ଽᑖϷέُ፡ᡐᏢ೩ॎПݲϞंـ
ݓס݂! ೨Мᎃ
ҳᄔϽৱጒσᏰώཾఀىᏰف
ᄢ! ौ
ႆၷоЅߨጣܒᐇհ࣏೩ॎଽᑖϷέُ፡ᡐᏢॶሯՃኌޟڍএкौ୰
ᚠȄ༈ಛΰȂ፡ᡐᏢ೩ॎޱӑӫԙ࢜ᄺϾޟᘮݰᏢᙽಋڒኵЙȄծԪᆍ Пݲܾܻҡྖ՝ȃϚᛧۡȃᇄଟၯ߽ኵᜲоᄂ౪้ીᘈȄӵҏ፣МϛȂרঈ ඪюΟΙৈԤਝޟ೩ॎଽᑖϷέُ፡ᡐᏢޟࢺแᇄПݲȂԪ೩ॎПݲоӫԙ ϞᘮݰᏢᙽಋڒኵ࣏ߑۖనӇپӫԙ፡ᡐᏢᙽಋڒኵȄငҥ߽ኵШᄇᇄਮ፡
ȂӵᏑ໔ؑுၶଽϞଉဴᚕଉШЅޢࢺᒯΣጒ൜ՄάϚѶᛧۡޟݷήȂ
࡞פӴؑு߽ኵԻϷШၶωϞଟၯ߽ኵȄᔣ๖ݎᡗҰȂҏПݲܚ೩ॎюޟ
፡ᡐᏢӵଟၯ߽ኵШȃଉဴᚕଉШȃЅޢࢺᒯΣጒ൜้П७ࣱၶ༈ಛПݲᇄ࢜
ᄺԤԁޟ๖ݎȄ
ᜰᗤຠȈ ଽᑖϷέُ፡ᡐᏢȃଟၯ߽ኵШȃଉဴᚕଉШȃޢࢺᒯΣጒ൜Ȅ
DESIGN METHODOLOGY FOR THE DESIGN OF HIGH ORDER SIGMA-DELTA MODULATORS
Zhi-Ming Lin! Wen-Huei Sheu
Department of Industrial Education National Changhua University of Education
Changhua, Taiwan 500, R. O. C.
Key Words: high-order sigma-delta modulator, coefficient ratio, SNR, DC input range.
ABSTRACT
Overloading and non-linear operation are the two major problems in the design of high order sigma-delta modulators. Traditionally, designers design modulators based on synthesizing the transfer function of a struc- ture-matched filter. This kind of design process is vulnerable to over- loading and instability, and quite often obtains unrealizable circuit coeffi- cients. In this paper, we present an efficient design method for the design of high order sigma-delta modulator. The proposed method uses the transfer function of the structure-matched filter as an initial solution to synthesize the transfer function of the modulator. By using the mapping and scaling techniques, the method is able to obtain loop coefficients with low coefficient ratio. The goal of mapping and scaling is to increase the value of signal-to-noise ratio and the dc input range of modulator without causing instability. Simulation result shows that the proposed method ob- tained better coefficient ratio, higher signal-to-noise ratio, and wider dc in- put range than that of the conventional methods and structures.
ʾˀ ˬʻ̍ʼˬʻ̍ʼˬʻ̍ʼˬʻ̍ʼ
̈ʻ̍ʼ
̈ʻ̍ʼ
̈ʻ̍ʼ
̈ʻ̍ʼ Hn ʾ H3 ʾ H2 ʾ H1
˴˴˴˴́́́́ ˴˴˴˴˄˄˄˄
ʾ ˀ
˵˵˵˵́́́́ ˵˵˵˵ˆˆˆˆ ˵˵˵˵˅˅˅˅ ˵˵˵˵˄˄˄˄
ʾ ˀ
ˀ ˀ ˀ ˀ
˵˵˵˵́ˀ˄́ˀ˄́ˀ˄́ˀ˄
Ιȃࠉ! ِ
ӵ౪ф຺σᑖᡝႫၯޟኵ՝߬ဴ౩ϛȂШ- ኵ՝ᙽᏢȞA/D converter; ADCȟϐϚџܖીޟ१ौϯ ӇȂӰ࣏Ѻᜰ߽ᐌএفಛޟᆠ࡙Ѕഀ࡙Ȃᐌӫᑖ ᡝႫၯӵӣΙ༵වаޟᜰᗤϞΙ[1]ȇӵ༈ಛޟ A/D ᙽᏢ ϛȂࠉޟШ߬ဴ౩Ꮲ࣏ІҺᜦȞanti-aliasingȟᘮݰ ᏢȂᒯΣ߬ဴོӑငႆІҺᜦᘮݰᏢپ३ڙᓜளቶȂՄᒯ ю߬ဴӔငႆѻ࠸ЪᓜȞNyquist frequencyȟήᐇհޟڥ ኺ-߳ࡻȞsample-and-holdȟႫၯᇄ໔ϽհҢޟ໔ϽᏢЅጡ ጆᏢپᙽ࣏ኵ՝߬ဴȄծҥܻڥኺ-߳ࡻႫၯЅ໔ϽᏢ
