Intermodulation analysis of dual-gate FET mixers

1544 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 50, NO. 6, JUNE 2002

Intermodulation Analysis of Dual-Gate FET MixersJunghyun Kim, Student Member, IEEE,and Youngwoo Kwon, Member, IEEE

Abstract—A detailed intermodulation analysis of dual-gate FET(DG-FET) mixers is presented. The analysis method is based ona large-signal/small-signal analysis using time-varying Volterra-series methods. The analysis program allows one to probe theinternal nodes of DG-FETs to evaluate the nonlinear currentcomponents. Therefore, it helps physical understanding of inter-modulation distortion (IMD) mechanisms in DG-FET mixers. Theprogram was used to identify the major sources of IMD generation.It was found from the analysis that the nonlinearities due to theoutput conductance ( 3 and 2) of the lower common-sourceFET were most responsible for IMD generation. The impact of theupper common-gate FET on IMD generation was also found to benonnegligible, especially at high local oscillator (LO) power levels.The analysis also predicted the presence of IMD “sweet spots”using bias optimization, which was experimentally proved by thefabricated mixers at - and -bands. The optimized -bandhybrid mixer showed measured intermodulation characteristics(OIP3 13 6 dBm) comparable to those of the resistive mixers(OIP3 15 3 dBm) with low LO and dc power conditions.Very good agreement between the measurement and simulationwas found for the two mixers using different types of transistors,which validates our analysis method and supports the generaladequacy of our approach. This paper presents a comprehensiveIMD analysis and design methodology for DG-FET mixers, andshows that well-designed DG-FET mixers are very promising formodern monolithic applications requiring high linearity.

Index Terms—Dual-gate FET, HEMT, intermodulation, mixer,MMIC.

I. INTRODUCTION

M ODERNdigital communicationsystemsrequirehigh lin-earity, characterized by low intermodulation distortion

(IMD), in order to reduce the error rates. The intermodulationperformance of a front-end receiver is often limited by that of themixer. This is due to the fact that the mixermust handle the largestRF signal, and the IMD performance of a mixer is usually worsethan that of other components. For this reason, accurate inter-modulation analysis of the mixers has recently become a criticalpart of the receiver analysis and design.

The intermodulation analysis of diode mixers has been avail-able since the late 1980s [1]. On the contrary, few works havebeen published on the IMD analysis of FET mixers, except forthe case of FET resistive mixers [2]–[5], which offer good lin-earity characteristics. The wide availability of IMD analysis ofFET resistive mixers is due to the fact that they are essentiallypassive mixers and, thus, the analysis method is basically iden-

Manuscript received June 20, 2000; revised May 15, 2001. This work wassupported by the Korean Ministry of Science and Technology under the CreativeResearch Initiative Program.

The authors are with the Center for 3-D Millimeter-Wave Integrated Systems,School of Electrical Engineering, Seoul National University, Seoul 151-742,Korea.

Publisher Item Identifier S 0018-9480(02)05202-X.

tical to that of the diode mixers. In the case of active FET mixers,few studies have been available. Penget al. [6] recently pre-sented an intermodulation analysis of single-gate FET mixersusing the large- and small-signal analysis method pioneeredby Maas to calculate the IMD of diode mixers [1]. However,the analysis was limited to the single-gate common-source FET(CS-FET) mixers in [6].

Among various mixer types using FETs, dual-gate FET(DG-FET) mixers are of particular interest for monolithicapplications. DG-FETs offer on-chip RF/local oscillator (LO)combining capability using the two isolated gates as LO andRF ports. DG-FET mixers also provide the possibility ofconversion gain. In this way, the need for a bulky couplerand IF amplifier can be eliminated, resulting in a small diesize. Monolithic DG-FET mixers have been successfullyimplemented up to -band [7]. Decent IMD performanceshave also been achieved experimentally using monolithic mi-crowave integrated circuit (MMIC) DG-FET mixers [8]–[10].Measured ’s (third-order intercept points referred to theoutput) ranging from 5 to 10 dBm were reported. However, noresearch has been reported on the comprehensive analysis ofintermodulation characteristics of DG-FET mixers, probablydue to the complexity of dual-gate devices. Accordingly,design methodology to optimize the circuit for linearity and/orconversion gain has not been available for DG-FET mixers.

In this study, a general intermodulation analysis method ofa DG-FET mixer has been developed at low transistor levels.The analysis is based on a time-varying Volterra series method[6]. Since the method was developed at the individual transistorlevels, it allows one to probe the internal nodes of DG-FETsto evaluate the nonlinear current components, and, thus, helpsto physically understand IMD generation mechanisms insidethe DG-FET mixers. It also provides a way of assessingthe role of each nonlinear component on the generation ofIMD products. To prove the validity and generality of theproposed analysis method, two types of DG-FET mixers com-posed of cascode-connected high electron-mobility transistors(HEMTs) were designed and fabricated at- and -bands. Ahybrid-type -band mixer has been implemented using com-mercially available HEMTs, and a monolithic -band mixerhas been realized using pseudomorphic high electron-mobilitytransistors (pHEMTs) fabricated in-house at Seoul NationalUniversity, Seoul, Korea. Both mixers showed excellent agree-ment between measured and simulated IMD characteristics,validating the analysis method. IMD “sweet spots” predictedby the analysis have also been verified experimentally for bothcases. The bias-optimized -band DG-FET mixer showedintermodulation characteristics comparable to those of theresistive mixers ( dBm versus 15.3 dBm forresistive mixers) with low LO power requirement.

