非線性器件振幅調(diào)制,失真和平衡對消

高頻電子線路多媒體教學課件西安電子科技大學電子工程學院趙建勛MultimediaTeachingCoursewareofHigh-FrequencyElectronicCircuitsZhaoJianxunSchoolofElectronicEngineeringXidianUniversity開始Start西安電子科技大學XidianUniversity本課件講授大學本科《高頻電子線路》課程的代表內(nèi)容——非線性器件振幅調(diào)制，失真和平衡對消。課件主要配合教師課堂教學使用，講授過程中始終以教師講述為主，課件只提供必要的文字和圖像信息。學生本人使用該課件預習和復習功課時，可以選擇向?qū)У膸椭?。向?qū)Ъ皶r提供豐富的文字講解，起到了教師指導的作用。因為集成了向?qū)Чδ埽菊n件也可以作為網(wǎng)絡(luò)課件使用。

Thecoursewareismaterializedonnonlinear-deviceamplitudemodulation,distortion,andbalancedcancellation,whicharerepresentativecontentsofHigh-FrequencyElectronicCircuits,acourseforundergraduatestudents.Withthemajorpurposetoassisttheclassroomlecturing,thecoursewareprovidesnecessaryliteralandimageinformationtohelptheteacher,whoplaysthemainroleinthelecturing.Thecoursewareitselfisalsoanet-basedone.Theintegratedguidetimelyprovidesdetailedliteralexplanationsforstudentsinpreparingandreviewingthecourse.Theguidanceservesastheinstructionsfromteachers.簡介Introduction西安電子科技大學XidianUniversity結(jié)束End封面Cover目錄

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Content結(jié)束End翻到幫助頁面Tothehelppage翻到目錄Tothecontent返回上一頁Tothelastpage結(jié)束放映Endthescreening第五章振幅調(diào)制與解調(diào)結(jié)束End向?qū)uide封面

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HelpChapter5Amplitudemodulationanddemodulation振幅調(diào)制方法的分類Typesofamplitudemodulationapproaches西安電子科技大學XidianUniversity您好，歡迎使用高頻電子線路多媒體教學課件，請選擇是否需要向?qū)Аello,welcometoTeachingCoursewareofHigh-FrequencyElectronicCircuits.Pleasechooseifyouwillneedaguide.使用向?qū)Вū阌跒g覽課件，課程預習和復習）Usetheguide(Forcoursewarebrowsing,coursepreparationandreviewing)不使用向?qū)Вū阌诮M織課堂教學）Noguide(Forclassroomlecturingorganization)第五章振幅調(diào)制與解調(diào)目錄ContentChapter5Amplitudemodulationanddemodulation振幅調(diào)制方法Amplitudemodulationapproaches非線性器件調(diào)幅Amplitudemodulationwithnonlineardevices線性時變電路調(diào)幅AMwithlineartime-varyingcircuits步驟[1]Stepone步驟[2]Steptwo步驟[3]Stepthree非線性器件調(diào)幅失真Distortionsofnonlinear-deviceAM振幅調(diào)制的關(guān)鍵問題Keyproblemofamplitudemodulation失真來源

Sourceofdistortions減小失真的方法

Methodstoreducedistortions平衡對消Balancedcancellation非線性器件調(diào)幅分析

Analysisofnonlinear-deviceAM振幅調(diào)制與解調(diào)Amplitudemodulation(AM)anddemodulation振幅調(diào)制方法的分類Typesofamplitudemodulationapproaches振幅調(diào)制信號Amplitudemodulatedsignals西安電子科技大學XidianUniversity結(jié)束End封面

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Help第五章振幅調(diào)制與解調(diào)目錄ContentChapter5Amplitudemodulationanddemodulation振幅調(diào)制方法Amplitudemodulationapproaches非線性器件調(diào)幅Amplitudemodulationwithnonlineardevices線性時變電路調(diào)幅AMwithlineartime-varyingcircuits步驟[1]Stepone步驟[2]Steptwo步驟[3]Stepthree非線性器件調(diào)幅失真Distortionsofnonlinear-deviceAM振幅調(diào)制的關(guān)鍵問題Keyproblemofamplitudemodulation失真來源

