非线性器件振幅调制,失真和平衡对消

高频电子线路多媒体教学课件西安电子科技大学电子工程学院赵建勋MultimediaTeachingCoursewareofHigh-FrequencyElectronicCircuitsZhaoJianxunSchoolofElectronicEngineeringXidianUniversity开始Start西安电子科技大学XidianUniversity本课件讲授大学本科《高频电子线路》课程的代表内容——非线性器件振幅调制，失真和平衡对消。课件主要配合教师课堂教学使用，讲授过程中始终以教师讲述为主，课件只提供必要的文字和图像信息。学生本人使用该课件预习和复习功课时，可以选择向导的帮助。向导及时提供丰富的文字讲解，起到了教师指导的作用。因为集成了向导功能，本课件也可以作为网络课件使用。

Thecoursewareismaterializedonnonlinear-deviceamplitudemodulation,distortion,andbalancedcancellation,whicharerepresentativecontentsofHigh-FrequencyElectronicCircuits,acourseforundergraduatestudents.Withthemajorpurposetoassisttheclassroomlecturing,thecoursewareprovidesnecessaryliteralandimageinformationtohelptheteacher,whoplaysthemainroleinthelecturing.Thecoursewareitselfisalsoanet-basedone.Theintegratedguidetimelyprovidesdetailedliteralexplanationsforstudentsinpreparingandreviewingthecourse.Theguidanceservesastheinstructionsfromteachers.简介Introduction西安电子科技大学XidianUniversity结束End封面Cover目录

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Content结束End翻到帮助页面Tothehelppage翻到目录Tothecontent返回上一页Tothelastpage结束放映Endthescreening第五章振幅调制与解调结束End向导Guide封面

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HelpChapter5Amplitudemodulationanddemodulation振幅调制方法的分类Typesofamplitudemodulationapproaches西安电子科技大学XidianUniversity您好，欢迎使用高频电子线路多媒体教学课件，请选择是否需要向导。Hello,welcometoTeachingCoursewareofHigh-FrequencyElectronicCircuits.Pleasechooseifyouwillneedaguide.使用向导（便于浏览课件，课程预习和复习）Usetheguide(Forcoursewarebrowsing,coursepreparationandreviewing)不使用向导（便于组织课堂教学）Noguide(Forclassroomlecturingorganization)第五章振幅调制与解调目录ContentChapter5Amplitudemodulationanddemodulation振幅调制方法Amplitudemodulationapproaches非线性器件调幅Amplitudemodulationwithnonlineardevices线性时变电路调幅AMwithlineartime-varyingcircuits步骤[1]Stepone步骤[2]Steptwo步骤[3]Stepthree非线性器件调幅失真Distortionsofnonlinear-deviceAM振幅调制的关键问题Keyproblemofamplitudemodulation失真来源

Sourceofdistortions减小失真的方法

Methodstoreducedistortions平衡对消Balancedcancellation非线性器件调幅分析

Analysisofnonlinear-deviceAM振幅调制与解调Amplitudemodulation(AM)anddemodulation振幅调制方法的分类Typesofamplitudemodulationapproaches振幅调制信号Amplitudemodulatedsignals西安电子科技大学XidianUniversity结束End封面

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Help第五章振幅调制与解调目录ContentChapter5Amplitudemodulationanddemodulation振幅调制方法Amplitudemodulationapproaches非线性器件调幅Amplitudemodulationwithnonlineardevices线性时变电路调幅AMwithlineartime-varyingcircuits步骤[1]Stepone步骤[2]Steptwo步骤[3]Stepthree非线性器件调幅失真Distortionsofnonlinear-deviceAM振幅调制的关键问题Keyproblemofamplitudemodulation失真来源

