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Lecture 17: Analog to Digital Converters

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.

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Lecture 17: Analog to Digital Converters

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  1. Lecture 17: Analog to Digital Converters Lecturers: Professor John Devlin Mr Robert Ross

  2. Overview • Introduction to ADCs • Types of ADCs • Further Reading: • R.J. Tocci, Digital Systems, Principles and Applications, Prentice Hall (Chapter 10)

  3. 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)

  4. 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

  5. Calculations Afs: Analog full scale voltage n: Number of bits Resolution = Analog Input = K X Digital Output Digital Output = Analog Input / K Number of voltage levels = 2n Number of voltage steps = 2n -1

  6. 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

  7. 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

  8. 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

  9. Types of ADC’s • Flash • Ramp-Compare (Integrating) • Successive Approximation • Sigma-Delta

  10. 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 Flash ADC

  11. 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

  12. Two different implementations: Timing of a charging capacitor Driving a DAC with a counter Ramp-Compare (Integrating) ADC

  13. 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 Ramp-Compare (Integrating) ADC

  14. 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

  15. 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 Successive Approximation ADC Bit 2 = 0 Bit 0 = 0 Bit 1 = 1 Bit 3 = 1 4 Bit SAC

  16. 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

  17. 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)

  18. 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

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