Transcript 9_EMBEDDED_GR_ppapag_ADC

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