Sourceofdistortions减小失真的方法

Methodstoreducedistortions平衡对消Balancedcancellation非线性器件调幅分析

Analysisofnonlinear-deviceAM振幅调制与解调Amplitudemodulation(AM)anddemodulation振幅调制方法的分类Typesofamplitudemodulationapproaches振幅调制信号Amplitudemodulatedsignals西安电子科技大学XidianUniversity继续Continue一种比较重要和常见的减小失真的方法是平衡对消技术，这是本次课程最后要学习的内容。Balancedcancellationisanimportantandusualmethodfordistortionreduction,whichwillbestudiedattheendofthislesson.我们从本次课程开始学习振幅调制方法，这是第五章，振幅调制与解调的一个重要部分。Inthislesson,webegintolearnapproachesofamplitudemodulation,whichisanimportantportionofChapter5,Amplitudemodulationanddemodulation.为了解决失真问题，我们接下来寻找失真的来源，并由此提出减小失真的方法。Totacklethedistortionproblem,we’llsearchforthedistortionsource,andthenbringforwardmethodsfordistortionreduction.非线性器件调幅通过三个步骤来实现。Thenonlinear-deviceamplitudemodulationisperformedinthreesteps.首先，我们简要复习三种振幅调制信号，即普通调幅信号，双边带调制信号和单边带调制信号。First,we’llbrieflyreviewthethreesignalsoutofamplitudemodulation,namely,theamplitudemodulatedsignal,thedouble-sidebandmodulatedsignal,andthesingle-sidebandmodulatedsignal.为了生成这些信号，我们进行振幅调制时需要解决一个关键问题，即调制信号与载波的相乘。Weneedtosolveakeyproblemintheamplitudemodulationtogeneratethesesignals,thatis,themultiplicationofthemodulatingsignalandthecarrierwave.感谢使用向导。首先，我们简略浏览本次课程的内容和结构。Thankyouforusingtheguide.Atfirst,let’sbrieflybrowsethecontentandstructureofthislesson.从分类上看，有两种基本方法可以解决该问题，即非线性器件调幅和线性时变电路调幅。本次课程学习非线性器件调幅。Forsolution,therearetwobasictypesofamplitudemodulationapproach,namely,theamplitudemodulationwithnonlineardevices，andtheamplitudemodulationwithlineartime-varyingcircuits.Theformeristobestudiedinthislesson.非线性器件的应用解决了前面提到的振幅调制的关键问题，但又产生了新的失真问题。Theabove-mentionedkeyproblemofamplitudemodulationissolvedbyusingnonlineardevices.However,thedistortionoccursasanewproblem.结束End目录

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页Page1Chapter5Amplitudemodulationanddemodulation西安电子科技大学XidianUniversity普通调幅信号

Amplitudemodulatedsignal双边带调制信号

Double-sidebandmodulatedsignal单边带调制信号Single-sidebandmodulatedsignal调制信号Modulatingsignal

u(t)=U

mcost载波

carrierwaveuC

(t)=U

Cmcos

Ct

C

C+

C－

CUmUCm继续Continue经过调制，得到的振幅调制信号可能包含三个频率分量。角频率为

C，

C+和

C-的频率分量可以分别叫做载频分量，上边频分量和下边频分量。Afterthemodulation,theobtainedamplitudemodulatedsignalmaycontainthreefrequencycomponents.Thosewiththeangularfrequenciesof

C,

C+and

C-aretermedasthecarriercomponent,theupperside-frequencycomponentandthelowerside-frequencycomponentrespectively.现在，我们开始学习本次课程的内容。进行振幅调制的目的是把低频的语音、图象等调制信号寄载到高频载波上，从而实现信息的远程无线传输。Now,let’sstartthelesson.Theamplitudemodulationisaimedatmountingthelow-frequencyaudioorvisualmodulatingsignalontoahigh-frequencycarrierwave,sothattheinformationcanbetransmittedwirelesslyatalongdistance.为简单起见，我们认为调制信号和载波都是单频信号。这里给出了它们的时域表达式。Forsimplicity,themodulatingsignalandthecarrierwavearesupposedtobesingle-frequencysignals.Thesearetheirtime-domainexpressions.在频域上，调制信号和载波都可以用其角频率和振幅表示。Themodulatingsignalandthecarrierwaveareexpressedinthefrequencydomainbyusingtheirangularfrequenciesandamplitudes.包含所有三个频率分量的信号称为普通调幅信号，只包含上边频分量和下边频分量的信号称为双边带调制信号，而单边带调制信号则只有上边频分量或下边频分量中的一个。Thesignalwithallthreefrequencycomponentsiscalledanamplitudemodulatedsignal.Thatonlywiththeupperandthelowerside-frequencycomponentsiscalledadouble-sidebandmodulatedsignal.Thesingle-sidebandmodulatedsignalhasonlyoneoftheside-frequencycomponents.结束End目录

