EECS 247 Lecture 11: Introduction to Data Converters © 2008 H. K. Page 1EE247Lecture 11• Data converters– Areas of application– Data converter transfer characteristics– Sampling, aliasing, reconstruction– Amplitude quantization– Static converter error sources•Offset• Full-scale error• Differential non-linearity (DNL)• Integral non-linearity (INL)EECS 247 Lecture 11: Introduction to Data Converters © 2008 H. K. Page 2Material Covered in EE247Where are We?9Filters – Continuous-time filters• Biquads & ladder type filters• Opamp-RC, Opamp-MOSFET-C, gm-C filters• Automatic frequency tuning– Switched capacitor (SC) filters• Data Converters– D/A converter architectures– A/D converter • Nyquist rate ADC- Flash, Pipeline ADCs,….• Oversampled converters• Self-calibration techniques• Systems utilizing analog/digital interfacesEECS 247 Lecture 11: Introduction to Data Converters © 2008 H. K. Page 3Converter ApplicationsEECS 247 Lecture 11: Introduction to Data Converters © 2008 H. K. Page 4Data Converter Basics• DSPs benefited from device scaling• However, real world signals are still analog:– Continuous time– Continuous amplitude• DSP can only process:– Discrete time– Discrete amplitudeÆ Need for data conversion from analog to digital and digital to analog Analog PostprocessingD/AConversionDSPA/D ConversionAnalog PreprocessingAnalog InputAnalog Output000...001...110FiltersFilters??EECS 247 Lecture 11: Introduction to Data Converters © 2008 H. K. Page 5A/D & D/A ConversionA/D ConversionD/A ConversionEECS 247 Lecture 11: Introduction to Data Converters © 2008 H. K. Page 6Data 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• Various hand-held measurement equipment• Low cost digital oscilloscopesEECS 247 Lecture 11: Introduction to Data Converters © 2008 H. K. Page 7Data Converters• Embedded data converters– Integration of data conversion interfaces along with DSPs and/or RF circuits Æ Cost, reliability, and performance– Main issues• Feasibility of integrating sensitive analog functions in a technology typically optimized for digital performance• Down scaling of supply voltage as a result of downscaling of feature sizes• Interference & spurious signal pick-up from on-chip digital circuitry and/or high frequency RF circuits• Portable applications dictate low power consumptionEECS 247 Lecture 11: Introduction to Data Converters © 2008 H. K. Page 8Embedded ConvertersExample: Typical Cell PhoneContains in integrated form:• 4 Rx filters• 4 Tx filters• 4 Rx ADCs•4 Tx DACs• 3 Auxiliary ADCs• 8 Auxiliary DACsTotal: Filters Æ 8ADCs Æ 7DACs Æ 12Dual Standard, I/QAudio, Tx/Rx powercontrol, Battery chargecontrol, display, ...EECS 247 Lecture 11: Introduction to Data Converters © 2008 H. K. Page 9D/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 VFS…….…b1b2bNVo or IoMSBLSBFSFSNFS2N # of bitsV full scale outputmin. step size 1LSBV2Vor N log resolution==Δ= →Δ==→ΔNomenclature:D/AEECS 247 Lecture 11: Introduction to Data Converters © 2008 H. K. Page 10D/A Converter Transfer CharacteristicsFSFSNN#of bitsV full scale outputmin. step size 1LSBV2==Δ= →Δ=N0FSi1Ni1iNibiVV2bi 2 , bi 0 or 1==−==Δ× × =∑∑binary-weighted()imaxoFSmaxoFSNNote:Db1,alliVV11VV2=→=−Δ⎛⎞−→=⎜⎟⎝⎠…….…b1b2bNVo or IoMSBLSBD/AEECS 247 Lecture 11: Introduction to Data Converters © 2008 H. K. Page 11D/A Converter Exampe: D/A with 3-bit Resolutionb1b2b3V0MSBLSB()()01233FS00NFSFS210210Vb2 b2 b2Then: V /2 0.1VV0.1V12 02 12V0.5VNote:MSB V / 2 & LSB V / 2=Δ×+×+×Δ= =→= =×+×+×→=→→1 0 1Example: for N=3 and VFS=0.8Vinput codeÆ 101Find the output value V0D/AEECS 247 Lecture 11: Introduction to Data Converters © 2008 H. K. Page 12Ideal 3-Bit 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 11: Introduction to Data Converters © 2008 H. K. Page 13A/D Converter Transfer Characteristics• An ideal analog-to-digital converter:– Accepts analog input in the form of either voltage or current – Produces digital output either in serial or parallel form– Assumption (will be revisited) • Unipolar input ranging from 0 to VFS• Uniform, binary digital encoding …….…b1b2bNMSBLSBVin FSFSNFS2N # of bitsV full scale outputmin. resolvable input 1LSBV2Vor N log resolution==Δ= →Δ==→ΔA/DEECS 247 Lecture 11: Introduction to Data Converters © 2008 H. K. Page 14Ideal A/D Transfer CharacteristicExample: 3Bit A/D Converter• Ideal ADC introduces error with max peak-to-peak:Æ(+-1/2Δ) Δ =VFS/2N N= # of bits•This error is called ``quantization error``111110101 100011010001000DigitalOutputAnalog input0 Δ 2Δ 3Δ 4Δ 5Δ 6Δ 7Δ1LSBVFSEECS 247 Lecture 11: Introduction to Data Converters © 2008 H. K. Page 15Non-Linear Data Converters• So far data converter characterisitics studied are with uniform, binary digital encoding• For some applications to maximize dynamic range non-linear coding is used e.g. Voice-band telephony, – Small signals Æ larger # of codes– Large signals Æ smaler # of codesEECS 247 Lecture 11: Introduction to Data Converters © 2008 H. K. Page 16Example: Non-Linear A/D ConverterFor Voice-Band Telephony ApplicationsNon-linear ADC and DAC used in voice-band
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