Ethernet 1000BASE-T (Gigabit Ethernet) is currently the state-of-the-art in residential computer connections (transmission lines). Category 5e (Cat5e = enhanced Cat5) cables, as shown below, can transport up to 1Gbps of digital data over lengths up to 100 meters. Cat5e cables typically consist of four twisted pairs of color-coded wires. Each twisted pair consists of two balanced 24 AWG (American Wire Gauge 24 diameter d=0.5106mm ) wires made of copper (Cu). The PVC insulator around the individual wires and spacing D is manufactured to create a characteristic impedance of Zc=100 and a signal that propagates at 0.64 times the speed of light in free space (up=0.64c). (a) Calculate the relative permittivity of the PVC dielectric. (b) If the Cat5e twisted wire pairs are lossless up to 100MHz, calculate this inductance per unit length (L) and capacitance per unit length (C). (c) To achieve a 100 characteristic impedance, calculate the spacing D between the conductors. (d) Assume the conductive losses are the dominant ones and calculate the resistance per unit length (R) of this twisted wire pair at 100MHz. (e) Now including R, calculate the complex characteristic impedance Zc and complex propagation constant at 100MHz. State what the loss () is in units of db/m at 100MHz