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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: EXPRESS BRIEFS 1

A 1- to 10-GHz RF and Wideband IF Cross-CoupledGilbert Mixer in 0.13-μm CMOS

Hu Zijie, Student Member, IEEE, and Koen Mouthaan, Member, IEEE

Abstract—A modified Gilbert-cell mixer exhibiting both wide-band radio-frequency (RF) and wideband IF performance ispresented. With the proposed common-gate RF stage with thecross-coupled complementary transistors, a measured conversiongain of 3–8 dB over an RF band of 1–10 GHz is demonstrated,together with an RF input return loss better than 10 dB. Theproposed mixer also incorporates wideband active local oscillator(LO) and IF baluns for matching and testing purposes. An IFbandwidth from 100 MHz to 1 GHz is achieved with a conversiongain variation of less than 2 dB. The measured output return losswithin the IF band is better than 10 dB. Fabricated in a standard0.13-μm CMOS technology, the chip only draws 7 mA from a1.2-V supply due to the current reuse in the proposed RF stage.The measured input referred 1-dB compression point IP1-dB,third-order input intercept point IIP3, and single-sideband noisefigure are better than −16 dBm, −7 dBm, and 15 dB throughoutthe entire RF band.

Index Terms—Common-gate (CG) radio-frequency (RF) stage,cross-coupled complementary transistors, current reuse, wide-band IF, wideband RF.

I. INTRODUCTION

M IXERS have been indispensable building blocks inwireless communication systems for decades. Since

the Federal Communications Commission allocated 7.5 GHz(3.1–10.6 GHz) of unlicensed spectrum, the development ofwideband mixers in this band has received considerable atten-tion. The emerging wideband applications call for an opera-tional frequency range from 1 GHz up to about 6 GHz forsoftware-defined radio and up to 10 GHz for ultrawideband(UWB). In addition, for monolithic microwave integrated cir-cuits (MMICs), a wideband mixer catering for multiple applica-tions is also attractive and advantageous, in light of applicationflexibility, economies of scale, and improved inventory costs.

Owing to the continuous downscaling and low cost require-ment, deep-submicron CMOS technologies have become themost appealing and promising candidate for radio-frequency(RF) applications. Gilbert-cell-based mixers are commonlyused in CMOS RF integrated circuits, which offer high spursuppression due to the double-balanced implementation. Toimprove the bandwidth of CMOS Gilbert-cell mixers, novelcircuit techniques have been extensively studied, such as em-ploying LC-ladder networks [1] and transformers [2] at theinput (RF and LO) ports, and the distributed architecture with

Manuscript received March 7, 2013; revised June 9, 2013; acceptedAugust 7, 2013. This brief was recommended by Associate Editor S. Levantino.

The authors are with the Department of Electrical and Computer Engineer-ing, National University of Singapore, Singapore 119077 (e-mail: huzijie@nus.edu.sg; k.mouthaan@nus.edu.sg).

Color versions of one or more of the figures in this brief are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TCSII.2013.2278130

Fig. 1. Block diagram of the proposed mixer.

input artificial transmission lines [3]. These techniques are con-sidered robust for the design of wideband mixers at the cost of alarger chip area due to additional passive networks. In addition,most of previously published wideband mixers tend to achievetheir wideband behavior by tuning the LO frequency acrossthe intended RF frequency range, while exhibiting a relativelysmall IF bandwidth. Therefore, these mixers are widebandRF but narrowband IF [1]–[6]. The IF bandwidth is also animportant parameter as it determines the channel bandwidth orthe number of channels in UWB systems [7]. However, to date,only a few published mixers have demonstrated both widebandRF and wideband IF performance [7], [8]. Here, we proposewideband techniques in a modified Gilbert-cell mixer, to realizeboth wideband RF and wideband IF performance. To the bestof our knowledge, the proposed mixer is the first Gilbert-cellmixer using the cross-coupled common-gate RF stage, whichexhibits a flat conversion gain and good input/output matchingover both wide RF and IF bands.

II. PROPOSED WIDEBAND MIXER DESIGN

Two key requirements for MMIC wideband mixers aregood input- and output-matching and adequate conversiongain flatness. To meet these demands, various design aspectsare discussed in the following sections, including the devicesize selection, bandwidth limitation, conversion gain boosting,conversion gain flattening, and circuit realization. Fig. 1 il-lustrates the block diagram of the proposed mixer, which isdivided into three functional blocks, namely, a mixer core basedon the Gilbert-cell multiplier, an active wideband LO balun,and an active wideband IF balun. Notably, the RF signal isintentionally designed differentially for application in differ-ential communication systems, which facilitates second-orderdistortion suppression, as well as noise reduction from powersupply and substrate. Active baluns are designed for the LO andIF ports, mostly for convenience of measurements. All build-ing blocks are designed and simulated using GlobalFoundries0.13-μm CMOS design kits.