Sourceofdistortions減小失真的方法

Methodstoreducedistortions平衡對消Balancedcancellation非線性器件調(diào)幅分析

Analysisofnonlinear-deviceAM振幅調(diào)制與解調(diào)Amplitudemodulation(AM)anddemodulation振幅調(diào)制方法的分類Typesofamplitudemodulationapproaches振幅調(diào)制信號Amplitudemodulatedsignals西安電子科技大學XidianUniversity繼續(xù)Continue一種比較重要和常見的減小失真的方法是平衡對消技術(shù)，這是本次課程最后要學習的內(nèi)容。Balancedcancellationisanimportantandusualmethodfordistortionreduction,whichwillbestudiedattheendofthislesson.我們從本次課程開始學習振幅調(diào)制方法，這是第五章，振幅調(diào)制與解調(diào)的一個重要部分。Inthislesson,webegintolearnapproachesofamplitudemodulation,whichisanimportantportionofChapter5,Amplitudemodulationanddemodulation.為了解決失真問題，我們接下來尋找失真的來源，并由此提出減小失真的方法。Totacklethedistortionproblem,we’llsearchforthedistortionsource,andthenbringforwardmethodsfordistortionreduction.非線性器件調(diào)幅通過三個步驟來實現(xiàn)。Thenonlinear-deviceamplitudemodulationisperformedinthreesteps.首先，我們簡要復習三種振幅調(diào)制信號，即普通調(diào)幅信號，雙邊帶調(diào)制信號和單邊帶調(diào)制信號。First,we’llbrieflyreviewthethreesignalsoutofamplitudemodulation,namely,theamplitudemodulatedsignal,thedouble-sidebandmodulatedsignal,andthesingle-sidebandmodulatedsignal.為了生成這些信號，我們進行振幅調(diào)制時需要解決一個關(guān)鍵問題，即調(diào)制信號與載波的相乘。Weneedtosolveakeyproblemintheamplitudemodulationtogeneratethesesignals,thatis,themultiplicationofthemodulatingsignalandthecarrierwave.感謝使用向?qū)?。首先，我們簡略瀏覽本次課程的內(nèi)容和結(jié)構(gòu)。Thankyouforusingtheguide.Atfirst,let’sbrieflybrowsethecontentandstructureofthislesson.從分類上看，有兩種基本方法可以解決該問題，即非線性器件調(diào)幅和線性時變電路調(diào)幅。本次課程學習非線性器件調(diào)幅。Forsolution,therearetwobasictypesofamplitudemodulationapproach,namely,theamplitudemodulationwithnonlineardevices，andtheamplitudemodulationwithlineartime-varyingcircuits.Theformeristobestudiedinthislesson.非線性器件的應(yīng)用解決了前面提到的振幅調(diào)制的關(guān)鍵問題，但又產(chǎn)生了新的失真問題。Theabove-mentionedkeyproblemofamplitudemodulationissolvedbyusingnonlineardevices.However,thedistortionoccursasanewproblem.結(jié)束End目錄

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頁Page1Chapter5Amplitudemodulationanddemodulation西安電子科技大學XidianUniversity普通調(diào)幅信號

Amplitudemodulatedsignal雙邊帶調(diào)制信號

Double-sidebandmodulatedsignal單邊帶調(diào)制信號Single-sidebandmodulatedsignal調(diào)制信號Modulatingsignal

u(t)=U

mcost載波

carrierwaveuC

(t)=U

Cmcos

Ct

C

C+

C－

CUmUCm繼續(xù)Continue經(jīng)過調(diào)制，得到的振幅調(diào)制信號可能包含三個頻率分量。角頻率為

C，

C+和

C-的頻率分量可以分別叫做載頻分量，上邊頻分量和下邊頻分量。Afterthemodulation,theobtainedamplitudemodulatedsignalmaycontainthreefrequencycomponents.Thosewiththeangularfrequenciesof

C,

C+and

C-aretermedasthecarriercomponent,theupperside-frequencycomponentandthelowerside-frequencycomponentrespectively.現(xiàn)在，我們開始學習本次課程的內(nèi)容。進行振幅調(diào)制的目的是把低頻的語音、圖象等調(diào)制信號寄載到高頻載波上，從而實現(xiàn)信息的遠程無線傳輸。Now,let’sstartthelesson.Theamplitudemodulationisaimedatmountingthelow-frequencyaudioorvisualmodulatingsignalontoahigh-frequencycarrierwave,sothattheinformationcanbetransmittedwirelesslyatalongdistance.為簡單起見，我們認為調(diào)制信號和載波都是單頻信號。這里給出了它們的時域表達式。Forsimplicity,themodulatingsignalandthecarrierwavearesupposedtobesingle-frequencysignals.Thesearetheirtime-domainexpressions.在頻域上，調(diào)制信號和載波都可以用其角頻率和振幅表示。Themodulatingsignalandthecarrierwaveareexpressedinthefrequencydomainbyusingtheirangularfrequenciesandamplitudes.包含所有三個頻率分量的信號稱為普通調(diào)幅信號，只包含上邊頻分量和下邊頻分量的信號稱為雙邊帶調(diào)制信號，而單邊帶調(diào)制信號則只有上邊頻分量或下邊頻分量中的一個。Thesignalwithallthreefrequencycomponentsiscalledanamplitudemodulatedsignal.Thatonlywiththeupperandthelowerside-frequencycomponentsiscalledadouble-sidebandmodulatedsignal.Thesingle-sidebandmodulatedsignalhasonlyoneoftheside-frequencycomponents.結(jié)束End目錄

