adc 采样交流信号计算有效值误差

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1、⬉ᄤ⌟䞣ϢҾ఼ᄺ᡹2008ᑈ๲ߞ䞛ḋ䅵ㅫᮍ⊩⌟䞣Ѹ⌕⬉य़᳝ᬜؐ䇃Ꮒߚᵤहྱѐ˄࣫Ҁϰᮍ䅵䞣⌟䆩ᡔᴃⷨお᠔ˈ࣫Ҁ100086˅ᨬ㽕˖ߚᵤњ߽⫼䞛ḋ䅵ㅫᮍ⊩⌟䞣Ѹ⌕ো᳝ᬜؐⱘЏ㽕䇃Ꮒ಴㋴DŽᇍѢ䅵ㅫᮍ⊩ǃ਼ᳳ䇃ᏂǃA/D䕀ᤶ఼䞣࣪䇃Ꮒ੠A/D䕀ᤶ఼⿃ߚ䴲㒓ᗻ䇃Ꮒ䖭ಯ⾡Џ㽕ⱘ䇃Ꮒᴹ⑤བԩᕅડ⬉य़᳝ᬜؐ⌟䞣㒧ᵰ䖯㸠њᅮ䞣ߚᵤˈ೼ᅲ䰙ᑨ⫼ⱘ䖛⿟Ёৃҹ᳝䩜ᇍᗻⱘ䞛প᥾ᮑᴹޣᇣ䇃Ꮒ಴㋴ᇍ⌟䞣㒧ᵰⱘᕅડDŽ݇䬂䆡˖䞛ḋ䅵ㅫ˗᳝ᬜؐ˗䇃ᏂߚᵤErrorAnalysisofSamplingComputationMethodforRMSMeasurementLIYicheng(Beijing

2、OrientInstituteofMeasurement&Test,Beijing100086,China)Abstract:Theerrorgenesis,measuringeffectivevalueofACsignalwithsamplingcomputationmethod,isanalyzedinthispaper.Fourprimarygeneses,includingcomputationalgorithm,measurementerrorsinnon-synchronous,quantizationerrorsofanaloguedigitalcon

3、verter(ADC),integralnonlinearityerrorsofADC,arediscussed;meanwhile,expressionsaregiveninthispaper.Theresultmaybetakenasareferenceforminimizinginfluencecausedbysucherrors.Keywords:samplingcomputation;effectivevalue;erroranalysisѸ⌕⬉य़᳝ᬜؐⱘ⌟䞣ᮍ⊩᳝ᕜ໮⾡ˈᇍѢԢⶀᯊؐDŽ䗮ᐌᡞ⬅˄1˅ᓣ᠔⹂ᅮⱘ⬉य़᳝ᬜؐ⿄乥ҹঞ䍙Ԣ乥ো⬉य़᳝ᬜؐⱘ⌟䞣ˈⳂ

4、ࠡ↨䕗ᐌПЎ㹿⌟⬉य़u(t)ⱘⳳ᳝ᬜؐDŽ⫼ⱘᰃ෎Ѣ䞛ḋ䅵ㅫⱘ⌟䞣ᮍ⊩DŽ䖭Џ㽕ᰃ಴Ў⫼೼᭄ᄫ࣪⌟䞣㋏㒳Ёˈ佪ܜ㽕ḍ᥂䞛ḋᅮ⧚ᇍᐌ㾘ⱘ⌟䞣ᮍ⊩੠῵ᢳᡔᴃϡԚ㽕∖⌟䞣Ҿ㸼ᴀu(t)䖯㸠ㄝ䯈䱨䞛ḋˈ㦋ᕫϔϾᯊ䯈⾏ᬷোᑣ߫䑿݋᳝ᵕ催ⱘ〇ᅮᗻˈ㗠ϨҾ㸼ᵕ䭓ⱘડᑨᯊ䯈੠ৢؐᬜ᳝ⳳⱘ)t(u∖ᴹߚ⿃᭄ؐ䖛䗮ݡˈ㢹ᇍϞ䗄ϡড়⧚ⱘ⬉䏃ܗӊখ᭄Փᕫ⌟䞣೼ᶤѯഎড়ᕜ䲒u(t)ো೼ϔϾো਼ᳳTݙҹDt=T/Nㄝ䯈䱨ᅲ⦄DŽ䞛ḋ䅵ㅫⱘ⌟䞣ᮍ⊩ܟ᳡䖭ѯӴ㒳ϡ߽಴㋴䞛ḋN⚍ˈᕫࠄϔϾ⾏ᬷোᑣ߫˖ⱘৠᯊгѻ⫳њᮄⱘ䯂乬ˈߚᵤ䇃Ꮒ಴㋴ᇍ⌟䞣㒧U(n)=u(n∂Dt),(n=,2,1,0∂∂∂,N-)1(

