Oversampling Analog to Digital Converters 21st International Conference on VLSI Design, Hyderabad Shanthi Pavan Nagendra Krishnapura DepartmentofElectricalEngineering IndianInstituteofTechnology,Madras Chennai,600036,India 4 January 2008 1 ShanthiPavan NagendraKrishnapura OversamplingAnalogtoDigitalConverters Outline Introduction to sampling and quantization Quantizationnoisespectraldensity Oversampling Noiseshaping-∆Σmodulation High order multi bit ∆Σ modulators Stability of ∆Σ A/D converters Implementation of ∆Σ A/D converters Loopfilterdesign Multibitquantizerdesign Excessdelaycompensation Clockjittereffects Mitigation of feedback DAC mismatch Dynamicelementmatching DACcalibration Case study 15bitcontinuous-time∆ΣADCfordigitalaudio 2 ShanthiPavan NagendraKrishnapura OversamplingAnalogtoDigitalConverters Signal processing systems Sensor(s) Digital Processing Actuator(s) . . . DSP . . . ...0100011011... . . . Continuous-time Discrete -time Continuous-time Continuous-amplitude Discrete -amplitude Continuous-amplitude Interface Electronics (Signal Conditioning) (A-D and D-A Conversion) 3 ShanthiPavan NagendraKrishnapura OversamplingAnalogtoDigitalConverters Signal processing systems Natural world: continuous-time analog signals Storage and processing: discrete-time digital signals Data conversion circuits interface between the two Wide variety of precision and speed 4 ShanthiPavan NagendraKrishnapura OversamplingAnalogtoDigitalConverters Continuous time signals Continuous−time analog signal 7V LSB 6V LSB 5V LSB 4V LSB 3V LSB 2V LSB V LSB 0 0 T 2T 3T 4T 5T 6T 7T 8T 9T 10T s s s s s s s s s s Signals defined for all t Signals can take any value in a given range 5 ShanthiPavan NagendraKrishnapura OversamplingAnalogtoDigitalConverters Discrete time signals Discrete time signal 7V LSB 6V LSB 5V LSB 4V LSB 3V LSB 2V LSB V LSB 0 0 1 2 3 4 5 6 7 8 9 10 Signals defined for discrete instants n Signals can take any value in a given range 6 ShanthiPavan NagendraKrishnapura OversamplingAnalogtoDigitalConverters Digital signals Sampled quantized(digital) signal 7V LSB 6V LSB 5V LSB 4V LSB 3V LSB 2V LSB V LSB 0 0 1 2 3 4 5 6 7 8 9 10 Signals defined for discrete instants n Signals can take discrete values kV LSB 7 ShanthiPavan NagendraKrishnapura OversamplingAnalogtoDigitalConverters Sampling and quantization A segment of a continuous-time signal has an infinite number of points of infinite precision Discretization of time(sampling) and amplitude(quantization) results in a finite number of points of finite precision Sampling and quantization = Analog to digital conversion Errors in the process? 8 ShanthiPavan NagendraKrishnapura OversamplingAnalogtoDigitalConverters Signals in time and frequency domains Continuous time signal x (t) ct Frequency domain representation using its Fourier transform X (f) ct ∞ X (f) = x (t)exp( j2πft)dt ct ct Z − −∞ Discrete time signal x [n] d Frequency domain representation using its Fourier transform X (ν) d ∞ X [ν] = x [n]exp( j2πνn) d d − n=X −∞ X [ν] periodic with a period of 1 d 9 ShanthiPavan NagendraKrishnapura OversamplingAnalogtoDigitalConverters Signals in time and frequency domains Continuous−time analog signal Fourier transform of a continuous−time signal 7V LSB 6V LSB 5VLSB 1.0 4V LSB 3V LSB 2V LSB V LSB f b 0 0 0 Ts 2Ts 3Ts 4Ts 5Ts 6Ts 7Ts 8Ts 9Ts 10Ts 0 fs 2fs ∞ X (f) = x (t)exp( j2πft)dt ct ct Z − −∞ Signal bandwidth f : X (f) = 0 for f > f b ct b | | 10 ShanthiPavan NagendraKrishnapura OversamplingAnalogtoDigitalConverters