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页Page2Chapter5Amplitudemodulationanddemodulation振幅调制方法Amplitudemodulationapproaches非线性器件调幅Amplitudemodulationwithnonlineardevices线性时变电路调幅Amplitudemodulationwithlineartime-varyingcircuits频域：

C+，

C-Frequencydomain:

C+，

C-振幅调制的关键问题

Keyproblemofamplitudemodulation时域：uC

uTimedomain:

uC

u西安电子科技大学XidianUniversity继续Continue为了生成前面的三种振幅调制信号，进行振幅调制时，在时域上要将调制信号和载波相乘，在频域上看，这样的相乘会生成上边频分量和下边频分量，这个关键问题的解决需要用到非线性电路。Inordertogeneratetheabovethreeamplitudemodulatedsignals,duringtheamplitudemodulation,themodulatingsignalwillbemultipliedbythecarrierwaveinthetimedomain,whichwillproducetheupperandthelowerside-frequencycomponentsinthefrequencydomain.Nonlinearcircuitsaretobeusedtosolvethiskeyproblem.用非线性电路进行振幅调制的方法有两种，一种是利有源器件，如晶体管或场效应管的非线性实现调幅，另一种是基于线性时变电路实现调幅。Therearetwotypesofamplitudemodulationapproachwiththeuseofnonlinearcircuits.Oneapproachistomakeusethenonlinearpropertyofactivedevices,suchasthetransistorandtheFET.Theotherapproachisbasedonlineartime-varyingcircuits.结束End目录

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页Page3Chapter5Amplitudemodulationanddemodulation+++++++西安电子科技大学XidianUniversity继续Continueube

(t)经过EB的偏置，产生晶体管的输入电压uBE(t)。WiththebiasingofEBuponube

(t),wegetuBE(t),theinputvoltageonthetransistor.接下来，在uBE(t)的作用下，晶体管产生输出电流iC(t)。Inthefollowing,thetransistorgeneratestheoutputcurrentiC(t)inresponsetouBE(t).该图实际上给出了一个放大器电路。首先，载波uC

(t)和调制信号u(t)叠加产生交流输入电压ube

(t)。Thediagramisactuallyanamplifiercircuit,wherethecarrierwaveuC

(t)andthemodulatingsignalu(t)areaddedupfirsttoproducethealternatinginputvoltageube

(t).最后，iC(t)经由LC并联谐振回路选频，产生普通调幅信号uAM

(t)。Finally,iC

(t)flowsthroughthefrequency-selectingLCparallelresonantcircuit,andproducesanamplitudemodulatedsignaluAM

(t).现在我们学习第一种振幅调制方法，即非线性器件调幅方法。该方法的原理电路如图所示。Nowwecometolearnthefirstamplitudemodulationapproach,i.e.,thenonlinear-deviceamplitudemodulation.Hereisthebasiccircuitdiagramofthisapproach.结束End目录

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页Page4Chapter5AmplitudemodulationanddemodulationtuC(t)0tu(t)0tube(t)0步骤[1]载波和调制信号相加产生输入电压Addingupthecarrierwaveandthemodulatingsignaltoproducetheinputvoltage+++++西安电子科技大学XidianUniversity继续Continue前面简要描述了非线性器件调幅的过程，在此基础上，我们接下来观察并研究该过程中一些值得注意的细节。非线性器件调幅的原理电路可以分解为输入级回路，晶体管和输出级回路三部分，每部分各自完成振幅调制过程的一个步骤。Theprocessofthenonlinear-deviceamplitudemodulationhasbeenbrieflydescribed,basedonwhich,wenowcometoobserveandstudysomedetailsintheprocess.Thebasiccircuitcanbedecomposedintothreeparts,namely,theinputloop,thetransistor,andtheoutputloop.Eachpartofthecircuitperformsonestepoftheamplitudemodulation.现在我们实时观察

uC

(t)，u(t)和

ube

(t)的波形。注意载波的频率远大于调制信号的频率，而其振幅也大于调制信号的振幅。二者叠加产生的交流输入电压ube

(t)的高频振荡与载波一致，其起伏与调制信号同步。Now,let’smakeareal-timeobservationofthewaveformsofuC

(t),u(t)andube

(t).Itshouldbenoticedthatthecarrierwavefrequencyismuchhigherthanthemodulatingsignalfrequency.Thesamecanbesaidoftheiramplitudes.Thealternatinginputvoltageube

