LSU 06/04/2007Electronics 71 Analog to Digital Converters Electronics Unit – Lecture 7 Representing a continuously varying physical quantity by a sequence.

LSU 06/04/2007 Electronics 7 1

Analog to Digital Converters Electronics Unit – Lecture 7

Representing a continuously varying physical quantity by a sequence of discrete numerical values.

03 07 10 14 09 02 00 04


Conversion Methods(selected types, there are others)

Ladder Comparison

Successive Approximation

Slope Integration

Flash Comparison


Ladder Comparison


Single slope integration• Charge a capacitor at constant

current

• Count clock ticks

• Stop when the capacitor voltage matches the input

• Cannot achieve high resolution– Capacitor and/or comparator

-

+IN

C

R

S Enable

N-bit Output

Q

Oscillator Clk

Co

un

ter

StartConversion

StartConversion

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101214161820

0 2 4 6 8 10 12 14 16

Time

Vo

lta

ge

acc

ross

th

e c

ap

aci

tor

Vin

Counting time




Flash Comparison

If N is the number of bits in the output word….

Then 2N comparators will be required.

With modern microelectronics this is quite possible, but will be expensive.


Pro and Cons

Slope Integration & Ladder Approximation

Cheap but Slow


Pro and Cons

Flash Comparison

Fast but Expensive


Cheap but Slow


Pro and Cons


The Happy Medium ??


Cheap but Slow

Flash Comparison

Fast but Expensive


Resolution

Suppose a binary number with N bits is to represent an analog value ranging from 0 to A

There are 2N possible numbers

Resolution = A / 2N


Resolution Example

Temperature range of 0 K to 300 K to be linearly converted to a voltage signal of 0 to 2.5 V, then digitized with an 8-bit A/D converter

2.5 / 28 = 0.0098 V, or about 10 mV per step

300 K / 28 = 1.2 K per step


Resolution Example

Temperature range of 0 K to 300 K to be linearly converted to a voltage signal of 0 to 2.5 V, then digitized with a 10-bit A/D converter

2.5 / 210 = 0.00244V, or about 2.4 mV per step

300 K / 210 = 0.29 K per stepIs the noise present in the system well below 2.4 mV ?


Quantization NoiseEach conversion has an average uncertainty of one-half of the step size ½(A / 2N)

This quantization error places an upper limit on the signal to noise ratio that can be realized.

Maximum (ideal) SNR ≈ 6 N + 1.8 decibels (N = # bits)

e.g. 8 bit → 49.8 db, 10 bit → 61.8 db


Signal to Noise RatioRecovering a signal masked by noise

Some audio examplesIn each successive example the noise power is reduced by a factor of two (3 db reduction), thus increasing the signal to noise ratio by 3 db each time.

Example 1 Example 2 Example 3 Example 4


Conversion Time

Time required to acquire a sample of the analog signal and determine the numerical representation.

Sets the upper limit on the sampling frequency.

For the A/D on the BalloonSat board, TC ≈ 32 μs, So the sampling rate cannot exceed about 30,000 samples per second (neglecting program overhead)


Data Collection – Sampling RateThe Nyquist RateA signal must be sampled at a rate at least twice that of the highest frequency component that must be reproduced.

Example – Hi-Fi sound (20-20,000 Hz) is generally sampled at about 44 kHz.

External temperature during flight need only be sampled every few seconds at most.


Activity E7a

Do the HuSAC ®

a party game for techies...

Human Successive Approximation Converter


Activity

Data Acquisition Using BalloonSat

LSU 06/04/2007Electronics 71 Analog to Digital Converters Electronics Unit – Lecture 7 Representing a continuously varying physical quantity by a sequence.

Documents

step slide

time slide

db slide

slow slide

expensive slide

ladder comparison slide

successive approximation

n bits