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
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