New Fibonacci Recurrent Systems Applied to Transmission Lines Input Impedance and Admittance

In this paper, new Fibonacci wave functions are introduced for the first time. These transfer functions are derived from a first order transfer function source. Their characteristics and behaviors are quiet impressive and their output signals present multiple intermediate steady-states. Their polynomial coefficients follow specific distribution with respect to the Golden ratio. The pole locations of these transfer functions follow the Fibonacci pattern and they can be created to an infinite degree following a simple recurrent process. They have multiple resonance and anti-resonance frequencies organized in a perfect way with respect to each other. Each Fibonacci system has two well defined Fibonacci boundary systems using Pascal's triangle. These systems describe perfectly transmission lines LC ladder model input impedance and admittance.