0018-9480/02$17.00 © 2002 IEEE

KIM AND KWON: INTERMODULATION ANALYSIS OF DG-FET MIXERS 1545

Fig. 1. Equivalent circuit schematic of a DG-FET mixer.

This paper provides a detailed IMD analysis and designmethodology of DG-FET mixers for high linearity. It alsoshows that well-designed DG-FET mixers are very promisingfor modern monolithic applications requiring high linearity.

II. I NTERMODULATION ANALYSIS METHOD

The goal of this study was to understand the intermodulationmechanisms in DG-FET mixers and to identify the dominantsources of intermodulation and, finally, based on such infor-mation, to come up with a design method to optimize DG-FETmixers for high linearity. For this purpose, a custom computerprogram to analyze the IMD in DG-FET mixers has been de-veloped on the basis of a time-varying Volterra-series method[11]. To simplify the analysis, a DG-FET was replaced by a cas-code connection of two single-gate FETs so that the intermod-ulation analysis could be performed at single transistor levelsrather than multitransistor ones. Fig. 1 shows the equivalent cir-cuit schematic of a DG-FET mixer as represented by the cas-code connection. Also shown in Fig. 1 is the circuit topology ofthe DG-FET mixer designed in this study, the details of whichwill be presented in Section V. As will be shown later, mixingmostly occurs in the lower CS-FET, which operates much like adrain-pumped mixer. The upper CG-FET provides LO pumpingto the lower FET by changing the intermediate drain voltage (in Fig. 1) in response to the LO signal. Nevertheless, the upperFET, which also works as a common-gate IF post-amplifier andmixer, may contribute to the overall IMD, as will be shown inSection IV.

A. Intermodulation Analysis Procedure

The analysis started by calculating the intermodulation prod-ucts in the CS-FET, and is followed by a similar calculation inthe CG-FET with different termination impedances and inputsignals. Thus, the nonlinear effects of the upper CG-FET werefully included in our analysis to generalize the analysis, as wellas to quantify the contribution of the CG-FET on IMD genera-tion.

Each calculation at the single-transistor levels was per-formed using an FET IMD analysis method presented in [6].The method is based on a large-signal/small-signal analysis

using a method of nonlinear currents, and was developed in [6]to analyze the single-gate mixers using CS-FETs. In this paper,the method has been extended and generalized so that it can beapplied to the upper common-gate FET (CG-FET) as well.

The flowchart of the analysis program is shown in Fig. 2. TheLO voltage waveform at each CS- and CG-FET was first eval-uated by a single-tone harmonic-balance simulation using theLO signal as the only input. A commercial harmonic-balancesimulator was used for this purpose. Once the LO waveformwas found, perturbed small-signal current components were ex-pressed in Taylor’s series up to third order as follows:

(1)

where is the drain current, and are the gate and drainvoltage, respectively, and

(2)

where

ifotherwise

In (2), subscripts with zeroes and ones were omitted to sim-plify the notation, e.g., denotes and represents

.Fast Fourier transform (FFT) was followed to find harmonic

frequency components of . Ten harmonics were includedin the analysis. A set of Kirchoff’s voltage law (KVL) equa-tions was then derived at each mixing frequency using the small-signal equivalent circuit, and was solved by the method of non-linear currents. The detail of the KVL equations and solutionprocedures will be presented in the following sections. After te-dious, but straightforward calculations, each component of thethird-order intermodulation currents shown in (1) was evaluatedat the internal node ( in Fig. 1).

Among various IMD products generated by the CS-FET atIF and RF bands, only those with mathematical significancewere selected and employed as the inputs to the lower CG-FET.The detailed selection criteria are given in Section IV. The IMDcalculation procedure was then repeated for an upper CG-FETusing different equations and input signals. Finally, the IMDproducts at the drain terminal of the cascode-connected FETswere found. The entire procedure was implemented in a com-puter program to speed up the simulation. The custom programallows one to probe any internal nodes to evaluate the nonlinearcurrent components and, thus, helps to understand the mixingand intermodulation mechanisms inside the device.

B. Device Models

The analysis requires accurate knowledge of thevoltage dependence of and their derivatives

, which were provided by the voltagedependence tables of and . It also requires accurate es-timation of the single-tone instantaneous LO voltage waveform


Fig. 2. Flowchart of the IMD analysis program of DG-FET mixers.

at each terminal of the FETs, which requiresgood nonlinear FET models.

The complete equivalent circuit of the DG-FETs used inthis study is shown in Fig. 3. It includes nonlinear componentsas represented by two current sources and linear capacitivecomponents, as well as parasitic elements such as accessresistances and stray capacitances. Also included in this figureis the internal impedance labeled as “ ,” which representsconnecting transmission lines between the two transistors, ifany, and also the interstage matching circuits in cascode mixers,which may be included to improve performance.

The basic assumptions for the analysis are as follows. First,the capacitive effects due to nonlinear gate–source andgate–drain capacitances were neglected since they werefar less significant than the nonlinear conductance effectsdue to and . Thus, they were considered as linearelements. Similar assumptions have been made for the analysis

Fig. 3. Complete equivalent circuit of the DG-FETs used in this study.

of single-gate FET mixers in [6]. Second, the reflections fromthe CG-FET was neglected to simplify the analysis. In this


way, multiple reflections between the CS- and CG-FETs couldbe ignored. Third, the effects of parasitic capacitances such as

and were not included in the analysis.The voltage dependence tables of have been extracted

from the -parameter measurements at various bias points. Toimprove the accuracy of the table,-parameters were measuredat fine steps ( V V) over the entire op-eration bias range of the DG-FET mixers. and valueswere extracted using the small-signal extraction program de-veloped in-house. The accuracy of the extraction program hasbeen verified through successful demonstration of MMICs upto -band [12], [13].

