EECS 247 Lecture 12: Data Converters © 2006 H. K. Page 1EE247Lecture 12• Administrative issues Midterm exam Tues. Oct. 24tho You can only bring one 8x11 paper with your own written notes (please do not photocopy)o No books, class or any other kind of handouts/notes, calculators, computers, PDA, cell phones....o Midterm includes material covered to end of lecture 14EECS 247 Lecture 12: Data Converters © 2006 H. K. Page 2EE247Lecture 12Today:– Example of Switched-Capacitor filters NOT followed by an ADC!– Data converters• ADC & DAC transfer curve• Sampling, aliasing, reconstruction• Amplitude quantization• Static converter error sources– Offset & full-scale error– DNL & INLEECS 247 Lecture 12: Data Converters © 2006 H. K. Page 3Summary of Last Lecture• Switched-Capacitor Filters (continued)–Effect of non-idealities–Bilinear switched-capacitor filters–Filter design summary • Comparison of various filter topologies• Data Converters (continued today)EECS 247 Lecture 12: Data Converters © 2006 H. K. Page 4Last Lecture Questions• Based on the CODEC example, class may have the impression that S.C. filters are always followed by an ADC!• Assumption not accurate– Example- Switched-capacitor filters used in the transmit path of ISDN ICsEECS 247 Lecture 12: Data Converters © 2006 H. K. Page 5Data Transmission Over Existing Twisted-Pair Phone LinesXmitterReceiverCentral OfficeBackboneDigital NetworkPOTSXmitterReceiver• Data transmitted over existing voice grade phone lines covering distances close to 3.5miles– Voice-band MODEMs–ISDN– HDSL, SDSL,……–ADSLCustomerTwisted Pair3 to 5kmEECS 247 Lecture 12: Data Converters © 2006 H. K. Page 6Data Transmission Over Twisted-Pair Phone LinesISDN (U-Interface) Transceiver• Full duplex transmission (RX & TX signals sent simultaneously)• 160kbit/sec baseband data (80kHz signal bandwidth)• Standardized line code 2B1Q (4 level code 3:1:-1:-3)• Max. desired loop coverage 18kft (~36dB signal attenuation)• Final required BER (bit-error-rate) 10-7Æ (min. SNDR=27dB)XmitterReceiverCentral OfficeBackboneDigital NetworkPOTSXmitterReceiverCustomerTwisted Pair3 to 5kmEECS 247 Lecture 12: Data Converters © 2006 H. K. Page 7Analog Front-End2b S.C.DAC2ndorderButterworthS.C. FilterClass A/BLine Driver13bitDouble-LoopTo avoid stringent requirements for non-linear echo canceller:Æ high linearity analog circuitry needed (~ 75dB)Peak signal frequency Æ80kHzfs=2.56MHzfs=20.48MHzEECS 247 Lecture 12: Data Converters © 2006 H. K. Page 8Data ConvertersEECS 247 Lecture 12: Data Converters © 2006 H. K. Page 9Data Converters• Stand alone data converters– Used in variety of systems– Example: Analog Devices AD9235 12bit/ 65Ms/s ADC- Applications:• Ultrasound equipment• IF sampling in wireless receivers• Hand-held scopemeters• Low cost digital oscilloscopesEECS 247 Lecture 12: Data Converters © 2006 H. K. Page 10Data Converters• Embedded data converters– Cost, reliability, and performance Æ integration of data conversion interfaces along with DSPs– Main challenges• Feasibility of integrating sensitive analog functions in technologies optimized for digital performance• Down scaling of supply voltage• Interference & spurious signal pick-up from on-chip digital circuitry• Portable applications dictate low power consumptionEECS 247 Lecture 12: Data Converters © 2006 H. K. Page 11D/A Converter Transfer Characteristics• An ideal digital-to-analog converter:–Accepts digital inputs b1-bn–Produces either an analog output voltage or current –Assumption (will be revisited) • Uniform, binary digital encoding • Unipolar output ranging from 0 to VFSD/A……..…b1b2b3bnV0MSBLSBFSFSNFS2N # of bitsV full scale outputmin.step size 1LSBV2Vor N log resolution==Δ= →Δ==→ΔNomenclature:EECS 247 Lecture 12: Data Converters © 2006 H. K. Page 12D/A Converter Transfer CharacteristicsFSFSNN#of bitsV full scale outputmin. step size 1LSBV2==Δ= →Δ=N0FSi1Ni1iNibiVV2bi 2 , bi 0 or 1==−==Δ× × =∑∑D/A……..…b1b2b3bnV0MSBLSBbinary-weightedEECS 247 Lecture 12: Data Converters © 2006 H. K. Page 13D/A Converter Exampe: D/A with 3-bit ResolutionD/Ab1b2b3V0MSBLSB()()FS01233FS00NFS FS210210Example:N 3Assume V 0.8VInputcode is101Vb2 b2 b2Then: V /2 0.1VV0.1V12 02 12V0.5VNote:MSB V /2 & LSB V / 2===Δ×+×+×Δ= =→= =×+×+×→=→→1 0 1EECS 247 Lecture 12: Data Converters © 2006 H. K. Page 14Ideal D/A Transfer Characteristic• Ideal DAC introduces no error!• One-to-one mapping from input to output000 001 010 011 100 101 110 111Step Height (1LSB =Δ)Ideal ResponseDigital InputCodeAnalog OutputVFSVFS /2VFS /8EECS 247 Lecture 12: Data Converters © 2006 H. K. Page 15A/D Converter Transfer Characteristic• For an ideal analog-to-digital converter with uniform, binary digital encoding & a unipolar input range for 0 to VFS()FSiFSNNote:D Vb1,alli11V2→−Δ=⎛⎞−→⎜⎟⎝⎠FSFSNwhere N # of bitsV full scale outputstep sizeV2==Δ=Δ=……..…b1b2b3bmVinMSBLSBA/DEECS 247 Lecture 12: Data Converters © 2006 H. K. Page 16Ideal A/D Transfer Characteristic• Ideal ADC introduces error Æ(+-1/2Δ) Δ = VFS/2N N= # of bits•This error is called ``quantization error``111110101 100011010001000Digital OutputAnalog input0 Δ 2Δ 3Δ 4Δ 5Δ 6Δ 7Δ1LSBEECS 247 Lecture 12: Data Converters © 2006 H. K. Page 17Example: Non-Linear A/D ConverterFor Voice-Band Telephony ApplicationsNon-linear ADC and DAC used in voice-band CODECs• To maximize dynamic range with lower # of bits• Coding scheme called A-law & μ-law• Also called companding Ref: P. R. Gray, et al. "Companded pulse-code modulation voice codec using monolithic weighted capacitor arrays," IEEE Journal of Solid-State Circuits, vol. 10, pp. 497 - 499, December 1975. -VFS/2-VFS-VFS/4Coder Input(ANALOG)Coder Output(DIGITAL)EECS 247 Lecture 12: Data Converters © 2006 H. K. Page 18Data Converter Performance Metrics• Data Converters are typically characterized by static, time-domain, & frequency domain performance metrics :– Static• Monotonicity• Offset• Full-scale error• Differential nonlinearity (DNL)• Integral nonlinearity (INL)– Dynamic• Delay, settling time• Aperture uncertainty• Distortion- harmonic content• Signal-to-noise ratio (SNR), Signal-to-(noise+distortion) ratio (SNDR)• Idle channel
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