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頁Page2Chapter5Amplitudemodulationanddemodulation振幅調(diào)制方法Amplitudemodulationapproaches非線性器件調(diào)幅Amplitudemodulationwithnonlineardevices線性時變電路調(diào)幅Amplitudemodulationwithlineartime-varyingcircuits頻域：

C+，

C-Frequencydomain:

C+，

C-振幅調(diào)制的關(guān)鍵問題

Keyproblemofamplitudemodulation時域：uC

uTimedomain:

uC

u西安電子科技大學XidianUniversity繼續(xù)Continue為了生成前面的三種振幅調(diào)制信號，進行振幅調(diào)制時，在時域上要將調(diào)制信號和載波相乘，在頻域上看，這樣的相乘會生成上邊頻分量和下邊頻分量，這個關(guān)鍵問題的解決需要用到非線性電路。Inordertogeneratetheabovethreeamplitudemodulatedsignals,duringtheamplitudemodulation,themodulatingsignalwillbemultipliedbythecarrierwaveinthetimedomain,whichwillproducetheupperandthelowerside-frequencycomponentsinthefrequencydomain.Nonlinearcircuitsaretobeusedtosolvethiskeyproblem.用非線性電路進行振幅調(diào)制的方法有兩種，一種是利有源器件，如晶體管或場效應(yīng)管的非線性實現(xiàn)調(diào)幅，另一種是基于線性時變電路實現(xiàn)調(diào)幅。Therearetwotypesofamplitudemodulationapproachwiththeuseofnonlinearcircuits.Oneapproachistomakeusethenonlinearpropertyofactivedevices,suchasthetransistorandtheFET.Theotherapproachisbasedonlineartime-varyingcircuits.結(jié)束End目錄

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頁Page3Chapter5Amplitudemodulationanddemodulation+++++++西安電子科技大學XidianUniversity繼續(xù)Continueube

(t)經(jīng)過EB的偏置，產(chǎn)生晶體管的輸入電壓uBE(t)。WiththebiasingofEBuponube

(t),wegetuBE(t),theinputvoltageonthetransistor.接下來，在uBE(t)的作用下，晶體管產(chǎn)生輸出電流iC(t)。Inthefollowing,thetransistorgeneratestheoutputcurrentiC(t)inresponsetouBE(t).該圖實際上給出了一個放大器電路。首先，載波uC

(t)和調(diào)制信號u(t)疊加產(chǎn)生交流輸入電壓ube

(t)。Thediagramisactuallyanamplifiercircuit,wherethecarrierwaveuC

(t)andthemodulatingsignalu(t)areaddedupfirsttoproducethealternatinginputvoltageube

(t).最后，iC(t)經(jīng)由LC并聯(lián)諧振回路選頻，產(chǎn)生普通調(diào)幅信號uAM

(t)。Finally,iC

(t)flowsthroughthefrequency-selectingLCparallelresonantcircuit,andproducesanamplitudemodulatedsignaluAM

(t).現(xiàn)在我們學習第一種振幅調(diào)制方法，即非線性器件調(diào)幅方法。該方法的原理電路如圖所示。Nowwecometolearnthefirstamplitudemodulationapproach,i.e.,thenonlinear-deviceamplitudemodulation.Hereisthebasiccircuitdiagramofthisapproach.結(jié)束End目錄

