# Analog digital conversion by MikeJenny

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```									      Analog-to-Digital Conversion
Terminology
analog: continuously valued signal, such as temperature or
speed, with infinite possible values in between

digital: discretely valued signal, such as integers, encoded in
binary

analog-to-digital converter: ADC, A/D, A2D; converts an
analog signal to a digital signal

digital-to-analog converter: DAC, D/A, D2A

An embedded system’s surroundings typically involve many
analog signals.
Analog-to-digital converters
Vmax = 7.5V         1111                      4                                                         4
7.0V          1110
6.5V          1101                      3                                                         3

analog output (V)
6.0V          1100
5.5V          1011
2                                                         2
5.0V          1010
4.5V          1001
4.0V                                    1                                                         1
1000
3.5V          0111
3.0V          0110                                                     time                                                          time
t1    t2      t3     t4                                   t1       t2      t3      t4
2.5V          0101
2.0V          0100                          0100   0110 0110 0101                                     0100     1000 0110        0101
1.5V          0011                                 Digital output                                             Digital input
1.0V          0010
0.5V          0001
0V          0000

proportionality                                 analog to digital                                        digital to analog

Embedded Systems Design: A Unified
Hardware/Software Introduction, (c) 2000 Vahid/Givargis
Proportional Signals
Simple Equation                               Vmax       1..1 = 2n-1

Assume minimum voltage of 0 V.
Vmax = maximum voltage of the
analog signal
a = analog value                                     …
n = number of bits for digital
encoding
2n = number of digital codes
M = number of steps, either 2n or 2n – 1
d = digital encoding

a / Vmax = d / M                              0V         0..0 = 0
Resolution
Let n = 2
Vmax   3=11

M = 2n – 1                                            r

3 steps on the digital scale                              3=11
d0 = 0 = 0b00
2=10
dVmax = 3 = 0b11

M = 2n                                                    2=10

4 steps on the digital scale
1=01
d0 = 0 = 0b00
1=01
dVmax - r = 3 = 0b11 (no dVmax )

r, resolution: smallest analog change
0V     0=00       0=00
resulting from changing one bit

DAC:                                          x0
x1
n digital inputs for digital encoding d                        DAC
…
a

analog output a

converter know what binary value to assign to d in order to
satisfy the ratio?
–    may use DAC to generate analog values for comparison with a
–    ADC “guesses” an encoding d, then checks its guess by inputting d
into the DAC and comparing the generated analog output a’ with
–    How does the ADC guess the correct encoding?
Guessing the encoding is similar to finding an item in a list.

0, then 1, then 2, etc. until find a match.
• 2n comparisons: Slow!
encoding for half of maximum; then compare analog result
original, set the new encoding to halfway between this one
and the minimum (maximum); continue dividing encoding
range in half until the compared voltages are equal
• n comparisons: Faster, but more complex converter

    Takes time to guess the encoding: start conversion input,
conversion complete output
approximation
should range from 0 to 15 volts, and an 8-bit
digital encoding, calculate the correct encoding for
5 volts. Then trace the successive-approximation
approach to find the correct encoding.
• Assume M = 2n – 1
a / Vmax = d / M
5 / 15 = d / (256 - 1)
d = 85 or binary 01010101
approximation
Step 1-4: determine bits 0-3

½(Vmax – Vmin) = 7.5 volts
0     0     0      0     0     0   0   0
Vmax = 7.5 volts.
½(7.5 + 0) = 3.75 volts
0     1     0     0      0     0   0   0
Vmin = 3.75 volts.

½(7.5 + 3.75) = 5.63 volts                       0     1     0     0      0     0   0   0
Vmax = 5.63 volts

½(5.63 + 3.75) = 4.69 volts                      0     1     0     1      0     0   0   0
Vmin = 4.69 volts.

Embedded Systems Design: A Unified
Hardware/Software Introduction, (c) 2000 Vahid/Givargis
approximation
Step 5-8: Determine bits 4-7

½(5.63 + 4.69) = 5.16 volts                     0     1     0      1     0     0   0   0
Vmax = 5.16 volts.
½(5.16 + 4.69) = 4.93 volts                     0     1     0      1     0     1   0   0
Vmin = 4.93 volts.

