ADC transfer curve types — A review
Introduction
The purpose of an analog to digital converter (ADC) is to convert the values of voltage or current present at the input, which is a continuous variable, into a digital word that should represent that input. That relationship, between input and output digital words (or codes) is known as the ADC transfer curve and is determined by the ADC manufacturer. There are different types of transfer curves. One of them, used with bipolar ADCs, is the one represented in Fig. 1. Variable N represents the ADC number of bits. Without loss of generality we will consider, in the remainder of this paper, that we are dealing with ADCs with a voltage input.
Each output code corresponds to a range of input voltage values (horizontal lines). Given an output code one cannot determine exactly which was the input voltage at the time of the analog to digital conversion. It is convention to adopt the middle point of the ranges mentioned as the value of the input voltage for a given output code (black circles in Fig. 1).
The Ideal Straight Line is the straight line that goes through the mid points of the ideal ADC transfer curve steps (dashed line in Fig. 1).
The transition voltages, Tk, define the ADC transfer curve, that is, the relation between input voltage and output code, k. The definition of transition voltage k is “the value of DC input voltage that results in the output codes of half the samples acquired being equal to or greater than k.” Since there are 2N different output codes, there are 2N − 1 different transition voltages, usually named T1 through T2N − 1.
Note that there is no transition voltage designated by T0, however when representing the ADC transition voltages on a computer, for the implementation of an algorithm, for instance, it is customary to use an array to do so. In some cases one may choose to place the lowest transition voltage in the first element of the array which traditionally has an index of “0” (but depends on the programming language). Care must be taken not to forget that the designation of the lowest transition voltage is T1.
Most ADCs have a uniform transfer curve, that is, the transition voltages are equally spaced by a quantity designated by Q, the ideal code bin width. There are however some ADCs that have a non-uniform transfer curve and which are used in specific applications, for instance, as an interface to a sensor with a non-linear characteristic. In this case the ADC has a transfer curve with a complementary non-linearity in order for the output codes to be linearly related with the quantity being measured. This case of ADCs will not be discussed here.
There are different types of transfer curves designations resulting from the manufacturers design choices: unipolar, bipolar with true zero, bipolar with no true zero, mid-tread and mid-riser. We will show here what they mean.
The specification of an N-ADC transfer curve can be done in several ways. Different manufacturers and technicians use different variables to specify the same transfer curve: Full scale, Nominal Full Scale, Practical Full Scale, Positive Full Scale, Negative Full Scale, Input Range, etc… The symbols used to represent these definitions also change according to the authors.
The goal of this paper is to present the different variations found in the literature in order for the user or technician working with ADCs to have a global view of this subject and to shed some light about the different definitions and their reason of existing. The systematization of this knowledge is useful as a reference for everyone working with ADCs and to understand and compare each others works on these devices. Note that two important parameters used when describing the performance of an ADC are the integral and differential nonlinearity. These parameters describe how well the actual transfer curve of an ADC matches the expected one. The comparison of the actual transfer curve estimated when testing an ADC with an ideal transfer curve that is not the correct, for a given ADC, will lead to erroneous values for those parameters and the consequent misrepresentation of the ADC performance.
In section II we will present the different types of transfer curves. In section 0 we will present the different approaches taken by different standardization bodies, namely the Institute of Electrical and Electronics Engineers (IEEE), the International Electrotechnical Commission (IEC), different manufacturers and a standardization effort made by a European Project known as DYNAD. Finally, in section 0 we will summarize and make a few concluding remarks.
Section snippets
Types of transfer curves
There are 3 major types of transfer curves usually encountered. For ADC that can only convert positive valued voltages the “Unipolar” transfer curve as depicted in Fig. 2 is used.
Note that the lowest transition voltage is half a step width (Q / 2) above 0.
In the case of ADCs that can convert both positive and negative voltage values, the transfer curve is called “Bipolar”. There are however two kinds of bipolar transfer curve depending where the zero input voltage is on the transfer curve. If it
Transfer curve definitions
The type of transfer curve is not all there is to the definition of an ADC transfer curve. The values of the lowest and highest transition voltages can be specified in different ways. In the following we will review some of the definition found in the literature.
Conclusions
We presented an overview of the different ways the transfer curve of an ADC is defined by different standardization organizations and manufacturers. Light was shed on the various parameters usually encountered to specify a given transfer curve. When testing ADCs, it is important to know what the ideal transfer curve is supposed to be in order for the ADC performance to be correctly quantified.
Due to the similarity of names between the different parameters care must be taken not to get them
Acknowledgments
This work was sponsored by the Portuguese national research project entitled “New error correction techniques for digital measurement instruments”, reference POCTI/ESE/46995/2002, whose support the authors gratefully acknowledge.
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