# EE 319K - Introduction To Microcontrollers by xSo9LLp

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```									EE 319K – Introduction to
Embedded Systems

EE 319K - Summer 2012 - Bill Bard - w.bard@mail.utexas.edu   1
Today’s Agenda
• QUIZ 2 – Friday, 7/27
• Analog to Digital Conversion

EE 319K - Summer 2012 - Bill Bard - w.bard@mail.utexas.edu   2
Analog To Digital
Conversion

EE 319K - Summer 2012 - Bill Bard - w.bard@mail.utexas.edu   3
Sample-And-Hold Circuit

Analog Input (AI) is sampled when the switch is closed
and its value is held on the capacitor where it becomes
the Analog Output (AO)

EE 319K - Summer 2012 - Bill Bard - w.bard@mail.utexas.edu   4
Analog to Digital Converter - ADC
• Successive Approximation
– VIN is approximated as a static                                        end of conversion
value in the sample and hold
circuit
– the successive approximation
register is a counter that
increments each clock as long
as it is enabled by the
comparator
– the output of the SAR is fed to
a DAC that generates a
voltage for comparison with
VIN
– when the ouput of the DAC =
VIN the value of SAR is the
digital representation of VIN
EE 319K - Summer 2012 - Bill Bard - w.bard@mail.utexas.edu              5

D            C             B
E                                                        A

EE 319K - Summer 2012 - Bill Bard - w.bard@mail.utexas.edu   6
Analysis
• Assume that the voltage for each bit (bi) is
either 0 or 1V.
– At point A, the voltage will be one half b0
considering the 2R-2R voltage divider
– The Thevenin equivalent circuit is a voltage
source having the value b0/2 in series with a
resistor, R (2R||2R)
– This voltage is applied through a series
resistor R to point B

EE 319K - Summer 2012 - Bill Bard - w.bard@mail.utexas.edu   7
Digital To Analog Conversion

R-2R Network

EE 319K - Summer 2012 - Bill Bard - w.bard@mail.utexas.edu   8
Analog to Digital Converter

EE 319K - Summer 2012 - Bill Bard - w.bard@mail.utexas.edu   9
Cortex M3                    Systick
System Bus Interface            NVIC

GPIO Port A                           GPIO Port B
PA7/I2C1SDA
PA6/I2C1SCL            I2C1                                             PB7/TSRT
Analog                PB6/C0+
PA5/SSI0Tx                                                            PB5/C1-
PA4/SSI0Rx                                PF4 Comparator
SSI0                                             PB4/C0-
PA3/SSI0Fss                                                            PB3/I2C0SDA
PA2/SSI0Clk                                          I2C0              PB2/I2C0SCL
PA1/U0Tx                                 PF6                         PB1/CCP2
PA0/U0Rx           UART0
Timer0            PB0/CCP0
GPIO Port C                           GPIO Port D
PC7/C2-          Analog                                            PD3/U1Tx
PC6/C2+                                          UART1              PD2/U1Rx
PC5/C1+
Comparator
PD1/PWM1
PC4/PHA0                                                             PD0/IDX0
PC3/TDO/SWO                       PB7
PC2/TDI                                          GPIO Port F        PF7
PC1/TMS/SWDIO
JTAG
PF6/CCP1
PC0/TCK/SWCLK                                                              PF5
GPIO Port E                  PH3                         PF4/C0o
PWM2               PF3/PWM5
PE3/SSI1Tx                                                            PF2/PWM4
PE2/SSI1Rx                                PC4               PD0
SSI1                          QEI0               PF1/IDX1
PE1/SSI1Fss                                                            PF0/PHB0
PE0/SSI1Clk                                         GPIO Port G
GPIO Port H                                    PF1
PH3/Fault                                         QEI1               PG7/PHB1
PH2                                                             PG6/PHA1
PB1
PH1/PWM3            PWM1                                              PG5
PH0/PWM2                                           Timer1             PG4/CCP3
ADC7                                  PH3               PD1       PG3
PG1/U2Tx
Peripheral Bus

EE 319K - Summer 2012 - Bill Bard - w.bard@mail.utexas.edu                           10
Analog to Digital Converter - ADC

LM3S1968 Analog to Digital Converter

EE 319K - Summer 2012 - Bill Bard - w.bard@mail.utexas.edu   11
Analog to Digital Converter - ADC
•   Single-ended and differential-input configurations
•   On-chip internal temperature sensor
•   Sample rate of one million samples/second
•   Flexible, configurable analog-to-digital conversion
•   Four programmable sample conversion sequences from one to eight entries
long, with corresponding conversion result FIFOs
•   Flexible trigger control
–   Controller (software)
–   Timers
–   Analog Comparators
–   PWM
–   GPIO
•   Hardware averaging of up to 64 samples for improved accuracy
•   Converter uses an internal 3-V reference