(t)outoftheadditionoscillatesaccordingtothecarrierwave,whereasitrisesandfallsinaccordancewiththemodulatingsignal.首先，我们看第一个步骤。这是在输入级回路中完成的，载波

uC

(t)和调制信号u(t)在这里相叠加产生交流输入电压

ube

(t)。First,let’sfocusonstepone,whichisaccomplishedintheinputloop,wherethecarrierwaveuC

(t)andthemodulatingsignalu(t)areaddeduptoproducethealternatinginputvoltageube

(t).结束End目录

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HelptuC(t)0tu(t)0tube(t)0iC0uBEtuBE0EBiC0QICQEBICQt第五章振幅调制与解调第5

页Page5Chapter5Amplitudemodulationanddemodulation步骤[2]非线性器件产生输出电流Thenonlineardevicegeneratestheoutputcurrent+西安电子科技大学XidianUniversity继续Continue我们现在把第一个点垂直投影到转移特性曲线上。Now,weverticallyprojectthefirstpointontothetransfercharacteristiccurve.对uBE(t)中的每个点都进行这样的投影，我们就最终可以得到iC

(t)的波形。We’llfinallygettheiC

(t)waveformaftereachuBE(t)pointisthusprojected.在该投影过程中，我们可以发现，晶体管的非线性，更确切地说，其转移特性的非线性，引起了

iC

(t)波形的变化。Intheprojectingprocess,wediscoverthat,thenonlinearityofthetransistor,ormoreaccurately,thenonlinearityofthetransistor’stransfercharacteristic,shouldberesponsibleforthealterationintheiC

(t)waveform.下面我们研究这样的波形变化是如何产生的。我们首先在uBE

(t)的波形上选取若干个点，接下来观察这些点是怎样投影确定iC(t)的波形的。Next,let’sfindouthowthewaveformalterationoccurs.First,weselectacoupleofpointsontheuBE

(t)waveform,thenwe’llobserveinwhatwayiC(t)isdeterminedbytheprojectionofthesepoints.接下来把该点水平投影到iC

(t)图中该点对应的时刻。Next,wepojectthepointhorizontallyontoitscorrespondinginstantintheiC

(t)diagram.借助于该特性曲线，我们可以通过投影方式从uBE

(t)的波形画出

iC(t)的波形。Withthecharacteristiccurve,wecandrawthewaveformofiC(t)fromuBE

(t)bywayofprojection.这里给出了晶体管的转移特性曲线，它描述了晶体管的输入电压uBE

和输出电流iC

的关系。Hereisthetransfercharacteristiccurveofthetransistor,whichdescribestherelationbetweentheinputvoltageuBEandtheoutputcurrentiC.这样我们得到了iC

(t)波形上的一个点。Therefore,onepointontheiC

(t)waveformisobtained.如果将波形放大，我们会注意到iC(t)的波形和uBE

(t)的波形并不一样。与uBE

(t)比较而言，iC(t)的上半周变得较为尖锐，而下半周则变得较为平缓。Ifthewaveformsaremagnified,itwillcometoourattentionthatthewaveformsofiC(t)anduBE

(t)arenotidentical.ComparedtouBE

(t),theupperpartofiC(t)becomessharper,whereasitslowerpartbecomessmoother.接下来，我们看第二个步骤。这是在晶体管中完成的，交流输入电压

ube

(t)经过EB

的偏置后，成为晶体管的输入电压uBE

(t)，在其作用下，晶体管产生输出电流iC(t)。Next,let’sfocusonthesecondstep,whichisaccomplishedinthetransistor,wherethealternatinginputvoltageube