For the evaluation of large-signal LO voltage waveform, amodified table-based model presented in [14] has been usedtogether with a commercial harmonic-balance simulator. Con-ventional table-based models are directly constructed from themeasured data by numerical interpolation and integration. How-ever, they may give erroneous results and cause ambiguity inI–V characteristics in the low drain voltage region due to thefact that the extracted conductance data may not satisfy numer-ical conservation condition. This may cause significant errorsfor simulations performed near the knee voltages, which is thecase for the lower CS-FET of this study.

To improve the accuracy, a modified table-based model thatcombines the advantages of table-based and analytical modelshas been developed by Kwonet al. in [14]. Over the bias rangeswhere conservation condition is acceptably satisfied, the mi-crowave current is calculated by integration using (3). On theother hand, for the bias regions where the current calculatedby integration is questionable, the current is determined simplyfrom the analytical – formula using the function as fol-lows:

(3)

(4)

Finally, to satisfy the necessary continuity conditions, analyticalformulas shown in (5)–(9) [15] are employed to fit the currentand charge data calculated either from the integration or analyt-ical methods as follows:

(5)

The two individual current terms are

(6)

(7)

where

(8)

(9)

Fig. 4. Equivalent-circuit schematic of the lower CS-FET used for IMDanalysis.

, and are parameters that are determined by fittingto the microwave current data with weighting factors.

The model is numerically stable and produces accurate re-sults. The model has been verified in [14] for millimeter-wavepower amplifiers. In this study, the model has been refined,making use of the fact that the bias region required for mixeroperation is limited compared to general circuits such as poweramplifiers. For example, the lower CS-FET in DG-FET oper-ates near the knee region only; the LO swing typically mod-ulates the drain voltage from 0 V only up to 1.5–2 V. Hence,the model was primarily constructed based on the data mea-sured densely in the knee region. The model was, in this way,capable of reproducing the conductances and their derivativesin the bias region of interest with high accuracy, as well as thecurrent data themselves. The following two sections present de-tailed intermodulation analysis and results in the lower CS- andupper CG-FETs.

III. I NTERMODULATION IN THE LOWER CS-FET

The lower CS-FET operates like a drain-pumped mixer,where the LO signal modulates the drain voltage (inFig. 1). Subsequent variation of the transconductance andoutput conductance results in mixing operation. The RF signalis applied to the gate terminal and, thus, transconductancemodulation with the LO signal is most responsible for mixing.As will be shown later, the nonlinear action of the CS-FET isnot only responsible for mixing, but is also the largest sourceof IMD. A detailed intermodulation study has, consequently,been performed on the nonlinear effects of the CS-FET. Inorder to understand IMD mechanisms and to identify the majorcontributors to IMD inside the lower FET, the analysis beganby investigating the intermodulation coefficients and proceededto calculating each nonlinear current component of (1) and,finally, expressing them as phasors.

The equivalent circuit shown in Fig. 4 has been used toderive perturbed nonlinear current equations for the CS-FET.Frequency-dependent termination impedances

were employed to represent the impedances at eachterminal of the CS-FET. represents the input impedanceof the CG-FET seen at the drain port of the CS-FET and mayinclude if it exists for the case of cascode mixers. Using


KVL, the small-signal incremental current loop equations canbe written in the following matrix forms [6]:

(10)

where superscript denotes the CS-FET. Impedance matrix, current vector , and voltage vector are as shown

in (11)–(14), at the bottom of this page, where small-signal in-cremental currents and , and small-signal incre-mental voltages and are specified in Fig. 4.is the voltage source that is determined according to the ordersduring the method of nonlinear currents.

Once the Taylor’s expansion of all the small-signal drain cur-rent of (1) is substituted in (10), and all the time-varying func-tions are expanded in the frequency domain, the node voltagevector can be expressed as

(15)

where the admittance matrix takes the form of a conversionmatrix in mixers, and includes the nonlinear submatricesand , as well as the linear submatrices andas

(16)

where is a diagonal submatrix whose diagonal elements cor-respond to the harmonic frequencies.

The method of nonlinear currents [11] is then applied to findthe first-, second-, and third-order nonlinear currents. For thefirst-order calculations, the voltage source vector is

(17)

As soon as the first-order voltages are determined, thefirst-order output currents and the second-order current sourcescan be determined. This second-order current sources can thenbe transformed to the second-order voltage sources to solvethe second-order equation. The calculation is repeated until the

Fig. 5. I–V characteristic of a DG-FET at a fixedV of �0.2 V. AccordingtoV , three different bias regions of interest can be found and are denoted bycircles.

third-order nonlinear currents are found. Detailed simulationresults are presented in the following sections.

A. Intermodulation Coefficients

As can be seen from (1), the third-order intermodulationproducts are most affected by the coefficientsand . Accordingly, intermodulation can be minimizedby studying these coefficients and selecting the bias and LOpumping conditions that minimize these coefficients. Similarstudies have been performed for resistive mixers in [16] and[17], where Taylor-series coefficients of the– formulawere related to IMD characteristics, and used to optimize thelinearity of the resistive mixers.

