IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 16, NO. 12, DECEMBER 2006 705

A 0.13-�m CMOS Phase Shifter Using TunablePositive/Negative Refractive

Index Transmission LinesMohamed A. Y. Abdalla, Khoman Phang, and George V. Eleftheriades

Abstract—This letter presents a tunable positive/negative re-fractive index transmission line (TL) phase shifter utilizing activecircuits. It comprises a microstrip TL loaded with series varactorsand a shunt monolithic microwave integrated circuit (MMIC) tosynthesize a tunable inductor. This implementation increases thephase tuning range and maintains the input and output matchingof the phase shifter across the entire phase tuning range, whileeliminating the need for bulky passive inductors. The phaseshifter is capable of providing both positive and negative phaseshifts. The MMIC tunable inductors are fabricated in a 0.13- mCMOS process and operate from a 1.5-V supply. The phase shifterachieves a phase of 40 to +34 at 2.5 GHz from a single stagewith less than 19 dB return loss, and better than 1.1-dB insertionloss at 2.5 GHz. The phase shifter has a 1-GHz bandwidth overwhich the return loss remains better than 12.1 dB.

Index Terms—Active inductors, CMOS, metamaterials, mono-lithic microwave integrated circuit (MMIC), negative refractiveindex (NRI), phase shifters, transmission lines (TLs).

I. INTRODUCTION

RECENTLY there has been a strong interest in buildingphase shifters by cascading negative-refractive-index

(NRI) metamaterial lines with positive-refractive-index (PRI)transmission lines (TLs) [1]. This allows building broadbandcompact phase shifters with linear frequency response. ThePRI/NRI phase shifters are centered on the zero-degree markand are capable of achieving positive and negative phase shifts.Centering the phase shift on 0 is necessary for scanningabout the broadside direction in series-fed steerable antennaarrays. These composite one-dimentional metamaterial linesare realized by loading a host TL with series capacitors andshunt inductors [2], [3]. Several designs [4]–[6] have recentlybeen published, which use a single variable loading elementto tune the phase characteristics of NRI lines. This results inonly positive phase shifts. Furthermore, tuning a single loadingelement (varactors in [4] and [5], and active inductors in [6]),results in high return losses. A composite PRI/NRI TL phaseshifter is presented in [7] using two tunable loading elements;series and shunt ferroelectric varactors, which however, requirehigh control voltages (15 V). Furthermore, the design in [7]

Manuscript received May 22, 2006. This work was supported by the CanadianMicroelectronics Corporation (CMC) and the Center for Excellence in Commu-nication and Information Technology Ontario (CITO).

The authors are with the Edward S. Rogers, Sr. Department of Electronic andComputer Engineering, Toronto, ON M5S 3G4 Canada (e-mail: abdulla@eecg.utoronto.ca; kphang@eecg.utoronto.ca; gelefth@waves.utoronto.ca).

Digital Object Identifier 10.1109/LMWC.2006.885648

Fig. 1. PRI/NRI metamaterial phase shifter unit-cell.

uses a fixed shunt inductor which makes it impossible to satisfythe matching condition across the entire phase tuning range.Ferroelectric varactors also result in a modest phase tuningrange of 12.5 unit–stage.

This letter presents a tunable active PRI/NRI phase shifter im-plementation based on loading a host TL with series varactorsand shunt monolithic microwave integrated circuit (MMIC) tun-able inductors fabricated in a 0.13- m CMOS process. It willbe shown that, using both varactors and tunable inductors ex-tends the phase tuning range and maintains the input and outputmatching across the entire phase tuning range. Using a stan-dard low-cost, low-voltage (1.5 V) CMOS process to imple-ment the MMIC inductors eliminates the need for bulky lumped-element inductors and allows integration with radio frequency(RF) and digital circuits. Furthermore, the MMIC inductors fea-ture a quality factor enhancement circuit that is used to minimizethe phase shifter insertion loss.

II. THEORY

Fig. 1 shows a unit-cell of the PRI/NRI phase shifter [1]. It iscomposed of a regular microstrip line loaded with series capaci-tors and shunt inductors. Cascading a PRI line with an NRI linecompensates the phase shift incurred by the propagating signal.Using periodic analysis one can show that the insertion phaseof the unit-cell is given by [1], [2]

(1)

where is the phase lag due to one section of the PRI micro-strip line, given by 2.

To match the phase shifter to the characteristic impedanceone equates the input reflection coefficient to zero, whichresults in the following condition:

(2)

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706 IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 16, NO. 12, DECEMBER 2006

Fig. 2. Proposed tunable PRI/NRI phase shifter unit-cell based on series var-actors and shunt MMIC inductors.

If we assume that the signal incurs a small phase shift prop-agating through the microstrip line, the matching condition canbe approximated as

(3)

The same result can be reached by investigating the stop-bandsof the periodic structure and finding the condition to elimi-nate the stop-band close to the zero-phase region. Under thismatching condition the phase can be approximated as [1]

(4)

Equation (4) indicates that positive and negative phase shifts canbe realized by a single unit-cell without having to go througha complete phase rotation as in a traditional left-handed (high-pass) or right-handed (low-pass) architecture.

