13RFDesign:ConceptsandTechnologyPout小OIP3PinIM3△P△P/2IIP3PinFigureI.4.Input IP3 as a function of the/M3and input powerPin.Both axes are in decibels.From (1.37)and (1.34)wecan seethat the difference betweenthe1dBcompression point and the input I P3 is roughly-9.6 dBIf stage (1.32)is cascadedwitha second non-linear stage,z(t) =ky(t)+ay2(t) +μy3(t)theoverallArp3results inQK(1.39)AIP3.all+2+3whichcanbeapproximatedtoQ23β入11(1.40)Aip3.22kAip3.allAip3.1where Arp3.1and Aip3,2 represent the input I P points of the first and secondstages,respectively.Increasing thegainof thefirst stage results in a decrease ofthe overall I P3; the second stage senses a large input signal thereby producingmuchgreaterIM3products.Equation(1.39)canbeextendedformorecascaded8We have used the relationship Ix + yl ≤ IxI + lyl
14CIRCUITDESIGNFORRFTRANSCEIVERSstages into the general expressionQ211αk2(1.41)Aip3.allAip3.1Aip3.2Aip3.3where we should emphasize that the expression is still an approximation.1.1.4SensitivityThe minimum signal level that a system can detect with an acceptable SNRis called the sensitivity of that system. This minimum input signal Pin.min isfoundtobetheintegral over thebandwidthB of theproductofnoisefactorF,the acceptable SNR at the output, and the source resistance noise power PnoisesyieldingPin.min =B.SNR·Pnoise-F(1.42)This expression can be simplified by assuming power matching at the input.Under this condition, Puoixe equals kT, which for room temperature results inPuoise =-174 dBm/Hz. The noise floor is total integrated noise of the sourceavailable at the input of the system and can be obtained from B. Pnoixe. Itrepresents the minimum amount of noise that a system must be able to copewith, assuming the system itself is noiseless.The maximum amount of noisethat the system should cope with is found to bethedifference betweenthesensitivity level and the minimum accepted SNR. This noise level is knownas the total in-band noise.The difference between the in-band noise and thenoiseflooristheamountof noisethesystemmay contribute,that is,thenoisefactor.The noise foor is also important in the definition of the dynamic range (DR)of the system.In RF design,thedefinition is based on the sensitivityand theintermodulation,and is called thespurious-freedynamic range (SFDR).1.2 RFDEVICETECHNOLOGYDrawing an analogy with digital integrated circuit technology,we would ex-pectthe optimumtechnologychoiceforradio frequencyICapplicationstofollowthe samepaththatdigitalIC implementationsfollowed,thatis,towardsCMOs.However,technical requirements for a transceiverfunction are consid-erably more complex than that of a digital integrated circuit.Issues such asnoise (near the carrier), linearity and gain are performance specifications thatingeneral,theDRisdfined astheratioothemaxmumtolerableinput signaltotheminimum input level(often the noise floor)
RFDesign:ConceptsandTechnology15RF transceivers have to deal with.As a result, the optimum integrated circuittechnology choices for RF transceivers are still evolving, Designers currentlyhaveawiderangeofpossibilities:CMOS,BiCMOS,GaAs,bipolar technologies,etc.In addition, improvements ofexisting technologies have resultedin technologies such as double poly devices, SiGe and Silicon-on-Anything(SOA).The remainder of this chapter includes a short discussion on technologyperformance factors and device modeling for RF, followed by an explanationof afew technologies suitable forRF applications.1.2.1CharacterizationandModelingItisoftendesirabletoconsidertheperformanceofatransistorintermsof somesimple,andpreferableeasilymeasurableparameters.SomecommonlyusedFigures Of Merits (FOMs)are discussedhere, enabling us to choose the righttechnology for a particular application. However, we have to bear in mind thatnon-technical factors very often dictate the technology choice as well. Thesefactors include cost, production volume, yield, time to market, etc. After abrief discussion on modeling, we will focus on the technical parameters in theremainderof this section.ModelingModeling of devices is as important as characterization.Without good models.it becomes difficult to analyse and predict circuitbehaviour on transistor level.Bipolar devices have a long history in modeling, even for radio frequencies.Models