Department of Electrical and Computer Engineering Pipelined Analog-to-Digital Converters Vishal Saxena, Boise State University ([email protected]) Vishal Saxena -1- Multi-Step A/D Conversion Basics Vishal Saxena -22- Motivation for Multi-Step Converters Flash A/D Converters   Area and power consumption increase exponentially with  number of bits N  Impractical beyond 7-8 bits Multi-step conversion-Coarse conversion followed by fine  conversion  Multi-step converters  Sub-ranging converters Multi step conversion takes more time   Pipelining to increase sampling rate Objective: Understand digital redundancy concept in multi-step  converters Vishal Saxena -3- Two-step A/D Converter - Basic Operation Second A/D quantizes the quantization error of first A/D converter  Concatenate the bits from the two A/D converters to form the final  output Also called as two-step Flash ADC  Vishal Saxena -4- Two-step A/D Converter - Basic Operation A/D1, DAC, and A/D2 have the same range V  ref Second A/D quantizes the quantization error of first A/D   Use a DAC and subtractor to determine residue V q  Amplify V to full range of the second A/D q Final output n from m, k   A/D1 output is m (DAC output is m/2MV ) ref  A/D2 input is at kth transition (k/2KV ) ref  V = k/2KV × 1/2M + m/2MV in ref ref  V = (2Km + k)/2M+KV in ref Resolution N = M + K   output  n = 2Km + k  Concatenate the bits from the two A/D converters to form the final output Vishal Saxena -5- Two-step A/D Converter – Example with M=3, K=2 Second A/D quantizes the quantization error of first A/D  Transitions of second A/D lie between transitions of the first, creating  finely spaced transition points for the overall A/D Vishal Saxena -6- Residue V q V vs. V : Discontinuous transfer curve  q in  Location of discontinuities: Transition points of A/D1  Size of discontinuities: Step size of D/A  Slope: unity Vishal Saxena -7- Two-step A/D Converter—Ideal A/D1 A/D1 transitions exactly at integer multiples of V /2M  ref Quantization error V limited to (0,V /2M)  q ref 2MV exactly fits the range of A/D2  q Vishal Saxena -8- Two-step A/D converter—M bit accurate A/D1 A/D1 transitions in error by up to V /2M+1 (= 0.5 LSB)  ref Quantization error V limited to  q  (−V /2M+1, 3V /2M+1)—a range of V /2M−1 ref ref ref 2MV overloads A/D2  q Vishal Saxena -9- Two-step A/D with Digital Redundancy (DR) Reduce interstage gain to 2M−1  Add V /2M+1 (0.5 LSB ) offset to keep V positive  ref 1 q Subtract 2K−2 from digital output to compensate for the added offset   Digital code in A/D2 corresponding to 0.5 LSB = (V /2M+1)/(V /2K+1)= 2K−2 1 ref ref Overall accuracy is N = M + K − 1 bits   A/D1 contributes M − 1 bits  A/D2 contributes K bits; 1 bit redundancy Output n = 2K−1m + k − 2K−2  Vishal Saxena -10-