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On the Validity of the Noise Model of Quantization for the Frequency-Domain Amplitude Estimation of Low-Level Sine Waves

Bellan D.

Metrology and Measurement Systems

2015

Vol. 22, nr 1

89--100

This paper deals with the amplitude estimation in the frequency domain of low-level sine waves, i.e. sine waves spanning a small number of quantization steps of an analog-to-digital converter. This is a quite common condition for high-speed low-resolution converters. A digitized sine wave is transformed into the frequency domain through the discrete Fourier transform. The error in the amplitude estimate is treated as a random variable since the offset and the phase of the sine wave are usually unknown. Therefore, the estimate is characterized by its standard deviation. The proposed model evaluates properly such a standard deviation by treating the quantization with a Fourier series approach. On the other hand, it is shown that the conventional noise model of quantization would lead to a large underestimation of the error standard deviation. The effects of measurement parameters, such as the number of samples and a kind of the time window, are also investigated. Finally, a threshold for the additive noise is provided as the boundary for validity of the two quantization models.

Mechanical-stress analytical modeling for the design of coils in power applications

Bellan D.

Archives of Electrical Engineering

2014

Vol. 63, nr 4

579--590

Modern electrical-power systems are often exploited for transmitting highfrequency carrier signals for communications purposes. Series-connected air-core coils represent the fundamental component allowing such applications by providing a proper filtering in the frequency domain. They must be designed, however, to withstand also the line short-circuit current. When a high-magnitude current flows through a coil, strong mechanical stresses are produced within the conductor, leading to possible damage of the coil. In this paper, an approximate analytical model is derived for the relationship between the maximum mechanical stress and the electrical/geometrical parameters of the coil. Such a model provides the guidelines for a fast and safe coil design, whereas numerical simulations are only needed for the design refinement. The presented approach can be extended to other applications such as, for example, the mechanical stress resulting from the inrush currents in the coils of power transformers.