឴ܻШႫၯ࢜ᄺȂڏᄇܻႫၯϯӇޟᆠแ࡙ौؑၶ ଽȂՄиζौҢၶ࣏ፒᚕޟШႫၯಢӫϗႀڗيԁޟ ໔ϽਝݎȇِϞȂ࣏Οौႀڗၶଽޟ၌ݙ࡙Ȃרঈሯौ
ၶፒᚕޟІҺᜦᘮݰᏢЅӻ՝ϯޟ໔ϽᏢȂծШϯӇޟ ᆠ࡙оЅႫၯϯӇޟϾแ࡙ࠓᝒ१ኇفಛޟਝ
[2]Ȅ
ᑖϷέُ፡ᡐᏢ A/D ᙽႫၯޟശσᓺᘈ൷ѫौቨ ёΙٲኵ՝ႫၯȂ൷σσЍفಛᄇᆠծάፒᚕޟ
ШႫၯޟሯؑՄᕕுྥጂޟኵ՝-Шᙽਝݎ[3]Ȃყ 1 ܚҰ࣏ΙᑖϷέُ ADC ޟفಛᙽП༵ყȄҥყϛרঈ џоޣၾѺҥᖂڷܹσᏢȞsumming amplifierȟȃᑖϷᏢ ȞintegratorȟȃШၶᏢȞcomparatorȟȃᇄ 1-bit D/A ᙽᏢ ܚᄺԙޟȄڏᐇհন౩࣏ӱ௲߬ဴᇄᒯΣ߬ဴོӵёᖂܹ
σᏢҡΙᇲ৯߬ဴȂԪᇲ৯߬ဴӵᑖϷᏢޟճᘮݰհ ҢࡣȂആႆШၶᏢپ໔ก߬ဴ৯ޟྥ՝Ȃ࿋ᒯΣ߬ဴࣱ
࣏ႭޟݷήȂШၶᏢޟᒯюߝਢޟȶ0ȷ߬ဴȇ࿋
ᒯΣ߬ဴ࣏ཌ໔ޟω߬ဴਢȂࠌौငႆӻԩޟώհ໊ϗ
ٺШၶᏢޟᒯю࣏ȶ1ȷ߬ဴȇՄ࿋ᒯΣ࣏Ιএᅖ
Ȟfull-scaleȟޟ߬ဴσωਢȂᑖϷᏢפഀޟшܹႫՄٺ ШၶᏢޟᒯюҡ៉ޟȶ0ȷᇄȶ1ȷ߬ဴȂِܾϞȂᒯ Σޟ߬ဴཕσȂШၶᏢޟᒯюོҡၶσԻϷШޟȶ1ȷ
߬ဴȄ
ौᕕுଽ၌ݙ࡙ޟᑖϷέُ፡ᡐᏢȂலџҥήӖڍ এПԒЙ[4,5]ȈΙ௴ҢႆڥኺȂ։ඪଽڥኺᓜ
ȇΠ࣏ඪଽ፡ᡐᏢޟኵȄலࡣޱШࠉޱԤਝȇծ ӵଽ፡ᡐᏢϛϫԤ೨ӻኇفಛਝޟᡐኵȂԃଽߨ ጣܒᐇհȃ՛ᑖϷᏢޟএኵᇄᑖϷᏢᒯюႹڷȃܖޢ ࢺᒯΣڧڗ३ڙ้้ሯёоՃኌȂМϛרঈоყ 2 ޟ ӻ१ӱ௲ଟၯȞmultiple feedbackȟ፡ᡐᏢ࢜ᄺ[6,7]࣏அ ᙃȂଆኇ፡ᡐᏢᛧ࡙ۡޟᡐӰоЅӨᡐኵᄇܻᐌএ፡
ᡐᏢفಛޟኇȂרঈٮඪюΙৈ೩ॎ፡ᡐᏢޟ೩ॎࢺ แȂԪ೩ॎࢺแџоΙٲԆӵܻଽفಛϛޟીᘈȂ ԃ፡ᡐᏢܾܻϚᛧۡȃܾܻྖ՝ᇄޢࢺᒯΣϚଽڷଟၯ
߽ኵԻϷШЊωՄϚܾհႫၯᄂ౪ޟીᘈȇӵႫၯᄂ౪ ΰȂרঈᄇܻୋኵޟ፡ᡐᏢفಛζඪюΟΙৈϽᙏጣၯ ޟПݲپЍӓਏଟၯ೩ॎਢޟፒᚕ࡙ȇרঈବᄇέ
ყ 1! ᑖϷέُ፡ᡐᏢϞ A/D ᙽП༵ყ
ყ 2! ӻ१ӱ㕞Ԓ࢜ᄺޟ፡ᡐᏢ
ՍϤޟӻ१ӱ௲ଟၯپ၏ёଆӓਏӱ௲ଟၯᄇܻفಛ ਝޟኇȇശࡣȂᙤҥኵᏰԒυޟᙽȂרঈџо࡞ৠ
ܾӴ N ճ፡ᡐᏢᙽ࣏ 2N ޟள፡ᡐᏢȂٮᒯ юڏᓜᜊپᢎᄆڏ࣏ԒȄ
Πȃଽ፡ᡐᏢ೩ॎՃ໔
ԤڍᆍٺҢӵᚔඹਢᄂ౪ޟᑖϷᏢڒኵȂϷտ឴
ܻ۽ᒶޟөࠉЎܜȞforward Eulerȟᇄ឴ܻߨ۽ᒶޟ өࡣЎܜȞbackward EulerȟڍᆍᑖϷᏢלԒȄΙ፡ᡐᏢ ڏᙽಋڒኵޟߒҰԒ࣏
) ( ) 1 ( ) ( )
(z z 1 X z z 1 E z
Y = − ⋅ + − − ⋅ (1)
ڏϛ E(z)࣏໔ϽᚕଉȂڏᚕଉᐌӰશ࣏Ȟ1ɯz-1ȟȂᚕଉ ᐌӰኵޟԩཕଽཕفಛޟਝȂӵଽޟᑖϷ έُ፡ᡐᏢϛல՛ӻޟᑖϷᏢپᕕுၶٹޟᚕଉ ᐌਝݎȄଽ፡ᡐᏢޟᙽಋڒኵޟߒҰԒџජक़ԃήȈ
) ( ) 1 ( ) ( )
(z z 1 X z z 1 E z
Y = − ⋅ + − − k⋅ (2) ڏϛ(1−z )−1 kάᆎ࣏፡ᡐᏢޟᚕଉᙽಋڒኵȞnoise-transfer
function; NTFȟȂҢپߒҰᒯю߬ဴϛᚕଉܚլޟШٽȂՄ ԃݎװz=ejωфΣԒ(1−z )−1 kϛȂרঈџоுޣڏ࣏Ιଽ
ᔖޟ࣏ԒȂٮџҥԒϛџоுޣȂ፡ᡐᏢޟ໔Ͻ ᚕଉӵ߬ဴᓜቶϱԤߨலσޟ૾Ȃζ൷ᇳȂᓜቶϱ ޟᚕଉђೝڙڗശճȂՄٺுӵӣኺڥኺᓜޟన ӇήȂଽ፡ᡐᏢᕕுၶٹޟ၌ݙ࡙ȄณՄȂᛧ࡙ۡல
ଽ፡ᡐᏢϛޟ१σ୰ᚠ[8, 9]Ȃҥܻ՛ӻޟᑖϷᏢ ٺுفಛܻᑖϷᏢڎσ߬ဴᇄճᓜᎪᕝޟݷȂᑖϷ ᏢޟᒯюႫᔆᗘቨՄഅԙߨጣܒޟᐇհޑᄘȂӰԪϚᛧۡ
ޟߨጣܒݷலଽفಛޟ೩ॎ౭ᓛȄ
ଽ՛Ԓ࢜ᄺȞcascade architectureȟலҢپպ݈ᛧ
࡙ۡޟ୰ᚠȄӻ१ଟၯӱ௲Ԓ࢜ᄺϛޟӻ१ӱ௲ଟၯ biᗶ
ʾ
˄ˀۯցᑇۯ ᣊֺ᠏ངᕴ
ៀंᕴᑇۯ
˫ʻ̍ʼ
˫ʻ̍ʼ
˫ʻ̍ʼ
˫ʻ̍ʼ ˬʻ̍ʼˬʻ̍ʼˬʻ̍ʼˬʻ̍ʼ
ᗨ։ᕴ ֺለᕴ
ᓳ᧢ᕴ ʾ
−
ყ 3! ᑖϷέُ፡ᡐᏢ೩ॎࢺแყ
ณџоЍ߬ဴڥኺਢޟᇲ৯Ȃծીᘈ࿋ᒯΣ߬ဴྥ՝
ωܻᛧۡᐇհጒ൜ਢȂ፡ᡐᏢϛؐΙᑖϷᏢޟᒯюོ
ЍՄٺுӵင६ᓜᏢհҢࡣޟᒯю߬ဴᓜᜊོШনپғல ᐇհጒ൜ϱޟ࣏ω[4]ȇѪΙᆍலٺҢپᛧ࡙ۡ୰ᚠ ޟࠉ㕞ԒȞfeedforward typeȟ࢜ᄺ፡ᡐᏢȂծԪᆍ࢜ᄺ ޟીᘈ҆ωЖӴ३ڙᒯΣ߬ဴσωоᗗջᒯю߬ဴޟ Ѷઍ[9]Ȅٲ࢜ᄺϛϞଟၯ߽ኵᄂሬΰܚфߒޟϸႫ ৠȞswitch capacitorȟϛႫৠޟШȂଟၯ߽ኵԻϷШ ࠌۡဎ࣏߽ኵശσᇄശωޟШȂ൷Ⴋၯޟᄂ౪ᜲܾแ࡙
