非線性器件振幅調(diào)制,失真和平衡對(duì)消

高頻電子線路多媒體教學(xué)課件西安電子科技大學(xué)電子工程學(xué)院趙建勛MultimediaTeachingCoursewareofHigh-FrequencyElectronicCircuitsZhaoJianxunSchoolofElectronicEngineeringXidianUniversity開(kāi)始Start西安電子科技大學(xué)XidianUniversity本課件講授大學(xué)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(duì)消。課件主要配合教師課堂教學(xué)使用，講授過(guò)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(xué)生本人使用該課件預(yù)習(xí)和復(fù)習(xí)功課時(shí)，可以選擇向?qū)У膸椭?。向?qū)Ъ皶r(shí)提供豐富的文字講解，起到了教師指導(dǎo)的作用。因?yàn)榧闪讼驅(qū)Чδ?，本課件也可以作為網(wǎng)絡(luò)課件使用。

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

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HelpChapter5Amplitudemodulationanddemodulation振幅調(diào)制方法的分類(lèi)Typesofamplitudemodulationapproaches西安電子科技大學(xué)XidianUniversity您好，歡迎使用高頻電子線路多媒體教學(xué)課件，請(qǐng)選擇是否需要向?qū)?。Hello,welcometoTeachingCoursewareofHigh-FrequencyElectronicCircuits.Pleasechooseifyouwillneedaguide.使用向?qū)Вū阌跒g覽課件，課程預(yù)習(xí)和復(fù)習(xí)）Usetheguide(Forcoursewarebrowsing,coursepreparationandreviewing)不使用向?qū)Вū阌诮M織課堂教學(xué)）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(shí)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(wèn)題Keyproblemofamplitudemodulation失真來(lái)源

Sourceofdistortions減小失真的方法

Methodstoreducedistortions平衡對(duì)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(lèi)Typesofamplitudemodulationapproaches振幅調(diào)制信號(hào)Amplitudemodulatedsignals西安電子科技大學(xué)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(shí)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(wèn)題Keyproblemofamplitudemodulation失真來(lái)源

Sourceofdistortions減小失真的方法

Methodstoreducedistortions平衡對(duì)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(lèi)Typesofamplitudemodulationapproaches振幅調(diào)制信號(hào)Amplitudemodulatedsignals西安電子科技大學(xué)XidianUniversity繼續(xù)Continue一種比較重要和常見(jiàn)的減小失真的方法是平衡對(duì)消技術(shù)，這是本次課程最后要學(xué)習(xí)的內(nèi)容。Balancedcancellationisanimportantandusualmethodfordistortionreduction,whichwillbestudiedattheendofthislesson.我們從本次課程開(kāi)始學(xué)習(xí)振幅調(diào)制方法，這是第五章，振幅調(diào)制與解調(diào)的一個(gè)重要部分。Inthislesson,webegintolearnapproachesofamplitudemodulation,whichisanimportantportionofChapter5,Amplitudemodulationanddemodulation.為了解決失真問(wèn)題，我們接下來(lái)尋找失真的來(lái)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(guò)三個(gè)步驟來(lái)實(shí)現(xiàn)。Thenonlinear-deviceamplitudemodulationisperformedinthreesteps.首先，我們簡(jiǎn)要復(fù)習(xí)三種振幅調(diào)制信號(hào)，即普通調(diào)幅信號(hào)，雙邊帶調(diào)制信號(hào)和單邊帶調(diào)制信號(hào)。First,we’llbrieflyreviewthethreesignalsoutofamplitudemodulation,namely,theamplitudemodulatedsignal,thedouble-sidebandmodulatedsignal,andthesingle-sidebandmodulatedsignal.為了生成這些信號(hào)，我們進(jìn)行振幅調(diào)制時(shí)需要解決一個(gè)關(guān)鍵問(wèn)題，即調(diào)制信號(hào)與載波的相乘。Weneedtosolveakeyproblemintheamplitudemodulationtogeneratethesesignals,thatis,themultiplicationofthemodulatingsignalandthecarrierwave.感謝使用向?qū)?。首先，我們?jiǎn)略瀏覽本次課程的內(nèi)容和結(jié)構(gòu)。Thankyouforusingtheguide.Atfirst,let’sbrieflybrowsethecontentandstructureofthislesson.從分類(lèi)上看，有兩種基本方法可以解決該問(wèn)題，即非線性器件調(diào)幅和線性時(shí)變電路調(diào)幅。本次課程學(xué)習(xí)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(wèn)題，但又產(chǎn)生了新的失真問(wèn)題。Theabove-mentionedkeyproblemofamplitudemodulationissolvedbyusingnonlineardevices.However,thedistortionoccursasanewproblem.結(jié)束End目錄

