Practical Synthesis Of Irrational Impedance Based On Solutions Of The Quadratic Equation

This article presents the rational approximations of recursively obtained solutions of the quadratic equation which lead to networks with lattice or tree structure. The impedance of a similar electrical circuit, composed of resistors and capacitors, has a module, depending on the square root of the frequency and its phase is equivalent to -45°. After considering the effect that the number of elements and their tolerances have on the accuracy of the impedance function of the networks, an eight section lattice cascade was constructed. The deviation between the theoretically and experimentally obtained magnitude and phase characteristics of such a device in the frequency interval 0,05÷1MHz did not exceed -1,2% and -1,3° respectively. Furthermore, it was found that the lattice network performance had impedance close to the expected one but in parallel with a capacity.