½(5.16 + 4.93) = 5.05 volts                     0     1     0      1     0     1   0   0
Vmax = 5.05 volts.
½(5.05 + 4.93) =                                0     1     0      1     0     1   0   1
4.99 volts

Embedded Systems Design: A Unified
Hardware/Software Introduction, (c) 2000 Vahid/Givargis

Analog        State
input        machine
Timing
control
Vmax                                      SAR
DAC
Vmin                                      BUF    Digital
output

Comparator                    SAR

SAR: Successive
approximation register
Bit Weight
Notice the concept of bit weight      Digital Bit   Bit Weight (V)
in the last example:
bit 7 = 7.5 V = 15/2                      7         10/2 = 5
bit 6 = 3.75 V = 15/4
6         10/4 = 2.5
Each bit is weighted with an              5         10/8 = 1.25
analog value, such that a 1 in that
bit position adds its analog value        4         10/16 = 0.625
to the total analog value
3         10/32 = 0.313
represented by the digital
encoding.                                 2         10/64 = 0.157

Example: -5 V to +5 V analog              1         10/128 = 0.078
range, n=8                                0         10/256 = 0.039
Bit Weight
Example (continued): -5 V to              Analog (V)       Digital (hex)
+5 V analog range, n=8
-5               00

Digital numbers for a few analog             -3.75              20
values                                        -2.5              40
–   Values shown increment by 6
bits (weight for bit position 5       -1.25              60
is 1.25 V)                              0                80
–   Maximum digital number
only approximates the                  1.25              A0
maximum analog value in the            2.5               C0
range
•   Try (-5) + sum of all bit         3.75              E0
weights
5-0.039 = 4.961        FF
Terms & Equations
Offset: minimum analog value

Span (or Range): difference between maximum and minimum analog values
Max - Min
n: number of bits in digital code (sometimes referred to as n-bit resolution)

Bit Weight: analog value corresponding to a bit in the digital number

Step Size (or Resolution): smallest analog change resulting from changing one
bit in the digital number, or the analog difference between two consecutive
digital numbers; also the bit weight of the
Span / 2n                        (Assume M = 2n)

Let AV be Analog Value; DN be Digital Number:
AV = DN * Step Size + Offset = (DN / 2n )* Span + Offset
DN = (AV - Offset) / Step Size = (AV - Offset) * 2n / Span
Analog to Digital
Converter Module-64

• 16 analog channels via
internal multiplexing

• Converts voltage to an
integer value (0-1023)

• Polling or interrupt driven

• Programmable channels
AN0-ANx
CCW Table
CCW0           A CCW tells the ADC
CCW1           which channel to
AN0                         scan and how long to
…              sample the signal.
AN1
CCW63
AN2
QACR1: start a scan by setting SSE bit

QASR0: CF flag is set after conv is done

Result Table
Result0      A Result is stored for
Result1      each scan of a channel
when the conversion is
…            complete.
Result63
Scan Sequence and Conversion
• After the ADC is initialized, a sequence of scans is set up as a “queue”
in the CCW Table.
• Each channel to be scanned is added to the queue at successive
positions 0, 1, 2, etc. For example: CCW0, CCW1, CCW2, CCW3.
– An end-of-queue marker should be added at the next position.
• The ADC starts the scan and conversion when it is triggered by the
enable bit.
• The ADC reads the CCWs, one after another until end-of-queue is
reached, and for each CCW, it converts the signal on the specified
channel.
– A conversion on a channel stores a result in the respective position of the
Result Table, e.g., the result for CCW0 is stored at Result0, etc.
• When the scan and conversion is complete for all CCWs, then the ADC
sets the completion flag to 1. Now all digital results are available to be
• Programmability using a queue
– Scan a few channels quickly
– Scan a channel multiple times
– Scan large number of channels
• QACR1 – QADC64 Control Register 1
o 16 bit register at 0x30480C
o SSE1 – bit 2 – Single Scan enable (bit 0 is MSb)
o MQ1 – bits 3-7
o Set to binary 00001 to identify Queue 1
• QASR0 – QADC64 Status Register 0
o 16 bit register at 0x304810
o ADC sets a flag when the conversion is done
o CF1 – bit 0 – Conversion Complete flag (bit 0 is MSb)
• CCW Table
o table of Conversion Command Words, where each command word specifies how
to perform a scan/conversion operation for an input channel
o CCW: 16 bit command word, starting at address 0x304A00
o A queue is a scan sequence of one or more input channels.
o A queue is started by a trigger event, which is a way to cause the QADC64 to
begin executing the command words.
o Each CCW requests the conversion of an analog channel to a digital result. The
CCW specifies the analog channel number, the input sample time, and whether
the queue is to pause after the current CCW.
CCW Table