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頁(yè)P(yáng)age1Chapter5Amplitudemodulationanddemodulation西安電子科技大學(xué)XidianUniversity普通調(diào)幅信號(hào)

Amplitudemodulatedsignal雙邊帶調(diào)制信號(hào)

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

u(t)=U

mcost載波

carrierwaveuC

(t)=U

Cmcos

Ct

C

C+

C－

CUmUCm繼續(xù)Continue經(jīng)過(guò)調(diào)制，得到的振幅調(diào)制信號(hào)可能包含三個(gè)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(kāi)始學(xué)習(xí)本次課程的內(nèi)容。進(jìn)行振幅調(diào)制的目的是把低頻的語(yǔ)音、圖象等調(diào)制信號(hào)寄載到高頻載波上，從而實(shí)現(xiàn)信息的遠(yuǎn)程無(wú)線傳輸。Now,let’sstartthelesson.Theamplitudemodulationisaimedatmountingthelow-frequencyaudioorvisualmodulatingsignalontoahigh-frequencycarrierwave,sothattheinformationcanbetransmittedwirelesslyatalongdistance.為簡(jiǎn)單起見(jiàn)，我們認(rèn)為調(diào)制信號(hào)和載波都是單頻信號(hào)。這里給出了它們的時(shí)域表達(dá)式。Forsimplicity,themodulatingsignalandthecarrierwavearesupposedtobesingle-frequencysignals.Thesearetheirtime-domainexpressions.在頻域上，調(diào)制信號(hào)和載波都可以用其角頻率和振幅表示。Themodulatingsignalandthecarrierwaveareexpressedinthefrequencydomainbyusingtheirangularfrequenciesandamplitudes.包含所有三個(gè)頻率分量的信號(hào)稱為普通調(diào)幅信號(hào)，只包含上邊頻分量和下邊頻分量的信號(hào)稱為雙邊帶調(diào)制信號(hào)，而單邊帶調(diào)制信號(hào)則只有上邊頻分量或下邊頻分量中的一個(gè)。Thesignalwithallthreefrequencycomponentsiscalledanamplitudemodulatedsignal.Thatonlywiththeupperandthelowerside-frequencycomponentsiscalledadouble-sidebandmodulatedsignal.Thesingle-sidebandmodulatedsignalhasonlyoneoftheside-frequencycomponents.結(jié)束End目錄

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頁(yè)P(yáng)age2Chapter5Amplitudemodulationanddemodulation振幅調(diào)制方法Amplitudemodulationapproaches非線性器件調(diào)幅Amplitudemodulationwithnonlineardevices線性時(shí)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(wèn)題

Keyproblemofamplitudemodulation時(shí)域：uC

uTimedomain:

uC

u西安電子科技大學(xué)XidianUniversity繼續(xù)Continue為了生成前面的三種振幅調(diào)制信號(hào)，進(jìn)行振幅調(diào)制時(shí)，在時(shí)域上要將調(diào)制信號(hào)和載波相乘，在頻域上看，這樣的相乘會(huì)生成上邊頻分量和下邊頻分量，這個(gè)關(guān)鍵問(wèn)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(jìn)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(chǎng)效應(yīng)管的非線性實(shí)現(xiàn)調(diào)幅，另一種是基于線性時(shí)變電路實(shí)現(xiàn)調(diào)幅。Therearetwotypesofamplitudemodulationapproachwiththeuseofnonlinearcircuits.Oneapproachistomakeusethenonlinearpropertyofactivedevices,suchasthetransistorandtheFET.Theotherapproachisbasedonlineartime-varyingcircuits.結(jié)束End目錄

