# Molecular Electronic Devices - UVACollab Transmission Lines Neurons in the hippocampus (Image courtesy Slice of Life Project) Carbon nanotube 1 When should we worry about transmission lines? l Transmission Line Asin[t-x]

LOAD Reflection, Distortion, Loss Phase difference between two ends: l Non-negligible if l > 0.01 x 2, i.e., l > 0.01 Lumped Model Distributed Model if long/high-speed Optical Signal 1015 Hz, = 0.3m Radio Wave 1 KHz,= 300km! 2 Lumped model for TL

L R G COPPER WIRE C INSULATION COPPER MESH 3

Distributed model for TL Lz Rz Gz Lz Rz Cz Gz COPPER WIRE Cz INSULATION

COPPER MESH 4 Typical formulae for C, G, L, R Two parallel plates C = w/d L = d/w R = 2R/w G = w/d A d

Note ! LC = G/C = / 5 AC Circuit model Zz ejt Yz Z = R + jL (Impedances in series) Y = G + jC (Admittances in series) 6

Kirchhoffs Voltage Law V(z) ejt Zz V(z+z) Yz Z = R + jL (Impedances in series) Y = G + jC (Admittances in series) KVL: V(z) - V(z+z) = IZz 7

Kirchhoffs Voltage Law V(z) ejt Zz V(z+z) Yz Z = R + jL (Impedances in series) Y = G + jC (Admittances in series) dV/dz = -Z 8

Kirchhoffs Current Law Zz I(z) ejt I(z+z) Yz Z = R + jL (Impedances in series) Y = G + jC (Admittances in series) KCL: I(z) - I(z+z) = -VYz 9 Kirchhoffs Current Law

Zz I(z) ejt I(z+z) Yz Z = R + jL (Impedances in series) Y = G + jC (Admittances in series) dI/dz = -YV 10 Telegraphers Equations dV/dz = -Z dI/dz = -YV

d2V/dz2 = 2V 11