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.