Fast Square Root Calculation without Division for High Performance Control Systems of Power Electronics

The calculation of square roots is a frequently used operation in control systems of power electronics for different applications:motor drives,power converters,etc.At the same time,the execution of this procedure significantly loads microcontrollers and uses its power,which can be utilized for performing other important tasks.Therefore,it restricts the size of code,which can be processed by the microcontroller and compels developers to limit the number of functions,or to decrease execution frequency of a program.Thus,the calculation of square roots is a bottle-neck in implementation of high-performance control systems,thus effective optimization of this task is extremely important in modern and efficient devices.In respect that many applications do not need precise calculation of square roots,the optimization of execution time can be achieved by decreasing of precision of the result.The proposed technique is based on the approximation of parabola with hyperbola,which allows you to rapidly find the approximate value of a square root.Taking into account that many digital signal processors(DSP)are not equipped with an effective divider,the developed algorithm does not use divisions,so it can be executed faster.The payback for this optimization is approximation error with a maximum of 0.5%,however,it is acceptable for the overwhelming majority of control systems.

Comparative Analysis of the Characteristics of Polar and Non-Polar Spiral Polarization Rotators

Spiral polarization rotators, rotating polarization ellipse axes clockwise or counterclockwise, depending on the azimuth angle in the transverse plane, are considered. It is shown that spiral polarization rotators lead to a change in the order of optical vortices with circular polarization. A comparative analysis of spiral rotators of two types (polar and non-polar) is carried out, using a mirror that allows light to pass in the opposite direction through the rotator. The effect of spiral rotators on optical vortices in a resonator is studied. It is shown that spiral rotators can preserve or accumulate changes of the vortex order during the passage of the beam in both directions. The properties of the spiral rotator and the cube-corner reflector with a special phase-correcting coating, as a diffractive polarization-optical element, are compared.

Comparison between Theoretical and Experimental Radial Electron Temperature Profiles in a Low Density Weakly Ionized Plasma

Experimental and theoretical studies of the radial distribution function of the electron temperature (RDFT) in a low-density plasma and weakly ionized gas for the abnormal glow region are presented. Experimentally, the electron temperatures and densities are measured by a Langmuir probe moved radially from the center to the edge of the cathode electrode for helium gas at different pressures in the low-pressure glow discharge. The comparison of the final experimental data for the radial distribution of electron temperatures and densities for different low pressures ranging from 0.2 to 1.2 torr, with the final proved equation of RDFT confirms that the electron temperatures decrease with increasing product of radial distance and gas pressures, showing a radial decrement dependence of the electron temperature from the center to the edge of the electrode. This is attributed to the increase of the number of electron-atom collisions at higher gas pressures and consequently of the rate of ionization. For the axial distance (L) from the tip of the probe to cathode electrode and the cathode electrode radius (R), a theoretical and experimental comparison for the two conditions L R and L > R, for both cases the produced plasma temperatures decrease and densities increase. It is concluded that the RDFT accurately shows a dramatic decrease for L R by 60% less than RDFT values for L > R similar as for conditions of magnetized and unmagnetized effect for DC plasma. This means that the rate of plasma loss by diffusion decreased for L R, agrees well with the applied of magnetic field