ՄِȂ߽ኵԻϷШູσႫၯູϚৠܾᄂ౪Ȅ
רঈоඁএПөپᇳ݂ӵ౪ԤଽᑖϷέُ፡ᡐᏢϛ லԆӵޟીᘈоЅרঈԃդᄇԪёо໌ȂശࡣӔᇳ݂ר ঈܚඪюޟ೩ॎࢺแᇄПݲȈ
1.ҥ࢜ᄺՄِ
ᏰޱҀܜȞBurraȟЅܚඪѻȞSodiniȟܚඪ࢜ᄺܚᒵ ڥޟଟၯ߽ኵԤ߽ኵԻϷШЊωՄᜲоᄂ౪ϞဲȂՄଽ
፡ᡐᏢһџ७ᖝ߽ኵϾޟ୰ᚠȂӰԪרঈඪюΙৈᒵ ڥଽ፡ᡐᏢଟၯ߽ኵޟၐᒿࢺแȂҬޟौӵϚኇ፡
ᡐᏢᐇհᛧۡޟݷήுڗ߽ኵԻϷШၶωޟଟၯ߽ኵ
Ȅ
2.൷೩ॎПݲՄِ
ӵרঈޟၐᒿࢺแϛרঈΙૡலٺҢᘮݰᏢלԒޟ ᙽಋڒኵ࿋࣏ϐޣޟߑۖనӇȂӔپᇄيႫၯᙽಋڒኵ ϛޟҐޣ߽ኵհШᄇȂՄܻଟၯ߽ኵޟШᄇႆแϛȂרঈ ӑӵࡾۡጒ൜ 0ʂ1 ϛᄇܻᓜᔖᡐଢ଼ኇϚσޟ߽
ኵႱ೩ڏߑۖȂһ։ӵԪӑؚనӇήȂרঈϗ໌ӑ ᙏϽҐޣᡐኵȃؑ၌ᖒҳПแԒȃཌ፡Ⴑ೩ᡐኵȃᢎᄆྃ
Ⴍᘈ՝ညȃоЅก໔፡ᡐᏢޟ SNRȞsignal-noise ratioȟ
้Өࢲ؏ޟႆแȄ 3.൷ᄂᡛޟႫၯՄِ
רঈоӻ१ӱ௲ଟၯڎӓਏӱ௲ଟၯȞchain of inte- grators with distributed feedback and local resonator feedback;
CRFBȟϞ࢜ᄺ࣏அᙃپհଽ፡ᡐᏢޟيᇄ੫ܒޟ
ଆȂᒵᐅڎӓਏӱ௲ଟၯޟনӰרঈҥႫၯ௰ுޟᙽ ಋڒኵԒϛࣼюȂڏӓਏӱ௲ၯ৷߽ኵ giؚۡᚔඹፒ ኵႭᘈᄇޟኵҬȂՄ߽ኵ biࠌؚۡ፡ᡐᏢྃᘈ֏ဣӵ
՝༫ϱȇᙤԪȂרঈџоޢᡐࢺแϛଟၯ߽ኵޟ σωپ፡ᐌႫၯ੫ܒȄ
4.൷ਝՄِ
࣏Οौଽ፡ᡐᏢᒯΣޢࢺጒ൜ЊճޟીᘈȂר ঈٺҢਮ፡ȞscalingȟޟПݲپቨёᒯΣ߬ဴޟޢࢺо Ѕ۽ڏଢ଼ᄘጒ൜Ȟdynamic range; DRȟ[7]Ȃٮቨёӓਏ ӱ௲ၯ৷پҡၶӻኵҬޟፒኵႭᘈᄇоுڗၶٹޟᚕଉ ᐌלȄ
έȃଽ፡ᡐᏢޟ೩ॎࢺแ
ᒵڥ፡ᡐᏢޟଟၯ߽ኵоࡾۡӫԙᘮݰᏢޟᙽಋڒ ኵ ࣏ அ ᙃ Ȃ Ι ૡ ᘮ ݰ Ꮲ ᙽ ಋ ڒ ኵ ல о Б ੫ գ ȞButterworthȟܖІ਼ШഡЉȞInverse-Chebyshevȟӻ
Ԓ࣏кौלԒȂӵӫԙڒኵਢ҆ौٲӻԒ S ሴ
ᙽ࣏ Z ሴϗҢپؚۡଟၯ߽ኵȂଟၯ߽ኵޟؚۡ
নࠌ։ौӵ๘ᄇᛧۡޟనӇήӫԙᘮݰᏢޟᙽಋڒኵٮ иौٺفಛႀڗၶଽޟ၌ݙ࡙ЅၶଽޟଉဴᚕଉШ SNR
ȂڎӓਏଟၯϞ፡ᡐᏢᎌӫҢІ਼ШഡЉᘮݰᏢپӫ ԙȂ֏ࠌџҢБ੫գᘮݰᏢپӫԙȄყ 3 ։࣏רঈܚඪ юޟᑖϷέُ፡ᡐᏢ၏ಠޟ೩ॎࢺแყᇄؚۡଟၯ߽ኵޟ ၐᒿႆแȂרঈоέ CRFB ޟᑖϷέُ፡ᡐᏢپᇳ݂
ଟၯ߽ኵ၏ಠޟ೩ॎ؏Ȉ
؏ΙȈ
ყ 4 Ιএέ CRFB ࢜ᄺޟᑖϷέُ፡ᡐᏢȂԒ(3) ޟG(z)mЅԒ(4)ޟH(z)mࠌϷտфߒ፡ᡐᏢޟ߬ဴᙽಋ ڒኵȞsignal-transfer function; STFȟᇄ NTF ߒҰԒȂᙽ ܒࡳᐙߓอհ
ڂై
ᒔࡳៀंᕴհী
ኪፖࠡᑇ ࠉᖕࠐٽګ
ᠧಛ᠏ངࠤᑇ
ᙇᖗ᠏ངᕴਮዌ
֗ࠡᓤᑇሿរኙ
ࠉᖕբव˛ʻ̍ʼࠐ
ֺኙಱሁᑇ
ଥإಱሁᑇ
ᛀᄕሿរۯᆜ
ၲࡨ
۩ᑓᚵ
ழᑓᚵ
ᗨ։ᕴᙁנ ጤآመሉ
᙮ᑓᚵ
᠏ངᕴᙁנ
ຏ᙮ᢜ
ߓอய౨ေ۷
ٽޣߓอய౨
ࠩಱሁএᑇଖ ܡ
ਢ
ܡ
ਢ
ܡ
ਢ ਢ
ܡ
˕
˕
ޡᨏԫ ޡᨏԫ ޡᨏԫ ޡᨏԫ
ޡᨏԲޡᨏԲ ޡᨏԲޡᨏԲ
ޡᨏԿ ޡᨏԿ ޡᨏԿ ޡᨏԿ
ޡᨏն ޡᨏն ޡᨏն ޡᨏն
˔
˔
ʻʳଥإ˨̀ʳʼ
ޡᨏޡᨏ
ޡᨏޡᨏ
ኙଖʳˏʳ˄ᄕរ
ȉ ȉ ȉ
ȉ
ʾ ʾ ʾ ʾ
̈
ʾ
ˀ ˀ ˀ
˘ʻ̍ʼ
˘ʻ̍ʼ˘ʻ̍ʼ
˘ʻ̍ʼ ˬʻ̍ʼˬʻ̍ʼ ˬʻ̍ʼˬʻ̍ʼ
˖˄
˖˄
˖˄
˖˄ ˖˅˖˅˖˅˖˅ ˖ˆ˖ˆ˖ˆ˖ˆ
˵˅
˵˅
˵˅
˵˅ ˵ˆ˵ˆ˵ˆ˵ˆ
˵˄
˵˄
˵˄
˵˄
˺˅
˺˅˺˅
˺˅
z-11 z
z-1 1
z-1 ˀ
ყ 4! Ιএέ CRFB ࢜ᄺϞᑖϷέُ፡ᡐᏢ
ყ 5! ؏Ιޟ၏ಠࢺแყ
ಋڒኵϛרঈџоுޣԪ࢜ᄺϛޟӱ௲ၯ৷ g2ؚۡ፡
ᡐᏢޟႭᘈ՝ညȂՄᚔඹႭᘈȞdistributed-zerosȟࠌӰ࣏
Ϛဣӵޢࢺޟ՝ညȞz=1ȟܚоڎԤၶቶᓜޟ߬ဴᙽਝ ݎȂᢎᄆԪᙽಋڒኵџޣڏӓڎԤΙএႭᘈ࣏ 1 ЅΙᄇፒ ኵႭᘈȂܚоҢڎഞᘈᔖ੫ܒޟІ਼ШഡЉᘮݰᏢپ հᄂ౪Ȅ
2 3
2 3 3 3 2 2
1=bcc +bc +cg − p
3 23 3
2 2 3 2 2 3 2 1 1
2=bccc −bcc −cg − bc + p
(3 3 1)
2 2 1
3 112 3
− +
⋅ +
⋅ +
= ⋅
c b p z p z z
z c c c ) b
z (
G m (3)
( )( ( ) )
(2 11)
1
3 3 2 2 1
3 2 2 2
− +
⋅ +
⋅ +
+
− +
= −
c b p z p z z
g c z z ) z