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頁Page4Chapter5AmplitudemodulationanddemodulationtuC(t)0tu(t)0tube(t)0步驟[1]載波和調(diào)制信號相加產(chǎn)生輸入電壓Addingupthecarrierwaveandthemodulatingsignaltoproducetheinputvoltage+++++西安電子科技大學XidianUniversity繼續(xù)Continue前面簡要描述了非線性器件調(diào)幅的過程，在此基礎(chǔ)上，我們接下來觀察并研究該過程中一些值得注意的細節(jié)。非線性器件調(diào)幅的原理電路可以分解為輸入級回路，晶體管和輸出級回路三部分，每部分各自完成振幅調(diào)制過程的一個步驟。Theprocessofthenonlinear-deviceamplitudemodulationhasbeenbrieflydescribed,basedonwhich,wenowcometoobserveandstudysomedetailsintheprocess.Thebasiccircuitcanbedecomposedintothreeparts,namely,theinputloop,thetransistor,andtheoutputloop.Eachpartofthecircuitperformsonestepoftheamplitudemodulation.現(xiàn)在我們實時觀察

uC

(t)，u(t)和

ube

(t)的波形。注意載波的頻率遠大于調(diào)制信號的頻率，而其振幅也大于調(diào)制信號的振幅。二者疊加產(chǎn)生的交流輸入電壓ube

(t)的高頻振蕩與載波一致，其起伏與調(diào)制信號同步。Now,let’smakeareal-timeobservationofthewaveformsofuC

(t),u(t)andube

(t).Itshouldbenoticedthatthecarrierwavefrequencyismuchhigherthanthemodulatingsignalfrequency.Thesamecanbesaidoftheiramplitudes.Thealternatinginputvoltageube

(t)outoftheadditionoscillatesaccordingtothecarrierwave,whereasitrisesandfallsinaccordancewiththemodulatingsignal.首先，我們看第一個步驟。這是在輸入級回路中完成的，載波

uC

(t)和調(diào)制信號u(t)在這里相疊加產(chǎn)生交流輸入電壓

ube

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

(t)andthemodulatingsignalu(t)areaddeduptoproducethealternatinginputvoltageube

(t).結(jié)束End目錄

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HelptuC(t)0tu(t)0tube(t)0iC0uBEtuBE0EBiC0QICQEBICQt第五章振幅調(diào)制與解調(diào)第5

頁Page5Chapter5Amplitudemodulationanddemodulation步驟[2]非線性器件產(chǎn)生輸出電流Thenonlineardevicegeneratestheoutputcurrent+西安電子科技大學XidianUniversity繼續(xù)Continue我們現(xiàn)在把第一個點垂直投影到轉(zhuǎn)移特性曲線上。Now,weverticallyprojectthefirstpointontothetransfercharacteristiccurve.對uBE(t)中的每個點都進行這樣的投影，我們就最終可以得到iC

(t)的波形。We’llfinallygettheiC

(t)waveformaftereachuBE(t)pointisthusprojected.在該投影過程中，我們可以發(fā)現(xiàn)，晶體管的非線性，更確切地說，其轉(zhuǎn)移特性的非線性，引起了

iC

(t)波形的變化。Intheprojectingprocess,wediscoverthat,thenonlinearityofthetransistor,ormoreaccurately,thenonlinearityofthetransistor’stransfercharacteristic,shouldberesponsibleforthealterationintheiC

(t)waveform.下面我們研究這樣的波形變化是如何產(chǎn)生的。我們首先在uBE

(t)的波形上選取若干個點，接下來觀察這些點是怎樣投影確定iC(t)的波形的。Next,let’sfindouthowthewaveformalterationoccurs.First,weselectacoupleofpointsontheuBE

(t)waveform,thenwe’llobserveinwhatwayiC(t)isdeterminedbytheprojectionofthesepoints.接下來把該點水平投影到iC

(t)圖中該點對應(yīng)的時刻。Next,wepojectthepointhorizontallyontoitscorrespondinginstantintheiC

(t)diagram.借助于該特性曲線，我們可以通過投影方式從uBE

(t)的波形畫出

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

(t)bywayofprojection.這里給出了晶體管的轉(zhuǎn)移特性曲線，它描述了晶體管的輸入電壓uBE

和輸出電流iC

的關(guān)系。Hereisthetransfercharacteristiccurveofthetransistor,whichdescribestherelationbetweentheinputvoltageuBEandtheoutputcurrentiC.這樣我們得到了iC

(t)波形上的一個點。Therefore,onepointontheiC

(t)waveformisobtained.如果將波形放大，我們會注意到iC(t)的波形和uBE

(t)的波形并不一樣。與uBE

(t)比較而言，iC(t)的上半周變得較為尖銳，而下半周則變得較為平緩。Ifthewaveformsaremagnified,itwillcometoourattentionthatthewaveformsofiC(t)anduBE

(t)arenotidentical.ComparedtouBE

(t),theupperpartofiC(t)becomessharper,whereasitslowerpartbecomessmoother.接下來，我們看第二個步驟。這是在晶體管中完成的，交流輸入電壓

ube

(t)經(jīng)過EB

的偏置后，成為晶體管的輸入電壓uBE

(t)，在其作用下，晶體管產(chǎn)生輸出電流iC(t)。Next,let’sfocusonthesecondstep,whichisaccomplishedinthetransistor,wherethealternatinginputvoltageube