(t)isbiasedbyEBandtheinputvoltageuBE

(t)isproduced,activatedbywhich,thetransistorgeneratestheoutputcurrentiC(t).结束End目录

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HelpiC0uBEtuBE0EBiC0QICQEBICQt第五章振幅调制与解调第5

页Page5Chapter5Amplitudemodulationanddemodulation+++++西安电子科技大学XidianUniversity继续Continue为了对iC

进行分析，我们将其近似表示成前三项级数和。利用已知的

ube，uC

和u的表达式，我们可以得到iC

的一个具体结果。InordertoanalyzeiC

,weusethefirstthreeseriestoapproximateit.AdetailedresultofiCisderivedbyusingtheavailableexpressionsofube,uCandu.我们写出晶体管转移特性曲线的表达式，当然这里的函数f是非线性函数。Wewritedowntheexpressionofthetransistor’stransfercharacteristiccurve,wherethefunctionfisofcourseanonlinearone.这种非线性过程导致的波形变化暗示了iC

(t)中含有uBE

(t)中没有的新的频率分量，下面我们通过解析方法确定iC

(t)中有哪些频率分量。ThewaveformalterationcausedbythenonlinearprocessindicatesiC

(t)containssomenewfrequencycomponentsbesidesthoseofuBE

(t).Inthefollowing,we’lldeterminetheiC

(t)components.参考原理电路中的输入级回路，我们还可以写出晶体管输入电压uBE(t)。WecanalsowritedownuBE(t),theinputvoltageofthetransistor,referringtotheinputloopofthebasiccircuitdiagram.这里，我们把iC

展开成泰勒级数，展开的中心位置选在EB

，这样就把晶体管输出电流

iC

表示成了交流输入电压ube

的级数和的形式。Next,weexpandiCintoaTaylorseries.TheexpansioniscenteredatEB,thereforetheoutputcurrentofthetransistor,iC,isexpressedasthesummationoftheseriesaboutube,thealternatinginputvoltage.结束End目录

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页Page6Chapter5Amplitudemodulationanddemodulation步骤[3]滤波产生已调波Producethemodulatedwavebyfiltering++IC()0

西安电子科技大学XidianUniversity中间三项分别是载频分量，下边频分量和上边频分量。Thethreeitemsinthemiddlearerespectivelythecarrier,theupperside-frequency,andthelowerside-frequencycomponents.我们根据其角频率和振幅在频域上画出该频率分量。Wedrawthiscomponentinthefrequencydomainaccordingtoitsangularfrequencyandamplitude.现在画出该频率分量。Now,wedrawthiscomponent.最后一项的角频率为2

C。Thelastitemhasanangularfrequencyof2

C.我们也画出该频率分量。Wedrawthiscomponenttoo.这三个频率分量对我们是有用的。Thesethreecomponentsareusefulforus.这样我们就可以方便地画出iC

的频谱，从而由前面的时域分析过渡到后面的频域分析。SowecaneasilyplotthespectrumofiC,andadvancefromtheprevioustime-domainanalysistothefollowingfrequency-domainanalysis.现在，我们来到非线性器件调幅的第三步。前面得到的iC

的具体结果经过整理，可以写成其各个频率分量叠加的形式。Wenowcometothethirdstepofthenonlinear-deviceamplitudemodulation.ThepreviouslyderivediCisreorganizedandwrittendownhereintheadditionformofitsvariousfrequencycomponents.现在画出该分量。Now,let’sdrawthiscomponent.表达式的第一项是直流分量。

Thefirstitemintheexpressionisadirectcomponent.第二项是角频率为的分量。

Theseconditemisacomponentwiththefrequencyof.第三项是角频率为2的分量。

Thethirditemisacomponentwiththefrequencyof2.进行滤波，就可以得到普通调幅信号。Anamplitudemodulatedsignalisobtainedbyfiltering.结束End目录

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页Page6Chapter5Amplitudemodulationanddemodulation步骤[3]滤波产生已调波Producethemodulatedwavebyfiltering++IC()0

