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

Analog Input = K X Digital Output

12

n

fsAKResolution = Afs: Analog full scale voltage

n: Number of bits

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

• 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

Bit 3 =

1B

it 2 = 0

Bit 1 =

1

Bit 0 =

0

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