Abstract
Operations in the Delta-Sigma ( Δ Σ ) domain are a broad field of research. In this article the main, focus is on applications in control systems, nevertheless the results are generally applicable for Δ Σ -signal processing ( Δ Σ SP) in other fields. As the bit-stream does not have an instantaneous value, algebraic operations cannot be executed directly. The first approaches were made in the 1980s based on small-scale integration logic chips by Kouvaras and by Lagoyannis. Further algebraic operations and other implementations were introduced by Zrilic, by Ng, by Bradshaw and by Homann. Other publications utilize complex networks and operations to achieve the desired algebraic operations. These presented operations can be divided into different operation classes by the based implementation idea. In this paper, the known algebraic operation classes are further developed and new operation classes are presented. All implementations are compared and evaluated. For linear operations in control applications, the introduced Bipolar Interpretation is best rated. It compensates for the signal offset of bipolar bit-streams and results in the best signal quality by mapping the logic values true and false of bit-stream to plus and minus one before the algebraic operation. The output of the algebraic operation is a multibit value, to achieve a bit-stream as output value a third step is taken. The result is modulated by a digital Δ Σ -modulator ( Δ Σ -M). For nonlinear operations the most universal implementation is also based on three steps. In the first stage, the bit-streams are processed with short sinc 3 filters, resulting in multibit values. This signal is processed by digital signal processing (DSP). The output stage is a Δ Σ -M. For some nonlinear algebraic operations there can be better solutions than DSP, like shown for limiting. In short, this paper gives a detailed overview about different Δ Σ SP classes for linear and nonlinear operations. Newly presented are the scaling with Bit-Stream Modification, the Bipolar Interpretation class, the nonlinear operation class based on digital signal processing (DSP), the modified multiplication based on Delta Adder and benchmarks of all presented operations.
Highlights
The control of mechatronic systems is usually performed using time-discrete signal processing
Presented are the scaling with Bit-Stream Modification, the Bipolar Interpretation class, the nonlinear operation class based on digital signal processing (DSP), the modified multiplication based on Delta Adder and benchmarks of all presented operations
The Bipolar Interpretation shows the same performance as the Advanced Quanta Decoding in this setting, as there is an even number of input signals and no previous scaling, both operation classes result in the same bit-stream and the signals quality is plotted only once
Summary
The control of mechatronic systems is usually performed using time-discrete signal processing. Analog-to-digital conversion of actual values such as current or position is frequently realized by oversampling ADCs to increase the effective resolution by filtering in a faster time frame. The filtering followed by decimation requires, as in bus systems, a synchronization of the data words This is stressed in [2], where it is demonstrated that the small signal bandwidth of a current control with Delta-Sigma (∆Σ) ADCs depends strongly on the correct sequence of the time discrete control. In terms of small signal bandwidth, a purely analog current control in conjunction with a linear power amplifier is best rated. This approach is no longer being pursued in practice for various reasons. In combination with the presented operations complex control loops with a high small signal bandwidth can be realized
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