Two independent gate biases determine the operating point ofthe DG-FETs. The gate bias to the lower FET ( in Fig. 1)determines the tradeoff between the conversion gain and noisefigure, as shown in [18]. However, it has little effect on the lin-earity as long as the device is biased above pinchoff. The gatebias to the upper FET ( in Fig. 1), on the other hand, deter-mines the operating point on the – curve of the lower FET,as illustrated in Fig. 5. Since it determines the operating regionof the CS-FET, it is expected to have strong effects on the co-efficients. Fig. 6(a) and (b) shows measured transconductance,

(11)

(12)

(13)

(14)


(a)

(b)

Fig. 6. Measured: (a)G ;G ; and G and (b)G ;G ; and Gcoefficients of the 80-�m HEMT as a function ofV .

output conductance, and their derivatives, as a function of thesecond gate bias for a fixed of 0.2 V. was setto 3 V for this measurement. The conversion gain of the mixerlargely depends on the variation of transconductance with LOpumping. To be more specific, the fundamental harmonic com-ponent of under LO pumping determines conver-sion gain [12]. Fig. 6(a) shows that the highest conversion gainis expected near the knee voltage V: “knee re-gion” in Fig. 5), where curve shows the greatest change.However, poor intermodulation characteristics are also expectedin this bias region, as shown in Fig. 6(b). Fig. 6(b) shows that

, which will be shown to have the greatest impact ongeneration later, presents the largest value and change near theknee voltage ( V). This means that poor intermod-ulation performance is unavoidable when the DG-FET mixeris bias tuned for maximum conversion gain. In order to clarifythis point, the first harmonic components of the intermodula-tion coefficients of (2) are calculated and plotted in Fig. 7 asa function of . For this calculation, the LO voltage wave-form was found from the harmonic-balance simulation, and asubsequent FFT was performed using the time-domain conduc-tance data. As expected, the first harmonic components ofand coefficients show peak values near the knee voltage.It is also worthwhile to note that the peak is broader thanthe peak. The rapid decrease of the coefficient outsidethe knee region suggests that excellent intermodulation charac-teristics can be achieved together with decent conversion gainby choosing the just outside of the knee region ( near

0.5 V: “linear region” and 0.2 V: “half-saturated region” in

(a)

(b)

Fig. 7. First harmonic components of: (a)G and (b)G ;G ;G ; andG as a function ofV at a fixed LO power of 0 dBm.

Fig. 8. First harmonic components ofG andG as a function of LO power.V was fixed at�0:5 V.

Fig. 5). This point will be verified by further simulation andmeasurement.

Besides the gate bias, the LO pumping level also has a strongeffect on the conversion gain and linearity. Fig. 8 shows thefirst harmonic components of and as a function of LOpower. The rapid increase of the coefficient at high LOpower levels implies that the LO pumping level must be main-tained below a certain level (4 dBm) to achieve good linearity.The decrease of the component at high LO power levelsalso suggests that optimum LO power be around 0–3 dBm.

B. Phasor Diagram Analysis and Simulation Results

The third-order intermodulation current is composed of var-ious components, as shown in (1). Each term in (1) is a vector


(a) (b)

(c)

Fig. 9. Phasor diagrams comparing nonlinear current components, corresponding to: (a) linear region, (b) knee region, and (c) half-saturated region.

quantity with both magnitude and phase. Thus, it can be repre-sented as a complex phasor, as in [19], and the total intermodula-tion current as a vector sum of each component. In order to iden-tify dominant terms generating IMD, terms of (1) are expressedwith the help of phasors in the two-dimensional (2-D) complexplane, as shown in Fig. 9. In the previous section, the intermod-ulation coefficients were shown to be strongly dependent on thesecond gate bias. Similar characteristics are expected for the in-termodulation current terms. Thus, Fig. 9 shows three differentphasor diagrams corresponding to the following bias regions:

1) linear region;2) knee region;3) half-saturated region;

according to the notations in Fig. 5. The LO power is fixedat 0 dBm for this calculation, corresponding to the optimumpumping level judged from Fig. 8.

Even though the phase and magnitude of intermodulationphasors vary according to bias, it can be generally stated fromFig. 9 that the nonlinearities related to the output conductance( and ) dominate the overall intermodulation in mostbias regions. The largest intermodulation occurs in the knee re-gion [see Fig. 9(b)]. In this region, the two output conductancenonlinearities and add nearly in-phase, producing thelargest intermodulation products. Terms due tononlineari-ties decreases rapidly as the bias is shifted away from the kneeregion. Minimum intermodulation is observed in the linear re-gion [see Fig. 9(a)], which shows greatly reduced terms

and almost negligible transconductance terms. The relative im-portance of transconductance nonlinearities ( and )grows as the bias moves toward saturation. In the half-saturatedregion [see Fig. 9(c)], the and current terms con-tribute to about 40% of the total IMD. However, the overall in-termodulation in this region still remains much smaller than thatin the knee region. On the whole, the dominant intermodulationsources are -related terms, and the intermodulation can begreatly reduced by selecting , which minimize terms.

