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Lecture 17: Analog to Digital Converters Lecturers: Professor John Devlin Mr Robert Ross Overview • Introduction to ADCs • Types of ADCs • Further Reading: – R.J. Tocci, Digital Systems, Principles and Applications, Prentice Hall (Chapter 10) Introduction ADC’s • The real world is full of analog, continuous signals • Microprocessors use digital electronics (encoded with discrete binary values) for processing • Analog to Digital Converters (ADC or A/D) convert continuous analog signals to discrete digital numbers – allowing digital electronics to sample real world signals • ADC’s are ‘Mixed Signal Devices’ as they combine analog circuits with DSP • Reverse of the operation of the DAC (Digital to Analog Converter) Important Terms • Resolution: Smallest analog increment corresponding to a 1 LSB change in conversion • Voltage Reference: the voltage against which the input is compared, taken as the full scale voltage • Conversion Time: Time required for a complete measurement • Number of Bits: Number of bits used to digitally encode the measured signal Calculations Resolution = K A fs 2n 1 Afs: Analog full scale voltage n: Number of bits Analog Input = K X Digital Output Digital Output = Analog Input / K Number of voltage levels = 2n Number of voltage steps = 2n -1 Example • A 10 bit ADC is used to sample over the range 0 to 5 Volts (VREF+ = 5V, VREF-=0V) • What is the step size? – 5/ (210-1)= 4.89mV/step • How would 2.1V be encoded? – (2.1/4.89mV) = 429 (Binary: 0110101101) • What voltage would correspond to 321 being returned by the ADC? – (321) x 4.89mV = 1.57V Example • A 8 bit ADC is used to sample over the range 0 to 2 Volts (VREF+ = 2V, VREF-=0V) • What is the step size? – 2/ (28 - 1)= 7.84mV/step • How would 0.5V be encoded? – 0.5/7.84mV = 64 (Binary: 01000000) • How would 0.75V be encoded? – 0.75/7.84mV = 96 (Binary: 01100000) • How would 2V be encoded? – 2/7.84mV = 255 (Binary: 11111111) • What voltage would a code of 5 belong to? – 5 x 7.84mV = 39mV • What voltage would a code of 190 belong to? – 190 x 7.84mV = 1.49V ADC Interface Signals • Data: Digital I/O pins the ADC uses to supply data • Start: Pulse high to start conversion • EOC (End of Conversion): Typically active low – will pulse low when conversion is complete • Clock: Clock used for conversion Types of ADC’s • • • • Flash Ramp-Compare (Integrating) Successive Approximation Sigma-Delta Flash ADC • Flash ADC (AKA Direct or Parallel ADC) uses a linear ladder of comparators to compare many different voltage references at the same time • Very fast -> High Bandwidth • Requires many comparators – expensive (2n – 1) comparators for n-bit conversion • Therefore typically low resolution Ramp-Compare (Integrating) ADC • A comparison voltage VAX is ramped up • When the comparison voltage matches the sampled voltage (VA) the comparator is triggered – the sampled voltage has been determined Ramp-Compare (Integrating) ADC • Two different implementations: – Timing of a charging capacitor – Driving a DAC with a counter Ramp-Compare (Integrating) ADC • Variable Conversion Time (depends when ramp signal matches actual signal) • Best case = 1 cycle • Worst case = 2n cycles • Average conversion time: 2n/2 Cycles, where n is the number of bits • Slower than Flash, but much less comparators – allows for higher accuracy Successive Approximation ADC • Successive Approximation ADC’s use a binary search to converge on the closest quantisation level • Binary search uses a divide and conquer algorithm • Binary search: – Select middle element – If too high select middle element of lower group – If too low select middle element of upper group – Repeat until 1 element remains Successive Approximation ADC Bit 0 = 0 Bit 1 = 1 Bit 2 = 0 Bit 3 = 1 • Slower than Flash, but far fewer comparators – allows for higher accuracy • Constant conversion time: n cycles • Each cycle allows the next MSB to be determined 4 Bit SAC Sigma-Delta ADC • Analog input used to drive a Voltage controlled oscillator (VCO) • Using a counter and a specified time period the frequency of the VCO can be determined • Since the frequency of the VCO is known, the input driving the VCO can be calculated • Negative feedback is used to generate the oscillator – which is in the form of a 1 bit serial bit stream Sigma-Delta ADC • Oversampling (more than the minimum sampling rate of 2*fmax) • Taking the mean of a series of over sampled measurements increases the resolution • One bit (density of ‘1’s and ‘0’s represents the analog voltage) Summary • Analog to Digital converters allow digital electronics to sample real world analog signals • Depending on the resolution and bandwidth requirements different methods of performing ADC can be used