## 1.2 ANALOG SIGNALS

• 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%.

### 1.2.1 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.

#### 1.2.1.1 - 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.

### 1.2.2 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,