CMOS Digitally Programmable InductanceHussain Alzaher Noman Tasadduq

Department of Electrical Engineering Department of Electrical EngineeringKing Fahd University of Petroleum & Minerals King Fahd University of Petroleum & Minerals

Dhahran, Saudi Arabia Dhahran, Saudi ArabiaEmail: alzaher@kfupm.edu.sa Email: nomangkfupm.edu.sa

used in data converters is used here to provide digital tuningAbstract-A CMOS digitally programmable active lossless of the inductance value. It is expected that the proposed

inductor realization is proposed. The proposed inductor is inductor will provide the advantage of high frequencybased on current and voltage followers and uses R-2R operation and programmability, like those of OTA basedladder to provide digital tuning of the inductance value. circuits, while offering improved linearity. Also, the proposedThe followers support the use of the simulated inductor circuit can realize large inductance values in relatively smallfor applications in few MHz range. Whereas the use of R- area which will permit the implementation of large time2R provide an additional advantage of realizing high constant circuit in integrated circuit (IC) chips. Moreover, itinductance value suitable for very low frequency will be seen that any filter built using the proposed inductorapplications. The proposed inductor is used in synthesizing will be automatically cascadable. Furthermore, the proposedcascadable biquadratic filters. Simulation results are circuit and unlike other grounded inductors can realizepresented. lowpass filter function. As demonstrating applications, the

proposed inductor is used in synthesizing a new voltage modeIndex Terms- Analog signal processing, Current mode resonator filter that provides both bandpass and lowpass

circuits, Active filters. functions, simultaneously. Simulation results obtained from a0.5,m CMOS technology are included.

I. INTRODUCTION

Active simulation of inductor is a common design problem II. BASic BUILDING BLOCKSin analog integrated circuits. Various topologies based on op This section briefly describes the terminal characteristicsamps, nullors, current feedback amplifiers and current and realizations of the basic building blocks of the proposedconveyors can be found in the literature, for example [1-2]. inductor circuit.However, such active-RC realizations rely on the inaccurate A. Current FollowerRC time constant to determine the inductance value. On theother hand, inductance simulation based on the operational An ideal current follower (CF) has zero input impedancetransconductance amplifier (OTA) provides electronic and infinite output impedance. Hence the terminalprogrammability such that of [3]. Unfortunately, characteristics of an ideal CF, symbolically shown in Fig. 1,transconductor-C (gm-C) based circuit suffers from linearity can be described by the following matrix equation.problems.

Ir

Recently, unity gain cells have been used in several z 0 ±1 (1)applications such as filters and oscillators. This is attributed to VL Lo 0oLI_their inherent wide bandwidth and low power consumption x x[4]. More recently, digitally programmable devices [5-8] have where the plus and minus signs of the current transfer ratiobecome attractive for mixed digital-analog applications. denote the CF+ or CF- respectively. The X terminal is held atDigital tuning of analog devices not only provides wide virtual ground, which results in a simple input stage that doesprogrammability range but also allows direct interface with not require rail-to-rail operation. A CMOS realization of thedigital signal processing (DSP) controller. CF is shown in Fig. 2 [5].

In this paper, a new simulated inductance based on currentfollowers, unity gain buffers, and digitally controlled R-2Rladder is proposed. The R-2R ladder which is conventionally

Manuscript received June 14, 2006.The authors are with King Fahd University of Petroleum & Minerals,

Dhahran 31261, KSA (Dr. Hussain Alzaher phone: +966-3-8601434; fax:+966-3-8603535; e-mail: alzaherh@ kfupm.edu.sa).

1-4244-07 5-6 06$.OC0.0 ©2006 fIEEIE 138

C. R-2R Ladderx x CF I The R-2R ladder shown in Fig. 4 can be considered as a

digitally programmable resistor. Incorporating the R-2Rladder as a circuit element into the circuit design will provide

Fig. 1. Current follower symbol precise frequency characteristics that can be tuned over a widerange. Unlike the case of the gm-C technique, the tuning

VDD feature of the proposed approach does not degrade thedynamic range of the circuit, since it is independent of the

M13 M9 MIO active element operating point. It can be seen that the outputcurrent (I) is given by:

M3 M7 M8

(i)VDD L, t 5 5 5 I = T -1 i-l where (2)

Mil I X ~~~~~~~~~~~Therefore, the equivalent resistance, seen between the inputA M12Vb lqMcl60 and output nodes, is given by

M4 |Re =-,R where q =n (3)

vssFig. 2. A CMOS low power current follower where bi, equaling 0 or 1, is the ith bit in an n bit digital control

word. This programmable resistance can be incorporated ininductor simulation designs to provide wide tuning of

B. Voltage Buffer inductance value without component spreading. This can beIdeally, a voltage buffer exhibits infinite input resistance, applied as long as those resistors are connected to virtual

zero output resistance, and unity gain voltage transfer ground, which simulates the proper operating condition of thecharacteristics. A CMOS class-AB realization of a voltage R-2R ladder. This property is inherently provided by the CF.buffer is shown in Fig. 3 [5]. The circuit utilizes a class-ABloop to boost the transconductance of a MOS transistoroperating in the saturation region. Hence, low outputimpedance can be achieved with low standby power _E b< Eb) 4 b Rconsumption. The voltage tracking of the buffer is achieved v

by forcing a constant biasing current through transistor Ml IT1 2R 2' 12 4 2R 8 12R 2'i l2RandM2. R R R 2R

aM v ----X--

(input) I, 112 1A4 118 11J2VDD

Fig. 4. Digitally controlled R-2R ladder.M16 M15 M19

M3 M11III. PROPOSED CIRCUIT

lb Using the building blocks of the pervious section, a

M1 M2 digitally programmable active inductor can be implemented.+ vi t t1 ,> 4 Vo The inductor is obtained from the basic circuit of Fig. 5

