FE8113 ”High Speed Data Converters”

Course outline Focus on ADCs. Three main topics:  1: Architectures ”CMOS Integrated Analog-to-Digital and Digital-to- Analog Converters,” 2nd ed., Rudy van de Plassche, Kluwer Academic Publishers, Ch. 1-3  2: Digital background calibration Selected papers  3: State-of-the-art converters Selected papers

Part 1: Architectures First three chapters of van de Plassche’s textbook  Ch.1: The Converter as a black box  Ch.2: Specifications of converters  Ch.3: High-Speed A/D Converters

Chapter 1 The converter as a black box

Basic A/D converter function Digital output:

Classification of signals A/D conversion:  Amplitude quantization  Sampling

Quantization errors Quantization error ε: Mean squared error: S/N for sinewave input (amplitude 2 (n-1) q s ):

Quantization errors Nioise density: System with BW=f sig: Definition of dynamic range: The dynamic range is equal to the signal-to-noise ratio measured over a bandwith equal to half the sampling frequency

Oversampling of converters Oversampling distributes the quantization noise over a larger spectrum However: Improvement in resolution is only obtained if the linearity of the converter is at least equal to the dynamic range obtained by oversampling

Quantization error spectra Sawtooth error signal, described by odd harmonics:

Quantization error spectra For a sinewave input, the error signal will get a kind of frequency modulation: Simplifying: where odd p even p p=1 p≠1p≠1

Amplitude dependence of quantization components ?

Multiple signal distortion Two input signals: Cross-modulation: Quantization results in errors correlated with the signal mostly as odd harmonics This analysis allows for investigation of inter-modulation and harmonic distortion  With resolutions above 10b these effects can practically be ignored

Accurate dynamic range calculation Fundamental signal amplitude for an n-bit converter (p=1): Quantization error calculated as sum of power of all odd harmonics: Signal to noise ratio:

Accurate dynamic range calculation Number of bits nS/N Accurate dBS/N 6.02*n

Sampling time uncertainty Assume full scale sine wave input  Sampling time error must be within 1LSB Inserting for t=0 (worst-case):

Sampling time uncertainty Reduction of ENOB  Error power due to jitter:  Average power:  Including quantization noise:  Dynamic range: where

Sampling clock time uncertainty Clock noise due to thermal noise over squaring amplifier bandwith With equivalent noise resistance R n of squaring amplifier, the noise is expressed as Differentiating V cl =Asin(ωt) we obtain the time uncertainty (rms)

Sampling clock time uncertainty Total time uncertainty, inserting at zero crossing For a first-order system,, which yields In amplifier systems, ther is a general relation between rise time at the output and bandwith Total clock time uncertainty from first order squaring circuit:

Ch Design specific, supplementary reading  Ch 1.13 Nyquist filtering in A/D converter systems  Ch 1.14 Combined analog and digital filter  Ch 1.15 Output filtering in D/A converter systems  Ch 1.16 Dynamic range and alias filter order  Ch 1.17 Analog filter designs

Minimum required stop band attenuation If the ADC system has an internal bandwith greater than the overall bandwith, quantization noise will fold down to the baseband  Example: SAR converters, where the comparator bandwith, f comp, is N times higher than the input bandwith Due to the sampling of the input signal all frequencies that are in the aliasing signal bands are folded back into the baseband of the system At which point the aliasing occurs depends on the architecture of the ADC and the point in the system where the sampling is performed

Minimum required stop band attenuation With f comp denoting the internal bandwith, the number of unwanted bands that fold back to the baseband is given by: The ”noise” in the baseband now increases to Stop-band rejection of low-pass filter must be increased by This increase in stop-band rejection (A foldback ) is equal to Which gives the minimum required stop-band rejection A stopmin This stopband rejection requirements yields an 3dB overall reduction of dynamic range (S/N)

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