final project thesis presentation rodrigo lorente sanjurjo thessaloniki, mar.12, 2010

FINAL PROJECT THESIS PRESENTATION RODRIGO LORENTE SANJURJO THESSALONIKI, Mar.12, 2010

OBJETIVES Give a general idea about the importance of the converters (ADCs). Help to understand the characteristics and behavior of an ADC. Analysis of non-idealities. Study the effects of real converters in bigger circuits.

INTRODUCTION It is said that the world is becoming digital. Evolution: Originally mechanical -> Electrical -> Solid-State. Optimization of resources and performance. E.g.: Audio.

INTRODUCTION

THEORY The analog-to-digital conversion consists in the transformation of analog signals into digital ones. A digital signal have discrete time and amplitude. An analog signal is one whose amplitude can (in principle) take any value, which does not mean that it have infinite precision.

Advan & Disad. of digitizing a signal Advantages Disadvantages Easy reconstruction when attenuated or disturbed. Systems of detection/correction of errors. Easy signal processing. Multigeneration infinitely without quality loss. Data compression techniques. It needs the conversion and the decoding. If not enough quantization levels, it decreases SNR. It is necessary a low-pass filter to avoid aliasing (also during the reconstruction).

Concepts Resolution: number of discrete values in what the entire range of analog values can be transformed. Limited by the SNR. Sampling rate: speed at which the analog signal is sampled. Signal to Noise Ratio (SNR) Signal to Noise and Distortion (SINAD) Effective Number of Bits (ENOB) Spurious-Free Dynamic Range (SFDR)

Concepts Quantization Error: due to the finite resolution of an ADC. Offset Error Full-Scale Error Gain Error Non-linearity: DNL and INL Missing Codes

Architectures Direct Conversion ADC or Flash ADC: bank of comparators in parallel, the fastest, limited resolution, exponential growth.

Architectures Successive-Approximation ADC: it constantly compares the value with different references until the best approximation is achieved.

Architectures Wilkinson ADC: it compares the input with the voltage of a load capacitor that discharges linearly when both voltages are equal, generating a pulse with the duration of the discharge which operates a logic gate that allows the pass of a pulse train. Sigma-Delta ADC (-): it uses oversampling to limit the quantization noise to the bandwidth of the signal. Pipeline ADC Integrating ADC (dual-slope or multi-slope) Ramp-compare ADC Time-interleaved ADC

HISTORY The first noticed kind of converter was in Turkey at 18 th century. An 8-bit DAC to measure water. Communications field, the main force behind the development of electronic data converters. Need for multiplexing: Pulse Code Modulation (PCM), first time in a patent of Paul M. Rainey, then developed by Alec Harley Reeves, covering the counter-based design for 5-bit ADCs and DACs

HISTORY At the beginning they used vacuum tube technology: expensive, bulky and high energy consumption. Migration to transistor (1950s-1960s). 1954 1966 1978

HISTORY Three different technologies: Monolithic Modular Hybrid Until 1990s predominance of modular and hybrid.

HISTORY

Present and future: Converter closer to the original signal. Integrate converters with other functions. Performance saturation. Very high level of transistor density. Digital post-processing to compensate analog non-idealities.

CODE Steps: Thresholds of decision. Comparison matrices. Calculation of the digital output. Calculation of non-idealities. Graphical representation.

Thresholds of decision Initially all the thresholds correspond to the ones of the ideal case (each multiple value of LSB).

Thresholds of decision Two parameters: Steps Slopes Two operation modes: Single value Vector of values

Steps steps = -0.5 steps = [0 -0.7 0 -0.5 0.5 0 0.7 0]

Slopes

slopes = 2 slopes = [1.2 1 1.5 1 1 0.5 1 1]

Thresholds of decision % ADC's real transfer function converter = zeros(2,2^nbits); % Thresholds of conversion slope_steps = ((ones(1,2^nbits)./slopes)- 1)*triu(ones(2^nbits,2^nbits)); converter(1,:) = ((1:2^nbits)+slope_steps+steps)*vlsb; % Digital output values converter(2,:) = (1:2^nbits)-1;

Comparison matrices With the thresholds we generate two matrices Reference matrix Matrix with the input information

Comparison matrices % Auxiliary (2^nbits)x(length(vin)) matrix with the square of each digital % value in the columns aux = vin*0+1; % Weight up the new matrix with the reference voltage and the number of % bits aux = (converter(1,:)'.^2*aux); % Weight up the input and compare it with the auxiliary matrix conversion = converter(1,:)'*(vin*vref/2);

Calculation of the digital output conversion = conversion>aux; % After fixing the problem of bubbles the output will be the number of ones % in each column out = max(((1:2^nbits)'*ones(1,length(conversion))).*conversion); % Limit maximum output value out(out>2^nbits-1) = 2^nbits-1;

Calculation of the digital output Two problems: Negative Thresholds Bubbles

Negative Thresholds R is the highest negative or zero threshold Avoid problems % Readjust negative thresholds R = find(converter(1,:)

Negative Thresholds E.g.: R=2 The problem are the outputs equal to zero % Compensation of the 0s for non-positive thresholds if R>0 out(out==0) = R; end

Bubbles Caused by Missing Codes Common in real converters

Bubbles E.g.: It does not affect thanks to the implementation. Alternative code that finds the positions of the bubbles

Bubbles

Calculation of non-idealities Best linear approximation. Offset Error Full-Scale Error Gain Error DNL INL % ADC's transfer function's linear interpolation approxFunction = polyfit([steps(1) converter(1,1:end- 1)/vlsb],converter(2,:),1); approxConverter = (converter(2,:)- approxFunction(2))*vlsb/approxFunction(1);

Calculation of non-idealities It uses all the values to calculate the non-idealities. Results in LSB units. % Output info offset = approxConverter(1)/vlsb; FSError = (idealConverter(end-1)-approxConverter(end))/vlsb; GError = FSError+offset; aux_inl = converter(1,1)-vlsb/slopes(1); % INL Adjustment INL = abs(approxConverter-[aux_inl converter(1,1:end- 1)])/vlsb; DNL = ([converter(1,1:end-1) vref]-[0 converter(1,1:end- 1)])/vlsb-1; DNL(DNL

Graphical representation % Number of points in the plot voltPoints = 2^14; converterRep = zeros(1,voltPoints); ---------------------------------------------------------- % Representation of the ADC transfer function scaling = voltPoints/vref; scaledConverter = converter(1,:)*scaling; scaledConverter(scaledConverter2^nbits-1) = 2^nbits-1;

EXAMPLES Ideal 3-bit converter

EXAMPLES steps = 0.75 & slopes = 1.4

EXAMPLES steps = [0 0 0.3 0.5 -0.3 0.4 0.3 0]

EXAMPLES steps = [0 0.2 0.2 0.8 -0.5 0.7 0 0]

EXAMPLES steps = [1 1.3 1.5 2 2.5 2.7 4 0]

EXAMPLES steps = [0 0.3 0.5 0 0 -0.2 0 0] & slopes = [1.5 1 1 0.8 0.8 2 2 1]

QUESTIONS

final project thesis presentation rodrigo lorente sanjurjo thessaloniki, mar.12, 2010

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