EE 319K - Summer 2012 - Bill Bard - w.bard@mail.utexas.edu   12
Analog to Digital Converter - ADC

• Sampling Range/Resolution
– 3V internal reference voltage
– 0x000 at 0 V input
– 0x3FF at 3 V
– resolution = range/precision
= 3V/1024 alternatives = 0.00293V

EE 319K - Summer 2012 - Bill Bard - w.bard@mail.utexas.edu   13
Nyquist Sampling Theorem
• A bandlimited analog signal that has been sampled can be perfectly
reconstructed from an infinite sequence of samples if the sampling
rate exceeds 2B samples per second, where B is the highest
frequency in the original signal.
– Harry Nyquist
• Valvano Postulate: If fmax is the largest frequency
component of the analog signal, then you must sample
more than ten times fmax in order for the reconstructed
digital samples to look like the original signal when
plotted on a voltage versus time graph.

EE 319K - Summer 2012 - Bill Bard - w.bard@mail.utexas.edu   14
Sampling
100 Hz signal sampled at
1600 Hz

100 Hz signal sampled at
1600 Hz

EE 319K - Summer 2012 - Bill Bard - w.bard@mail.utexas.edu        15
Sampling
800 Hz signal sampled at
1600 Hz

1500 Hz signal sampled at
1600 Hz

EE 319K - Summer 2012 - Bill Bard - w.bard@mail.utexas.edu        16
Sampling

A signal with DC, 100 Hz and 400 Hz is sampled
at 1600 Hz

EE 319K - Summer 2012 - Bill Bard - w.bard@mail.utexas.edu   17
Analog to Digital Converter - ADC

• Transducer – A device actuated by power
from one system that supplies power in
the same or other form to another system.

EE 319K - Summer 2012 - Bill Bard - w.bard@mail.utexas.edu   18
Data Acquisition System
• Hardware                             • Software
– Transducer                         • ADC device driver
• Timer routines
– Electronics
– Output compare
• LCD driver
• Measurement system
– How fast to update
– Fixed-point number
system
– Algorithm to convert
EE 319K - Summer 2012 - Bill Bard - w.bard@mail.utexas.edu   19
Data Acquisition System

Transducer – position to voltage

EE 319K - Summer 2012 - Bill Bard - w.bard@mail.utexas.edu   20
Data Acquisition System

Data Flow Graph

EE 319K - Summer 2012 - Bill Bard - w.bard@mail.utexas.edu   21
Data Acquisition System

Call Graph
EE 319K - Summer 2012 - Bill Bard - w.bard@mail.utexas.edu   22
Analog-to-Digital Converter
Precision
• Observable x(t) is sensed via transducer
as signal y(t)
– assume a relation, y = f(x)
– range of x is rx and range of y is ry
– precision of x and y is nx and ny respectively
– resolution of x and y is Dx and Dy respectively
• and Dx = rx/nx

EE 319K - Summer 2012 - Bill Bard - w.bard@mail.utexas.edu   23
Analog-to-Digital Converter Precision
• The output of the transducer is related to the
input such that:
– Dy = min{f(x + Dx) – f(x)} for all x in rx
– and ny = ry/Dy
• Consider y = x2 with 0  x  1
– then 0  y  1
• If Dx = 0.01, Dx = rx/nx = 1/0.01 = 100
– log2(100) ~ 7 bits
 Dy = min{(x + 0.01)2 – x2} = 0.0001
– ny = ry/Dy = 1/10-4 = 104;
– log2(104) ~ 15 bits

EE 319K - Summer 2012 - Bill Bard - w.bard@mail.utexas.edu   24
Time Jitter
• Definition of time-jitter, δt:
– Let nΔt be the time a task is scheduled to be
run and tn the time the task is actually run
– thenδtn= tn – nΔt
• Real time systems with periodic tasks,
must have an upper bound, k, on the time-
jitter
– -k ≤ δtn ≤ +k for all n
EE 319K - Summer 2012 - Bill Bard - w.bard@mail.utexas.edu   25
Delayed Service
• Consequences
– Nyquist’s theorem no longer holds
• requires constant sampling interval
– data acquisition and control systems operate
using incorrect calculated values
• consider derivative dx/dt = ((x(t)-x(t-Δt))/Δt
– errors in signal generation
• the sound is distorted
• the picture is blurry

EE 319K - Summer 2012 - Bill Bard - w.bard@mail.utexas.edu   26
Measurement Resolution
• Limiting factors
– Transducer noise
– Electrical noise
– Software errors

EE 319K - Summer 2012 - Bill Bard - w.bard@mail.utexas.edu   27
Measurement Accuracy
• Limiting factors
– Resolution
– Calibration
– Transducer stability

EE 319K - Summer 2012 - Bill Bard - w.bard@mail.utexas.edu   28

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