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首页> 外文会议>Conference on Ph.D. Research in Microelectronics and Electronics >A general formula for impulse-invariant transformation for continuous-time Delta-Sigma Modulators
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A general formula for impulse-invariant transformation for continuous-time Delta-Sigma Modulators

机译：连续时间Delta-Sigma调制器的脉冲不变变换的一般公式

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摘要

This paper presents a generalised new formula for impulse-invariant transformation which can be used to convert an nth-order Discrete-Time (DT) ΔΣ modulator to an nth-order equivalent Continuous-Time (CT) ΔΣ modulator. Impulse-invariant transformation formulas have been published in many open literature articles for s-domain to z-domain conversion and vice-versa. However, some of the published works contain omissions and oversights. To verify the newly derived formulas, very many designs of varying orders have been tested and a representative 4th-order single-loop DT ΔΣ modulator converted to an equivalent CT ΔΣ modulator through the new formulas are presented in this paper. The simulation results confirm that the CT ΔΣ modulator which has been derived by these formulas works in accordance with the initial DT specifications without any noticeable degradation in performance in comparison to its original DT ΔΣ modulator prototype.
机译：本文提出了一种用于脉冲不变变换的通用新公式，该公式可用于将n阶离散时间（DT）ΔΣ调制器转换为n阶等效连续时间（CT）ΔΣ调制器。脉冲不变变换公式已在许多开放文献中发表，涉及s域到z域的转换，反之亦然。但是，某些已出版的作品包含疏漏和疏忽。为了验证新推导的公式，已经测试了许多不同阶数的设计，并提出了通过新公式转换为等效CTΔΣ调制器的代表性四阶单环DTΔΣ调制器。仿真结果证实，由这些公式得出的CTΔΣ调制器与其原始DTΔΣ调制器原型相比，按照初始DT规范工作，而性能没有任何明显下降。

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