5、2)ᵰⱘᕅડᮍᓣˈህ㛑໳೼ᅲ䰙⌟䞣ᯊ᳈᳝ᬜⱘ䙓ܡ䖭ѯ಴㋴ⱘᕅડˈ᳝߽Ѣޣᇣ⌟䞣ⱘϡ⹂ᅮᑺDŽᴀ߭˄1˅ᓣЁⱘ⿃ߚᓣ䞛⫼ϡৠⱘ᭄ؐ∖⿃݀ᓣৢ᭛ᇍᕅડ䞛ḋ䅵ㅫᮍ⊩ⱘЏ㽕䇃Ꮒ಴㋴䖯㸠њᅮৃҹ㦋ᕫ⬉य़ⳳ᳝ᬜؐⱘϡৠㅫ⊩DŽ䞣ߚᵤDŽ]1[བᵰҹ᭄ؐ⿃ߚЁⱘẃᔶ݀ᓣ1䅵ㅫᮍ⊩ⱘᕅડbb-a³f(x)dxö[f(a)+f(b)](3)a2ḍ᥂᳝ᬜؐⱘᅮНˈ೼ϔϾো਼ᳳݙˈ䗮䖛ᡞu(t)ᣝᯊ䯈തᷛߦߚЎNㄝߚˈ↣ϔㄝߚⱘ䖍⬠ᶤ㒃䰏䋳䕑᠔ѻ⫳ⱘ⛁䞣ϢϔϾⳈ⌕⬉य़೼ৠϔؐህᰃ˄2˅ᓣ᠔⼎ⱘ䞛ḋ⚍U(n)DŽ㢹⬅Ⳍ䚏ϸϾ䋳䕑Ϟѻ⫳ⱘ⛁䞣Ⳍㄝᯊˈ䆹Ⳉ⌕⬉य़ⱘ᭄ؐህᰃ䞛ḋ⚍ⱘ䖲㒓ǃҪӀߚ߿Ϣᯊ䯈䕈

6、ⱘൖ㒓ǃ䞛ḋ⚍Ѹ⌕⬉य़ⱘ᳝ᬜؐDŽ᭄ᄺ㸼䖒ᓣབᓣ˄1˅᠔⼎˖䯈ⱘᯊ䯈䕈ᵘ៤ϔϾẃᔶˈ߭ৃ㒘៤NϾẃᔶDŽᇍҪӀ䞡໡Փ⫼˄3˅ᓣৃᕫࠄ໡࣪ẃᔶ∖⿃݀ᓣDŽ1T2U=u(t)dt(1)݊⬉य़ⳳ᳝ᬜؐЎ˖rms³T0N-11Dt22˄1˅ᓣЁⱘTᰃѸ⌕োⱘ਼ᳳˈu(t)Ў⬉य़Urmsö∂∂ƒ[U(n)+U(n+1)](4)T2n=062⬉ᄤ⌟䞣ϢҾ఼ᄺ᡹2008ᑈ๲ߞ⬅Ѣu(t)ᰃ਼ᳳোˈᇚU(N)=U(0)ҷܹ˄4˅ᵰ᳝ӬѢ0.01%ⱘޚ⹂ᑺDŽᓣᑊ㒣䖛ㅔ࣪ˈৃҹᕫࠄѢᖂ໘⧚఼ᅲ⦄ⱘ݀ᓣ˖2਼ᳳ䇃ᏂⱘᕅડN-112UrmsöƒU(n)(5)Ңᓣ˄5˅ᕫࠄⱘ䖛⿟ৃҹⳟߎˈབᵰ㽕ᣝ

7、✻Nn=0ℸᓣ䖯㸠䞛ḋ䅵ㅫ߭䳔⒵䎇U(N)=U(0)ˈे㹿⌟䞛⫼໡࣪ẃᔶ∖⿃݀ᓣᴹ䅵ㅫ⬉य़᳝ᬜؐᯊˈোⱘ਼ᳳᘏᰃৃҹ㹿䞛ḋ乥⥛NㄝߚⱘDŽԚᰃˈ⬅ᰃ⬅੠ᓣᴹҷ᳓⿃ߚˈϡৃ䙓ܡⱘӮѻ⫳⿃ߚԭѢ䞛ḋᯊ䩳ⱘ乥⥛ᰃϔᅮⱘˈ㗠Ϩϡৃ㛑᮴䰤ࠊⱘ乍DŽḍ᥂໡࣪ẃᔶ݀ᓣⱘ䇃ᏂԄ䅵া᳝ᔧDtç0催ˈ䙷Мህϡৃ㛑↣⃵䞛ḋ䛑⒵䎇ㅔ࣪ᯊⱘᴵӊDŽेNçÑᯊˈ⿃ߚԭ乍ᠡ㛑䍟䖥Ѣ0ˈ㗠䖭ϔᴵ؛䆒䞛ḋ䯈䱨ЎDtᓻᑺˈϔϾ਼ᳳݙ䞛ḋ⚍᭄Ўӊ೼⦄ᅲⱘ⌟䞣䖛⿟Ёᰃϡৃ㛑⒵䎇ⱘDŽ᠔ҹ㽕ߚNˈ䙷МD=T-N∂DtᑊϡᘏᰃЎ䳊ˈ៪㗙䇈ᘏᵤ䞛ḋ⚍᭄ᇍ᳔㒜⌟䞣㒧ᵰⱘᕅડˈḍ᥂⌟䞣ϡ⹂ᰃϡЎ䳊ˈ݊ЁDህ⿄԰਼ᳳ䇃Ꮒ