Nonlinear D/A and A/D converters some new techniques and applications

Abstract

The development of new techniques for realizing nonlinear D/A and A/D converters, followed by their hardware implementation and/or computer simulation, has been described in this thesis. Also covered in the thesis are many applications of the above D/A and A/D converters, which demonstrate their usefulness. Important aspects of these investigations and the results derived are briefly described below.

a) Nonlinear D/A Converters: The following techniques have been developed to provide a generalized approach to the design of nonlinear D/A converters:

i) Code conversion ii) Conversion using Haar functions iii) Iteration iv) Cascade connection of linear D/A converters

While the first three techniques facilitate the design of D/A converters for a wider range of functions, the last one is useful in the generation of polynomial functions. The salient features of these converters are summarized below.

A computer program for synthesizing a variety of nonlinear functions has been developed. For example, this program has been employed to generate nonlinear Boolean equations to synthesize a square-root type converter. The advantages of this method are: (a) ease of realization using state-of-the-art hardware, and (b) high speed of operation.

It is expected that these D/A converters can be useful in the realization of high-speed successive-approximation type A/D converters.

ii) Conversion using Haar functions: Nonlinear D/A conversion can also be realized using Haar functions, a particular class of digital orthogonal functions. As an example, an exponential D/A converter has been implemented in the laboratory following this approach. The main advantage of this technique is the low distortion of the output analog signal, which makes this technique highly suitable for digital function generators. However, this technique suffers from disadvantages such as: (a) requirement of precision resistors, and (b) large hardware complexity.

iii) Iteration: In this technique, a difference equation is written to represent the given nonlinear function. Based on this equation, an iterative type of circuit can be realized to synthesize the given function. An exponentially decaying function has been realized following this approach, as an example. The main advantage of this technique is the simplicity of hardware required for system implementation. However, this technique suffers from the disadvantage of longer conversion periods.

iv) Cascade technique: Linear D/A converters are cascaded to generate a polynomial function. A converter that can generate a second-degree polynomial function has been realized using this approach, as an example. The advantages of this technique are: (a) ease of realization using state-of-the-art hardware, and (b) high speed of operation. This converter is particularly suitable for linearizing A/D converters.

The important characteristics of these D/A converters are summarized in Table 5.1, which clearly shows the usefulness and importance of these building blocks.

b) Nonlinear A/D Converters: Nonlinear A/D converters for both DC and time-varying signals have been developed and implemented in the laboratory. While A/D converters for DC signals employ the nonlinear D/A converters described above in their feedback paths, new algorithms are utilized in the realization of converters for time-varying signals. For the former, logarithmic characteristics have been implemented as an example. Both successive-approximation and counter-ramp type converters are realized for high- and low-speed applications. While the successive-approximation type logarithmic A/D converter can be utilized in analog multiplexed systems, the counter-ramp type converter, which has very low hardware complexity, can be employed in simple multiplexed systems. An exponential A/D converter for time-varying signals has been implemented as an example.

The important characteristics of different logarithmic A/D converters, realized in the laboratory, are given in Table 5.2, which indicates their usefulness in practical systems. Also, a new averaging technique has been developed to reduce the error of those converters. This technique has been simulated on the computer to determine the optimum conditions.

To demonstrate the usefulness of these converters, a few typical applications, viz., a linearizing A/D converter and a POM encoder, have been tried out in the laboratory, and the results are encouraging. In all these cases, the resolution and conversion interval are mainly limited by the linear ICs such as OPAMPs and comparators employed in the converters. With readily available OPAMPs (type LF356), a 5-bit converter with a conversion period of 60 ?s could be easily synthesized. The resolution and speed of operation of these converters can be vastly improved by using high-input-impedance, high slew-rate OPAMPs (e.g., type LH003). Although these devices are available in advanced countries, their non-availability in some regions did not permit practical implementation of high-speed and high-resolution A/D converters using the approaches described.

Table 5.2: Important characteristics of logarithmic A/D converters implemented in the laboratory

Technique System Complexity Conversion Interval Input Dynamic Range Successive Approximation Type High Low (60 ?s with 1 MHz clock) 0–10 V Haar Functions High Low (60 ?s with 1 MHz clock) 0–10 V Iteration Very Low High (320 ?s with 100 kHz clock) 0–10 V Counter-ramp Type Very Low Moderate 0–10 V

The main advantage of the different techniques developed is their suitability for realizing a wide range of nonlinear characteristics with very few modifications in the hardware. Hence, these converters are expected to be useful for a variety of applications in electronic systems.