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EE 319K�Introduction to Embedded Systems

Lecture 11: Sampling, �Analog-to-Digital Conversion

http://users.ece.utexas.edu/~valvano/Volume1/E-Book/C13_Interactives.htm

http://users.ece.utexas.edu/~valvano/Volume1/E-Book/C14_Interactives.htm

Today and cover lab 8, lec11

Exam2 Friday 4/8: hard cutoff at 8:30pm

Please attempt Quiz 9 and Quiz 10

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Agenda

Recap

Local Variables
Stack frames
Recursion
Fixed-point numbers
LCD device driver (Lab 7)

Outline

Sampling, Nyquist theorem
Analog to Digital Conversion

Push {R11}

SUB SP,SP,#32

MOV R11, SP

;*********

;*********(

ADD SP,SP#32

POP {R11}

X86

ENTER #32

LEAVE (moves BP into, POP BP

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Analog to Digital Converter (ADC)

Four limitations of digital sampling

Finite precision (4096 alternatives)
Finite voltage range (0 to 3.3V)
Discrete time sampling, f_s
Finite number of samples, N

Voltage resolution = 3.3V/4095 =0.8 mV

Frequency range = 0 to ½ f_s

Frequency resolution = f_s / N

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Nyquist Theorem

A bandlimited analog signal that has been sampled can be perfectly reconstructed from an infinite sequence of samples if the sampling rate f_sexceeds 2f_max samples per second, where f_max is the highest frequency in the original signal.

If the analog signal does contain frequency components larger than (1/2)f_s, then there will be an aliasing error.
Aliasing is when the digital signal appears to have a different frequency than the original analog signal. �

Valvano Postulate: If f_max is the largest frequency component of the analog signal, then you must sample more than ten times f_max in order for the reconstructed digital samples to look like the original signal when plotted on a voltage versus time graph.

http://users.ece.utexas.edu/~valvano/Volume1/E-Book/C13_Interactives.htm

http://users.ece.utexas.edu/~valvano/Volume1/E-Book/C14_Interactives.htm

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Sampling (option 1)

200Hz signal sampled at 2000Hz

http://www.ece.utexas.edu/~valvano/Volume1/Nyquist.xls

Look at

200 Hz

2200 Hz

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Sampling (option 1)

1000Hz signal sampled at 2000Hz

http://www.ece.utexas.edu/~valvano/Volume1/Nyquist.xls

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Sampling (option 1)

2200Hz signal sampled at 2000Hz

This is aliasing

http://www.ece.utexas.edu/~valvano/Volume1/Nyquist.xls

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Sampling (option 2)

100Hz signal sampled at 1600Hz

http://www.ece.utexas.edu/~valvano/EE345L/Labs/Fall2011/FFT16.xls

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Sampling (option 2)

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

http://www.ece.utexas.edu/~valvano/EE345L/Labs/Fall2011/FFT16.xls

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Sampling (option 2)

1500Hz signal sampled at 1600Hz

This is aliasing

http://www.ece.utexas.edu/~valvano/EE345L/Labs/Fall2011/FFT16.xls

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Analog to Digital Converter (ADC)

Successive approximation ADC

V_IN is approximated as a �static value in a sample and hold (S/H) circuit
the successive approximation register (SAR) is a counter that increments each clock �as long as it is enabled by �the comparator
output of the SAR is fed �to a DAC that generates a voltage to compare with V_IN
when the output of the DAC = V_IN the value of SAR is the digital representation of V_IN

end of conversion

http://users.ece.utexas.edu/~valvano/Volume1/E-Book/C14_Interactives.htm

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Play the 6-bit SAR game

http://users.ece.utexas.edu/~valvano/Volume1/E-Book/C14_Interactives.htm

Interactive Tool 14.1
I choose a number from 0 to 63
You control the DAC

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Sample-And-Hold Circuit

The software writes to PSSI to start conversion
Writing to PSSI latches the analog input and the actual conversion starts
The essence of sampling is to write to PSSI with a fixed and known period
The sampling rate, f_s , is 1/period
Lab 8 will use interrupts to establish f_s

