Reconfigurable, Power Efficient, and High IP3 Passive

FET Mixers For Wideband Communication Systems

Ulrich L. Rohde, Fellow, IEEESynergy Microwave Corporation

Paterson, NJ 07504, USAulrgsynergymwave.com

Abstract Wireless systems operate in high interferenceenvironments, therefore very much prone to distortion, wheremixers are frequently the dominant circuit components inestablishing the overall system's distortion performance. Theemerging wireless standards have pushed researchers to look forcost-effective, power-efficient, and high IP3 (third order interceptpoint) wideband mixer that can satisfy the present and futurerequirement of wireless service, which comes with the necessity ofmulti-band, multi-mode, and multi-standard trans-receiverssystems. The passive FET mixer using hybrid-resonanceswitching and feedback mechanism demonstrated in this workoffers low cost, low distortion, low-LO power, high inputintercept points (IIP3), broadband operation, compact size,reconfigurable, and easily amenable for integration in integratedcircuit (IC) form.

Keywords- FET; IC; IIP3, LO; RF.

I. INTRODUCTION

Despite numerous advances in the technology, mixer stillremains as one of the critical modules in the RF transreceiversystem. Mixers have a wide variety of applications incommunication systems. The superheterodyne RX (receiver)architecture often has several frequency translation stages (IFfrequencies), to optimize image rejection, selectivity, anddynamic range. Through the act of heterodyning, a mixer beatsincoming RF (radio frequency) signals with tuned LO (localoscillator) signals to produce desired IF (intermediatefrequency) outputs, and as part of the process, mixer alsogenerates spurious signal products that can limit the sensitivityof a receiver circuits. This becomes more critical especially,when these unwanted signals are close in the frequency to thedesired carrier signals, they can mix and then generateundesirable intermodulation distortions (IMD)[ 1-4]. Directconversion receiver architectures such as used in pagers usemixers at the input to both downconverts and demodulate thedigital information. Mixer circuit can be used fordemodulation, although the trend is to digitize following a lowIF frequency and implement the demodulation functiondigitally. Mixer circuit can be used as analog multipliers toprovide gain control.

With the recent progress in wireless communicationsystems, the demand for high performance mixer iscontinuously increasing in terms of performance parameterssuch as operation frequency, bandwidth, conversion loss

Ajay K. Poddar, Senior Member, IEEESynergy Microwave Corporation

Paterson, NJ 07504, USAakpoddarwsynergymwave.com

(gain), linearity, noise figure, and dynamic range for reducedBER (bit error rate). In addition to this, circuit size andrequired LO power level has to be minimized to keep in pacewith the growing improvements, concerning miniaturizationand power consumption for the application of present and latergeneration of warless communication systems.

The influences of distortions (second order, third order,and other higher order distortions) are being recognized as alimitation in the performances of the communication systems.The second order distortion degrades the performance of thebase band circuits of wireless receivers that down-convert thechannel of interest to zero IF. The offset and mismatches in apractical mixer circuits, lead to imbalance, and generatesproportional second order nonlinearities. Hence, detection ofinterferers in the pass band by second order nonlinearitiescreates associated spectral components at or closer to dc,where the channel of interest is being downconverted to zeroIF. This limitation has made it more attractive to pursuealternative approaches, such as switched mode balancedfeedback passive reflection FET mixers.

This work relates the double balanced passive reflectionFETs mixer by using novel configuration that operates withreduced level of nonlinearity and intermodulation distortion.The double balanced configuration cancels the strong second-order nonlinearity of the FET I-V (current-voltage)characteristic, but does not minimize the third-ordernonlinearity. Moreover, the inadequate swing and finite slopeof the gate voltage (LO signal) give rise to a dynamicnonlinearity that further increases third-order distortion. Anovel and innovative approach is to resonate the gatecapacitances by hybrid resonance network, and drive the gatesof switching device (FETs) with maximum slew rate. Thisleads to the improvement in energy transfer to the mixing cell(switching network), and at the same time increases thedynamic slope of the LO level used for switching the FETsnetwork. By incorporating feedback mechanism, second andthird order intercept point can be raised and optimized for lowLO drive level and low conversion loss in a double balancedswitch mode passive FETs mixers circuits.

II. THEORY

Mixer is a frequency translation device, as name appearsmixing but it does not really 'mix' or 'sum' signals; it simplymultiplies them. Figure 1 shows the typical ideal mixer, note

This work was supported in part by the U.S. government (DARPA and U.S Army).Ulrich. L. Rohde is with the University of Cottbus, Germany and Chairman of

Synergy Microwave Corporation, NJ 07504 USA (Phone: 973-881-8800; Fax: 973-881-8361; e-mail: ulr synergymwave.com).