such as those in Figure 1.7 are usually used, and they give very accuratesimulationresultswhencomparedtomeasurements.Wewill thereforenotfocuson bipolar device modeling, but will concentrate on MOS device modelingwhere this accuracy is still lacking.For thepastfew years, intensive researchhas beengoing on in thefield of RFMOSmodeling.Studieshaveshownthatthe“standard"(digital oriented)MOSmodelsdonot allowforRFmodeling.Threemajoreffectsplayanimportantroleathighfrequencies:theterminal resistors,bulkeffects,and non-quasistaticeffects.We will brieflydiscuss each ofthese effects below.The gate resistance is an important parameter and can be approximated by1 W(1.43)Rg=3LR.polywhere R.poly is the sheet resistance of polysilicon, used in the gate of thedevice.The valueof thegate resistancecanbereduced belowafew Ohms if
16CIRCUITDESIGNFORRFTRANSCEIVERSthere is a proper MOST layout. Resistances in series with the drain (Ra) andsource(R,)degrade the drain current and transconductance of the MOST.The source resistance will degrade the noise performance and the maximumoscillationfrequency.Thedrainresistancewill reducetheoutputimpedanceofthedevice.Deviceoperationsareinfluenced by signals on thebulk nodeas aresult of thebody effect.Aproperbulkresistancenetwork is thereforemandatoryintheintrinsic devicemodel.The values of these resistors are highlydependenton the substrate used,i.e.a high-ohmic orlow-ohmic substrate beneath anepilayer.-When signal frequencies are in the same order ofthe maximum operatingfrequencies as theMOsdevice,non-quasi static effects can occur. To explain the effect of non-quasi static behavior, consider a MOs device witha sinusoidal signal on its gate terminal. At low frequencies, the thicknessof the channel will change due to the gate modulation, but the change willbe the same everywhere in the channel. In other words,there will be nophase differences in the channel. The dynamics of the device can be mod-eled byapplying the charge equations to the static DC equations.This isno longertrue at highfrequencies,as the channel thickness will be modu-lated.This effect is strongest for long devices and can only be measured forminimum device lengths near the cut-off frequencies.As a consequencethe device equation should be solved in a non-quasi static approach.One oftheimportant results ofnon-quasi staticeffects is the valueof thegateinputresistance.At low frequencies, the gate is assumed to be purely capacitive,i.e. Re (Zi) -- O. This is no longer true at high frequencies, as there will alsobe a resistive part (see Figure 1.5). In fact, we “see" the channej10. Theseeffects result in an extra real contribution to the input impedance,which canbe taken into account by adding an additional resistance of approximately(inthecaseofsaturation)1Rin=(1.44)ngmto the gate resistance, where n ~ 5 - 7. Note that this effect cannot bemodeledby including external gate and sourceresistances as canbe seen inFigure 1.5.utrsisanweoiwounitowgincaussipatakes place at the input. This is impossible of course
17RFDesign:ConceptsandTechnologyRin(ohm)500400300200non-quasistatic100externalgateandsource?1.01.52.02.53.00.00.51/gm(Kohm)(varying channel)Figure 1.5.The measured input resistanceofa MOSTis inversely proportional to the transcon-ductance.Theeffects mentionedabovecanbe incorporatedintoa low-frequency MOSTmodel such as the one depicted in Figure l.6.The resulting model is accuratefor RF analysis,although it only partly includes the non-quasi static effectsIf a complete non-quasi static behavior has to be included, the low-frequencyMOST should be divided into a chain of smaller MOSTs ina very particularway [2].Cut-offFrequencyProbably themost usedFOMfor abipolar device is thecut-offrequency fr,biposometimes called thetransition frequency or unity-current-gain frequency.Thelatter name refers to the definition of the cut-off frequency: the fr is defined asthe transition frequency at which the common-emitter small signal gain dropsto unityfora short-circuitload.We can use theequivalent circuit from Figure1.7to calculate the small-signalcommon-emittercurrentgainβwithβo(1.45)Cu=Cje,Cn= Trgm+Cjergmand trtheforward transit time.The junction capacitances Cjeand Cje arefunctions of the voltage u across the junction,CJ(1.46)Cj(u) =(1+)M)