Abstract
In this paper, the general model for an infinite LC ladder network using Fibonacci wave functions that were applied to lossless transmission lines will be extended to transmission lines including losses. The general model that was derived from a first order system transfer function representing a simple RC or RL circuit will be used to model and analyze transmission lines presenting losses. The LC ladder network model can be applied to any order for each inductor current with its parasitic rc resistor and for each capacitor voltage with its parasitic rL resistor. The extension of the proposed general model to transmission lines with losses is subject to Heaviside condition for both resistors rc and rL .
Highlights
In the previous papers [1] and [2], Fibonacci wave functions (FWFs) were introduced to model an infinite LC ladder network without losses
Most other papers used only lossless modeling and analysis. Introducing losses in such systems leads to another level of difficulties in modelling and analyzing these systems [3], [5] and [6]
Studies confirm that these electrical LC ladder circuits for different orders representing different transmission lines length with losses defined by rL and rC follow the same recurrent Fibonacci sequence modelled by FWFs [1]
Summary
In the previous papers [1] and [2], Fibonacci wave functions (FWFs) were introduced to model an infinite LC ladder network without losses. Most other papers used only lossless modeling and analysis Introducing losses in such systems leads to another level of difficulties in modelling and analyzing these systems [3], [5] and [6]. The extension of FWFs with its general model to LC ladder network with losses to model a transmission lines with resistive losses will be modeled and analyzed for different orders and will be compared to MATLAB-Simulink LC model presenting the same losses.
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