Analog to Digital Converters

Analog to Digital
Converters
Anas mujahid

Presentation Outline
Introduction: Analog vs. Digital?
Examples of ADC Applications
Types of A/D Converters
A/D Subsystem used in the
microcontroller chip
Examples of Analog to Digital Signal
Conversion
Successive Approximation ADC

Analog Signals
Analog signals – directly measurable quantities
in terms of some other quantity
Examples:
 Thermometer – mercury height rises as
temperature rises
 Car Speedometer – Needle moves farther
right as you accelerate
 Stereo – Volume increases as you turn the
knob.

Digital Signals
Digital Signals – have only two states. For
digital computers, we refer to binary states, 0
and 1. “1” can be on, “0” can be off.
Examples:
 Light switch can be either on or off
 Door to a room is either open or closed

Examples of A/D Applications
 Microphones - take your voice varying pressure waves in the
air and convert them into varying electrical signals
 Strain Gages - determines the amount of strain (change in
dimensions) when a stress is applied
 Thermocouple – temperature measuring device converts
thermal energy to electric energy
 Voltmeters
 Digital Multimeters

Just what does an
A/D converter DO?
 Converts analog signals into binary words

Two main steps of process
1.Sampling and Holding
2.Quantization and Encoding
ADC Conversion Process

Analog  Digital Conversion
2-Step Process:
 Quantizing - breaking down analog value is a
set of finite states
 Encoding - assigning a digital word or
number to each state and matching it to the
input signal

Step 1: Quantizing
Example:
You have 0-10V
signals. Separate them
into a set of discrete
states with 1.25V
increments. (How did
we get 1.25V? See
next slide…)
Output
States
Discrete Voltage
Ranges (V)
0 0.00-1.25
1 1.25-2.50
2 2.50-3.75
3 3.75-5.00
4 5.00-6.25
5 6.25-7.50
6 7.50-8.75
7 8.75-10.0

Quantizing
The number of possible states that the
converter can output is:
N=2n
where n is the number of bits in the AD converter
Example: For a 3 bit A/D converter, N=23
=8.
Analog quantization size:
Q=(Vmax-Vmin)/N = (10V – 0V)/8 = 1.25V

Encoding
 Here we assign the
digital value (binary
number) to each
state for the
computer to read.
Output
States
Output Binary Equivalent
0 000
1 001
2 010
3 011
4 100
5 101
6 110
7 111

Accuracy of A/D Conversion
There are two ways to best improve accuracy of
A/D conversion:
 increasing the resolution which improves the
accuracy in measuring the amplitude of the
analog signal.
 increasing the sampling rate which increases the
maximum frequency that can be measured.

Resolution
 Resolution (number of discrete values the converter can
produce) = Analog Quantization size (Q)
(Q) = Vrange / 2^n, where Vrange is the range of analog
voltages which can be represented
 limited by signal-to-noise ratio (should be around 6dB)
 In our previous example: Q = 1.25V, this is a high
resolution. A lower resolution would be if we used a 2-bit
converter, then the resolution would be 10/2^2 = 2.50V.

CONVERSATION OF
ANALOG TO DIGITAL
SIGNAL

SAMPLING
 Sampling is the process of recording an
analog signal at regular discrete moments of
time.
 The sampling rate fs is the number of
samples per second.
 The time interval between samples is called
the sampling interval
Ts=1/fs.

The signal v(t)=cos(2πft) in Fig. 1 is sampled uniformly with 3 sampling intervals within each signal period T.
Therefore, the sampling interval Ts=T/3 and the sampling rate fs=3f.

The samples from above figure are shown as the sequence v[n] indexed by integer values of n.

NYQUIST THEOREM
 The Nyquist-Shannon sampling theorem states that
“the sampling rate for exact recovery of a signal
composed of a sum of sinusoids is larger than twice
the maximum frequency of the signal”.
 This rate is called the Nyquist sampling rate
fNyquist.
 fs>fNyquist=2fmax(5)

QUANTIZATION
 A sequence of samples like v[n] in Fig. 2 is not a
digital signal because the sample values can
potentially take on a continuous range of values.
 In order to complete analog to digital conversion,
each sample value is mapped to a discrete level
(represented by a sequence of bits) in a process
called quantization.
 In a m-bit quantizer, each quantization level is
represented with m bits, so that the number of
levels equals 2^m.

Overlaid on the samples v[n] from Fig. 2 is a 3-bit quantizer with 8 uniformly spaced quantization levels.
The quantizer approximates each sample value in v[n] to its nearest level value (shown on the left),
producing the quantized sequence vQ[n].

ADC Process
t
Continuous Signal
Sampling & Hold
Measuring analog signals
at uniform time intervals
 Ideally twice as fast as what
we are sampling
Digital system works with
discrete states
 Taking samples from each
location
Reflects sampled and hold
signal
 Digital approximation

ADC Process
t
Sampling & Hold
we are sampling
discrete states
 Taking samples from each
location
signal

ADC Process
t
Sampling & Hold
we are sampling
discrete states
 Taking a sample from each
location
signal

Sampling Rate
Frequency at which ADC evaluates analog signal. As we
see in the second picture, evaluating the signal more often
more accurately depicts the ADC signal.

