Abstract
In this paper, new general model for an infinite LC ladder network using Fibonacci wave functions (FWF) is introduced. This general model is derived from a first order resistive-capacitive (RC) or resistive-inductive (RL) circuit. The order Fibonacci wave function of an LC ladder denominator and numerator coefficients are determined from Pascal’s triangle new general form. The coefficients follow specific distribution pattern with respect to the golden ratio. The LC ladder network model can be developed to any order for each inductor current or flux and for each capacitor voltage or charge. Based on this new proposed method, nth order FWF general models were created and their signal propagation behaviors were compared with nth order RC and LC electrical circuits modeled with Matlab-Simulink. These models can be used to represent and analyze lossless transmission lines and other applications such as particles interaction behavior in quantum mechanics, sound propagation model.
Highlights
Fibonacci wave functions (FWFs) are transfer functions with high degree that are irreducible
Simulations of[(%a,%) = C ∗ g[(%a,%)(s) FWF model and Matlab-Simulink RC-Fibonacci electrical circuits (FECs) electrical circuit model order 40 are illustrated in figure 6
The 2nd order RL FIBONACCI ELECTRICAL CIRCUIT (RL-FEC) will be defined with current input and voltage output and its FWF expressed in (10)
Summary
Fibonacci wave functions (FWFs) are transfer functions with high degree that are irreducible. A step by step development methodology of new electrical circuit application of FWFs called Fibonacci electrical circuits (FECs) is introduced to model perfectly the recurrent LC ladder network. These FECs can be used to model transmission cables [3], [4], the behavior and interaction of the infinitely small particles using the infinite LC networks [5] in quantum mechanics, the neural dynamic in biology [6], etc. For nEF odd order RC-FEC with current as input and voltage as output have a final steady-state value L V
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