z (
H m (4)
ყ 5 ࣏؏Ιޟ၏ಠࢺแყȂӵ؏ΙޟႆแϛȂר ঈӑؚۡ፡ᡐᏢ࢜ᄺȂӔҥ፡ᡐᏢᙽಋڒኵ NTFȞzȟپ
ࡾۡᘮݰᏢלԒȄᒵۡ፡ᡐᏢᇄᘮݰᏢ࢜ᄺࡣȂרঈџо ٺҢߒΙޟߑۖనӇپܚӫԙᘮݰᏢޟᙽಋڒኵȂԃԒȞ6ȟ ܚҰȄԪᙽಋڒኵӔپᇄ CRFB ፡ᡐᏢϛޟҐޣଟၯ߽ኵ
ߒΙ! έ CRFB ፡ᡐᏢߑۖనӇ ߑ! ۖ! న! Ӈ
(1) І਼ШഡЉଽᘮݰᏢ (2) ኵɶ3
(3) ႆڥኺɶ128 (4) NTF(z)∞ɶ1.5 (5) Asɶ81dB
(6) Шኵ՝ᙽᏢᒯюɶᑖϷڒኵ
پհ࣏፡ᡐᏢଟၯ߽ኵШᄇȂٺ፡ᡐᏢӵ๘ᄇᛧۡޟ
ݷήհ߽ኵШᄇᇄཌ፡Ȅ
፡ᡐᏢޟႆڥኺȞover-sample ratio; OSRȟȂۡဎ
࣏ڥኺᓜᇄڍॻஅᓜϞШȂᄇܻفಛਝኇࣥ႞Ȃ
Мᝦ[1]ޟଆ፣ϛרঈџоுޣȈॻቨڥኺᓜོٺ໔ Ͻᚕଉ६ճ 3(2N+1)dBȂٮȞN+0.5ȟѴ՝ϯޟ၌
ݙ࡙Ȃڏϛ N ࣏፡ᡐᏢޟኵȇູଽޟ፡ᡐᏢ༉ሯၶω ޟႆڥኺ߯џԤၶٹޟᚕଉڙਝݎȂӵרঈհଟၯ ᘮݰᏢޟ೩ॎᔣਢȂശкौޟҬޟ߯װ໔Ͻᚕଉڙ ӵ-100dB ѾѡȇΙૡՄِȂኵσܻ 3 Ϟ፡ᡐᏢڏႆڥኺ
ڥ 64Ȃωܻܖ้ܻ 3 ࠌڥ 128Ȅӵ೩ॎႫၯޟႆแϛՃ ኌᑖϷέُ፡ᡐᏢᛧ࡙ۡޟ३ڙనӇ࣏ȶNTF ޟቨઉȷ ᇄȶശσޢࢺᒯΣᛧۡጒ൜ȷȂՄ NTF ޟቨઉࠌџМ ᝦଆپհ೩ॎޟ೩ȂרঈМᝦ[1]ޟଆ፣ϛுڗή Ӗޟᜰ߽ԒȈOSR ቨё→SNR ቨё→ NTF(z)∞ή६→ف ಛᛧ࡙ۡቨёȇٮਲ਼ᐃ Lee’s rule[2]Ȃᚕଉቨઉޟ३ڙనӇ
࣏Ȉ
6 . 1 ) (z ∞<
NTF (5)
ڏϛ NTF(z)∞ࠌۡဎ࣏ maxNTF(z)ޟȂרঈ҆р ಠӴՃኌႆڥኺᇄ NTF(z)∞Ϟޟኇᜰ߽Ȃ֏ࠌ
ོٺு፡ᡐᏢϛؐΙᑖϷᏢޟᒯюႹڷȂՄٺفಛี
ҡϚᛧۡޟޑݷȂӰԪӵרঈ೩ॎଟၯᘮݰᏢޟߑۖనӇ ϛȂרঈࡾۡ NTF(z)∞ɶ1.5[2]پհ࣏ၐᒿႆแϛޟߑ
ۖనӇȂٮрಠӴՃኌႆڥኺᇄ NTF(z)∞ޟȄ
4488 . 0 7015 . 1 2086 . 2
1 9995 . 2 9995 . ) 2
( 3 3 2 2
− +
−
− +
= −
z z
z
z z
z z
H filter (6)
רঈџоٺҢԪߒਿܚࡾۡޟᘮݰᏢኵپӫԙڏᙽ ಋڒኵՄհ࣏Ґޣଟၯ߽ኵޟШᄇҢȇӵհኵޟࡾۡᇄ ཌ፡ਢӰ࣏ளՍХளϞᚕଉ૾ As ᜰ߽فಛޟ SNR ᇄྃᘈ՝ည֏ဣӵ՝༫ϱȂڏᜰ߽։࣏ȈAs ቨёٺுᛧ࡙ۡή६ȂӰԪ҆рಠپհՃ໔ȇѪѴ൷Ȃ ԃݎᑖϷᏢޟᒯюีҡྖ՝Ȃ٥ߒҰޢࢺᒯΣ Umޟ ЊσȂ҆ωڏȄყ 6 ࠌԪ፡ᡐᏢӫԙᘮݰᏢޟྃ
Ⴍᘈ՝ညყȂყ 7 ࠌڏ NTF ளޟᓜᔖყȂԪਢڥ ኺᓜ fsample=1и OSR=128Ȃٮҥყ 7 רঈџоுޣȂᄇܻ
ճᑖϷέُ፡ᡐᏢޟ NTF ᓜᔖོڎԤଽޟ੫ܒȄ
ެࡳៀंᕴীኪ֗
ࠡᑇ ᒔࡳៀंᕴীኪΕ
ၸᑇΕመ࠷ᑌ
ઃڇփ חmax|NTF| = 1.5 As=70 dBʻॣࡨଖʼ
SNR>=100dB
ࡳΛ
ࠩࡳհ˔̆ ଖ
ᏺףʳ˔̆ ଖ ᠏ངៀंᕴ᠏ฝࠤ
ᑇط˦Ꮖࠩ˭Ꮖ
ቃ۷˦ˡ˥ଖ
ܡ
ਢ
-1 -0.5 0 0.5 1 -1
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
R eal Axis
Imag Axis
-1 -0 .5 0 0 .5 1
-1 -0 .8 -0 .6 -0 .4 -0 .2 0 0 .2 0 .4 0 .6 0 .8 1
R e a l Axis
Imag Axis
1 0-4 1 0-3 1 0-2 1 0-1
- 1 1 0 - 1 0 0 -9 0 -8 0 -7 0 -6 0 -5 0 -4 0 -3 0 -2 0 -1 0 0
NT F r e s p o n s e - C h e b y 2 h ig h - p a s s filte r
n o r m a lize d fre q u e n c y (Hz) fs = 1
Magnitude (dB)
8 2 d B
Magnitude (dB)
1 0-5 1 0-4 1 0-3 1 0-2 1 0-1 1 00
- 2 0 0 - 1 5 0 - 1 0 0 - 5 0 0 5 0
NT F r e s p o n s e - - B u tte r wo r th h ig h - p a s s filte r
n o r m a lize d fr e q u e n c y ( Hz) fs = 1
Magnitude (dB)
ყ 6! έ CRFB ፡ᡐᏢޟྃႭᘈ՝ညყ
Normalized frequency (Hz) fs = 1 ყ 7! έ CRFB ࢜ᄺϞ NTF ᓜᔖყ
ყ 8! έ CIFB ࢜ᄺᑖϷέُ፡ᡐᏢ
