In most applications, it is preferable to get the maximum resolution possible. The number of quantisation bits of a given analog to digital converter is know as its resolution.Ĭharacteristic 1: Resolution - The number of quantisation bits of an ADC. Nevertheless, determining the SQNR required for your application, by careful analysis and consideration of the analog signal, will aid in the selection process. Unfortunately, there are other sources of noise associated with the analog-to-digital conversion process. The SQNR value would be the signal to noise ration (SNR) for an ideal ADC. From this equation it becomes obvious that an ADC with a larger number of quantisation levels results in an improved SQNR ratio. Thus, the signal to quantisation noise ratio (SQNR) can be defined in decibels as shown below. The power of the signal can be defined as shown in the equation below. The equation below describes quantisation error.įrom this, the power in quantisation error can be defined as shown below.Ĭonsider the signal in the figure above. In order to do this, we need to do some more mathematics. Now that we have investigated quantisation, it is time to see what quantisation means for an ADC.
N represents the number of bits the signal is quantised to. One quantum can be described as shown above in which A represents the amplitude and the signal spans from A to -A. Quantisation error is a term used to describe the difference between the original signal and the discrete representation of the signal. For example, if we know our signal will never increase above 2.4 V, it would be inefficient to use a voltage reference of 5 V because over half of the quantisation levels would be unused. Bear in mind, however, that a value much larger than the value of V in will result in fewer quantisation levels representing the original signal. As such, it is important that V ref be larger, or the same as, the maximum value of V in. Vref represents the maximum input voltage that can be successfully converted to an accurate digital representation. For example, if we can represent the signal with 1024 quantisation levels instead of 256 levels, we have increased the precision of the ADC because each quantisation level represents a smaller amplitude range. It is intuitive that more quantisation levels result in a more precise digital representation of the original analog signal. In this formula 2 N represents the number of quantisation levels.
#DIGITAL TO ANALOG VIDEO CONVERTER FOR ANTENNA SERIES#
Here we are describing the input voltage V in as a series of bits b N-1.b 0. The equation above describes the analog-to-digital conversion process mathematically. Mathematically, an ADC can be described as quantising a function with a large domain to produce a function with a smaller domain. The term quantisation refers to the process of converting a large set of values to a smaller set, or discrete set, of values. QuantisationĪn analog-to-digital converter converts a continuous signal, either a voltage or a current, into a sequence of numbers represented by discrete logic levels. If you can bear through the mathematics and understand the concepts introduced, you will be able to narrow down the number of appropriate ADCs for your application and selection will become that much easier. The mathematics is important, but the concepts that it represents are even more important. What follows here are some mathematical descriptions of the terms associated with analog-to-digital conversion. In order to properly determine the correct resolution and the correct sampling rate for a specific application, a reasonable understanding of these characteristics should be obtained. They will affect everything in the selection process from price to the underlying architecture of the analog-to-digital converter required.
Before any selection can take place these two factors should be considered carefully. Perhaps two of the most important characteristics to consider during the selection process for analog-to-digital converters (ADCs) are the resolution and the sampling rate.
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