4.2 ANALOG SIGNALS

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A Continuous signal is sampled by the computer

The computer uses approximation techniques to estimate the analog value during the sampling window.

An example of an A/D, D/A control of a process is shown below

Multiplexers are used when a number of signals are to be input to a single A/D converter. This allows each of a number of channels to be sampled, one at a time

Signal conditioners are often to amplify, or filter signals coming from transducers, before they are read by the A/D converter.

Output drivers and amplifiers are often required to drive output devices when using D/A

Sampling problems occur with A/D conversion. Because readings are taken periodically (not continually), the Nyquist criterion specifies that sampling frequencies should be twice the frequency of the signal being measured, otherwise aliasing will occur.

Since the sampling window for a signal is short, noise will have added effect on the signal read. For example, a momentary voltage spike might result in a higher than normal reading.

When an analog value is converted to or from digital values, a quantization error is involved. The digital numbering scheme means that for an 8 bit A/D converter, there is a resolution of 256 values between maximum and minimum. This means that there is a round off error of approximately 0.4%.

4.2.1 Analog to Digital Conversion

When there are analog values outside a computer, and we plan to read these to digital values, there are a variety of factors to consider,

- when the sample is requested, a short period of time passes before the final sample value is obtained.

- the sample value is `frozen' after a sample interval.

- after the sample is taken, the system may change

- sample values can be very sensitive to noise

- the continuous values of the signal loose some accuracy when conversion to a digital number

Consider the conversion process pictured below,

Once this signal is processes through a typical A/D converter we get the following relations (these may vary slightly for different types of A/D converters).

In most applications a sample is taken at regular intervals, with a period of `T' seconds.

In practice the sample interval is kept as small as possible. (i.e., tau << T)

If we are sampling a periodic signal that changes near or faster that the sampling rate, there is a chance that we will get a signal that appears chaotic, or seems to be a lower frequency. This phenomenon is known as aliasing.

Quite often an A/D converter will multiplex between various inputs. As it switches the voltage will be sampled by a `sample and hold circuit'. This will then be converted to a digital value. The sample and hold circuits can be used before the multiplexer to collect data values at the same instant in time.

4.2.1.1 - Flash A/D Converter

On type of A/D converter is the flash converter shown below,

These converters are very fast, but they are hard to build for high resolutions.

The conversion rates for these devices are limited by inherent capacitance, and transistor switching times.

4.2.2 Digital to Analog Conversion

After we have used a controller equation to estimate a value to put into our process, we must convert this from a digital value in the computers memory, to a physical voltage.

This voltage is typically limited to 20mA in most computer board, and drawing near this current reduces accuracy and life of the board.

A simple circuit is shown below for a simple digital to analog converter.

The calculations for the A/D converter resolution and accuracy still apply.

Consider the example below,