From Thomson Formula to Resonant Equivalent Diagrams

L. Tomawskia, I. Mrózb, Z. Kukułac aUniversity of Silesia, August Chełkowski Institute of Physics, 75 Pułku Piechoty 1A, 41-500 Chorzów bUniversity of Wrocław, Institute of Experimental Physics, pl. M. Borna 9, 50-204 Wrocław, Poland cUniversity of Silesia, Institute of Computer Science, 75 Pułku Piechoty 1A, 41-500 Chorzów, Poland

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Until the 1970s, only three basic elements: R, C, and L have been used to construct RLC circuits. These elements are two-ports of zero order (resistances) and of first order (capacitances and inductances). Their presence in electronic circuits causes a certain phase shift between voltage and current. In 1969, Bruton published an inductorless filter. There are two two-ports of second order (supercapacitances) in this circuit. Supercapacitance causes a phase shift of 180 degrees. In the next years, many two-ports of higher orders (e.g. of second and third order) were developed and, in theory, their number may be infinite. The use of such two-ports in resonant circuits makes it possible to obtain other phase shifts. In this paper, we show how to transform basic circuits into their resonant equivalent diagram. The analysis of these diagrams allows us to describe precisely resonant phenomena occurring in the circuit and to identify all resonant circuits, even when the basic diagram does not indicate resonance properties.

DOI:10.12693/APhysPolA.139.304 topics: basic blocks of electronics, FDNR, FDNC, FDNCap