1549-7747 © 2013 IEEE

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2 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: EXPRESS BRIEFS

Fig. 2. Circuit schematic of the proposed mixer core.

A. Cross-Coupled CG RF Stage

The proposed mixer core is based on a Gilbert-cell mul-tiplier, as shown in Fig. 2. Since wideband input matchingis a primary objective to ensure effective RF power injec-tion, a cross-coupled common-gate stage is adopted as theRF transconductace stage. As commonly used in widebandLNA designs, the common-gate topology features desirableproperties for wideband operation, and exhibits superior sta-bility due to the absence of the Miller effect of Cgd. Ignoringthe loading effect of the following stages and the back-gatetransconductance gmb, the input impedance of the common-gate stage is given by

Zin =1

gm,M1 + sCgs,M1 + 1/RS(1)

where gm,M1 and Cgs,M1 are the transconductance and gate-to-source capacitance of the common-gate NMOS transistor M1,respectively. By selecting RS = 200 Ω and optimizing the sizeof M1 for impedance matching, an input return loss larger than10 dB can be easily achieved up to 10 GHz.

The conversion gain of the proposed common-gate Gilbert-cell mixer is determined by the transconductance of the CGtransistor gm,M1, which is restricted by the input matching,according to (1). Hence, a gm-boosting technique is proposedfor the RF stage. The RF stage of a Gilbert-cell mixer hasdifferential inputs and differential outputs, which allow thetwo branches to be cross coupled for transconductance en-hancement [9]. As shown in Fig. 2, the proposed RF stagecontains two CG transistors (M1 and M2) and two comple-mentary pairs (MN1/MP1 and MN2/MP2), where the drain ofeach complementary pair is cross coupled to the gate of theother. To illustrate how the effective transconductance of theproposed RF stage Gm,eff is boosted, the signal polarity andcurrent direction are labeled in Fig. 2. When the differential RFsignal vRF+ is in the positive half-cycle, a positive small-signalcurrent id1 results, whereas a negative small-signal current id2

results from the negative vRF−. Meanwhile, the drain voltagevd1 of M1 increases, and the vd2 of M2 decreases. With thecross-coupled connection, the decrease in vd2 would cause apositive iC2. Since the small-signal output current of the RFstage iRF+ consists of two current components id1 and iC2

with the same polarity, iRF+ is enhanced, which results in anincrease in Gm,eff . It is worth noting that a positive voltagefeedback is formed between node C1 and C2 due to the cross-coupled complementary pairs MP1/MN1 and MP2/N2, whichfurther improves Gm,eff .

To analyze the proposed gm boosting technique further, weconsider the left branch of the RF stage where the drain voltageand current of M1 are given by{

vC1 = (id1 + iC2)ZC

id1 = gm,M1vRF+(2)

where ZC denotes the node impedance at C1, and vC1 isthe small-signal voltage at node C1. Subsequently, the currentflowing into the complementary stage MP2/MN2 is derived

iC2 = − iC1

=(gm,MP1 + gm,MN1)vC1. (3)

Consequently, the output current of the left branch isexpressed as

iRF+ = id1 + iC2

=gm,M1

1− (gm,MP1 + gm,MN1)ZCvRF+. (4)

Therefore, the effective transconductance Gm,eff can be ob-tained, i.e.,

Gm,eff =gm,M1

1− (gm,MP1 + gm,MN1)ZC. (5)

Compared with the transconductance gm,M1 of the CG inputstage, the transconductance enhancement factor F is found, i.e.,

F =1

1− (gm,MP1 + gm,MN1)ZC. (6)

In addition, the node impedance ZC is given by

ZC =1

2gm,LO‖Rds,M1‖Rds,CP2‖

1

jωCC(7)

where Rds,M1 and Rds,CP2 denote the drain source resistanceof M1 and the complementary pair MN2/MP2, CC is the par-asitic capacitance at node C1, and the input resistance lookinginto the source of the LO stage is approximated by 1/(2gm,LO).Note that the term (gm,MP1 + gm,MN1)ZC from (5) is requiredto remain less than 1 for any frequency to ensure a stable circuitwith the cross-coupled positive feedback.