M 17 l l tconsisting of a voltage integrator with infinite inputM7 impedance followed by voltage to current converter with its

M189FjVb- M19 M4 + 4 output fed-back to the input node. The corresponding losslessM18 e4 Vsbinductor circuit is shown in Fig. 6. It can be shown that input

impedance of the circuit of Fig. 6 is given by:

Zi =sClAAR (4)

Fig. 3. A CMOS low power voltage buffer

139

where [I and [2 can be digitally controlled. Obviously, the simulated inductor as shown in Fig. 7(a). It is well known thatcircuit simulates a lossless inductor and inductance is given the bandpass response is given by:by:

V I V = sL ID(s) (6)L = CJ,8,8/2RIR2 (5) where D(s) =s2CLR+sL+R (7)

Clearly, the inductance can be tuned digitally via PI and/or and L is given by (5). Therefore, it can be shown that the32. On the other hand, a negative lossless inductor can be circuit of Fig. 7(b) provides bandpass and lowpass responsesobtained by changing the polarity of one of the CF. that are given by:

It can be observed that a large R-2R ladder equivalentresistance can be achieved using a relatively small passive V /V (8)resistance. For example, when b, = 0 for L

1 ~~~~Ln =1, 2... (n- 1) andbn 1, a n bit R-2R ladder exhibits VLP/ V (R ) /D(s) (9)

a large equivalent resistance of (2f )RQ while actuallyrequiring total resistance of only (3n + 1)RQ . Thus, the circuit It can shown from (5) and (7) that the center frequency (co)of Fig. 6 can simulate a very high inductance value and and the bandwidth (w0/QO) are given by:therefore can also be used for implementing very lowfrequency applications in ICs. For example, with C1=5pF, and } 1/ LC 1 /(CC /3/3R1R2) (10)8-bit R-2R ladder with R=10kQ, a 32H inductance can be ° l l 21 2achieved. On the other hand, the use of voltage buffer and o I QO = 1 / CR (11)current follower provides better linearity than OTA andtherefore can inherently be used for high frequency Clearly, co can be tuned digitally using .3 and/or /2withoutapplications.

disturbing wOIQO. Also, the filters are automaticallycascadable since they are available at the output of the voltagebuffers.

1 3 /Ck/[ vi R Bls ~~~converterc L

Fig. 5. Basic circuit for inductor realization.

Ai pI ~~~~Cti 02 c I cII 52(b)

Fig. 6. Proposed inductor realization.

Fig. 7. (a) Passive filter realization (b) Bandpass and lowpass active filterrealization using inductor simulation circuit.

IV. APPLICATIONS

Actively simulated inductors can be used in severalV IUAINREUT

applications such as active filters, oscillator designs andV.SMLTOREUScancellation of parasitic inductances. This section The proposed filter of Fig. 7(b) was simulated using SPICE.

demnsraes ha teropse idutorexibts evra Te 05p BIM CMS odls valalethruQ!MSI

proidd..Aecod rdev ltag mode bad1s filte canb

obtained~~~~~~~~~~~~~~~~~raizto usin inductornsiuato circuit.i arlllwihh

IV. APPLICATIONS~14

filters are varied for several different digital control word RiEFERENCESshowing fine and coarse tuning. [1] 5. J. Lui, and Y. S. Hwang, "Realization of R-L and C-D impedances

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e ~~~~~~~~~~~~~~~~~[2]P. V. Ananda Mohan, "Grounded capacitor based grounded and floating

1998, pp.1037-1038.-iC ~~~~~~~~~~~~~~~~~[3]Y. Sun, "OTA-C filter design using inductor substitution and Bruton

transformation methods," Electron. Lett., vol. 34, 1998, pp.2082-2083.[4] M. T. Abuelma'atti, and M. A. Al-Qahtani, "Current-mode universal

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Fig. 8. Simulation results for VBP with passive R= IOOkQ cuffent-division network and its applications," International Conferenceon Electrical, Electronic and Computer Engineering, ICEEC 5-7 Sept.

5.2004, pp. 520- 523.[8] C. Hsu, and J. Wu, "A highly linear 125-MHz CMOS switched-resistor

0 ~~~~~~~~~~~~~~~~~~programmable-gain amplifier," IEEE J. Solid State Circuits, vol. 38, no.10, Oct. 2003, pp. 1663-1670.

20)

.35102 1 03 10 4 1 0 06 107

frequency, Hz

Fig. 9. Simulation results for VLP with passive R IlOkQ

VI. CONCLUSION

A CMOS simulated inductor circuit based on current andvoltage followers and incorporates R-2R ladders is presented.The proposed circuit exhibit several advantages: (a) its valuecan be digitally tuned (b) it can be used for high frequencyapplication like the OTA based counterparts but withimproved linearity (c) It can be used to realize a very highinductance value required for ICs low frequency applications(d) it provide cascadable voltage-mode biquad filters whenused in filter design (e) it can be used to realize a lowpassbiquad which usually requires a floating inductor. Theproposed circuit is used to design a second order filter thatsimultaneously provides bandpass and lowpass functions.Simulation results based on manufacturer 0.5 !tm CMOS