Ajay K. Poddar is with the Synergy Microwave Corporation, NJ 07504 USA. (Phone:973-881-8800; Fax: 973-881-8361; e-mail: akpoddarg synergymwave.com).

1-4244-0398-7/06/$20.00 )2006 IEEE

that both sum and difference frequencies are obtained by themultiplication of the two input signals fJ(t) and f2(t). But inreality, practical mixer generates undesired output frequenciesdue to the nonlinear characteristic of the device used formultiplications.

Figure 2 shows the typical simple unbalance nonlinearmixer operation in which any diode or transistor will exhibitnonlinearity characteristic at sufficiently high input signallevel. The IF (intermediate frequency) output waveform f3(t)as shown in Figure 3 can be described by

VO (t) = ao + a1vi, (t) + a2v t) +a3v(t)+ an1v, (t)+anv (t)(1)

From (1), output may consist a DC term ao, RF and LOfeedthrough, and higher order terms at all harmonics of the RFand LO frequencies. However, only the second-order productterm in (1) produces the desired frequency translation(upconversion/downconversion). Moreover, when Vu(t)consists of multiple carriers, then power series given in (1),generates the cross-products that make the IF output productsdependent on the amplitude of other inputs. From (1), higherorder harmonics and spurious output signal strengths can beminimized when devices that are used for multiplicationpurpose are primarily obeying square-law characteristics; suchas FETs are good choice in place of diodes or bipolartransistors. In addition to this, incorporating switching orsampling mechanism can further minimize the spurious anddistortion contents in the desired IF output.

Figure 3 shows the simplified version of typical switchingmixer circuit, where switch circuit s(t) is operated by thesquare wave LO signal with a 5000 duty cycle.

Ideal Ilixer

fi (t) =A sinco, (t) f _(t) f(t)f (t)

RF IF

LO

f2(t) =Bsin 92(t)

Down convert Upconvert

IAO()

No harmonics

The switching mechanism depicted in Figure 3, can berepresented by Fourier series as

s(t) = + Lsin(woLOt) + sin(3woLot) + sin(5woLot) +* * * (2)

From (2), the symmetry causes the even-order harmonicsto drop out from the LO spectrum. The output waveform VO(t)can be described by multiplying switch circuit s(t) with asingle frequency cosine at RF frequency 'OtkF', yields togenerates second order desired output frequencies products atfkF-oQO and WORF+±Oto as

VO(t) =VRF(t)eS(t)

s(RRsin)oURt) 1 1os(3)R2COSORF0+ COSJ+ COSF3 RFt)sin0cLot) +.3

From (1) and (3), the harmonics of the LO present at 3 q_O,5 q_o, etc., which will further mix to generate spurious signals,and will convert broadband noise that is generated internal tothe mixer circuit (or allowed into the mixer input in theabsence of a pre selection filter) into the IF output band.

From (3), odd harmonics of the LO frequency are alsopresent due to square wave LO switching signal s(t). These arespurious signal at 4th, 6th, 8.....order products with respectiveoutputs at noAQO-fkF and nfOtO+±OF, where n is odd. We alsoget RF feedthrough directly to the output.

Ideally, none of the LO signals should appear in the outputif the mixer circuit behaves according to (3), but in presenceof a DC offset on the RF input, there will be a LO frequencycomponent in the output as well. The offset and mismatches ina practical mixer circuits, lead to imbalance, and generatesproportional second order nonlinearities. However, therequirement of a DC offset is not unusual, since many mixerimplementations require some bias current, which leads to aDC offset on the input. The efficiency performance criteria isgiven by mixer transducer voltage gain Av and conversiongain CG (which is usually defined as the ratio of the IF outputpower to the available RF source power); and can be describedfor mixer circuit shown in Figure 3 as

VI,,2 1 +cAv cos)RFt)Sin(COLot) [Sin[ORF WLO)t] +Sin[O)RF + COLO)t](VIN YZ

Output power at IF 1Available RF input power 20.