As can be seen from (6) and (7), Gm,eff can be enhanced byproperly designing the transconductance of the complementarypair and the LO stage. In order to effectively boost Gm,eff ,preferably wide transistors are used for the complementary pair.However, when the transistor width increases, the gate parasiticcapacitance increases too, which reduces the node impedanceZC at higher frequencies. Thus, a tradeoff should be made be-tween Gm,eff and the RF bandwidth. Alternatively, reducing the

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ZIJIE AND MOUTHAAN: A 1- TO 10-GHz RF AND WIDEBAND IF CROSS-COUPLED GILBERT MIXER 3

Fig. 3. Simulated frequency response of the proposed Gilbert mixer.

width of LO transistors M3–M6 also benefits Gm,eff boostingby increasing ZC . However, smaller LO transistors require alarger overdrive voltage, which results in a reduction of voltageheadroom in the RF stage and, therefore, degrades linearityand noise performance of the mixer [3]. Cadence simulationsshow a very good agreement with the presented analysis andindicate a stable circuit, even with PVT variations. Additionally,an approximately 3-dB increase in noise figure caused by theproposed cross-coupled complementary pair is also observed.

Furthermore, the proposed mixer also employs the current-reuse technique realized by the bias current difference inthe complementary transistors (MN1 and MP1). The relation-ship between the bias currents of RF and LO stage can beexpressed as

IM2 = (IMP1 − IMN1) + (IM5 + IM6) (8)

where (IM5 + IM6) refers to the bias current of the LO stage.By optimizing the size difference of MN1 and MP1, the biascurrent through the LO transistors can be reduced, whichimproves the switching function. Reduction of the dc currentthrough the resistive load RD also alleviates voltage headroomlimitations and, therefore, improves the mixer linearity andconversion gain.

B. Conversion Gain Flattening Technique

According to (5), the high parasitic capacitance CC lowersGm,eff at high frequencies, which is mainly due to Cgs ofthe LO transistors and the complementary pair. To investigatethe resulting conversion gain rolloff at higher RF frequencies,cadence harmonic balance (HB) simulations are performed bysweeping both RF and LO frequencies for a fixed IF frequencyof 200 MHz. Note that the LO and IF baluns are also includedin HB simulations, which will be discussed in Section II-C.The conversion gain frequency response of the mixer using theproposed RF stage is shown in Fig. 3, indicating a 3-dB RFbandwidth of approximately 3 GHz.

To reduce the effect of parasitic capacitance present at theinterstage nodes C1 and C2 and to realize a flat conversiongain over a wider frequency range, an inductor Linter is addedbetween LO and RF stages, as shown in Fig. 4. A complex

Fig. 4. Parasitic capacitance compensated by the interstage inductor at thedominant pole.

resonator is formed by the total parasitic capacitor at the sourceof LO transistors Cp,LO, the interstage inductor Linter, andthe total parasitic capacitor at the output node of the RF stageCp,RF, as shown in Fig. 4. Resonating with Cp,RF and Cp,LO

at a certain in-band frequency, the added inductor contributes toa peaking in the conversion gain. Taking into account processlimitations of CMOS inductors, such as low-Q and low self-resonant frequency, an optimum inductance Linter = 3.5 nH at10 GHz is adopted. As shown in Fig. 3, the gain peaking occursaround 8.5 GHz, which effectively improves the conversiongain flatness up to 10 GHz. Cadence simulations also showthat the noise performance is improved around the gain peakingfrequency. The main reason for the noise figure improvement isthe part of noise added by the circuit itself remains unchangeddue to the gain peaking, whereas the amplification of usefulsignal is enhanced.

C. Wideband LO and IF Active Baluns

For the convenience of measurements with the single-endedinterface, an on-chip active LO balun with wideband matchingis applied in the proposed mixer. A cascode common-gatecommon-source balun is adopted and designed at the LO port[4]. As shown in Fig. 5(a), the cascode common-gate topologyis employed to add phase delay to compensate for the phasedeviation between the two stages over a wide bandwidth. Ca-dence HB simulations are performed on the designed LO balun,loaded with the gate-source capacitance of LO transistorsM3–M6. The LO balun exhibits a phase imbalance better than6◦ and an amplitude imbalance within 2.6 dB in the frequencyrange from 1 to 10 GHz. Simulations also indicate a 5-dB gainvariation throughout the LO band, which slightly increases therequired LO power for the optimum conversion gain.

An on-chip active IF balun is also designed for matching andtesting purposes, as shown in Fig. 5(b). It combines a common-source amplifier and a source follower for the differential tosingle-ended conversion [10]. Owing to the inherently lowoutput impedance of the source follower stage, output matchingand conversion gain flatness can be achieved throughout theentire IF-band. However, due to the limited output swing ofthe source follower stage, the overall linearity of the mixeris degraded. Note that a simple source follower can be alsoutilized as the output buffer for achieving wideband matchingif the output signal intends to differentially maintain.

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4 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: EXPRESS BRIEFS

Fig. 5. Schematic diagrams of (a) LO balun and (b) IF balun.

Fig. 6. Microphotograph of the mixer chip (core size: 0.7× 0.4 mm2).