؏ΠȈ
Ⴋၯޟᔣ፡ᡐᏢޟᙽಋڒኵۖȂӰ࣏ᄇᔖڗႫ ၯ࢜ᄺȶඁಢӓፒኵႭᘈ൷Ԥඁన giଟၯȷȂӵႫၯϛ Ԥၶӻ१ӱ௲ၯ৷ giȂһ։ٺҢԤၶӻኵҬޟᚔඹፒኵ Ⴍᘈᄇفಛོுڗၶଽޟ SNR Ȃڏᄇܻᚕଉޟᐌלਝݎ ཕٹȄ
έ፡ᡐفಛџԤڍᆍџޟಢӫȈ{ΙᄇӓፒኵႭ ᘈڷΙᄂኵႭᘈ}ܖ{έᄂኵႭᘈ}ȂѲ፡ᡐᏢفಛࠌџԤ ڍᆍџޟಢӫȈ{ΠᄇӓፒኵႭᘈ}ܖ{ΙᄇӓፒኵႭ ᘈڷΠᄂኵႭᘈ}ȄΙనӓਏଟၯфߒΙᄇӓፒኵႭᘈȂ ζོӵ NTF ڒኵԢጣΰҡΙএഞᘈȂΙૡՄِȂູӻഞ ᘈູᔆᚕଉȂඪଽଉဴᚕଉШȄषџޟӓਏଟၯኵ
ߒΠ! έ CIFB ፡ᡐᏢߑۖనӇ ߑ! ۖ! న! Ӈ
(1) Б੫գଽᘮݰᏢ (2) ኵ=3
(3) ႆڥኺ=128 (4) NTF(z)∞=1.5 (5) As = 71dB
(6) Шኵ՝ᙽᏢᒯю=ᑖϷڒኵ
ყ 9! έ CIFB ፡ᡐᏢޟྃႭᘈ՝ညყ
ყ 10! έ CIFB ࢜ᄺϞ NTF ᓜᔖყ ၶӓፒኵႭᘈӻȂࠌџҢᔣײюȶӓਏଟၯཌ໔ᡐϽ ᄇ NTF ᓜᔖޟᜰ߽ȷՄپϽᙏޢࢺᚕଉ՝ྥЅႭᘈ՝
ညޟኇแ࡙ၶσϞӓਏଟၯȄ
ᄇέՄِԃ{έᄂኵႭᘈ}Ȃࠌ࣏ฒӓਏଟၯȞchain of integrators with distributed feedback; CIFBȟȂԃყ 8 Ι এέ CIFB ࢜ᄺޟᑖϷέُ፡ᡐᏢȂԒ(7)࣏ڏᙽಋڒኵ NTFޟߒҰԒȂ NTF ޟڒኵϛרঈџޣԪ࢜ᄺܚԤႭᘈ
࣏ 1ȂܚоҢБ੫գଽᘮݰᏢپᄂ౪Ȃڏ೩ॎଟၯ ᘮݰᏢޟߑۖనӇԃߒΠܚҰȄ
רঈџоٺҢߒΠܚࡾۡޟᘮݰᏢೣਿኵپӫԙڏ ᙽಋڒኵՄհ࣏ଟၯ߽ኵШᄇҢȂԃԒ(8)ܚҰȇყ 9 ࠌ
Ԫ፡ᡐᏢӫԙᘮݰᏢޟྃႭᘈ՝ညყȂყ 10 ࠌڏ NTF
ளޟᓜᔖყȂԪਢڥኺᓜ fsample=1и OSR=128Ȃ
̍ˀ˄˄
ʾ ʾ ̍ˀ˄̍ ʾ ̍ˀ˄˄ ʾ
̈
ʾ
ˀ ˀ ˀ
˘ʻ̍ʼ˘ʻ̍ʼ˘ʻ̍ʼ
˘ʻ̍ʼ ˬʻ̍ʼ ˬʻ̍ʼ ˬʻ̍ʼ ˬʻ̍ʼ
˖˄
˖˄˖˄
˖˄ ˖˅˖˅˖˅˖˅ ˖ˆ˖ˆ˖ˆ˖ˆ
˵˅
˵˅˵˅
˵˅ ˵ˆ˵ˆ˵ˆ˵ˆ
˵˄˵˄
˵˄˵˄
Magnitude (dB)
Normalized frequency (Hz) fs = 1
0 2 4 6 -200
-150 -100 -50 0 50
NTF of 3order mod-b1 vary
Normalized frequency(Hz)
Amplitude(dB)
0 2 4 6
-200 -100 0 100
NTF of 3order mod-b2 vary
Normalized frequency(Hz)
Amplitude(dB)
0 2 4 6
-300 -200 -100 0 100
NTF of 3order mod-b3 vary
Normalized frequency(Hz)
Amplitude(dB)
0 2 4 6
-300 -200 -100 0 100
NTF of 3order mod-c1 vary
Normalized frequency(Hz)
Amplitude(dB)
0 2 4 6
-300 -200 -100 0
100 NTF of 3order mod-c2 vary
Normalized frequency(Hz)
Amplitude(dB)
0 2 4 6
-400 -300 -200 -100 0
100 NTF of 3order mod-c3 vary
Normalized frequency(Hz)
Amplitude(dB)
ყ 11! ଟၯ߽ኵ biᄇفಛᙽಋڒኵޟኇ
ყ 12! ਮ፡߽ኵ ciᄇفಛᙽಋڒኵϞኇ
) c b ( ) c c b c c c b ( z ) c b c c b ( z z
) z ( )
z ( H m
1 3
3 1
3 3 3
2 2 3 2 1 1 3
3 3 2 2 2 3
3
− + +
− +
− + +
= −
(7) ٮҥԪყϛרঈџоޣၾȂᄇܻճᑖϷέُ፡ᡐᏢޟ
NTF ᓜᔖོڎԤଽޟ੫ܒȂиӵХளޟഋϷԤҁۄ ޟᓜᔖȄ
5321 . 0 9294 . 1 3741 . 2
1 3 ) 3
( 3 3 2 2
− +
−
− +
= −
z z
z
z z z z
H filter (8)
؏έȈ
Ԫ؏࣏ШᄇҐޣଟၯ߽ኵᇄϷݙᔣ๖ݎޟႆแȂ Ӱ࣏ᘮݰᏢޟኵᇄ፡ᡐᏢᛧ࡙ۡޟ୰ᚠϐೝՃኌȂӰ ԪרঈџоҢӣኺڎԤଽᘮݰ࣏ޟᘮݰᏢᙽಋڒኵپ հ࣏Шᄇ፡ᡐᏢ߽ኵਢޟϐޣనӇՄሯ၌ᖒҳПแԒȂծ Ӱ࣏ႫၯϛٺҢਮ፡ޟПݲȞᡐኵ ciȟȃҡፒኵႭᘈᄇޟ ଟၯȞᡐኵ giȟՄҡၶПแԒӻޟҐޣᡐኵȂרঈ၌ؚ
ޟᒲݲӑӵࡾۡޟጒ൜ 0ʂ1 ϛႱ೩ଟၯ߽ኵȂٮи ԪႱ೩ޟཌ፡໔ᡐϽᄇ፡ᡐᏢفಛਝٮฒᡗޟኇ
ȂԪџоؑுխყ 11ȃყ 12 ޟᜰ߽پհᒋ໔Ȃᅭ