(t)isbiasedbyEBandtheinputvoltageuBE

(t)isproduced,activatedbywhich,thetransistorgeneratestheoutputcurrentiC(t).結(jié)束End目錄

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HelpiC0uBEtuBE0EBiC0QICQEBICQt第五章振幅調(diào)制與解調(diào)第5

頁Page5Chapter5Amplitudemodulationanddemodulation+++++西安電子科技大學XidianUniversity繼續(xù)Continue為了對iC

進行分析，我們將其近似表示成前三項級數(shù)和。利用已知的

ube，uC

和u的表達式，我們可以得到iC

的一個具體結(jié)果。InordertoanalyzeiC

,weusethefirstthreeseriestoapproximateit.AdetailedresultofiCisderivedbyusingtheavailableexpressionsofube,uCandu.我們寫出晶體管轉(zhuǎn)移特性曲線的表達式，當然這里的函數(shù)f是非線性函數(shù)。Wewritedowntheexpressionofthetransistor’stransfercharacteristiccurve,wherethefunctionfisofcourseanonlinearone.這種非線性過程導致的波形變化暗示了iC

(t)中含有uBE

(t)中沒有的新的頻率分量，下面我們通過解析方法確定iC

(t)中有哪些頻率分量。ThewaveformalterationcausedbythenonlinearprocessindicatesiC

(t)containssomenewfrequencycomponentsbesidesthoseofuBE

(t).Inthefollowing,we’lldeterminetheiC

(t)components.參考原理電路中的輸入級回路，我們還可以寫出晶體管輸入電壓uBE(t)。WecanalsowritedownuBE(t),theinputvoltageofthetransistor,referringtotheinputloopofthebasiccircuitdiagram.這里，我們把iC

展開成泰勒級數(shù)，展開的中心位置選在EB

，這樣就把晶體管輸出電流

iC

表示成了交流輸入電壓ube

的級數(shù)和的形式。Next,weexpandiCintoaTaylorseries.TheexpansioniscenteredatEB,thereforetheoutputcurrentofthetransistor,iC,isexpressedasthesummationoftheseriesaboutube,thealternatinginputvoltage.結(jié)束End目錄

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Help第五章振幅調(diào)制與解調(diào)第6

頁Page6Chapter5Amplitudemodulationanddemodulation步驟[3]濾波產(chǎn)生已調(diào)波Producethemodulatedwavebyfiltering++IC()0

西安電子科技大學XidianUniversity中間三項分別是載頻分量，下邊頻分量和上邊頻分量。Thethreeitemsinthemiddlearerespectivelythecarrier,theupperside-frequency,andthelowerside-frequencycomponents.我們根據(jù)其角頻率和振幅在頻域上畫出該頻率分量。Wedrawthiscomponentinthefrequencydomainaccordingtoitsangularfrequencyandamplitude.現(xiàn)在畫出該頻率分量。Now,wedrawthiscomponent.最后一項的角頻率為2

C。Thelastitemhasanangularfrequencyof2

C.我們也畫出該頻率分量。Wedrawthiscomponenttoo.這三個頻率分量對我們是有用的。Thesethreecomponentsareusefulforus.這樣我們就可以方便地畫出iC

的頻譜，從而由前面的時域分析過渡到后面的頻域分析。SowecaneasilyplotthespectrumofiC,andadvancefromtheprevioustime-domainanalysistothefollowingfrequency-domainanalysis.現(xiàn)在，我們來到非線性器件調(diào)幅的第三步。前面得到的iC

的具體結(jié)果經(jīng)過整理，可以寫成其各個頻率分量疊加的形式。Wenowcometothethirdstepofthenonlinear-deviceamplitudemodulation.ThepreviouslyderivediCisreorganizedandwrittendownhereintheadditionformofitsvariousfrequencycomponents.現(xiàn)在畫出該分量。Now,let’sdrawthiscomponent.表達式的第一項是直流分量。

Thefirstitemintheexpressionisadirectcomponent.第二項是角頻率為的分量。

Theseconditemisacomponentwiththefrequencyof.第三項是角頻率為2的分量。

Thethirditemisacomponentwiththefrequencyof2.進行濾波，就可以得到普通調(diào)幅信號。Anamplitudemodulatedsignalisobtainedbyfiltering.結(jié)束End目錄

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Help第五章振幅調(diào)制與解調(diào)第6