III. MEASUREMENT RESULTS

The proposed wideband mixer is fabricated in Global-Foundries 0.13-μm CMOS technology. The die photographis shown in Fig. 6 with a chip size of 1.4× 1.1 mm2, inwhich the active area only occupies 0.28 mm2, excluding padsand dc decoupling capacitors. The mixer characteristics aremeasured using on-wafer probing on RF, LO, and IF pads,whereas dc pads are wire bonded to the mounted printed circuitboard. An external balun is used at the RF port to providethe differential RF signals. All losses from the external balun,probes, and cables are carefully extracted for precise powercalibrations. Operated with a 1.2-V supply voltage, the totalpower dissipation of the entire chip is 8.4 mW, whereas thesimulated power consumptions of the mixer core, LO and IFbalun are 2.55, 1.6, and 3.05 mW, respectively.

The measured and simulated port reflection coefficients areshown in Fig. 7. Due to the use of common-gate transistors inthe RF stage, a measured RF input return loss better than 10 dBis achieved from 0.6 to 12 GHz. The LO port exhibits an inputreturn loss better than 7 dB from 1 GHz to 10 GHz, and theoutput return loss at the IF port is better than 10 dB from 0.1 to4.4 GHz. The conversion gain frequency response is subse-quently measured at various RF and LO frequencies at anoptimum LO power of 0 dBm. As shown in Fig. 8, the measuredconversion gain is 5.5 ± 2.5 dB throughout the entire RF bandfrom 1 to 10 GHz, and the IF bandwidth from 100 MHz to1 GHz is measured with a conversion gain deviation less than2 dB. Compared with the simulated conversion gain in Fig. 3,the relatively large discrepancies at high frequencies are at-tributed to the inaccuracy of the device models at these frequen-cies, together with process variations and an underestimation ofparasitic effects.

Fig. 7. Measured and simulated reflection coefficient at RF, LO, and IF ports.

Fig. 8. Measured conversion gain versus RF frequency.

Fig. 9. Measured port-to-port isolation (LO-to-RF and LO-to-IF) with an LOpower of 0 dBm.

The measured port-to-port isolation is presented in Fig. 9.The LO-to-RF isolation is higher than 45 dB, whereas the LOleakage to the IF port is lower than −40 dB within the RFband. To evaluate the linearity of the proposed mixer, a two-toneintermodulation distortion test is performed over the entire RFband. In each case, RF signals spaced 1 MHz apart are down-converted to two-tone IF of 199 and 200 MHz. The measuredIP1-dB and IIP3 as a function of RF frequency are plotted inFig. 10. In addition to the linearity, the noise figure of thefabricated mixer is characterized at various RF frequencies. Ata group of fixed IF frequencies, the measured single-sideband(SSB) noise figure ranges from 11.3 to 15 dB within the entire

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ZIJIE AND MOUTHAAN: A 1- TO 10-GHz RF AND WIDEBAND IF CROSS-COUPLED GILBERT MIXER 5

Fig. 10. Measured IP1−dB and IIP3 of the proposed mixer.

Fig. 11. Measured SSB noise figure versus RF frequency.

RF band, as shown in Fig. 11. Note that the noise performanceat IF frequencies lower than 100 MHz dramatically deterioratesdue to the flicker noise of the transistors, which indicate that theproposed mixer in the present form is not suitable for zero-IFreceivers.

The performance summary and comparison with recentlypublished wideband CMOS mixers is shown in Table I. Thereported wideband mixers are implemented in CMOS technol-ogy and demonstrated in a similar frequency range. Note thatthe mixers in [4]–[6] are measured at a fixed IF frequency,and therefore, they are only wideband RF mixers. Comparedwith recently published wideband mixers in [4]–[6], [8], and[11], the mixer presented here has relatively wide RF andIF bandwidth, good input- and output-matching, low powerconsumption, along with moderate LO power requirement,conversion gain and gain flatness, which makes the proposedmixer suitable for wideband applications.

IV. CONCLUSION

A wideband RF and wideband IF mixer has been demon-strated in standard 0.13-μm CMOS technology. By employing acommon-gate RF stage with the cross-coupled complementarypair, a conversion gain of 5.5 ± 2.5 dB and RF return loss betterthan 10 dB are measured over the RF band from 1 to 10 GHz.The proposed mixer also exhibits a measured IF bandwidthfrom 100 MHz to 1 GHz with a conversion gain variation lessthan 2 dB, and an output return loss better than 10 dB. The chip

TABLE IPERFORMANCE SUMMARY AND REFERENCE TABLE

draws only 7 mA at a supply voltage of 1.2 V. The measuredIP1−dB, IIP3 and SSB noise figure are better than −16 dBm,−7 dBm, and 15 dB throughout the entire RF band. To the bestof our knowledge, the proposed mixer is the first demonstrationof a CMOS Gilbert mixer exhibiting a flat conversion gain andgood input/output matching over both wide RF and IF bands.

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