西安电子科技大学XidianUniversity继续Continue我们把这些频率分量写到新的位置。Let’swritethesecomponentsatnewpositions.下面，为了说明滤波过程，我们在时域和频域只保留下

iC

的这三个有用频率分量。Inthefollowing,weonlykeepthethreeusefulfrequencycomponentsofiCbothinthetimedomainandinthefrequencydomain.结束End目录

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页Page6Chapter5Amplitudemodulationanddemodulation步骤[3]滤波产生已调波Producethemodulatedwavebyfiltering++a1UCmcosCta2UmUCmcos(

C－)ta2UmUCmcos(

C+)ta1UCma2UmUCma2UmUCmC－C＋C西安电子科技大学XidianUniversity继续Continue需要注意的是，这些有用的频率分量都是电流，而我们要得到的普通调幅信号是电压，所以需要使晶体管的输出电流iC

流过一个支路，该支路只对iC

中这三个频率分量产生有效的电压输出，而不对其余的频率分量产生有效的电压输出。Itshouldbenoticedthattheseusefulfrequencycomponentsarecurrents,whereasweneedthevoltageoftheamplitudemodulatedsignal.Thereforetheoutputcurrentofthetransistor,iC,shouldbemadetoflowacrossabranchcircuit,whichproduceseffectivevoltageoutputforthethreeusefulcomponentsandnoeffectiveoutputfortheothercomponents.这种支路的阻抗应该具有带通的幅频特性，最为典型的设计就是LC并联谐振回路。Theimpedanceofsuchabranchcircuitshouldhaveaband-passamplitude-frequencycharacteristic.ThemosttypicaldesignistheLCparallelresonantcircuit.我们可以参照这三个有用频率分量的频谱画出LC并联谐振回路的幅频特性和相频特性。Wecandrawtheamplitude-frequencyandthephase-frequencycharacteristicsoftheLCparallelresonantcircuit,accordingtothespectrumofthethreeusefulfrequencycomponents.结束End目录

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页Page6Chapter5Amplitudemodulationanddemodulation步骤[3]滤波产生已调波Producethemodulatedwavebyfiltering++a1UCma2UmUCma2UmUCmC－C＋Ca1UCmcosCta2UmUCmcos(

C－)ta2UmUCmcos(

C+)t[][]Z|Ze|－/4/400.707Reo0.707ReoReo西安电子科技大学XidianUniversity这里给出的LC并联谐振回路的谐振电阻为Reo，其谐振角频率等于载频

C，带宽为2。因此在下边频

C-

和上边频

C+

处，其呈现的电阻为0.707Reo，而提供的相移则分别为

/4和-/4。TheresonantresistanceoftheLCparallelresonantcircuitgivenhereisReo.Theresonantangularfrequencyequalsthecarrierfrequency

C,andthebandwidthis2.Therefore,thesubcircuitactsasaresistorof0.707Reoandprovidesphaseshiftsof/4and-/4atthelowersidefrequency

C-

andtheuppersidefrequency

C+

respectively.因此我们给下边频分量乘上0.707R

eo，再添加/4的相移，就得到它产生的电压。Therefore,wemultiplythelowerside-frequencycomponentand0.707R

eo,andaddthephaseshiftof/4toobtainthevoltagegeneratedbyit.因此我们给载频分量乘上R

eo，就得到它产生的电压。Therefore,wemultiplythecarriercomponentandR

eotoobtainthevoltagegeneratedbyit.三个频率分量当中，载频分量流经LC并联谐振回路时，遇到的电阻为R

eo，生成电压时的相移为0。Amongthethreefrequencycomponents,thecarriercomponentmeetstheresistanceofR

eo

whileflowingacrosstheLCparallelresonantcircuit,andproducesavoltagewiththephaseshiftof0.最后，将这三部分电压求和就得到一个普通调幅信号。Atlast,thethreeportionsofvoltageareaddedupandanamplitudemodulatedsignalisproduced.上边频分量流经LC并联谐振回路时，遇到的电阻为0.707R

eo，生成电压时的相移为-/4。Theupperside-frequencycomponentmeetstheresistanceof0.707R

eo

whileflowingacrosstheLCparallelresonantcircuit,andproducesavoltagewiththephaseshiftof-/4.下边频分量流经LC并联谐振回路时，遇到的电阻为0.707R