頁Page6Chapter5Amplitudemodulationanddemodulation步驟[3]濾波產(chǎn)生已調(diào)波Producethemodulatedwavebyfiltering++IC()0

西安電子科技大學XidianUniversity繼續(xù)Continue我們把這些頻率分量寫到新的位置。Let’swritethesecomponentsatnewpositions.下面，為了說明濾波過程，我們在時域和頻域只保留下

iC

的這三個有用頻率分量。Inthefollowing,weonlykeepthethreeusefulfrequencycomponentsofiCbothinthetimedomainandinthefrequencydomain.結(jié)束End目錄

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Help第五章振幅調(diào)制與解調(diào)第6

頁Page6Chapter5Amplitudemodulationanddemodulation步驟[3]濾波產(chǎn)生已調(diào)波Producethemodulatedwavebyfiltering++a1UCmcosCta2UmUCmcos(

C－)ta2UmUCmcos(

C+)ta1UCma2UmUCma2UmUCmC－C＋C西安電子科技大學XidianUniversity繼續(xù)Continue需要注意的是，這些有用的頻率分量都是電流，而我們要得到的普通調(diào)幅信號是電壓，所以需要使晶體管的輸出電流iC

流過一個支路，該支路只對iC

中這三個頻率分量產(chǎn)生有效的電壓輸出，而不對其余的頻率分量產(chǎn)生有效的電壓輸出。Itshouldbenoticedthattheseusefulfrequencycomponentsarecurrents,whereasweneedthevoltageoftheamplitudemodulatedsignal.Thereforetheoutputcurrentofthetransistor,iC,shouldbemadetoflowacrossabranchcircuit,whichproduceseffectivevoltageoutputforthethreeusefulcomponentsandnoeffectiveoutputfortheothercomponents.這種支路的阻抗應(yīng)該具有帶通的幅頻特性，最為典型的設(shè)計就是LC并聯(lián)諧振回路。Theimpedanceofsuchabranchcircuitshouldhaveaband-passamplitude-frequencycharacteristic.ThemosttypicaldesignistheLCparallelresonantcircuit.我們可以參照這三個有用頻率分量的頻譜畫出LC并聯(lián)諧振回路的幅頻特性和相頻特性。Wecandrawtheamplitude-frequencyandthephase-frequencycharacteristicsoftheLCparallelresonantcircuit,accordingtothespectrumofthethreeusefulfrequencycomponents.結(jié)束End目錄

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Help第五章振幅調(diào)制與解調(diào)第6

頁Page6Chapter5Amplitudemodulationanddemodulation步驟[3]濾波產(chǎn)生已調(diào)波Producethemodulatedwavebyfiltering++a1UCma2UmUCma2UmUCmC－C＋Ca1UCmcosCta2UmUCmcos(

C－)ta2UmUCmcos(

C+)t[][]Z|Ze|－/4/400.707Reo0.707ReoReo西安電子科技大學XidianUniversity這里給出的LC并聯(lián)諧振回路的諧振電阻為Reo，其諧振角頻率等于載頻

C，帶寬為2。因此在下邊頻

C-

和上邊頻

C+

處，其呈現(xiàn)的電阻為0.707Reo，而提供的相移則分別為

/4和-/4。TheresonantresistanceoftheLCparallelresonantcircuitgivenhereisReo.Theresonantangularfrequencyequalsthecarrierfrequency

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

C-

andtheuppersidefrequency

C+

respectively.因此我們給下邊頻分量乘上0.707R

eo，再添加/4的相移，就得到它產(chǎn)生的電壓。Therefore,wemultiplythelowerside-frequencycomponentand0.707R

eo,andaddthephaseshiftof/4toobtainthevoltagegeneratedbyit.因此我們給載頻分量乘上R

eo，就得到它產(chǎn)生的電壓。Therefore,wemultiplythecarriercomponentandR

eotoobtainthevoltagegeneratedbyit.三個頻率分量當中，載頻分量流經(jīng)LC并聯(lián)諧振回路時，遇到的電阻為R

eo，生成電壓時的相移為0。Amongthethreefrequencycomponents,thecarriercomponentmeetstheresistanceofR

eo

whileflowingacrosstheLCparallelresonantcircuit,andproducesavoltagewiththephaseshiftof0.最后，將這三部分電壓求和就得到一個普通調(diào)幅信號。Atlast,thethreeportionsofvoltageareaddedupandanamplitudemodulatedsignalisproduced.上邊頻分量流經(jīng)LC并聯(lián)諧振回路時，遇到的電阻為0.707R

