Analysis of switching frequency variation in self-oscillating class-D audio amplifiers
In this letter, a mathematical model in self-oscillating class-D audio amplifiers is proposed to describe the switching frequency variation as a fuction of the modulation depth. It is alleged in a very simple form which can be applied to any general structure adopting phase-shifting in the feedback filter, time delay of the loop, and the hysteresis window at the comparator. The main focus is set on the analysis of the phase-shifting filter which shows the least dependency on the modulation depth, which is not yet revealed.
Efficient approximations for the arctangent function
This paper provides several efficient approximations for the arctangent function using Lagrange interpolation and minimax optimization techniques. These approximations are particularly useful when processing power, memory, and power consumption are important issues. In addition to comparing the errors and the computational workload of these approximations, we also extend them to all four quadrants.
The unfolded universe of elementary particles. A geometric explanation of the standard model structure
We propose a geometric explanation of the standard model of Glashow, Weinberg and Salam for the known elementary particles. Our model is a generic Quantum Field Theory in dimension four, obtained by developing along a Lorentz sub-manifold the lagrangian of Einstein and Dirac in dimension twelve. The main mechanism which gives birth to the standard model is a certain gauge fixing of triality, which permits to identify the multiplicity of fermions, as seen from the four dimensional world, with the eight unseen dimensions of the generating universe. In this way we get the known tables of particles, explaining the series of fermions and the gauge bosons. We suggest that the Higgs field dynamics could appear through a bosonization of the right handed neutrino and correspond to a displacement in the unseen dimensions. We also propose hypotheses for dark matter, and perhaps dark energy. Then we suggest predictions to go beyond the standard model.