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頁(yè)P(yáng)age3Chapter5Amplitudemodulationanddemodulation+++++++西安電子科技大學(xué)XidianUniversity繼續(xù)Continueube

(t)經(jīng)過(guò)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(lái)，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(shí)際上給出了一個(gè)放大器電路。首先，載波uC

(t)和調(diào)制信號(hào)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(hào)uAM

(t)。Finally,iC

(t)flowsthroughthefrequency-selectingLCparallelresonantcircuit,andproducesanamplitudemodulatedsignaluAM

(t).現(xiàn)在我們學(xué)習(xí)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(yè)P(yáng)age4Chapter5AmplitudemodulationanddemodulationtuC(t)0tu(t)0tube(t)0步驟[1]載波和調(diào)制信號(hào)相加產(chǎn)生輸入電壓Addingupthecarrierwaveandthemodulatingsignaltoproducetheinputvoltage+++++西安電子科技大學(xué)XidianUniversity繼續(xù)Continue前面簡(jiǎn)要描述了非線性器件調(diào)幅的過(guò)程，在此基礎(chǔ)上，我們接下來(lái)觀察并研究該過(guò)程中一些值得注意的細(xì)節(jié)。非線性器件調(diào)幅的原理電路可以分解為輸入級(jí)回路，晶體管和輸出級(jí)回路三部分，每部分各自完成振幅調(diào)制過(guò)程的一個(gè)步驟。Theprocessofthenonlinear-deviceamplitudemodulationhasbeenbrieflydescribed,basedonwhich,wenowcometoobserveandstudysomedetailsintheprocess.Thebasiccircuitcanbedecomposedintothreeparts,namely,theinputloop,thetransistor,andtheoutputloop.Eachpartofthecircuitperformsonestepoftheamplitudemodulation.現(xiàn)在我們實(shí)時(shí)觀察

uC

(t)，u(t)和

ube

(t)的波形。注意載波的頻率遠(yuǎn)大于調(diào)制信號(hào)的頻率，而其振幅也大于調(diào)制信號(hào)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(hào)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(gè)步驟。這是在輸入級(jí)回路中完成的，載波

uC

(t)和調(diào)制信號(hào)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(yè)P(yáng)age5Chapter5Amplitudemodulationanddemodulation步驟[2]非線性器件產(chǎn)生輸出電流Thenonlineardevicegeneratestheoutputcurrent+西安電子科技大學(xué)XidianUniversity繼續(xù)Continue我們現(xiàn)在把第一個(gè)點(diǎn)垂直投影到轉(zhuǎn)移特性曲線上。Now,weverticallyprojectthefirstpointontothetransfercharacteristiccurve.對(duì)uBE(t)中的每個(gè)點(diǎn)都進(jìn)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(guò)程中，我們可以發(fā)現(xiàn)，晶體管的非線性，更確切地說(shuō)，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(gè)點(diǎn)，接下來(lái)觀察這些點(diǎn)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(lái)把該點(diǎn)水平投影到iC

(t)圖中該點(diǎn)對(duì)應(yīng)的時(shí)刻。Next,wepojectthepointhorizontallyontoitscorrespondinginstantintheiC

(t)diagram.借助于該特性曲線，我們可以通過(guò)投影方式從uBE

(t)的波形畫(huà)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(gè)點(diǎn)。Therefore,onepointontheiC

(t)waveformisobtained.如果將波形放大，我們會(huì)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(lái)，我們看第二個(gè)步驟。這是在晶體管中完成的，交流輸入電壓

ube

(t)經(jīng)過(guò)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(yè)P(yáng)age5Chapter5Amplitudemodulationanddemodulation+++++西安電子科技大學(xué)XidianUniversity繼續(xù)Continue為了對(duì)iC

進(jìn)行分析，我們將其近似表示成前三項(xiàng)級(jí)數(shù)和。利用已知的

ube，uC

和u的表達(dá)式，我們可以得到iC

的一個(gè)具體結(jié)果。InordertoanalyzeiC

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

(t)中含有uBE

(t)中沒(méi)有的新的頻率分量，下面我們通過(guò)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(jí)回路，我們還可以寫(xiě)出晶體管輸入電壓uBE(t)。WecanalsowritedownuBE(t),theinputvoltageofthetransistor,referringtotheinputloopofthebasiccircuitdiagram.這里，我們把iC