eo，生成電壓時的相移為-/4。Theupperside-frequencycomponentmeetstheresistanceof0.707R

eo

whileflowingacrosstheLCparallelresonantcircuit,andproducesavoltagewiththephaseshiftof-/4.下邊頻分量流經(jīng)LC并聯(lián)諧振回路時，遇到的電阻為0.707R

eo，生成電壓時的相移為/4。Thelowerside-frequencycomponentmeetstheresistanceof0.707R

eo

whileflowingacrosstheLCparallelresonantcircuit,andproducesavoltagewiththephaseshiftof/4.因此我們給上邊頻分量乘上0.707R

eo，再添加-/4的相移，就得到它產(chǎn)生的電壓。Therefore,wemultiplytheupperside-frequencycomponentand0.707R

eo,andaddthephaseshiftof-/4toobtainthevoltagegeneratedbyit.結(jié)束End目錄

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Help第6

頁Page6電子工程學院SchoolofElectronicEngineering第五章振幅調(diào)制與解調(diào)第6

頁Page6Chapter5Amplitudemodulationanddemodulation步驟[3]濾波產(chǎn)生已調(diào)波Producethemodulatedwavebyfiltering++a1UCma2UmUCma2UmUCmC－C＋Ca1UCmcosCta2UmUCmcos(

C－)ta2UmUCmcos(

C+)t[][]Z|Ze|0.707Reo0.707ReoReo－/4/40iC(t)0tuAM(t)t0西安電子科技大學XidianUniversity繼續(xù)Continue我們還可以進一步寫出uAM(t)的標準形式。WemayfurtherwriteuAM(t)initsstandardform.接下來，我們對比一下iC(t)和uAM(t)的波形。由于LC并聯(lián)諧振回路的選頻作用，只有iC(t)的部分頻率分量可以產(chǎn)生有效的電壓輸出，因此uAM(t)和iC(t)的波形有較大差別，這與電流通過電阻產(chǎn)生電壓輸出的情況不同。Next,let’scomparethewaveformsofiC(t)anduAM(t).Becauseofthefrequency-selectivityoftheLCparallelresonantcircuit,onlyaportionoftheiC(t)componentsareabletoproduceeffectivevoltageoutputs.Consequently,thewaveformofuAM(t)differssignificantlyfromthatofiC(t),whichisquitedifferentfromthecasewheretheoutputvoltageisgeneratedbyacurrentflowingthrougharesistor.結(jié)束End目錄

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Helpa1UCma2UmUCma2UmUCmC－C＋CZ|Ze|0.707Re0.707ReRe－/4/40iC(t)0tuAM(t)t0第五章振幅調(diào)制與解調(diào)第7

頁Page7Chapter5Amplitudemodulationanddemodulation非線性器件調(diào)幅失真Distortionsofamplitudemodulationbynonlineardevices失真來源Sourceofdistortions高階項Higher-ordertermsIC()0

西安電子科技大學XidianUniversity繼續(xù)Continue下面，我們進一步深入研究非線性器件調(diào)幅的失真問題。Inthefollowing,we’lltakeanotherfurtherstepandstudythedistortionprobleminheritedfromthenonlinear-deviceamplitudemodulation.嚴格地說，iC

的表達式還應(yīng)該包括后面這些高階項。Rigorouslyspeaking,theexpressionofiCshouldincludethefollowinghigher-orderterms.這些高階項也可以具體寫成多個頻率分量疊加的形式，這些新的頻率分量的頻譜將疊加到前面的用前三項泰勒級數(shù)近似表示的iC

的頻譜上。Also,thesehigher-ordertermscanbedetailedasthesummationofmanyfrequencycomponents.ThespectrumofthesenewcomponentsaretobeaddeduptothatoftheiCpreviouslyapproximatedbythefirstthreeTaylorseries.這三個新的頻率分量和前面得到的iC

的有用頻率分量在頻率上是重合的，它們造成包絡(luò)失真。ThesethreecomponentsaresuperpositionedinfrequencyontothepreviouslyobtainedusefulcomponentsofiC.Theyleadtotheenvelopedistortion.如果濾波器的帶寬足夠大，則邊上這兩個頻率分量也可以產(chǎn)生有效電壓輸出，造成非線性失真。Onconditionthatthebandofthefilteriswideenough,thetwocomponentsonbothsidesmayalsoproduceeffectivevoltageoutput,thusthenonlineardistortionoccurs.我們現(xiàn)在看失真是怎樣產(chǎn)生的。在前面的分析中，我們只保留了泰勒級數(shù)展開式的前三項來近似晶體管的輸出電流iC