IV. I NTERMODULATION IN THE UPPERCG-FET

The upper FET operates much like a source follower. It pro-vides the LO signal to the lower CS-FET. The main action takingplace in the CG-FET was considered by many designers as mereIF post-amplification. Mixing in a CG-FET was thought to benegligible. Furthermore, its role for IMD generation has notbeen well understood. In order to accurately assess the role ofthe CG-FET in mixing and intermodulation generation, a fullintermodulation analysis similar to the case of the CS-FET de-scribed in the previous section was performed on the upper FET.The equivalent-circuit schematic shown in Fig. 10 has been em-ployed to derive perturbed nonlinear current equations for theCG-FET. A set of equations similar to those derived for theCS-FET [see (11)–(16)] has been derived for the CG-FET. Here,superscript represents the CG-FET as follows:

(18)


Fig. 10. Equivalent-circuit schematic of the upper CG-FET used for IMDanalysis.

and as and , shown in (19) and (20), at the bottomof this page, where represents the output impedance ofthe CS-FET seen at the source terminal of the CG-FET, andmay also include for cascode mixers. Overall matrix ele-ments and calculation procedures are very similar to the case ofthe CS-FET, except for the termination impedances and inputvoltage source vectors. For example, the following first-ordervoltage source vector is used for CG-FET calculation:

(21)

It is worthwhile to note that the first-order sources, or theinput signals to the CG-FET, are much more complicated thanthose of CS-FETs since, in principle, they should comprise allthe output components from the CS-FET. However, this makesanalytical derivation practically impossible. Thus, a selectionprocedure is needed at this stage. Selection was made to includeall the dominant frequency components that will eventually ap-pear at the IF load via mixing or amplification in the CG-FET.Eighteen components

have been selected as the inputs to the CG-FET; 9 compo-nents each with orders less than or equalto three have been chosen from IF and RFbands. The spectrum of the 18 input frequency components isshown in Fig. 11 together with the voltage magnitudes of eachcomponent in a separate table. The largest terms are the RF com-ponents at and , followed by the down-converted IF components at and . It isworthwhile to note that the components at the RF band (or ) are greater by a factor of two to three than the cor-responding components at the IF band ( or ). This can

Fig. 11. Spectrum of the 18 frequency components selected as the inputs to theupper CG-FET for IMD simulation. Shown in the separate table are the voltageamplitudes(V ) of each frequency component.

be easily understood if one considers that the IF components aredownconverted signals from their RF counterparts.

Given the inputs shown in Fig. 11, the following four fre-quency components of interest have been calculated at the load:

. Inorder to identify the major sources of intermodulation, each fre-quency component has been sorted according to the frequencyand the order of mixing. For example, the IF intermodulationproduct at (IM1) was sorted as follows:

higher order terms

(22)where

(23)

(24)

(25)

(26)

and represents theth harmonic component of .

(19)

(20)


TABLE IAMPLITUDE AND PHASE OFSORTEDCURRENTCOMPONENTS(I ; I ; I AND I OF (4)–(7)) CALCULATED AT VARIOUS LO PUMPING POWER

LEVELS. MIXING COMPONENTS AT! ARE LISTED IN (a), WHILE THE INTERMODULATION COMPONENTS AT! (=2! � ! ) ARE SHOWN IN (b)

(a)

(b)

represents linear amplification terms that are essen-tially the intermodulation terms generated by the lower CS-FETand linearly amplified in the upper FET. includes first-order mixing terms that have been frequency translated from

to . Thus, for this component, theintermodulation was generated in the CS-FET and downcon-verted to the IF band by mixing in the CG-FET. rep-resents the second- and third-order mixing terms resulting fromintermixing of and and , andso on. These terms were generated by intermodulation in theCG-FET and downconverted to the IF band by mixing in thesame device. Lastly, terms denote intermodulation prod-ucts at IF frequencies. No frequency translation is involved inthe CG-FET for this term. Thus, they represent intermodulationterms produced during post-amplification of IF-band signals inthe CG-FET. The generation of and IMD termsis attributed exclusively to the nonlinear effects of the CG-FET.Similar categorization can be carried out on other IF frequencycomponents. Table I shows each sorted current component cal-culated at four different LO pumping power levels. Mixing com-ponents at are listed in Table I(a), while the intermodula-tion components at are shown in Table I(b). Thefollowing observations can be made from the simulation resultsof Table I.

1) Higher order intermixing in the CG-FET has a negligibleeffect on the mixing component (IF1); andterms are insignificant compared to and[two orders of magnitude smaller, as shown in Table I(a)].

2) The downconverted IF1 component due to mixing in theCG-FET is smaller than the linearly post-am-plified term at low LO power levels. However, itgrows with LO power and becomes nonnegligible at highLO power levels, implying that the mixing effect in theupper FET needs to be considered for conversion-loss cal-culation at high LO power levels.

3) Unlike the mixing component (IF1), a significant portionof the intermodulation term IM1 is generated by higherorder intermixing in the CG-FET. As a matter of fact, thesecond– and third-order RF intermodulation termis comparable to the linear term over the entire LOpower range used in the simulation [see Table I(b)].

4) IMD during post-amplification of IF signals alsocannot be neglected. This, together with the importanceof , means that the CG-FET contributes signif-icantly to the overall IMD and, consequently, the inter-mixing effect of the CG-FET has to be included for accu-rate estimation of IMD in DG-FET mixers.

Following the above observations, it can be stated that theupper CG-FET operates more than just a simple linear post IFamplifier. It does indeed complicate the picture by adding itsown nonlinearities, especially at high LO power levels. To makematters worse, its effect is more pronounced in producing inter-modulation products than mixing terms; major mixing actionstill takes place in the lower CS-FET, but the intermodulationproducts will grow measurably after the signal passes throughthe upper FET. Therefore, the nonlinear effects of the CG-FEThave to be considered for accurate simulation of IMD, and spe-cial care has to be taken not to use excessive LO powers andto keep the CG-FET in the linear-operation region for high-lin-earity design.