16 bits
Entry
00     Begin Queue 1        0x304A00

0              5 6 7      8         9 10          15
Reserved    P   BYP       IST          CHAN

MSB                                                 LSB

n      End Queue 1
• Total conversion time: initial sample time, final sample time, and resolution
time
o Initial sample time – time during which the selected input channel is driven by
the buffer amplifier onto the sample capacitor (disabled by means of the BYP bit
in the CCW)
o Final sampling period – time to set up DAC array
o Resolution period – time to convert voltage in the DAC array to a digital value
• Result Word Table
o table of Result Words, where each result word is the digital result of a
conversion
o Results from a sequence of conversions are placed in the Result Word
Table.
o RW: 16 bit result word, starting at address 0x304A80

channels, 0 through 3 (AN0-AN3)
– Add an end-of-queue marker to terminate the scan sequence
– Start a conversion on the ADC, which begins reading each analog
input and converting it to a digital value
Bit 0                Bit 15   0x30 4A00
0x30 4800    Module Config. Reg.
64-entry 16-bit Conversion
0x30 4802           Test Reg.                      Command Word Table
0x30 4804         Interrupt Reg.                  (Configurable: one queue
0x30 4806   Port A Data Port B Data                    or two queues)
0x30 4808    Port A Direction Reg.        0x30 4A7E
0x30 480A         Control Reg. 0          0x30 4A80
0x30 480C         Control Reg. 1                       64-entry 16-bit
0x30 480E         Control Reg. 2                      Result Word Table
0x30 4810         Status Reg. 0                        64-entry, 16-bit
0x30 4812         Status Reg. 1           0x30 4AFE
The above is the memory-mapping for the 1st QADC64.

CCW Format:        6    7    8 9 10 11 12 12 14 15
P   BYP   IST       CHAN

Example: Write a CCW into CCW table to scan channel
nChannel with no amplifier bypassing and 4-cycle initial sample
time (16 cycles in total).
nQueueVal =   nChannel;
nQueueVal =   nQueueVal & 0xFF3F;
nQueueVal =   nQueueVal | 0x0040;
*(pCCWTable   + nQueue) = nQueueVal;
The Control Registers
The Status Registers

CF1     Queue1 completion flag
PF1     Queue1 pause flag
TOR1    Trigger over-run
QS      Queue status
CWP     Command word pointer
• Initialize the QADC: reset queue to be
empty; set up interrupt driven mode,
interrupt levels, clock rate.
• Write into the command word queue (a
sequence of A to D conversion commands).
• In software triggered mode, initiate the
conversion by writing into QACR[SSE] bit.
• Monitor the conversion finished flag (CF).
• Read the results, and reset CF and PF flags.
Example: Reset QADC64 by writing END-OF-QUEUE (63 in decimal) as
the first word of CCW table.

{
g_nNumChannels = 0;
}

QADCR64_SetQueue: Given CCW entry index, CCW channel/end-of-
queue command, and final sample setting, write the corresponding CCW.
Example: Start scanning in polling mode (interrupt disabled)
– Set up control register 1
{
unsigned short * pQACR1;
pQACR1 = (unsigned short *) 0x30480C;
// Bit 0 CIE1 Conversion Interrupt Enable 0
// Bit 1 PIE1 Pause Interrupt Enable 0
// Bit 2 SSE1 Single Scan Enable 1
// MQ=00001; software triggered single scan mode
*pQACR1 = 0x2100;
}
Example: Determine if all conversions has finished
–   Checking status register 0
{
unsigned short * pQASR0;
unsigned short nResult;
pQASR0 = (unsigned short *) 0x304810;
nResult = (*pQASR0 & 0x8000);
return nResult;
}