。Now,let’sfindouthowthedistortionsoccur.WehavepreviouslyreservedthefirstthreetermsintheTaylorseriestoapproximateiC,theoutputcurrentofthetransistor.包絡(luò)失真Envelopedistortion非線性失真Nonlineardistortion結(jié)束End目錄

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Help第五章振幅調(diào)制與解調(diào)第8

頁Page8Chapter5Amplitudemodulationanddemodulation減小失真的方法Methodstoreducedistortions方法[3]Methodthree:采用平衡對消

Applybalancedcancellation西安電子科技大學XidianUniversity繼續(xù)Continue方法[1]Methodone:采用平方率器件Usesquare-lawdevices方法[2]Methodtwo:減小ubeReduceube失真的起源是iC

中的高階項，平方率器件的輸出電流的泰勒展開式只到二次平方項為止，沒有高階項，因此用它們作有源器件時就可以從根本上消除失真。Thedistortionsoriginatefromthehigher-ordertermsofiC.Thesquare-lawdevicesproducetheoutputcurrentwhoseTaylorexpansionseriesterminateatthesquaretermwithnoadditionalhigher-orderterms.Usedastheactivedevice,theycanfundamentallyeliminatethedistortions.高階項中，ube

的冪n

取值較大，因此如果我們減小ube，則高階項會顯著變小，這也可以在一定程度上減弱失真。Theexponentnofubeisrelativelylargerinhigher-orderterms.Therefore,thehigher-ordertermsarereducedsignificantlyifwedecreasethevalueofube,whichhelpstoweakenthedistortionstosomeextent.我們還可以通過改進電路來處理失真問題，方法之一是采用平衡對消的電路設(shè)計。Wemayalsoimprovethecircuitstotacklethedistortionproblem.Thebalanced-cancellationcircuitisonesolution.現(xiàn)在我們接著討論可以采取哪些方法來減小失真。Nowwecontinuetodiscussthemethodsfordistortionreduction.結(jié)束End目錄

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Help第五章振幅調(diào)制與解調(diào)第9

頁Page9Chapter5Amplitudemodulationanddemodulation平衡對消

Balancedcancellation西安電子科技大學XidianUniversity繼續(xù)Continue從原理上看，平衡對消是通過多路輸入－輸出電路實現(xiàn)的，當輸出的多路電流疊加時，大多數(shù)會造成失真的頻率分量可以相互抵消。Theoretically,thebalancedcancellationisrealizedbyamultiple-input-outputcircuit。Whentheoutputcurrentsareaddedup,mostofthefrequencycomponentsresponsibleforthedistortionsarecancelledamongthemselves.基于晶體管輸出電流iC

的泰勒級數(shù)展開式，我們可以寫出一個四路輸入－輸出的平衡對消電路的表達式。在四路輸入中，交流輸入電壓由載波uC

和調(diào)制信號u

以四種不同方式組合而成，從而產(chǎn)生四路輸出電流iC1，iC2，iC3

和iC4。BasedontheTaylorseriesexpansionofthetransistor’soutputcurrentiC,wecanwritedowntheexpressionsofabalanced-cancellationcircuitwithfourinput-outputroutes.ThecarrierwaveuCandthemodulatingsignaluarecombinedinfourdifferentways,andthusproducingfouroutputcurrentsasiC1,iC2,iC3,andiC4.結(jié)束End目錄

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Help第五章振幅調(diào)制與解調(diào)第9

頁Page9Chapter5Amplitudemodulationanddemodulation步驟[2]Steptwo:iC3-iC4步驟[1]Stepone:iC1-iC2步驟[3]Stepthree:(iC1-iC2)+(iC3-iC4)西安電子科技大學XidianUniversity繼續(xù)Continue接下來，我們把iC1，iC2，iC3

和iC4

用其泰勒展開式的前五項級數(shù)來近似。Next,weusethefirstfiveseriesoftheTaylorexpansiontoapproximateiC1,iC2,iC3,andiC4.這里的平衡對消過程通過三個步驟進行。在步驟[1]中，我們使iC1減去iC2。

Thebalancedcancellationiscarriedoutinthreesteps.Inthefirststep,wesubtractiC2fromiC1.再引入iC2

的該頻率分量。WethenintroducethefrequencycomponentofiC2.繼續(xù)這個過程，我們就最終作出了iC1-iC2

的頻譜。Continuetheprocess,andwe’llfinallyfinishthespectrumofiC1-iC2.再引入iC2

的頻率分量。ThecomponentfromiC2isthenintroduced.最后，我們來作iC1-iC2的頻譜。在角頻率為0處，引入

iC1

的該頻率分量。Atlast,let’splotthespectru