eo，生成电压时的相移为/4。Thelowerside-frequencycomponentmeetstheresistanceof0.707R

eo

whileflowingacrosstheLCparallelresonantcircuit,andproducesavoltagewiththephaseshiftof/4.因此我们给上边频分量乘上0.707R

eo，再添加-/4的相移，就得到它产生的电压。Therefore,wemultiplytheupperside-frequencycomponentand0.707R

eo,andaddthephaseshiftof-/4toobtainthevoltagegeneratedbyit.结束End目录

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Help第6

页Page6电子工程学院SchoolofElectronicEngineering第五章振幅调制与解调第6

页Page6Chapter5Amplitudemodulationanddemodulation步骤[3]滤波产生已调波Producethemodulatedwavebyfiltering++a1UCma2UmUCma2UmUCmC－C＋Ca1UCmcosCta2UmUCmcos(

C－)ta2UmUCmcos(

C+)t[][]Z|Ze|0.707Reo0.707ReoReo－/4/40iC(t)0tuAM(t)t0西安电子科技大学XidianUniversity继续Continue我们还可以进一步写出uAM(t)的标准形式。WemayfurtherwriteuAM(t)initsstandardform.接下来，我们对比一下iC(t)和uAM(t)的波形。由于LC并联谐振回路的选频作用，只有iC(t)的部分频率分量可以产生有效的电压输出，因此uAM(t)和iC(t)的波形有较大差别，这与电流通过电阻产生电压输出的情况不同。Next,let’scomparethewaveformsofiC(t)anduAM(t).Becauseofthefrequency-selectivityoftheLCparallelresonantcircuit,onlyaportionoftheiC(t)componentsareabletoproduceeffectivevoltageoutputs.Consequently,thewaveformofuAM(t)differssignificantlyfromthatofiC(t),whichisquitedifferentfromthecasewheretheoutputvoltageisgeneratedbyacurrentflowingthrougharesistor.结束End目录

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Helpa1UCma2UmUCma2UmUCmC－C＋CZ|Ze|0.707Re0.707ReRe－/4/40iC(t)0tuAM(t)t0第五章振幅调制与解调第7

页Page7Chapter5Amplitudemodulationanddemodulation非线性器件调幅失真Distortionsofamplitudemodulationbynonlineardevices失真来源Sourceofdistortions高阶项Higher-ordertermsIC()0

西安电子科技大学XidianUniversity继续Continue下面，我们进一步深入研究非线性器件调幅的失真问题。Inthefollowing,we’lltakeanotherfurtherstepandstudythedistortionprobleminheritedfromthenonlinear-deviceamplitudemodulation.严格地说，iC

的表达式还应该包括后面这些高阶项。Rigorouslyspeaking,theexpressionofiCshouldincludethefollowinghigher-orderterms.这些高阶项也可以具体写成多个频率分量叠加的形式，这些新的频率分量的频谱将叠加到前面的用前三项泰勒级数近似表示的iC

的频谱上。Also,thesehigher-ordertermscanbedetailedasthesummationofmanyfrequencycomponents.ThespectrumofthesenewcomponentsaretobeaddeduptothatoftheiCpreviouslyapproximatedbythefirstthreeTaylorseries.这三个新的频率分量和前面得到的iC

的有用频率分量在频率上是重合的，它们造成包络失真。ThesethreecomponentsaresuperpositionedinfrequencyontothepreviouslyobtainedusefulcomponentsofiC.Theyleadtotheenvelopedistortion.如果滤波器的带宽足够大，则边上这两个频率分量也可以产生有效电压输出，造成非线性失真。Onconditionthatthebandofthefilteriswideenough,thetwocomponentsonbothsidesmayalsoproduceeffectivevoltageoutput,thusthenonlineardistortionoccurs.我们现在看失真是怎样产生的。在前面的分析中，我们只保留了泰勒级数展开式的前三项来近似晶体管的输出电流iC

。Now,let’sfindouthowthedistortionsoccur.WehavepreviouslyreservedthefirstthreetermsintheTaylorseriestoapproximateiC,theoutputcurrentofthetransistor.包络失真Envelopedistortion非线性失真Nonlineardistortion结束End目录