The phase can be tuned by changing the values of the loadingelements and . Fortunately, changing and simultane-ously will help maintain the matching condition of (3). If and

are varied from to and to respectively,the phase tuning range can be expressed as

(5)

where . For a typical valueof 3 , (5) results in at least doubling the tuning rangecompared to varying only.

III. DESIGN AND IMPLEMENTATION

Fig. 2 shows the proposed unit-cell of the tunable PRI/NRIphase shifter. Tunable capacitors are implemented using varac-tors, where the reverse voltage across the varactor controls itscapacitance. On the other hand, electronically tunable MMICinductors are implemented using the gyrator- architecture,shown in Fig. 2. The circuit’s equivalent inductance isgiven by

(6)

Fig. 3. Grounded CMOS active inductor circuit.

where and are the transconductances of the back-to-back transconductors, and is the total capacitance at the feed-back node. The circuit implementation of the grounded activeinductor is presented in Fig. 3. The first transconductor isreplaced by a differential pair , while the secondtransconductor is replaced by the common-source tran-sistor . This feedback loop is responsible for the inductivebehavior. An additional feedback resistance is added to theloop to enhance the inductor quality factor . The bias cur-rents and determine the transconductances and ,and are set through two off-chip bias networks. The currentis mirrored and another copy of it is used to bias . The cir-cuit inductance is controlled via the product of and ,while its quality factor is controlled via the feedback resistance

. This provides us with two sets of control inputs to set thedesired and . To implement , binary weighted NMOStransistors operating in the triode region are used, and this al-lows both coarse and fine tuning .

IV. EXPERIMENTAL RESULTS AND DISCUSSION

The MMIC inductors were fabricated in a 0.13- m CMOSprocess and operate from a 1.5-V supply. The chip area is1 mm ; the grounded inductor circuit occupies an area of150 m 170 m (excluding the pads). The inductors wereexperimentally characterized by probing the dies. The circuitinductance is tunable from 0.93 to 2.7 nH at 2.5 GHz whilemaintaining a high ( 40). The active inductor circuits werepackaged in a 4 mm 4 mm high-speed micro lead frame(MLF) QFN package to minimize the package and bondwireparasitics.

The phase shifter, shown in Fig. 4, is implemented on a low-loss 10 mil Rogers RT/duroid 5880 substrate with two layersof copper. A low substrate permittivity of 2.2 was chosen toreduce the phase shift incurred by the signal, hence making thephase shifter more wide-band. The varactors used are 1.7 mm0.9 mm plastic packaged silicon hyper-abrupt junction varactordiodes from Skyworks (SMV1232). The phase shifter unit-cellsize is 10.8 mm 10.4 mm; the TL and series varactors occupy10.8 mm 1 mm, while the chip and the bias lines roughlyoccupy 10.8 mm 9.4 mm. The unit-cell width is mainly setby the MMIC inductor package, which can be easily reducedby more than 22% by using a smaller package size (3 mm

ABDALLA et al.: 0.13- m CMOS PHASE SHIFTER 707

Fig. 4. Photograph of the tunable PRI/NRI phase shifter unit-cell.

Fig. 5. Measured phase andS versus frequency, for different bias conditions.

3 mm). The smaller package wasn’t used here, since the chipcontained other test circuits that needed to be packaged.

Fig. 5 shows the measured phase when both the MMIC in-ductance and varactor capacitance are varied. At the design fre-quency (2.5 GHz), the phase can be varied from 40 to 34passing through the zero-phase point. The phase shifter unit-cellis capable of achieving both positive and negative phase shiftsat the design frequency without going through an entire 360rotation ( 88 mm microstrip line). This corresponds to a 73%area saving compared to meandering the microstrip line. Fur-thermore, over the entire phase tuning range the matching con-dition is satisfied, and is maintained below 19 dB, asshown by Fig. 5. As the varactor reverse bias voltage in-creases its capacitance decreases, hence the MMIC has to de-crease to satisfy (3). When approaches 4.2 V it becomeshard to satisfy the matching condition, since the package adds afixed inductance to the MMIC inductance, which sets the min-imum achievable . Nevertheless, the phase shifter achieves a

12.1 dB over a bandwidth of 1 GHz centered about thedesign frequency of 2.5 GHz (see Fig. 5). The measuredis presented in Fig. 6, is set by the varactor losses and theMMIC inductor . The insertion loss at 2.5 GHz varies from0.55 dB to 1.1 dB over the entire phase tuning range. Over theentire 1-GHz bandwidth, the phase shifter insertion loss variesfrom 0.25 to 1.6 dB.

Fig. 6. Measured S versus frequency for different bias conditions.

V. CONCLUSION

This letter presented a PRI/NRI phase shifter unit-cell thatachieves both positive and negative phase shifts without goingthrough the entire 360 rotation. Using tunable MMIC inductorsand varactors extended the tuning range by a factor of two andat the same time maintained the input and output matching ofthe phase shifter. The phase shifter achieved an electronicallytunable phase from 40 to 34 at 2.5 GHz from a singlestage, with better than 19 dB return loss across the entirephase range. The MMIC inductors were implemented in a low-cost, low-voltage (1.5 V) standard CMOS process. The PRI/NRIphase shifter can be used in series-fed steerable antenna arraysor as the unit cell for two-dimensional tunable metamaterialstructures. In addition, more than one stage can be cascaded toextend the phase tuning range further according to the desiredapplication.

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