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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

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analog to digital converters electronics unit lecture 7

Analog to Digital ConvertersElectronics Unit – Lecture 7

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

03 07 10 14 09 02 00 04

Electronics 7

conversion methods selected types there are others

Conversion Methods(selected types, there are others)

Ladder Comparison

Successive Approximation

Slope Integration

Flash Comparison

Electronics 7

ladder comparison

Ladder Comparison

Electronics 7

single slope integration

-

+

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

Vin

Counting time

StartConversion

StartConversion

Enable

S

Q

R

N-bit Output

Counter

C

IN

Clk

Oscillator

Electronics 7

flash comparison

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.

Electronics 7

pro and cons

Pro and Cons

Slope Integration & Ladder Approximation

Cheap but Slow

Electronics 7

pro and cons1

Pro and Cons

Flash Comparison

Fast but Expensive

Slope Integration & Ladder Approximation

Cheap but Slow

Electronics 7

pro and cons2

Pro and Cons

Successive Approximation

The Happy Medium ??

Slope Integration & Ladder Approximation

Cheap but Slow

Flash Comparison

Fast but Expensive

Electronics 7

resolution

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

Electronics 7

resolution example

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

Electronics 7

resolution example1

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 step

Is the noise present in the system well below 2.4 mV ?

Electronics 7

quantization noise

Quantization Noise

Each 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

Electronics 7

signal to noise ratio recovering a signal masked by noise

Signal to Noise RatioRecovering a signal masked by noise

Some audio examples

In 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

Electronics 7

conversion time

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)

Electronics 7

data collection sampling rate

Data Collection – Sampling Rate

The Nyquist Rate

Asignal 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.

Electronics 7

activity e7a

Activity E7a

Do the HuSAC®

a party game for techies...

Human Successive Approximation Converter

Electronics 7

activity e7b

Activity E7b

Data Acquisition Using BalloonSat

Electronics 7