Aliasing
 Occurs when the input signal is changing much
faster than the sample rate.
For example, a 2 kHz sine wave being sampled
at 1.5 kHz would be reconstructed as a 500 Hz
(the aliased signal) sine wave.
Nyquist Rule:
 Use a sampling frequency at least twice as high
as the maximum frequency in the signal to avoid
aliasing.

Overall Better Accuracy
 Increasing both the sampling rate and the resolution
you can obtain better accuracy in your AD signals.

A/D Converter Types
 Converters
 Flash ADC
 Delta-Sigma ADC
 Dual Slope (integrating) ADC
 Successive Approximation ADC

Flash ADC
 Consists of a series of comparators, each
one comparing the input signal to a unique
reference voltage.
 The comparator outputs connect to the inputs
of a priority encoder circuit, which produces a
binary output

How Flash Works
 As the analog input voltage exceeds the
reference voltage at each comparator, the
comparator outputs will sequentially saturate
to a high state.
 The priority encoder generates a binary
number based on the highest-order active
input, ignoring all other active inputs.

Flash
Advantages
 Simplest in terms of
operational theory
 Most efficient in terms
of speed, very fast
 limited only in terms of
comparator and gate
propagation delays
Disadvantages
 Lower resolution
 Expensive
 For each additional
output bit, the number
of comparators is
doubled
 i.e. for 8 bits, 256
comparators needed

Sigma Delta ADC
 Over sampled input
signal goes to the
integrator
 Output of integration is
compared to GND
 Iterates to produce a
serial bit stream
 Output is serial bit
stream with # of 1’s
proportional to Vin

Sigma-Delta
Advantages
 High resolution
 No precision external
components needed
Disadvantages
 Slow due to
oversampling

Dual Slope Converter
 The sampled signal charges a capacitor for a fixed
amount of time
 By integrating over time, noise integrates out of the
conversion
 Then the ADC discharges the capacitor at a fixed
rate with the counter counts the ADC’s output bits.
A longer discharge time results in a higher count
t
Vin
tFIX tmeas

Dual Slope Converter
Advantages
 Input signal is averaged
 Greater noise immunity
than other ADC types
 High accuracy
Disadvantages
 Slow
 High precision external
components required to
achieve accuracy

Successive Approximation ADC
 A Successive Approximation Register (SAR)
is added to the circuit
 Instead of counting up in binary sequence,
this register counts by trying all values of bits
starting with the MSB and finishing at the
LSB.
 The register monitors the comparators output
to see if the binary count is greater or less
than the analog signal input and adjusts the
bits accordingly

Successive Approximation
ADC Circuit

Advantages
 Capable of high speed and
reliable
 Medium accuracy compared
to other ADC types
 Good tradeoff between
speed and cost
 Capable of outputting the
binary number in serial (one
bit at a time) format.
Disadvantages
 Higher resolution
successive approximation
ADC’s will be slower
 Speed limited to ~5Msps

ADC Resolution Comparison
0 5 10 15 20 25
Sigma-Delta
Successive Approx
Flash
Dual Slope
Resolution (Bits)
Type Speed (relative) Cost (relative)
Dual Slope Slow Med
Flash Very Fast High
Successive Appox Medium – Fast Low
Sigma-Delta Slow Low
ADC Types ComparisonADC Types Comparison

Example
 10 bit resolution or
0.0009765625V of Vref
 Vin= .6 volts
 Vref=1volts
 Find the digital value of
Vin

 MSB (bit 9)
 Divided Vref by 2
 Compare Vref /2 with Vin
 If Vin is greater than Vref /2 , turn MSB on (1)
 If Vin is less than Vref /2 , turn MSB off (0)
 Vin =0.6V and V=0.5
 Since Vin>V, MSB = 1 (on)

 Next Calculate MSB-1 (bit 8)
 Compare Vin=0.6 V to V=Vref/2 + Vref/4= 0.5+0.25 =0.75V
 Since 0.6<0.75, MSB is turned off
 Calculate MSB-2 (bit 7)
 Go back to the last voltage that caused it to be turned on
(Bit 9) and add it to Vref/8, and compare with Vin
 Compare Vin with (0.5+Vref/8)=0.625
 Since 0.6<0.625, MSB is turned off

 Calculate the state of MSB-3 (bit 6)
 Go to the last bit that caused it to be turned on (In
this case MSB-1) and add it to Vref/16, and
compare it to Vin
 Compare Vin to V= 0.5 + Vref/16= 0.5625
 Since 0.6>0.5625, MSB-3=1 (turned on)

 This process continues for all the remaining
bits.

DAC Performance Specifications
 Monotonicity means that the magnitude
of the output voltage increases every time
the input digital code increases.
 Absolute accuracy is the measure of the
DAC output voltage with respect to its
expected value.
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 Relative accuracy is the deviation of the
actual from the ideal output voltage as a
fraction of the full-scale voltage.
 Settling time is the time required for the
outputs to switch and settle within ±½ LSB
when the input switches form all 0s to all 1s.
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 Gain error occurs when the output saturates
before reaching the maximum output code.
 Linearity error is the deviation from a straight
line output with increasing digital input codes.
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 Differential nonlinearity is the difference
between actual and expected step size
when the input code is changed by 1 LSB.
 Offset error occurs when the DAC output
is not 0 V when the input code is all 0s.
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Analog to Digital Converters

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