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Help第五章振幅调制与解调第8

页Page8Chapter5Amplitudemodulationanddemodulation减小失真的方法Methodstoreducedistortions方法[3]Methodthree:采用平衡对消

Applybalancedcancellation西安电子科技大学XidianUniversity继续Continue方法[1]Methodone:采用平方率器件Usesquare-lawdevices方法[2]Methodtwo:减小ubeReduceube失真的起源是iC

中的高阶项，平方率器件的输出电流的泰勒展开式只到二次平方项为止，没有高阶项，因此用它们作有源器件时就可以从根本上消除失真。Thedistortionsoriginatefromthehigher-ordertermsofiC.Thesquare-lawdevicesproducetheoutputcurrentwhoseTaylorexpansionseriesterminateatthesquaretermwithnoadditionalhigher-orderterms.Usedastheactivedevice,theycanfundamentallyeliminatethedistortions.高阶项中，ube

的幂n

取值较大，因此如果我们减小ube，则高阶项会显著变小，这也可以在一定程度上减弱失真。Theexponentnofubeisrelativelylargerinhigher-orderterms.Therefore,thehigher-ordertermsarereducedsignificantlyifwedecreasethevalueofube,whichhelpstoweakenthedistortionstosomeextent.我们还可以通过改进电路来处理失真问题，方法之一是采用平衡对消的电路设计。Wemayalsoimprovethecircuitstotacklethedistortionproblem.Thebalanced-cancellationcircuitisonesolution.现在我们接着讨论可以采取哪些方法来减小失真。Nowwecontinuetodiscussthemethodsfordistortionreduction.结束End目录

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Help第五章振幅调制与解调第9

页Page9Chapter5Amplitudemodulationanddemodulation平衡对消

Balancedcancellation西安电子科技大学XidianUniversity继续Continue从原理上看，平衡对消是通过多路输入－输出电路实现的，当输出的多路电流叠加时，大多数会造成失真的频率分量可以相互抵消。Theoretically,thebalancedcancellationisrealizedbyamultiple-input-outputcircuit。Whentheoutputcurrentsareaddedup,mostofthefrequencycomponentsresponsibleforthedistortionsarecancelledamongthemselves.基于晶体管输出电流iC

的泰勒级数展开式，我们可以写出一个四路输入－输出的平衡对消电路的表达式。在四路输入中，交流输入电压由载波uC

和调制信号u

以四种不同方式组合而成，从而产生四路输出电流iC1，iC2，iC3

和iC4。BasedontheTaylorseriesexpansionofthetransistor’soutputcurrentiC,wecanwritedowntheexpressionsofabalanced-cancellationcircuitwithfourinput-outputroutes.ThecarrierwaveuCandthemodulatingsignaluarecombinedinfourdifferentways,andthusproducingfouroutputcurrentsasiC1,iC2,iC3,andiC4.结束End目录

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Help第五章振幅调制与解调第9

页Page9Chapter5Amplitudemodulationanddemodulation步骤[2]Steptwo:iC3-iC4步骤[1]Stepone:iC1-iC2步骤[3]Stepthree:(iC1-iC2)+(iC3-iC4)西安电子科技大学XidianUniversity继续Continue接下来，我们把iC1，iC2，iC3

和iC4

用其泰勒展开式的前五项级数来近似。Next,weusethefirstfiveseriesoftheTaylorexpansiontoapproximateiC1,iC2,iC3,andiC4.这里的平衡对消过程通过三个步骤进行。在步骤[1]中，我们使iC1减去iC2。

Thebalancedcancellationiscarriedoutinthreesteps.Inthefirststep,wesubtractiC2fromiC1.再引入iC2

的该频率分量。WethenintroducethefrequencycomponentofiC2.继续这个过程，我们就最终作出了iC1-iC2

的频谱。Continuetheprocess,andwe’llfinallyfinishthespectrumofiC1-iC2.再引入iC2

的频率分量。ThecomponentfromiC2isthenintroduced.最后，我们来作iC1-iC2的频谱。在角频率为0处，引入

iC1

的该频率分量。Atlast,let’splotthespectru