展開(kāi)成泰勒級(jí)數(shù)，展開(kāi)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(jí)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(yè)P(yáng)age6Chapter5Amplitudemodulationanddemodulation步驟[3]濾波產(chǎn)生已調(diào)波Producethemodulatedwavebyfiltering++IC()0

西安電子科技大學(xué)XidianUniversity中間三項(xiàng)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(huà)出該頻率分量。Wedrawthiscomponentinthefrequencydomainaccordingtoitsangularfrequencyandamplitude.現(xiàn)在畫(huà)出該頻率分量。Now,wedrawthiscomponent.最后一項(xiàng)的角頻率為2

C。Thelastitemhasanangularfrequencyof2

C.我們也畫(huà)出該頻率分量。Wedrawthiscomponenttoo.這三個(gè)頻率分量對(duì)我們是有用的。Thesethreecomponentsareusefulforus.這樣我們就可以方便地畫(huà)出iC

的頻譜，從而由前面的時(shí)域分析過(guò)渡到后面的頻域分析。SowecaneasilyplotthespectrumofiC,andadvancefromtheprevioustime-domainanalysistothefollowingfrequency-domainanalysis.現(xiàn)在，我們來(lái)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(guò)整理，可以寫(xiě)成其各個(gè)頻率分量疊加的形式。Wenowcometothethirdstepofthenonlinear-deviceamplitudemodulation.ThepreviouslyderivediCisreorganizedandwrittendownhereintheadditionformofitsvariousfrequencycomponents.現(xiàn)在畫(huà)出該分量。Now,let’sdrawthiscomponent.表達(dá)式的第一項(xiàng)是直流分量。

Thefirstitemintheexpressionisadirectcomponent.第二項(xiàng)是角頻率為的分量。

Theseconditemisacomponentwiththefrequencyof.第三項(xiàng)是角頻率為2的分量。

Thethirditemisacomponentwiththefrequencyof2.進(jìn)行濾波，就可以得到普通調(diào)幅信號(hào)。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(yè)P(yáng)age6Chapter5Amplitudemodulationanddemodulation步驟[3]濾波產(chǎn)生已調(diào)波Producethemodulatedwavebyfiltering++IC()0

西安電子科技大學(xué)XidianUniversity繼續(xù)Continue我們把這些頻率分量寫(xiě)到新的位置。Let’swritethesecomponentsatnewpositions.下面，為了說(shuō)明濾波過(guò)程，我們?cè)跁r(shí)域和頻域只保留下

iC

的這三個(gè)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(yè)P(yáng)age6Chapter5Amplitudemodulationanddemodulation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(xué)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(hào)是電壓，所以需要使晶體管的輸出電流iC

流過(guò)一個(gè)支路，該支路只對(duì)iC

中這三個(gè)頻率分量產(chǎn)生有效的電壓輸出，而不對(duì)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(jì)就是LC并聯(lián)諧振回路。Theimpedanceofsuchabranchcircuitshouldhaveaband-passamplitude-frequencycharacteristic.ThemosttypicaldesignistheLCparallelresonantcircuit.我們可以參照這三個(gè)有用頻率分量的頻譜畫(huà)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(yè)P(yáng)age6Chapter5Amplitudemodulationanddemodulation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(xué)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(gè)頻率分量當(dāng)中，載頻分量流經(jīng)LC并聯(lián)諧振回路時(shí)，遇到的電阻為R

eo，生成電壓時(shí)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(gè)普通調(diào)幅信號(hào)。Atlast,thethreeportionsofvoltageareaddedupandanamplitudemodulatedsignalisproduced.上邊頻分量流經(jīng)LC并聯(lián)諧振回路時(shí)，遇到的電阻為0.707R

eo，生成電壓時(shí)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(shí)，遇到的電阻為0.707R

eo，生成電壓時(shí)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(yè)P(yáng)age6電子工程學(xué)院SchoolofElectronicEngineering第五章振幅調(diào)制與解調(diào)第6