ࡣӔᙤҥӫ߽ኵཌ፡ᇄ၌ᖒҳПแԒޟႆแپײю഻ή ޟҐޣ߽ኵȂശࡣٮுڗΙಢശٹϽޟ߽ኵ၌ӫȇՄ ӵΰक़؏ϛШᄇҐޣ࢜ᄺ߽ኵᇄᄇਮ፡߽ኵ ciޟཌ፡ႆ
แਢȂרঈ҆ᕣ၌ਮ፡߽ኵ ciᇄؚۡ፡ᡐᏢྃᘈ՝ည ޟ biᄇفಛਝޟኇแ࡙࣏դȂԃԪϗپՃኌӵၐ ᒿႆแϛ߽ኵཌ፡ᡐ໔ޟσωȄӵყ 11 ᇄყ 12 ϛרঈ
ཌ፡໔೩࣏ 0.1 پᢎᄆ߽ኵ biᇄ ciཌ໔ᡐϽᄇܻفಛ ᙽಋڒኵޟᒯюȂһ։ᚕଉᐌלਝݎޟኇȂٮҥԪყ רঈџоுޣଟၯ߽ኵ biᄇفಛᙽಋڒኵޟኇแ࡙࣏
b2>b3>b1Ȃଟၯ߽ኵ ci ᄇفಛᙽಋڒኵޟኇแ࡙࣏
c3>c1≈c2ȂӰԪרঈ߯џоΰक़ٲᡐ໔Ϟᜰ߽پհ࣏ӵၐ ᒿႆแϛ߽ኵཌ፡ᡐ໔σωޟٷᐃȄ
ᡐϽኇၶωޟ೩࣏ၐᒿႆแϛϐޣ߽ኵޟߑ
ۖՄ٥ٲኇแ࡙ၶσޟᡐኵࠌо၌ᖒҳПแԒޟПԒ پؑுȂኺ൷џоЍၐᒿႆแϛޟᇲ৯Ȅ
רঈװᙏϽ߽ኵޟႆแජक़ԃήȈ
(1)ӨଟၯᡐኵᄇفಛਝޟኇԃήȈᡐኵ giҡፒኵႭ ᘈᄇȂኇ፡ᡐᏢޟᚕଉڙΨȇᡐኵ biؚۡኇف ಛᛧ࡙ۡޟྃᘈ՝ညȇᡐኵ ciࠌኇޢࢺᒯΣᇄଢ଼ ᄘጒ൜Ȅ
(2)հӨᡐኵޟ NTF ᓜᔖϷݙȂоቨ໔ 0.01 پհσ ωШၶȂᔖᡐϽၶωޟڥ 0.1 پհ߽ኵᒵڥਢޟߑ
ۖȂᔖᡐϽၶσޟࠌӱў၌ᖒҳПแԒȄ (3)ਲ਼ᐃ೩ॎࢺแყܚҰȂംԩཌ፡Өଟၯ߽ኵоؑுശٹ
ਝȄרঈٮӵؐΙԩޟཌ፡߽ኵؚۡࡣ१ፒӴӵᓜ
ޟᢎᄆڏྃᘈ՝ည֏՝ܻ z = 1 ՝༫ϱȂоᗗջี
ҡϚᛧۡޟᐇհݷȄ
؏ѲȈ
ܚ೩ॎ፡ᡐᏢޟᒯю੫ܒџငҥᓜЅਢΰޟ੫ܒ پհᒋ໔Ȅӵᓜΰרঈᢎᄆڏྃᘈ՝ည֏ဣܻ՝༫ ϱȂٮᢎᄆڏᒯюᓜᜊ֏࣏ଽȇӵਢΰࠌӵޢࢺ ᒯΣϞݷήȂᅾџ᠒фޑᄘПแԒپᢎᄆؐএᑖϷᏢ ޟᒯюശσȄӵਢޟਝก໔ΰȂڏޑᄘПแԒԃ(9) ܚҰȂרঈоᒯΣ߬ဴ-3dB ࣏ۖȂംԩ᠒фԪޑᄘП แԒپؑு፡ᡐᏢޟശσޢࢺᒯΣႫᔆ UmȂUmޟৠע ጒ൜ཕσȂᑖϷᏢཕϚৠܾีҡႹڷՄᄇܻفಛޟᛧۡܒ ԤߨலσޟᔓօȄ
)) 1 ( ( ) 1 (
0 ] [
) (
) (
) (
1 0 1
0
0 1
) 1 (
) 1 (
) 1 (
3
1 1
1
3 2 1 1 2 3
1
3 2 1 2 2
2 2 1 3
2 1
+
= +
⋅
+
⋅
−
−
−
−
+
⋅
−
⋅
−
⋅
=
+ + +
n x Sgn n
y
u c a
a n y b
b c b g b
b
n x
n x
n x g c
g c c n
x n x
n x
(9)
0 0 .1 0.2 0.3 0.4 0.5 -1
0 1 2 3 4 5
In te g ra to r m a x im u n o u tp u t (U n s c a le d )
Inpu t sign al le vel (V )
Max value (V)
X1
X2
X3
0 0.2 0.4 0.6 0.8 1 1.2
-0.5 0 0.5 1 1.5 2
2.5 Integrator maximun output (Scaled)
Input signal level (V)
Max value (V)
X1 X2 X3
0 2000 4000
0 0.5 1
Sampling point Magnitude (V) X1(n)
0 2000 4000
-0.5 0 0.5 1
Sampling point
Magnitude (V) X2(n)
0 2000 4000
-0.2 0 0.2 0.4 0.6
Sampling point Magnitude (V)X3 (n)
ߒέ! έ CRFB ࢜ᄺଟၯ߽ኵ ଟ! ၯ! ߽! ኵ
g2=0.0117 a1=0.15
a2=0 a3=0
b1=0.10 b2=0.19 b3=0.11
c1=0.33 c2=0.26
c3=4.72 ߽ኵШ=103
ყ 13! ፡ᡐᏢਝก໔ࢺแყ
ყ 14! έ CRFB ࢜ᄺϞਢϷݙ
ყ 15! έ CRFB ࢜ᄺҐਮ፡ᑖϷᏢޟᒯюႫᔆ
؏ϤȈ
ԃყ 13 ܚҰҢᓜϷݙپுڗؚۡفಛਝޟ SNR
ȂӔਲ਼ᐃԪ SNR پրᘞרঈܚᒵڥޟ߽ኵ၌֏ᎌ
࿋Ȅ
ߒѲ! έ፡ᡐᏢᒯюᓜᜊޟก໔ ђ! ! ᓜ! ᜊ! ໔! ก
ኵ ଉဴ ଽ! ᓜ! ᔖ! Ң
ᒯ Σ ՝ ྥ -3 dB
ႆ ڥ ኺ 128
ڥ ኺ ᓜ 2.56 MHz
ᒯ Σ ᓜ 5 KHz
ᓜ ள ቶ 20 KHz
פഀയҳဨᙽ 65536 points
ყ 16! έ CRFB ࢜ᄺਮ፡ࡣᑖϷᏢޟᒯюႫᔆ
ყ 17 έ CRFB ࢜ᄺ፡ᡐᏢޟڥኺᒯю(a)ШᒯΣ߬
ဴ(b)ኵ՝ᒯю߬ဴ
Ѳȃᔣ๖ݎ
ߒέ։ਲ਼ᐃ೩ॎࢺแЅߑۖనӇܚᒵڥޟέ
CRFB ࢜ᄺޟᑖϷέُ፡ᡐᏢ࢜ᄺ߽ኵȂרঈٺҢٲ߽
ኵپհӨᆍ࣏ᔣоᄺԙܾܻᄂ౪иܒيԁޟ፡ᡐ ᏢȂႫၯϛӻ१ӱ௲ၯ৷ؚۡϚӣޟᙽಋڒኵȂϷυ࣏