S/H

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ADC on TM4C123

Sampling Range/Resolution

3.3V internal reference voltage
0x000 at 0 V input
0xFFF at 3.3 V
resolution = range/precision

= 3.3V/4095 alternatives < 1mV

or = 3.3V/4096 alternatives < 1mV

Actual resolution dominated by noise

Improve signal to noise ratio (SNR)

Slow down ADC (take longer to sample)
Analog filtering, ground shield
Digital filtering (average multiple samples)

Use either

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ADC on TM4C123

Twelve analog input channels
Single-ended and differential-input configurations
On-chip internal temperature sensor
Sample rate up to one million samples/second 30 Hz
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) We will use software-initiated trigger
Timers
Analog Comparators (trigger if analog input crosses a threshold)
Pulse Width Modulator (another timer)
GPIO (input pin)
Continuous

Hardware averaging of up to 64 samples for improved accuracy
Converter uses an internal 3.3V reference

PD2=Ain5 used for Lab 8, 9, 10

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ADC on TM4C123

Ain5PD2

Software initiated

Bit 3 is done flag

Use sequencer 3

PD2=Ain5 used for Lab 8, 9, 10

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ADC on TM4C123

Twelve different pins can be used to sample analog inputs.

PD3=Ain4 used for TExaS oscilloscope

PD2=Ain5 used for Lab 8, 9, 10

PE4=Ain9 used in book and ADCSWTrigger_4C123

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ADC on TM4C123

TM4C ADC registers

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ADC on TM4C123

TM4C123 ADC Operation

select rate
select sequencer
select trigger
select channel
select sample mode

0 not temperature
1 set completion flag
1 end sequence
0 not differential

Speed bits in ADC0_PC_R

EM3, EM2, EM1, and EM0 bits in ADC_EMUX_R

ADC0_SSCTL3_R = 0x06;

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ADC on TM4C123

Initialization

Enable ADC clock: set bit 0 in SYSCTL_RCGCADC_R
Set 125kHz ADC conversion speed: write 0x01 to ADC0_PC_R
Set sequencer priority: 0,1,2,3 in ADC0_SSPRI_R
Disable selected sequence 3: zero bit 3 of ADC0_ACTSS_R
Set software start trigger event: zero bits 15-12 of ADC0_EMUX_R
Set input source (0-11): write channel number in bits 3-0 of ADC0_SSMUX3_R (channel 9 is PE4, channel 1 is PE2)
Set sample control bits: write 0110 in bits 3-0 ADC0_SSCTL3_R to disable temp measurement, notify on sample complete, indicate single sample in sequence, and denote single-ended signal mode
Disable interrupts: zero bit 3 of ADC0_IM_R
Enable selected sequencer 3: set bit 3 of ADC0_ACTSS_R

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ADC on TM4C123

Channel 9 is PE4

void ADC0_InitSWTriggerSeq3_Ch9(void){

SYSCTL_RCGCGPIO_R |= 0x10; // 1) activate clock for Port E

while((SYSCTL_PRGPIO_R&0x10) == 0){};

GPIO_PORTE_DIR_R &= ~0x10; // 2) make PE4 input

GPIO_PORTE_AFSEL_R |= 0x10; // 3) enable alternate fun on PE4

GPIO_PORTE_DEN_R &= ~0x10; // 4) disable digital I/O on PE4

GPIO_PORTE_AMSEL_R |= 0x10; // 5) enable analog fun on PE4

SYSCTL_RCGCADC_R |= 0x01; // 6) activate ADC0

delay = SYSCTL_RCGCADC_R; // extra time to stabilize

delay = SYSCTL_RCGCADC_R;

ADC0_PC_R = 0x01; // 7) configure for 125K

ADC0_SSPRI_R = 0x0123; // 8) Seq 3 is highest priority

ADC0_ACTSS_R &= ~0x0008; // 9) disable sample sequencer 3

ADC0_EMUX_R &= ~0xF000; // 10) seq3 is software trigger

ADC0_SSMUX3_R = (ADC0_SSMUX3_R&0xFFFFFFF0)+9; // 11) Ain9 (PE4)