頁(yè)P(yáng)age6Chapter5Amplitudemodulationanddemodulation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(xué)XidianUniversity繼續(xù)Continue我們還可以進(jìn)一步寫(xiě)出uAM(t)的標(biāo)準(zhǔn)形式。WemayfurtherwriteuAM(t)initsstandardform.接下來(lái)，我們對(duì)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(guò)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(yè)P(yáng)age7Chapter5Amplitudemodulationanddemodulation非線性器件調(diào)幅失真Distortionsofamplitudemodulationbynonlineardevices失真來(lái)源Sourceofdistortions高階項(xiàng)Higher-ordertermsIC()0

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

的表達(dá)式還應(yīng)該包括后面這些高階項(xiàng)。Rigorouslyspeaking,theexpressionofiCshouldincludethefollowinghigher-orderterms.這些高階項(xiàng)也可以具體寫(xiě)成多個(gè)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(xiàng)泰勒級(jí)數(shù)近似表示的iC

的頻譜上。Also,thesehigher-ordertermscanbedetailedasthesummationofmanyfrequencycomponents.ThespectrumofthesenewcomponentsaretobeaddeduptothatoftheiCpreviouslyapproximatedbythefirstthreeTaylorseries.這三個(gè)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?cè)斐砂j(luò)失真。ThesethreecomponentsaresuperpositionedinfrequencyontothepreviouslyobtainedusefulcomponentsofiC.Theyleadtotheenvelopedistortion.如果濾波器的帶寬足夠大，則邊上這兩個(gè)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(jí)數(shù)展開(kāi)式的前三項(xiàng)來(lái)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(yè)P(yáng)age8Chapter5Amplitudemodulationanddemodulation減小失真的方法Methodstoreducedistortions方法[3]Methodthree:采用平衡對(duì)消

Applybalancedcancellation西安電子科技大學(xué)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(xiàng)，平方率器件的輸出電流的泰勒展開(kāi)式只到二次平方項(xiàng)為止，沒(méi)有高階項(xiàng)，因此用它們作有源器件時(shí)就可以從根本上消除失真。Thedistortionsoriginatefromthehigher-ordertermsofiC.Thesquare-lawdevicesproducetheoutputcurrentwhoseTaylorexpansionseriesterminateatthesquaretermwithnoadditionalhigher-orderterms.Usedastheactivedevice,theycanfundamentallyeliminatethedistortions.高階項(xiàng)中，ube

的冪n

取值較大，因此如果我們減小ube，則高階項(xiàng)會(huì)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(guò)改進(jìn)電路來(lái)處理失真問(wèn)題，方法之一是采用平衡對(duì)消的電路設(shè)計(jì)。Wemayalsoimprovethecircuitstotacklethedistortionproblem.Thebalanced-cancellationcircuitisonesolution.現(xiàn)在我們接著討論可以采取哪些方法來(lái)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(yè)P(yáng)age9Chapter5Amplitudemodulationanddemodulation平衡對(duì)消

Balancedcancellation西安電子科技大學(xué)XidianUniversity繼續(xù)Continue從原理上看，平衡對(duì)消是通過(guò)多路輸入－輸出電路實(shí)現(xiàn)的，當(dāng)輸出的多路電流疊加時(shí)，大多數(shù)會(huì)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(jí)數(shù)展開(kāi)式，我們可以寫(xiě)出一個(gè)四路輸入－輸出的平衡對(duì)消電路的表達(dá)式。在四路輸入中，交流輸入電壓由載波uC

和調(diào)制信號(hào)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(yè)P(yáng)age9Chapter5Amplitudemodulationanddemodulation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(xué)XidianUniversity繼續(xù)Continue接下來(lái)，我們把iC1，iC2，iC3

和iC4

用其泰勒展開(kāi)式的前五項(xiàng)級(jí)數(shù)來(lái)近似。Next,weusethefirstfiveseriesoftheTaylorexpansiontoapproximateiC1,iC2,iC3,andiC4.這里的平衡對(duì)消過(guò)程通過(guò)三個(gè)步驟進(jìn)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(gè)過(guò)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(lái)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