-IOdB (5)CO - t) + )2

Fig. 1. Typical simplified ideal mixer circuit

Nonlinear Device

RL

VO (t)IF

f2 (t)LO

fE(t)R-F

VO ((t) a, +a,v (t) + a2v,(t)+ a3v, (t) + ..a, v- (t) + a,v, (t)

Fig.2. Typical simplified nonlinear mixer circuit operation

From (5), the simple switching mixer as shown in Figure3, shows high conversion loss since transducer voltage gain Avis only 1/ . In addition to this, RF feedthrough problem andin most instances, an LO feedthrough problem for mixercircuit shown in Figure 3, do exist. The above problems can beovercome by incorporating balanced topologies, whichprovide reasonable cancellation of RF, and LO signals at IFoutput as well minimizes the conversion loss. Byincorporating a differential IF output and a polarity reversingLO switch s(t) can eliminate the RF feedthrough from the IFoutput. Figure 4 shows the typical polarity reversing LOswitching function for the purpose of understanding about theoperation mechanism.

f3(t) -[Asin co, (t) *Bsin co,(t)_I..AB121-cos(Co,-c92)t-cos(co,-, C92) t]

From (6), the second order term is given by

2g_RLVR [sin(CRF + coLO)t + sin(CWRF CLO )t]VIt)IF

VRF(t)No even order harmonics

s(t) + Lsin(cot)++ sin(3cwot)+ sin(5cLot) +

VO (t) VRF (t)s(t) = LRCOS((RFt) +2 RF-Feddthrough

-[COS(WORFt) sin(coLOt)]2d-order-prodt +

2VR F_ cos(RFt) sin(3wLOt)JYz 3 4th-order- product

Fig.3 Typical switching operation ofunbalance mixer circuit

IF,

Linear V-IConversion

Linear I-VConversion

s,(t) = + 2sin( Lo t) + sin( 3cLot) + ...

sI(t)I Hn n n HH

s (t)

S2(t)_

(7)

From (6) and (7), we found that ideal conversion loss is(VIF/VR)2=(2/n)2 is 6dB lower than the the unbalanced mixercircuit operation (for gmRL=1) as shown in Figure 3. For mixercircuit shown in Figure 4, LO Feed through can be given by

VIF (t) RL[IDC + gm VR Cos(W RFt)]Lsin(wLot) + I sin(3wo0t) + sin(5wo0t) + X

(8)

(9)VIF (t) =4R {IDC sin(WoLot)+ <= LO Feedthroughz

2 gm VR [Sin(-)RF + 3)LO )t + sin(o&,, -(o9LO )t]}From (9), LO feedthrough will be present if we are taking

single-ended output or else, if there is a DC current in thesignal path. In general, there is presence of DC current sincethe output of the transconductance amplifier will have a DCcurrent component; therefore, this current shows up as adifferential output. This LO component is highly undesirablebecause it could desensitize a mixer post amplifier stage if theamplification occurs before IF filtering. Removal of the LOcomponent in presence of a DC current requires doublebalancing mixer circuit operation.

Figure 5 shows the typical ideal DBM (double balancedmixer), which consists of a switch driven by the LO thatreserves the polarity of the RF input at the LO frequency and adifferential transconductance amplifier stage. In this case,polarity reversing switch and differential IF cancels any outputat the RF input frequency because the DC term cancels as wasthe case for the single balanced design. The double LO switchcancels out any LO frequency component, even with currentsin the RF to IF path.

An IF Balun either active (a differential amplifier), orpassive (a transformer or hybrid), can be used depending uponthe level of conversion loss allowed by the system design. Tooptimize the mixer circuit performance, RF to IF path shouldbe as linear as possible and must minimize the switching timeof the LO switch. The ideal DBM switching mixer as shownin Figure 5 would not be effected by intermodulationdistortion (IMD) at the high end of the operating signal rangesince the ideal transconductance and resistors are linear andswitches are ideal but in reality this not the case.

It I It+S

Fig.4 Typical LO switching function with reverse polarityAs depicted in mixer circuit in Figure 4, by adding two

switching functions sl(t) and SA(, the DC terms (1/2 & -1/2)cancel in s(t). From above, DC term was responsible for RFfeedthrough in the unbalanced mixer due to multiplication ofCOS (OtkFt) term by sl(t). The expression for IF outputwaveform V0(t) for the mixer circuit shown in Figure 4 is

V0(t) =VIF =g,,RLVRCOS?OVF)4sinojt)+ ~sinQwot)+ ~sinocoot)+.

r-1 3 -r- 5'

IFTdtput

Fig.5. Typical ideal double balanced switching mixer circuit

1 2 I+ sin( coLO t) +-sin( 3 coLO t) +

2 ;T 3

The output ofDBM as shown in Figure 5 can be given by

VIF (t) RL[IDC + gm VR CS ORFt)1 Lsin(wLot) + sinfcLOt) +-sinflot)+.l

RL[IDC gm VR COSORFt)l Lsin(oLot) + sinfcoLOt) +-sinflLOt) +**

(10)

As discussed above, single balancing got rid of the RFfeedthrough, which was caused by the average DC value ofthe switching function, double balancing removes the LOfeedthrough as well, since the DC term cancels. From (10),there is no LO or RF feedthrough in this typical ideal DBM(Figure 5), even with a DC current in the signal path.