In order to visualize the nonlinear effect of the CG-FET,the calculated IF power and the power level of the third-orderintermodulation components are plotted in Fig. 12 as a functionof the LO power for two signals: one before and the other afterpassing through the upper FET. The RF power was20 dBm.The curves labeled as “IF-out” and “ -out” denote theoutput signals after the CG-FET and those labeled as “IF-in”and “ -in” are the input signals into the CG-FET. Asexpected earlier, IMD increases with the LO power. Rapidincrease of intermodulation above 0 dBm in Fig. 12 againindicates that the optimum LO power is around 0 dBm. At thisLO power level, the relative intermodulation power (referencedto the IF signal) increases from48 dBc to 44 dBc afterthe signal passes through the CG-FET. This corresponds to a2-dB decrease in the third-order intercept point , whichillustrates a nonnegligible impact of the CG-FET on linearity.

V. DESIGN AND RESULTS

To verify the analysis method and to demonstrate generalityof the proposed analysis, two types of linearity-optimizedDG-FET mixers composed of cascode-connected HEMTs


Fig. 12. Power of IF and third-order intermodulation signals as a function ofthe LO power. The curves labeled “-in” correspond to the signals before enteringthe CG-FET, and those labeled “-out” represent the signals after passing throughthe CG-FET.

Fig. 13. Measured and calculated conversion gain and relative intermodulationlevel(IMD ) of theX-band DG-FET mixer at a fixedV of�0:2V andVof 3 V. RF input power is�20 dBm and LO power is 0 dBm. Also shown inthe inset are the spectrums of IF andIM signals at two distinct bias points:V = �0:2 V (optimum conversion gain) and�0.5 V (optimumIMD ).

were fabricated at two different frequencies using differenttypes of transistors. First, commercially available HEMTs wereused to realize a hybrid-type -band mixer. Another mixerwas fabricated at the -band using 0.2-m GaAs pHEMTsdeveloped in-house. The -band mixer is a monolithic circuitand the epitaxial layer structure is different from the-banddevice, resulting in different nonlinear characteristics.

Fig. 1 shows the equivalent-circuit schematic of the-bandhybrid mixer. The gate bias network included a transmis-sion line terminated with a large capacitor for an IF short. AnLO short was provided at the output using a radial stub. RF andLO matching circuits were realized with open-ended stubs. NoIF matching was included in the circuit, making the IF loadimpedance 50 . The frequencies of the two-tone RF signalswere 10 and 10.001 GHz and the LO frequency was 9.7 GHz,resulting in IF two-tone signals at 300 and 301 MHz.

Fig. 13 shows the measured and calculated conversion gainand of the -band mixer as a function of at afixed of 0.2 V and of 3 V. RF input power was

20 dBm and LO power was 0 dBm. As expected earlier,

Fig. 14. Comparison of measuredIP between the resistive mixer and DG-FET mixer as a function of LO power. Both mixers used the same transistor, acommercial 80-�m HEMT.

maximum conversion gain was observed near the knee voltage( V), corresponding to the peak point of thefirst harmonic component of in Fig. 7(a). This bias point,however, showed the worst IMD characteristics with anof 28.6 dBc. As the bias is moved out of the knee region,IMD characteristics improved with a slight decrease in theconversion gain. Minimum IMD distortion was observed ata of 0.5 V. This point was consistent with the inter-modulation “sweet spot” predicted from the intermodulationcoefficient analysis in Section III. Also shown in the inset arethe spectrums of IF and IM signals at these two bias points.The measured level at V was 58.1 dBc,which was as much as a 29.5-dB improvement over the valueat the knee bias region ( V). The conversiongain decreased only by 3.4 dB from 8.1 to 4.7 dB. Fig. 13shows an important characteristic of a DG-FET mixer that thecircuit can be optimized either for conversion gain or linearityby simple tuning of bias. Fig. 13 also shows excellentcorrespondence between the measurement and simulation forboth conversion gain and ; measured conversion gainwas within 1 dB of the simulation, and measured waswithin 5 dB for most bias conditions. Good agreement betweenmeasured and simulated data proves the validity of our analysismethod.

To benchmark the linearity of the DG-FET mixer of thisstudy, a resistive mixer was designed and fabricated using thesame transistor at -band. Measured is compared as afunction of the LO power in Fig. 14. The resistive mixer showeda peak of 15.3 dBm at a high LO power of 10 dBm. TheDG-FET mixer showed a slightly lower peak of 13.6 dBm,but at a much lower LO power of 0 dBm. This demonstratesthat properly designed DG-FET mixer can show linearitycharacteristics not so much inferior to resistive mixers, but withlower LO power requirement, as well as favorable conversiongain and inherent RF/LO isolation capability.

To prove the general adequacy of the proposed intermod-ulation analysis, we also made two-tone measurements of a

-band HEMT MMIC mixer. Two transistors with a gateperiphery of 80 m have been used in a cascode configuration.The frequencies of the two-tone RF signals were 27 and


Fig. 15. Measured and calculated conversion gain and relative intermodulationlevel (IMD ) of theKa-band DG-FET mixer at a fixedV of �0.2 V andV of 3 V. RF input power is�20 dBm and LO power is 0 dBm:V = 0:4 Vcorresponds to optimum conversion gain and�0.1 V to optimumIMD biaspoints.

