1. EE 319K Introduction to Embedded Systems
Lecture 11: Data Acquisition, Numerical Fixed-Point Calculations, Lab 8
Bard, Tiwari, Telang, Janapa Reddi, Gerstlauer, Valvano, Yerraballi

2. Agenda Recap Agenda Sampling, Nyquist Analog to Digital Conversion
Data acquisition
Numerical fixed-point calculations
Lab 8
Bard, Tiwari, Telang, Janapa Reddi, Gerstlauer, Valvano, Yerraballi

3. Data Acquisition System (Lab 8)
Hardware
Transducer
Electronics
ADC
Software
ADC device driver
Timer routines
Output compare interrupts
LCD driver
Measurement system
How fast to update
Fixed-point number system
Algorithm to convert ADC into position
Bard, Tiwari, Telang, Janapa Reddi, Gerstlauer, Valvano, Yerraballi

4. Analog Input Device
Transducer – A device actuated by power from one system that supplies power in the same or other form to another system.
Bard, Tiwari, Telang, Janapa Reddi, Gerstlauer, Valvano, Yerraballi

5. Transducer Circuit Position to voltage
Bard, Tiwari, Telang, Janapa Reddi, Gerstlauer, Valvano, Yerraballi

6. Data Acquisition System
Data flow graph
ST7735 P o s i t n S e r V l a g +
3.3V A D C h d w v m p 4 9 5 y T c k I R L F x - 2 . M b
Bard, Tiwari, Telang, Janapa Reddi, Gerstlauer, Valvano, Yerraballi

7. Data Acquisition System
Call graph
ST7735
Bard, Tiwari, Telang, Janapa Reddi, Gerstlauer, Valvano, Yerraballi

8. Thread Synchronization in Lab 8
Background thread
Foreground thread
SysTick ISR
Sample ADC
Store in ADCmail
Set ADCstatus
Main loop
Wait for ADCstatus
Read ADCmail
Clear ADCstatus
Convert to distance
Display on LCD
Bard, Tiwari, Telang, Janapa Reddi, Gerstlauer, Valvano, Yerraballi

9. Sampling 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
Then δtn= tn – nΔt
Real time systems with periodic tasks, must have an upper bound, k, on the time-jitter
-k ≤ δtn ≤ +k for all n
Bard, Tiwari, Telang, Janapa Reddi, Gerstlauer, Valvano, Yerraballi

10. Measurement Resolution: Limiting factors Accuracy: Limiting factors
Transducer noise
Electrical noise
ADC precision
Software errors
Accuracy: Limiting factors
Resolution
Calibration
Transducer stability
Average accuracy (with units of x) =
Bard, Tiwari, Telang, Janapa Reddi, Gerstlauer, Valvano, Yerraballi

11. Fixed-Point Revisited
Why:
express non-integer values
no floating point hardware support (want it to run fast)
When:
range of values is known
range of values is small
How:
1) variable integer, called I.
may be signed or unsigned
may be 8, 16 or 32 bits (precision)
2) fixed constant, called  (resolution)
value is fixed, and can not be changed
not stored in memory
specify this fixed content using comments
value  integer • 
Bard, Tiwari, Telang, Janapa Reddi, Gerstlauer, Valvano, Yerraballi

12. Fixed-Point Numbers The value of the fixed-point number:
Fixed-point number  I•
Smallest value = Imin • D, where Imin is the smallest integer
Largest value = Imax • D, where Imax is the largest integer
Decimal fixed-point, =10m
Decimal fixed-point number = I • 10m
Nice for human input/output
Binary fixed-point, =2m
Binary fixed-point number = I • 2m
Easier for computers to perform calculations
Bard, Tiwari, Telang, Janapa Reddi, Gerstlauer, Valvano, Yerraballi

13. Fixed-Point Math Example
Consider the following calculation.
C = 2**R
The variables C, and R are integers
2p ≈ 6.283
C = (6283*R)/1000
Bard, Tiwari, Telang, Janapa Reddi, Gerstlauer, Valvano, Yerraballi

14. Fixed-Point Math Example
Calculate the volume of a cylinder
V = *R2 * L
The variables are binary fixed-point
R = I*2-4 cm L = J*2-4 cm
V = K*2-8 cm3 2p ≈ 201*2-5
K = (201*I*I*J)>>9
Bard, Tiwari, Telang, Janapa Reddi, Gerstlauer, Valvano, Yerraballi

15. Make a Voltmeter with ADC
Vin (V)
Analog in N
Digital out
I (1 mV)
Variable part
LCD
0.000
0.75
1024
750
0.750
1.5
2048
1500
1.500
2.25
3072
2250
2.250 3
4096
3000
3.000
=0.001 V
Vin = 3•N/4096 how ADC works
Vin = I • definition of fixed point
I = (3000*N)/ substitution
I = (m•N+b)/ calibrate to get m and b
Bard, Tiwari, Telang, Janapa Reddi, Gerstlauer, Valvano, Yerraballi

16. Lab 8 Calibration
Bard, Tiwari, Telang, Janapa Reddi, Gerstlauer, Valvano, Yerraballi