ӻԒ։ҡᚔඹፒኵᄇޟႭᘈȂԪᙽಋڒኵᄇܻᚕ ଉޟႆᘮΨၶٹȂفಛޟ SNR һၶଽȄყ 14 ࠌӵਢ
ϷݙϛؐΙᑖϷᏢޟᒯюȂҥԪყџоுޣȂӵޢࢺ ᒯΣ࣏ᛧۡޟጒ൜ήȂᑖϷᏢޟᒯюٮϚོีҡႆၷޟ ޑݷȇყ 15 ࣏ҐٺҢਮ፡ПݲޟᑖϷᏢᒯюȂՄყ 16 ࠌ
ٺҢਮ፡ПݲࡣᑖϷᏢޟᒯюȂҥყ 15ȃყ 16 רঈџ оுޣȂӵਮ፡ࡣᑖϷᏢޟശσޢࢺᒯΣџо 0.45V ᘗቨՍ 1.17V ѾѡȂޢࢺᒯΣጒ൜ޟቨёџоٺ፡ᡐᏢၶ
᠏ངᕴᑓڤ ݧ٨ᙁנ
ଊא࿗Ցࠤᑇ
֗شݶຒແܓᆺ
᠏ངࠐޣפ
᙮ᢜૠጩ࿓ݧ ߓอய౨ ۷
ʻ˦ˡ˥ʳၦྒྷʼ ඝंಛᇆᙁԵ
ِҁ
10-1 -60 -40 -20 0
normalized frequency
amplitude(dB)
-60 -40 -20 0
normalized frequency
amplitude(dB)
10-1 -60 -40 -20 0
normalized frequency
amplitude(dB)
-100 -90 -80 -70 -60
normalized frequency
amplitude(dB)
-80 -70 -60 -50 -40 -30 -20 -10 0
-40 -20 0 20 40 60 80 100
120 SNR response for scaled-unscaled
Input level (dB)
SNR (dB)
100
-1 -0 .5 0 0 .5 1
-1 -0 .8 -0 .6 -0 .4 -0 .2 0 0 .2 0 .4 0 .6 0 .8 1
R e a l Axis
Imag Axis
ߒϤ! ᔣ๖ݎШၶᇄϷݙ
ᙽᏢ࢜ᄺ ᛧ࡙ۡ ႆၷ ॸоШ ଉဴᚕଉШ ߽ኵШ ޢࢺᒯΣጒ൜
4th-order Burra [8] ԤనӇӴ ฒ ~105 dB 104 < 0.1V 4th-order Sodini [9] ԤనӇӴ ฒ ~102 dB 106 < 0.1V
CRFB(g2) 110.5 dB 1.17V 103
3rd-order CIFB ๘ᄇӴ ֏ Ԥ 103.5 dB ~1.17V 102
CRFB(g2, g3) 112.3 dB 1.16V 104
CRFB(g2) 109 dB 1.12V 103
4th-order
CIFB ๘ᄇӴ ֏ Ԥ
100 dB 1.09V 101
CRFB(g1, g2) 112.8 dB 0.9V 103
5th-order CIFB ๘ᄇӴ ֏ Ԥ 104.8 dB 0.89V 101
ყ 18! έ CRFB ࢜ᄺଽᓜ߬ဴޟᒯюᓜᜊ
ყ 19! έ CRFB ࢜ᄺਮ፡ࡣޟ SNR ᔖШၶყ
ყ 20! ϲள፡ᡐᏢޟྃႭᘈყ
ყ 21! ϲள CRFB ࢜ᄺᘮݰᏢޟ STF ᇄ NTF ᔖყ
ყ 22! ϲ CRFB ࢜ᄺள፡ᡐᏢᒯюᓜᜊ
ϚོีҡႹڷՄԤօܻفಛਝޟᛧۡȄყ 17 ࠌ፡ᡐᏢ ޟڥኺᒯюȂרঈٺҢШᒯΣ߬ဴᇄኵ՝ᒯю߬ဴپ
ᔣ፡ᡐᏢޟ࣏Ȃཕଽޟ፡ᡐᏢڏ၌ݙ࡙ཕଽȂܚоኵ
՝߬ဴᒯюޟแོ࡙ཕё݂ᡗȄߒѲࠌ፡ᡐᏢᒯю ᓜᜊޟก໔ೣਿߒȂרঈٺҢଽᓜ߬ဴپᢎᄆᒯюᓜᜊޟ
࣏Ȃശٹޟ౩དޑݷ࣏ΙଽᘮݰᏢȂԪਢ၌ݙ࡙࣏
65536ᘈޟയҳဨᙽȂ๖ݎԃყ 18 ܚҰȄყ 19 ࣏ਮ፡
ࡣ SNR ᔖޟШၶყȂSNR ӵਮ፡ࡣඪଽΟ 4.5dBȂи ଢ଼ᄘጒ൜ζඪЀΟ 7dB ՄٺுᐌএفಛਝᡐԁȄყ 20
CRFB ࢜ᄺޟϲள፡ᡐᏢྃႭᘈყȂڏᙽಋڒኵޟ Ⴍᘈࢎৢڗ±π/2ޟ՝ညȂڥኺᓜ fsample=4ॻஅᓜᓜи OSR=128ȇყ 21 ᄇܻ fsample=1ޟ STF ᇄ NTF σωᔖ ყȂყ 22 ࠌᄇܻԪϲள፡ᡐᏢޟᒯюୈ 65536 ᘈޟ യցဨᙽყȄ
Frequency (Hz)
רঈҢΰक़೩ॎࢺแپϷտ೩ॎέՍϤϞ፡ᡐ ᏢȂശࡣᔣޟ๖ݎШၶᇄϷݙࠌӖܻߒϤϛȂҥߒϛר ঈџоޣၾȂငҥਮ፡ПݲޟٺҢᇄӨኵೣਿޟՃ໔ ήȂҏ፣Мܚඪюޟ೩ॎПݲᇄுڗࢋᛧۡάϚོีҡ
ႆၷޟଽ፡ᡐᏢȂՄӵفಛਝП७һڎരԤၶଽޟޢ ࢺᒯΣጒ൜ᇄၶଽ SNR ޟ੫ܒȄҥߒϤϛζџᢎᄆ юȂӵ SNR П७Ȃ൷ࣺӣኵՄِȂ CRFB ࢜ᄺ֯ၶ CIFB
࢜ᄺԤၶٹߒ౪ȇӣਢȂၶӻӓਏଟၯ࢜ᄺζџுڗၶଽ Ϟ SNR Ȅ
Ϥȃ๖፣
ҏंـޟкौҬޟӵ໌ଽᑖϷέُ፡ᡐᏢޟ೩
ॎȂҥܻᑖϷέُ፡ᡐᏢҏ፴ΰ࣏ΙߨጣܒϯӇȂኇ፡
ᡐᏢ೩ॎޟᡐኵࣥӻȂՄ҆ौоጣܒޟಢپ໌ڏ
࣏ᔣȂஅܻԪᢎᘈȂרঈඪюΟΙৈ೩ॎଽᑖϷέُ
፡ᡐᏢޟࢺแȂӵՃኌӨᆍኇӰશޟݷήȂᄂሬў ᒵڥଽ፡ᡐᏢޟଟၯ߽ኵȂиӰ࣏ΙૡᑖϷέُ፡ᡐᏢ ޟ೩ॎޱၶЍўՃኌጣၯϛӓਏଟၯᄇܻفಛਝޟኇ
ȂӰԪҏंـବᄇέՍϤӨڎϚӣኵҬޟӓਏଟ ၯޟ፡ᡐᏢհϷݙᇄᔣȂٮᄇୋኵޟ࢜ᄺඪюΙᆍϽ ᙏጣၯޟПݲپᙏϽ೩ॎȇӵרঈޟ೩ॎࢺแϛȂॶӑବ ᄇᑖϷέُ፡ᡐᏢޟஅҏ੫ܒёоϷݙᇄଆȂٮٷܚு