Fig. 16. MeasuredOIP as a function of the LO power for theKa-bandmixer.

27.001 GHz and the LO frequency was 26.5 GHz, resulting inIF two-tone signals at 500 and 501 MHz.

The comparison of the measured and calculated conversiongain and as a function of is shown in Fig. 15. As inthe case of the -band hybrid mixer, the intermodulation “sweetspot” was observed at a of 0.1 V, showing 20-dBc im-provement over the value at the knee bias region ( V).Good agreement between simulation and measurement againverifies the accuracy of the proposed analysis. Fig. 16 showsthe measured as a function of the LO power. This provesthat there is also an optimum LO power ( dBm) for IMD forthe -band DG-FET mixer.

Fig. 17 shows measured and conversion gain as a func-tion of the drain bias for both mixers. Excellent char-acteristics hold out to a very low drain bias of 0.8 V at-band[see Fig. 17(a)]. High ’s more than 13 dBm were foundover a broad drain bias range from 0.8 to 3 V. At a drain bias of2 V, an of 13.6 dBm was obtained together with a low dcpower consumption of 6 mW. Similar characteristics have alsobeen observed for the -band monolithic mixer, as shown inFig. 17(b). higher than 10 dBm have been achieved downto a low drain bias of 1.2 V at -band.

(a)

(b)

Fig. 17. Measured conversion gain and third-order output intercept points(IP ): (a) of theX-band commercially available cascode mixer and (b) theKa-band monolithic cascode mixer as a function ofV .

VI. CONCLUSION

A detailed intermodulation analysis program has been de-veloped to simulate the IMD performance of DG-FET mixers.The program was based on a large-signal/small-signal analysismethod, where a commercial harmonic-balance program wasused to find large-signal LO waveforms, and Volterra series forperturbed small-signal analysis. For the analysis, the DG-FETwas broken down into a cascode connection of a CS-FET andCG-FET. A comprehensive IMD study was carried out at theindividual transistor levels to obtain physical understanding ofintermodulation mechanisms inside the DG-FETs.

A quantitative IMD comparison study has shown that the con-tribution of the CS-FET on IMD generation was found to be pre-dominant over that of the CG-FET. Yet it was also found that,at high LO power levels, nontrivial IMD can be added by theCG-FET due to its own nonlinearities. In other words, majormixing and IMD action takes place in CS-FET, but IMD cangrow measurably after passing through the CG-FET dependingon the LO power levels. Therefore, the nonlinear effects of theCG-FET should be included for accurate IMD simulation, andspecial care has to be taken not to use excessive LO powers forhigh linearity.

Since the CS-FET was found to be the largest source of IMD,a thorough intermodulation study has been performed to iden-tify the major contributors to IMD inside the CS-FET. After in-vestigating the intermodulation coefficients and comparing each


nonlinear current component with the help of phasors, it was re-vealed that the nonlinearities related to the output conductancedominate the overall IMD in the CS-FET. It was also found that

nonlinearities show strong dependence on the second gatebias . The largest intermodulation occurs in the knee re-gion, where nonlinearities add in-phase and produce largeintermodulation products. However, nonlinearities decreaserapidly as the bias is shifted away from the knee region. Min-imum IMD is observed in the linear region right next to the kneebias. Respectable conversion gain is also observed in this re-gion, suggesting that it correspond to a “sweet spot” for lin-earity. IMD dependence on LO power was also studied. Therapid increase of the coefficient at high LO power levelsimplies that the LO pumping level must be maintained below acertain level (4 dBm) to achieve good linearity.

Based on the analysis results, two types of illustrative DG-FET mixers, both optimized for linearity, have been designedand fabricated using different devices at- and -bands. Ex-cellent IMD characteristics were achieved using a drain bias aslow as 0.8 V at -band and 1.2 V at -band. Measuredof an -band DG-FET mixer (13.6 dBm) compares well withthat of the resistive mixers (15.3 dBm) using the same FET.The presence of IMD “sweet spots” predicted by the analysiswas also proven experimentally. Very good agreement betweenthe measurement and simulation was found for both types ofmixers, which validates our analysis method and supports thegeneral adequacy of our approach. This paper has shown thatwell-designed DG-FET mixers are very promising for modernmonolithic applications requiring high linearity. The analysisof this paper can be further used to optimize the linearity ofDG-FET or cascode mixers.

ACKNOWLEDGMENT

The authors would like to thank M. S. Jeon, WavIC Inc.,Seoul, Korea, for technical assistance during testing and mea-surement.

REFERENCES

[1] S. A. Maas, “Two-tone intermodulation in diode mixers,”IEEE Trans.Microwave Theory Tech., vol. MTT-35, pp. 307–315, Mar. 1987.

[2] R. S. Virk and S. A. Mass, “Modeling MESFET’s for intermodulationanalysis of resistive FET mixers,” inIEEE MTT-S Int. Microwave Symp.Dig., June 1995, pp. 1247–1250.

[3] S. Peng, P. McCleer, and G. I. Haddad, “Intermodulation analysis of FETresistive mixers using Volterra series,” inIEEE MTT-S Int. MicrowaveSymp. Dig., June 1996, pp. 1377–1380.

[4] J. A. Garcia, J. C. Pedro, N. B. De Carvalho, A. M. Sanchez, and A. T.Puente, “Resistive FET mixer conversion loss and IMD optimization byselective drain bias,”IEEE Trans. Microwave Theory Tech., vol. 47, pp.2382–2392, Dec. 1999.

