A/D Conversion

The heart of a PC-based measurement system is an electronic board that fits within the PC and is capable of analog-to-digital (AD) digital-to-analog (DA) conversion of signals. The conversion of data from analog to digital form and vice versa is necessitated by the fact that the real-world events and the output of probes and measurement systems are continuous (or analog) in nature while the computer is a digital device in the sense that it stores and transmits data as a string of binary digits 0 and 1. Thus data has to be converted into digital form before sending it to the computer. Instructions from the computer may have to be converted back to analog form so as to operate and control the analog devices. Different approaches may be used for this converstion leading to trade-offs between the cost of the converter, its simplicity and the speed of conversion. Digitization of an analog signal, called a trace results in a set of discrete values that is in turn called a time series. These are respectively given symbols and , where is time, is an index and is a dependent variable. Parameters that quantify digitization of a trace are the sampling frequency (Hz) and resolution (bits)

The time elapsed between successive value of is 1 (sec). With a resolution of -bits, a pre-determined voltage range, -1 to +1 volts for example is divided into parts and voltage is transmitted as integer multiples of this basic unit. As a rule-of-thumb, must be greater than twice the largest frequency to be resolved by the experiment. It is clear that should be as large as possible. Commonly used A D cards for laboratory applications use 8, 10, 12, 14 and 16 through 8, 12 and 16 are common. The signal corresponding to the measured quantity is in Volts and an integer after being digitized. Proper scaling is required to convert to dimensions appropriate to the experiment. If is the total time for which data is collected, the number of data points collected is . In practice is chosen to be of the form . A large value of A large value of and hence a large computer memory requirement. Hence there is always a trade-off between sampling frequency and the time duration for which data is collected.