– 1 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 Data Converter Basics

A/D and D/A Conversion – 2 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 A/D Conversion D/A Conversion

Quantization – 3 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 Quantization = division + normalization + truncation Full-scale range (V FS ) is determined by V ref

Quantization Error – 4 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 “Random” quantization error is usually regarded as noise N = 3

Quantization Noise – 5 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 Assumptions: N is large 0 ≤ V in ≤ V FS and V in >> Δ V in is active ε is Uniformly distributed Spectrum of ε is white Ref: W. R. Bennett, “Spectra of quantized signals,” Bell Syst. Tech. J., vol. 27, pp , July 1948.

Signal-to-Quantization Noise Ratio (SQNR) – 6 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 Assume V in is sinusoidal with V p-p = V FS, N (bits) SQNR (dB) SQNR depicts the theoretical performance of an ideal ADC In reality, ADC performance is limited by many other factors: –Electronic noise (thermal, 1/f, coupling/substrate, etc.) –Distortion (measured by THD, SFDR, IM3, etc.)

FFT Spectrum of Quantized Signal – 7 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 N = 10 bits 8192 samples, only f = [0, f s /2] shown Normalized to V in f s = 8192, f in = 779 f in and f s must be incommensurate SQNR = dB ENOB = bits Ref: W. R. Bennett, “Spectra of quantized signals,” Bell Syst. Tech. J., vol. 27, pp , July 1948.

Commensurate f s and f in – 8 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 f s = 8192 f in = 256 f s = 8192 f in = 2048 Periodic sampling points result in periodic quantization errors Periodic quantization errors result in harmonic distortion

Spectrum Leakage – 9 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 f s = 8192 f in = f s = 8192 f in = TD samples must include integer number of cycles of input signal Windowing can be applied to eliminate spectrum leakage Trade-off b/t main-lobe width and sideband rejection for different windows w/ Blackman window

FFT Spectrum with Distortion – 10 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 High-order harmonics are aliased back, visible in [0, f s /2] band E.g., 779x3+1=2338, x779+1=1182 HD3 HD9

Dynamic Performance – 11 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 Peak SNDR limited by large-signal distortion of the converter Dynamic range implies the “theoretical” SNR of the converter

Dynamic Performance Metrics – 12 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 Signal-to-noise ratio (SNR) Total harmonic distortion (THD) Signal-to-noise and distortion ratio (SNDR or SINAD) Spurious-free dynamic range (SFDR) Two-tone intermodulation product (IM3) Aperture uncertainty (related to the frontend S/H and clock) Dynamic range (DR) – misleading (avoid it if possible!) Idle channel noise or pattern noise in oversampled converters

Evaluating Dynamic Performance – 13 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 Signal-to-noise plus distortion ratio (SNDR) Total harmonic distortion (THD) Spurious-free dynamic range (SFDR) SNDR = dB THD = dB SFDR = dB ENOB = bits HD3 HD9

Static Performance Metrics – 14 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 Offset (OS) Gain error (GE) Monotonicity Linearity (unique to converters) –Differential nonlinearity (DNL) –Integral nonlinearity (INL)

– 15 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 Static Performance of DAC

DAC Transfer Characteristic – 16 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 Note: V out (b i = 1, for all i) = V FS - Δ = V FS (1-2 -N ) ≠ V FS N = # of bits V FS = Full-scale input Δ = V FS /2 N = 1LSB b i = 0 or 1 Multiplication

Ideal DAC Transfer Curve – 17 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014

Offset – 18 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 V os

Gain Error – 19 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014

Monotonicity – 20 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014

Differential and Integral Nonlinearities – 21 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 DNL = deviation of an output step from 1 LSB (= Δ = V FS /2 N ) INL = deviation of the output from the ideal transfer curve DNL < -1 ?

DNL and INL – 22 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 INL = cumulative sum of DNL

DNL and INL – 23 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 DNL measures the uniformity of quantization steps, or incremental (local) nonlinearity; small input signals are sensitive to DNL. INL measures the overall, or cumulative (global) nonlinearity; large input signals are often sensitive to both INL (HD) and DNL (QE). SmoothNoisy

Measure DNL and INL (Method I) – 24 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 Endpoints of the transfer characteristic are always at 0 and V FS -Δ Endpoint stretch

Measure DNL and INL (Method II) – 25 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 Least-square fit and stretch (“detrend”) Endpoints of the transfer characteristic may not be at 0 and V FS -Δ

Measure DNL and INL – 26 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 Method I (endpoint stretch) Σ(INL) ≠ 0 Method II (LS fit & stretch) Σ(INL) = 0

– 27 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 Static Performance of ADC

Ideal ADC Transfer Characteristic – 28 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 Note the systematic offset! (floor, ceiling, and round)

DNL and Missing Code – 29 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 DNL = deviation of an input step width from 1 LSB (= V FS /2 N = Δ) DNL = ? Can DNL < -1?

DNL and Nonmonotonicity – 30 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 DNL = deviation of an input step width from 1 LSB (= V FS /2 N = Δ) DNL = ? How can we even measure this?

INL – 31 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 INL = deviation of the step midpoint from the ideal step midpoint (method I and II …) Any code Missing? Nonmonotonic?

10-bit ADC Example – 32 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall codes No missing code! Plotted against the digital code, not V in Code density test (CDT) DNL must always be greater or equal to -1 LSB!

Code Density Test – 33 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 Ball casting problem: # of balls collected by each bin (n i ) is proportional to the bin size (converter step size)

CDT and Nonmonotonicity – 34 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 Two transition steps for one code?! How to plot INL/DNL? CDT can be misleading in determining the static nonlinearity

– 35 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 Nyquist-Rate ADC

– 36 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 Digitizes input signal up to Nyquist frequency (f N =f s /2) Minimum sample rate (f s ) for a given input bandwidth Each sample is digitized to the maximum resolution of converter Often referred to as the “black box” version of digitization

Nyquist-Rate ADC (N-Bit, Binary) – 37 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 Word-at-a-time (1 step) † ← fast –Flash Level-at-a-time (2 N steps) ← slowest –Integrating (Serial) Bit-at-a-time (N steps) ← slow –Successive approximation –Algorithmic (Cyclic) Partial word-at-a-time (1 < M ≤ N steps) ← medium –Subranging –Pipeline Others (1 ≤ M ≤ N step) –Folding ← relatively fast –Interleaving (of flash, pipeline, or SA) ← fastest † the number in the parentheses is the “latency” of conversion, not “throughput”

Accuracy-Speed Tradeoff – 38 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014

Building Blocks for Data Converters – 39 – Data Converters Data Converter BasicsProfessor Y. Chiu EECT 7327Fall 2014 Sample-and-Hold (Track-and-Hold) Amplifier Switched-Capacitor Amplifiers, Integrators, and Filters Operational Amplifier Comparators (Preamplifier and Latch) Voltage and Current DAC’s Current Sources Voltage/Current/Bandgap References