87-92.

[10] Soliman AM, Kerwin-Huelsman-Newcomb circuit using current conveyors, Electron Lett 1994, 30, 2019-20.

[11] Senani R, Singh VK, KHN-equivalent biquad using current conveyors, Electron Lett 1995, 31, 626-8.

[12] Toker A, Ozoguz S, Acar C, Current-mode KHN-equivalent biquad using CDBAs, Electron Lett 1999, 35, 1682-3.

[13] Altuntas E, Toker A, Realization of voltage and current mode KHN biquads using CCCIIs, AEU Int J Electron Commun 2002, 56, 45-9.

[14] Pal K, Modified current conveyors and their applications, Microelectron J 1989, 20, 37-40.

[15] Toumazou C, Lidjey F, Haigh D, Analog IC design: the current mode approach, Exeter, UK, Peter Peregrinus, 1990.

[16] Awad IA, Soliman AM, Inverting second generation current conveyors: the missing building blocks, CMOS realizations and applications, Int J Electron