However, in real mixers, there is always some imbalance.Transistors and baluns are never perfectly matched orbalanced. These nonlinearities will produce some LO to IF orRF to IF feedthrough (thus, isolation is not perfect). This isusually specified in terms of a power ratio relative to thedesired IF output power: dBc. Secondly, the RF to IF path isnot perfectly linear. This will lead to intermodulationdistortion. Odd-order distortion (typically third and fifth orderare most significant) will cause spurs within the IF bandwidthor cross-modulation when strong signals are present. Also, theLO switches are not perfectly linear, especially while in thetransistor region. This can add more distortion to the IF outputand will increase loss due to the resistance of the switches.This paper discusses about the novel approach to over comethe above problem in practical mixer circuits by usingfeedback mechanism and resonating the gate of the FETs.

III. DESISGN APPROACH

Due to the conversion constraints by nonlinear mixing cellin active mixer, device has to be operated in a stronglyoperating bias condition, but this imposes limiting conditionon breakdown voltage due to the technological scaling of thedevice. The scaling of the device (FET) causes reduction inbreakdown voltages, thereby, limits the dynamic range of thereceiver circuits. Whereas, passive mixers have the significantadvantages of not being much dependent on operating biascondition, therefore, well suited for scaled device havinghigher cut-off frequency. The advantages of the passive FETmixer is its high linearity and low levels of distortions but atthe cost of high conversion loss, and also require excessivelocal oscillator (LO) drive levels. There is some evidence thatpassive FET mixer exhibit lower levels of 1lfnoise than diodeor active mixers, and may be this could be sometimes thejustification for their increasing applications.

Thus, there exist a need to improve LO power transfermechanism and minimization of the conversion loss of thepassive mixer circuits for the requirement of the present andlater generation wireless communication systems. The presentapproach (patent pending) is based on reflection mechanism ofswitching devices where the mixing cell (dual FETs switchingnetwork) gate's capacitances are forced resonated by hybridresonant network (series and parallel tuned) for impulsivedriving action of LO power level. The driving power transfermechanism of the mixing cell is controlled by resonated LOsignal that activates switching or modulation mechanism of

the mixing cell (dual FETs switching network), and cause thedevice conductance/transconductance to switch between twostates (ON/OFF) such as low conductance/transconductanceand high conductance/transconductance corresponding to ONand 'OFF' state of the mixing cell network.

Figure 6 shows the typical balanced nonlinear circuit forthe purpose of analysis. The input-output characteristic of abalanced circuit (Figure 6) with differential input and outputcan be described by

vou (t) a1vi + a3v+inThe third order two-tone input intermodulation is [1-3]

VIIP3= al

(1 1)

(12)

Assume that there is offset voltage Voffset due to mismatchin the FETs or unbalanced bias currents in two sides of asymmetrical circuit shown in Fig. 6; the differential output is

vout (t) = a, (v,, + vo0 ) + a3 (vin + v0 )3 + (13)

v0u (t) =(al + 3a3v2 )vi + 3a3v0 v2 + (14)From (13) and (14), second term implies second-orderintermodulation, given by an intercept point that depends onthe offset and also on the value of VIIP3 as

(a,+ 3a3vOs) = P+ V I/P3 (15)3a3vos 4vos 4vos

From (11) to (15), second order distortion arises from thirdorder terms due to the third order intermodulation between aninput tone and dc tone due to the offset. For minimization ofthe second order intermodulation, or maximization of the VIIP2,Voffset should be reduced and VIIP3 should be increased.

Figure 7 shows the typical feedback (f) based balancednonlinear circuit for the purpose of the comparative analysis ofthe influence of second and third order intermodulation ascompared to Figure 6. Assuming that the feedback element isperfectly linear so that applied feedback will now try tocorrect and compensates the nonlinearities of the device as

(16)out = a vi a+ (3I A )4 Vm

From (16), the term a1p represents the small-signal feedbackloop gain. From (12), effective 11P3, OIP3, 11P2, and OIP2 canbe given by

[VjjP3 ]with feedback [ VIIP3 ] without feedback (1 + a g)3/2 (17)

[VOP3]Vwith feedback [IVOIP3 ] without feedback (1 + ag)l')

[VIIP2 ]with feedback [VIIP2 ]without feedback (1 + al)

(18)

(19)

[VOIP2 ]with feedback [[VOIP2 ]without feedback (1 + al/) (20)

From (17) to (20), feedback mechanism increases secondand third order input and output intercept points.