ኵᐃޟ੫ܒȂپᘪઽю೩ॎޟྥࠌȂӔپ߯໌ϽᙏҐ ޣ߽ኵȃؑ၌ᖒҳПแԒȃཌ፡Ⴑ೩ᡐኵȃᢎᄆྃႭᘈ՝
ညоЅ໔ก SNR ޟၐᒿࢺแȂ೩ॎϛٮሄо Matlab ᡝپհӨᆍ࣏ᔣȄ
ᙤҥҏंـϛ၏ᅾޟଽᑖϷέُ፡ᡐᏢޟ೩ॎႆแ Ѕᔣ๖ݎȂᄇܻؠԤငᡛޟ೩ॎޱȂ൷ԃӣඪټΟΙӋ ശׇᐌޟൢ֙Ȃٺ೩ॎޱඉוӴپᒵڥ፡ᡐᏢޟଟၯ߽
ኵȂׇԙ๘ᄇᛧۡȃڎଽ SNR Ѕၶωޟ߽ኵԻϷШՄܾ
ܻᄂ౪ޟଽᑖϷέُ፡ᡐᏢ೩ॎȄӰ࣏ٲଟၯ߽ኵᄂ ሬΰܚфߒޟϸႫৠϛޟႫৠШȂܚоஊޢ
ӵ VLSI ೩ॎΰپհᄂ౪Ȅ
ಒဴષЕ
ai i এӓਏଟ௲߽ኵ bi i এөࡣଟ௲߽ኵ ci i এॻ߽ኵ gi i এӓਏଟ௲߽ኵ X ᒯΣଉဴ
Y ፡ᡐᏢᙽಋڒኵ E ໔Ͻᚕଉ G ଉဴᙽಋڒኵ
H ᚕଉᙽಋڒኵ As ளՍХள૾໔ fs ڥኺᓜ
Um ശσޢࢺᒯΣႫᔆ
ՃМᝦ
1. Candy, J. C., “A Use of Double Integration in Sigma- Delta Modulation,” IEEE Trans. on Communications, Vol. 33, No. 3, pp.249-258 (1985).
2. Carley, R., and Kenney, J., “A 16-bit 4th Order Noise- Shaping D/A Converter,” Proceedings, IEEE Custom In- tegrated Circuits Conf., pp.21.7.1-21.7.4 (1988).
3. Candy, J. C. and Temes, G. C., Oversampling Delta- Sigma Data Converters, IEEE Press, New York, pp.1- 275 (1992).
4. Ritoniemi,T., Pajarre, E., Jugalsuo, S., Husu, T., Eorola, V., and Saramaki, T., “A Stereo Audio Sigma Delta A/D Converter,” IEEE Journal of Solid-State Circuits, Vol. 29, No. 12, pp.1514-1522 (1994).
5. King, E. T., Eshraghi, A., Galton, I. and Fiez, T. S., “A Nyquist-Rate Delta-Sigma A/D Converter,” IEEE Journal of Solid-State Circuits, Vol. 33, No. 12, pp. 45-42 (1998).
6. Burra, G., and Chao, K. S., “A High-Speed High Resolu- tion Oversampled A/D Converter,” Proceedings, IEEE In- ternational Symposium on Circuits and Systems, Vol. 2, pp. 1282-1285 (1993).
7. Chao, K. C. H., Nadeem, S., Lee, W. L., and Sodini, C. G.,
“A Higher Order Topology for Interpolative Modulators for Oversampling A/D Conversion,” IEEE Trans. on Cir- cuits and Systems, Vol. 37, No. 3, pp. 309-318 (1990).
8. Ju, P., and Suyama, K., “Design Consideration in High-Order Multi-Bit Sigma-Delta Modulators,” Pro- ceedings, IEEE International Symposium on Circuits and Systems, Vol. 1, pp. 389-392 (1997).
9. Baird, R. T., and Fiez, T. S., “Stability Analysis of High-Order Delta-Sigma Modulator for ADC’s,” IEEE Trans. on Circuits and Systems II: Analog and Digital Signal Processing, Vol. 41, No. 1, pp. 59-62 (1994).
88 ԑ 06 Т 17 Р! ԝገ 88 ԑ 12 Т 10 Р! ߑቷ 89 ԑ 03 Т 28 Р! ፒቷ 89 ԑ 04 Т 26 Р! ڧ