[5] K. Yhland, N. Rorsman, M. Garcia, and H. F. Merkel, “A symmet-rical nonlinear HFET/MESFET model suitable for intermodulation anal-ysis of amplifiers and resistive mixers,”IEEE Trans. Microwave TheoryTech., vol. 48, pp. 15–22, Jan. 2000.

[6] S. Peng, P. J. McCleer, and G. I. Haddad, “Nonlinear models for the in-termodulation analysis of FET mixers,”IEEE Trans. Microwave TheoryTech., vol. 43, pp. 1037–1045, May 1995.

[7] Y. Kwon, D. Pavlidis, P. Marsh, G. I. Ng, T. Brock, and D. C. Streit,“A miniaturizedW -band monolithic dual-gate InAlAs/InGaAs HEMTmixer,” in IEEE GaAs IC Symp. Tech. Dig., Oct. 1993, pp. 215–218.

[8] V. Nair, S. Tehrani, R. L. Vaitkus, and D. G. Scheitlin, “Low powerHFET down converter MMIC’s for wireless communication applica-tions,” IEEE Trans. Microwave Theory Tech., vol. 43, pp. 3043–3047,Dec. 1995.

[9] M. Nakayama, K. Horguchi, K. Yamamoto, Y. Yoshii, S. Suematsu,and T. Takagi, “A 1.9 GHz single-chip RF front-end GaAs MMIC withlow-distortion cascode FET mixer for personal handy-phone system ter-minals,” in IEEE MTT-S Int. Microwave Symp. Dig., June 1998, pp.171–174.

[10] H. I. Kang, J. H. Kim, Y. Kwon, and J. E. Oh, “An asymmetric GaAsMMIC dual-gate mixer with improved intermodulation characteristics,”in IEEE MTT-S Int. Microwave Symp. Dig., June 1999, pp. 795–798.

[11] S. A. Maas,Nonlinear Microwave Circuits. Norwood, MA: ArtechHouse, 1988.

[12] Y. Kwon, D. Pavlidis, P. Marsh, G. I. Ng, and T. Brock, “Experimentalcharacteristics and performance analysis of monolithic InP-basedHEMT mixers atW -band,”IEEE Trans. Microwave Theory Tech., vol.41, pp. 1–8, Jan. 1993.

[13] Y. Kwon, D. Pavlidis, T. Brock, and D. C. Streit, “AD-band mono-lithic fundamental oscillator using InP-based HEMT’s,”IEEE Trans.Microwave Theory Tech., vol. 41, pp. 2236–2344, Dec. 1993.

[14] Y. Kwon, K. Kim, E. A. Sovero, and D. S. Deakin, “Watt-levelKa-andQ-band MMIC power amplifiers operating at low voltages,”IEEETrans. Microwave Theory Tech., vol. 48, pp. 891–897, June 2000.

[15] Y. C. Chen, D. L. Lngram, H. C. Yen, R. Lai, and D. C. Streit, “Anew empiricalI–V model for HEMT devices,”IEEE Microwave GuidedWave Lett., vol. 8, pp. 342–344, Oct. 1988.

[16] J. C. Pedro and J. Perez, “An improved MESFET model for predictionof intermodulation load-pull characterization,” inIEEE MTT-S Int. Mi-crowave Symp. Dig., June 1992, pp. 825–828.

[17] , “Accurate simulation of GaAs MESFET’s intermodulation distor-tion using a new drain-source current model,”IEEE Trans. MicrowaveTheory Tech., vol. 42, pp. 25–33, Jan. 1994.

[18] C. Tsironis, R. Meirer, and R. Stahlmann, “Dual-gate MESFET mixer,”IEEE Trans. Microwave Theory Tech., vol. MTT-32, pp. 245–255, Mar.1984.

[19] Y. Kwon and D. Pavlidis, “Phasor diagram analysis of millimeter-waveHEMT mixers,” IEEE Trans. Microwave Theory Tech., vol. 43, pp.2165–2167, Sept. 1995.

Junghyun Kim (S’99) was born in Pusan, Korea, in1972. He received the B.S. degree from Sung KyunKwan University, Seoul, Korea, in 1998, the M.S.degree in electrical engineering from Seoul NationalUniversity, Seoul, Korea, in 2000, and is currentlyworking toward the Ph.D. degree at Seoul NationalUniversity.

His research is focused on MMIC design and inter-modulation analysis of mixer and power amplifiers.

Youngwoo Kwon (S’90–M’94) was born in Korea,in 1965. He received the B. S. degree in electronicsengineering from the Seoul National University,Seoul, Korea, in 1988, and the M.S. and Ph.D.degrees in electrical engineering from The Univer-sity of Michigan at Ann Arbor, in 1990 and 1994,respectively.

From 1994 to 1996, he was with the RockwellScience Center, where he was involved in thedevelopment of various millimeter-wave monolithicintegrated circuits based on HEMTs and hetero-

junction bipolar transistors (HBTs). In 1996, he joined the faculty of School ofElectrical Engineering, Seoul National University. His current research activi-ties include the design of MMICs for mobile communication and millimeter-wave systems, large-signal modeling of microwave transistors, applicationof micromachining techniques to millimeter-wave systems, nonlinear noiseanalysis of MMICs, and millimeter-wave power combining.

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Intermodulation analysis of dual-gate FET mixers