Fig.6 Typical balanced nonlinear circuit (Mixer)

Fig.7. Typical balanced nonlinear system with negative feedback

IV. VALIDATION

Figure 8 shows the block diagram of the low distortion,high dynamic range reflection mode commutating FET doublebalanced mixer (DBM) that is operable with low noise figureand high dynamic range without the penalty of increasedpower levels (LO drive signals). This work is based on novelapproach (patent pending) in which transistor's gatecapacitances are resonated by a dynamic slope optimizernetwork (hybrid-tuned network, which consists of parallel andseries resonance at fundamental and third harmonics) thatdrives the gates of FETs with low conduction and increaseddynamic slope. This leads to the improvement in energytransfer to the mixing cell (comprised of dual FETs connectedin balanced configuration), and at the same time increases theslope of the LO level used for switching the FETs network.

Distortion in a switched FET mixer can be evaluated interms of the signal-to-distortion ratio (SDR). The SDR in aFET mixer due to the switching mechanism as [3]

SDR _ 20OlogL A dB; s =(2)

where s is the slope of the gate voltage swing, fin is theinput frequency, vg is the gate voltage signal swing, and vi1 isthe input signal voltage. From (23), SDR can be improved byincreasing the slope (by increasing magnitude of the gatevoltage signal or reducing the rise/fall time of the gate voltageswing). It is seen from (23) that the reduction in the magnitudeof vin improves the distortion.

From (23), SDR and energy transfer to the mixing cell(comprised of dual FETs connected in balanced configuration)is improved, and at the same time optimizes the slope andslew rate of the LO level used for switching the FETsnetwork. Further improvement in the intercept point andconversion loss can be achieved by allowing LO signal tooperate in differential mode, which gives 180-degree phaseshifted outputs.

Figure 8 shows the LO circuit (differential outputwideband voltage controlled oscillator circuits) for the purposeof controlling the conduction angle and duty cycle of the LOsignal. The integrated mixer (in built VCOs) providesalternative solution for impedance transforner (BALUN);therefore, conversion loss can be minimized withoutsacrificing the 1-dB compression and intercept points.

Fig. 8. Block diagram of switched feedback passive reflection FETDBM (Patent pending)

a

a)U)

15-14-13-12-1 1109 e

8-7-6-5-800 1300 1800 2300

Frequency (MHz)

2800 3300

Fig. 9. Conversion loss vs frequency reflection mode FET DBM

The experimental results shows input IP3 in excess of +38dBm throughout the frequency bands (RF: 800-3100MHz,LO: 850-3300MHz, IF: 50-200MHz), with the conversion lossof typically 8.8dB and LO drive level +16dBm.

V. CONCLUSION

The reconfigurable passive FET mixer design approachdemonstrated in this work can satisfy the need for the presentdemand for low cost, low distortion, power-efficient, ultra-wideband operation.

REFERENCES

[1] S. A. Mass " Noise in Linear and Nonlinear Circuits, Artech House,MA, 2005.

[2] G. D. Vendelin, A. M. Pavio, and U. L. Rohde, " Microwave CircuitDesign Using Linear and Nonlinear Techniques, Wiley, NY, 2005.

[3] J. Browne, " Wideband Mixers Hit High Intercept Points", Microwave& RF Journal, pp. 98-104, September 2005.

[4] M. W. Vice, "Quasi-Double Balanced Passive Reflection FET Mixer",Aug 25,1998, US Patent No: 5799248.

[5] U. L. Rohde, A. K. Poddar, and G. Boeck, Modern MicrowaveOscillators for Wireless Applications: Theory and Optimization, JohnWiley & Sons Inc., 2005.

[6] E. W. Lin and W. H. Ku, "Device consideration and modeling for thedesign of an InP-based MODFET millimeter-wave resistive mixer withsuperior conversion efficiency," IEEE Trans. MTT, Vol.43, no. 8. pp.1951-1959, Aug. 2001.

[7] A. A. M. Saleh, Theory of Resistive Mixers, Cambridge, MA:MITPress, 1971.

[8] M. R. Barber, " Noise Figure and conversion loss of the Schottky barriermixer diode," IEEE Trans. MTTT., pp. 629-635, Nov. 1967.