• 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%.
• 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.
• A simple type of A/D converter is shown below. It is known as a successive approximation type.
• To input analog values into a PLC we use the block transfer commands. These allow control information to the input card and retrieve results.
• The example below shows ladder logic to do an analog input.
• The block that needs to be written to an 1771-IFE analog input card is shown below. This is a 12 bit card, so the range will have up to 2**12 = 4096 values.
• After the input card reads the values, the results are returned in a block. The structure of the block is shown below.
