Sampling. AD Conversion (Additional Material) Sampling: Band limited signal. Sampling. Sampling function (sampling comb) III(x) Shah.
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1 AD Coversio (Addiioal Maerial Samplig Samplig Properies of real ADCs wo Sep Flash ADC Pipelie ADC Iegraig ADCs: Sigle Slope, Dual Slope DA Coverer Samplig fucio (samplig comb III(x Shah III III ( x = δ ( x = ( ax = a = δ x a Muliplicaio of f(x wih III(x describes samplig a ui iervals III( x f ( x = f ( δ ( x = Samplig a iervals τ: x III f τ ( x = τ f ( τ δ ( x τ = Bracewell, R. he Fourier rasform ad Is Applicaios, 3rd ed. New York: McGrawHill,. 3 III ( x III( k Samplig Fourier rasform of he samplig fucio x III τ τ III( τk III( x III( k Samplig: Bad limied sigal Bad limied sigal: F(k = for k > f(x F(k τ III x III( k τ x k here: τ = Bracewell, R. he Fourier rasform ad Is Applicaios, 3rd ed. New York: McGrawHill,. Bracewell, R. he Fourier rasform ad Is Applicaios, 3rd ed. New York: McGrawHill,.
2 5 6 Samplig i he wo Domais Criical Samplig ad dersamplig f(x F(k f(x F(k τ x x III τ τ III( τk τ k III( x f ( x x k ( kc III F( k k c k = = x III f ( x τ III( τk F( k τ dersamplig τ > Bracewell, R. he Fourier rasform ad Is Applicaios, 3rd ed. New York: McGrawHill,. Bracewell, R. he Fourier rasform ad Is Applicaios, 3rd ed. New York: McGrawHill,. 7 8 Summary: Samplig Samplig heorem A fucio whose Fourier rasform is zero (F(k = for k > is fully specified by values spaced a equal iervals τ < /(. Aleraive (simplified saeme: he samplig frequecy mus be higher ha wice he highes frequecy i he sigal Descripio of samplig a iervals τ: Muliplicaio of f(x wih III(x/ τ Ideal ADCoverer: Quaizaio Error Recosrucio of he sigal: Muliplicaio of he Fourier k rasform ( τ III( τk F( k wih Π ad iverse rasformaio Or: Covoluio of he sampled fucio wih a sicfucio J. G. Webser (Edior: he Measureme, Isrumeaio, ad SesorsHadbook CRC Press, 999.
3 9 Offse Error Gai Error J. G. Webser (Edior: he Measureme, Isrumeaio, ad SesorsHadbook CRC Press, 999. J. G. Webser (Edior: he Measureme, Isrumeaio, ad SesorsHadbook CRC Press, 999. Differeial Nolieariy Iegral Nolieariy Ideal code widh: LSB Differeial olieariy describes deviaio from ideal code widh: DNL = Code widh Iegral Nolieariy: Deviaio of he code rasiios from he ideal sraigh lie, providig ha he liear errors (offse ad gai have bee removed J. G. Webser (Edior: he Measureme, Isrumeaio, ad SesorsHadbook CRC Press, 999. J. G. Webser (Edior: he Measureme, Isrumeaio, ad SesorsHadbook CRC Press, 999.
4 3 AD Coverers: Specificaios Rage AD Coverers: Specificaios Resoluio Ipu rage spa of volages over which a coversio is valid Rage = full scale full scale If =, he ADC is called uipolar full scale If =, he ADC is called bipolar full scale full scale Resoluio smalles chage i volage he ADC ca deec Resoluio Volage differece of LSB (leas sigifica bi bi ADC: Rage Rage = Example: 6 bis, Ipu rage 5 V Resoluio V = 5 76µV 6 Cusomary: Saeme of resoluio as umber of bis (e.g. 6 bis resoluio or effecive umber of bis (ENOB 5 6 Dyamic Rage Calculaio of he Noise Volage Calulaio of Noise Noise volage: N = d ( N = Roo mea square value of he sigal S = max Sigal = max si ( ω = d N = = = = ( ( ( ( ( 3 3 ( ( ( ( = ( d J. G. Webser (Edior: he Measureme, Isrumeaio, ad SesorsHadbook CRC Press, 999.
5 7 8 Dyamic Rage Effecive Number of Bis (ENOB Bipolar ADC:, max max Rage = max = = max S SNR = lg lg = SNR: Sigal o oise raio N lg max = 6 = lg 6 ( ( = lg( 6( = lg 6 6 = lg lg =.76dB 6. db 6 ( = lg lg( If oise (ad disorios are o give by LSB, ENOB is a quaiy ha allows compariso of differe ADCs Deermiaio of effecive umber of bis wih a measured SNR SNR.76dB ENOB = 6. 9 wo Sep Flash ADC Pipelie ADC Reducio of umber of comparaors Example 8 bis: Flash: 55 comparaors, wo sep flash: 3 comparaors S/H i S/H 3 N/ MSBs MSB ADC DAC Subracor LSBs LSB ADC Ipu 3bi Flash ADC 3bi DAC 3bi S/H Sage Sage Sage 3 Sage bi FADC 3bi 3bi 3bi 3bi bi Correcio Logic bi Ph. Farhoua N bis Lach Delay : cycles for sages Oe oupu every clocycle Lower power cosumpio ha flash coverer (less comparaors
6 IN REF IN R C Sigle Slope ADC (I Priciple IN REF Iegraor: IN = R C IN ( τ dτ =, IN = cos. (Sample ad hold IN IN = R C Measureme of ime uil IN = REF REF IN IN R C Sigle Slope ADC (II Priciple IN IN Iegraor: IN IN = R C REF = R C REF =, REF = cos. ( τ dτ Measureme of ime uil IN = IN ime IN IN ~ IN ime IN IN ~ IN 3 Sigle Slope ADC Sigle Slope ADC: imig Diagram x measurig comparaor K Zero comp. s K XOR (Quarz Couer Digial oupu measurig comparaor x K Zero comp. K s XOR (Quarz Couer Digial oupu S x Zero comparaor V REF Sar Corol ui REF Sar Corol ui Measurig comparaor
7 5 6 Dual Slope ADC DigialAalog Coverer Corol Differe archiecures Simple DA Coverer based o summig amplifier: C S N (z N S 3 (z 3 S (z S (z S (z Aalog ipu i Volage referece ref R iegraor Gae Digial couer u ref R/ N R/8 R/ R/ R/ R ref u A iegraor Sample ad hold ADCoversio Sample ad Hold 7 u E u A Digiisaio wih Sample ad hold AiAliasigFiler (Low pass filer Sample ad Hold ADCoverer
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