ADC0_SSCTL3_R = 0x0006; // 12) no TS0 D0, yes IE0 END0

ADC0_IM_R &= ~0x0008; // 13) disable SS3 interrupts

ADC0_ACTSS_R |= 0x0008; // 14) enable sample sequencer 3

}

Book shows Ain9=PE4 Lab 8, 9, 10 use Ain5=PD2

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ADC on TM4C123

Analog to digital conversion

Set software trigger

Write to PSSI bit 3

Busy-Wait

Raw Interrupt Status = RIS bit 3
Poll until sample complete

Read sample

Read from SSFIFO3

Clear sample complete flag

Write to ISC bit 3

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ADC on TM4C123

//------------ADC_InSeq3------------

// Busy-wait analog to digital conversion

// Input: none

// Output: 12-bit result of ADC conversion

uint32_t ADC0_InSeq3(void){

uint32_t data;

ADC0_PSSI_R = 0x0008;

while((ADC0_RIS_R&0x08)==0){};

data = ADC0_SSFIFO3_R&0xFFF;

ADC0_ISC_R = 0x0008;

return data;

}

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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

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Analog Input Device

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

3.3V

GND

PD2

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Transducer Circuit

Position to voltage

There are 6 ways to connect 3 pins to 3 connections; 4 of which will explode; 2 of which will operate

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Data Acquisition System

Data flow graph

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Data Acquisition System

Call graph

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Thread Synchronization in Lab 8

SysTick ISR producer

Sample ADC
Store in ADCmail
Set ADCstatus

Main loop

consumer

Wait for ADCstatus
Read ADCmail
Clear ADCstatus
Convert to distance
Display on LCD

Background thread

Foreground thread

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Sampling Jitter

Definition of time-jitter, δt:

Let nΔt be the time a task is scheduled to be run and t_n the time the task is actually run
Then δt_n= t_n – nΔt

Real time systems with periodic tasks, must have an upper bound, k, on the time-jitter

-k ≤ δt_n ≤ +k for all n

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Measurement

Resolution: Limiting factors

Transducer noise
Electrical noise
ADC precision
Software errors

Accuracy: Limiting factors

Resolution
Calibration
Transducer stability

Average accuracy (with units of x) =

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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 Δ (resolution)

value is fixed, and can not be changed

not stored in memory

specify this fixed constant using comments

value ≡ integer • Δ

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Fixed-Point Numbers

The value of the fixed-point number:

Fixed-point number ≡ I•Δ

Smallest value = I_min • Δ, where I_min is the smallest integer

Largest value = I_max • Δ, where I_max is the largest integer

Decimal fixed-point, Δ=10^m

Decimal fixed-point number = I • 10^m

Nice for human input/output

Binary fixed-point, Δ=2^m

Binary fixed-point number = I • 2^m

Easier for computers to perform calculations

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Fixed-Point Math Example

Consider the following calculation.

C = 2*π*R

The variables C, and R are integers

2π ≈ 6.283

C = (6283*R)/1000

2π ≈ 6434/1024 = 6.283203125

C = (6434*R)>>10

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Fixed-Point Math Example

Calculate the volume of a cylinder

V = π*R²*L

The variables are fixed-point

R = I*2^-4 cm L = J*2^-4 cm

V = K*2^-8 cm³ π ≈ 3217*2^-10 = 3.1416015625

K*2^-8 cm³ = (3217*2^-10)*(I*2^-4 cm)²*(J*2^-4 cm)

K = (3217*I*I*J)>>14

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V_in(V) Analog in	N Digital out	I (1 mV) Variable part	LCD
0	0	0	0.000
0.825	1024	825	0.825
1.650	2048	1650	1.650
2.475	3072	2475	2.475
3.3	4095	3300	3.300

Δ=0.001 V

V_in = 3.3•N/4095 how ADC works

or V_in = 3.3•N/4096 how ADC works

V_in = I • 0.001 definition of fixed point

I = (3300*N)/4096 substitution

I = (m•N+b)/ 4096 calibrate to get m and b

Make a Voltmeter with ADC

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Lab 8 Calibration (0.001)

Show Lab8_Accuracy

http://users.ece.utexas.edu/%7Evalvano/Volume1/E-Book/C14_ADCdataAcquisition.htm

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