Transmission Line Parameters Physical Dimensions and Material Properties d Α + jβ = propagation constant (inverse meters) Y = G + jB = admittance (Siemens) y = Y/Y0 = g + jb = normalized admittance (dimensionless) Γ = Γr + j Γi = complex reflection coefficient (dimensionless) γ= Z/Z0 = r + jx = normalized impedance (dimensionless) Z = R + jX = impedance (Ohms) ZL = Load impedance (Ohms) Zi = Input impedance (Ohms) Z0 = Characteristic impedance (Ohms) z= Shunt capacitance per unit length (Farads/meter) Shunt conductance per unit length (Siemens/meter)
Smith chart basics pdf series#
Series inductance per unit length (Henries/meter) Series resistance per unit length (Ohms/meter) Propagation constant γ = α + jβ = ( R + jωL)(G + jωC ) Traveling wave V ( x ) = Vo eγx V ( x) I( x) = Zo ∇ × E = − jωµH ∇ × H = (σ + jωε )E ∇⋅E = 0 ∇⋅H = 0Įquivalent circuit of infinitesimal segmentĭV = −( R + jωL) I ( x ) dx dI = −(G + jωC )V ( x ) dx ∂B ∇×E = − ∂t ∂D ∇×H = J+ ∂t ∇⋅D = ρ ∇⋅B = 0 D = εE B = µH “And God said, Let there be light and there was light.” Genesis 1:3 Heaviside’s Vector Formulation of Maxwell’s Theory Transatlantic cable, project delayed by civil warġ880s Vectors, vector calculus, reformulation of Maxwell’s theory, transmission line theory - Heaviside 1886Įxperimental confirmation of Maxwell’s Theory - Hertz and Europe 1851ĭistributed analysis of transmission line - Lord Kelvin Key Dates in Electrical Transmission 1830s Magnetic telegraphs - Gauss, Henry 1839Įlectromagnetic telegraph - Wheatstone & Cookġ850s Thousands of miles of telegraph line U.S. Matching ➤ Single frequency matching ➤ Multiple-frequency and broadband matching VG – 2 PSA-00527. ❏ Impedance Matching ➤ Why match? Impedance matching vs.
❏ The Smith Chart ➤ Bilinear complex functions ➤ Impedance and admittance coordinates (circles, circles, and more Outline ❏ Transmission Line Theory ➤ Historical development ➤ Heaviside’s rewrite of Maxwell’s theory, Telegrapher’s equations, ➤ Impedance, reflection coefficient, SWR, phase constant, and velocityįactor ➤ Special facts for λ/2, λ/4, and λ/8 lossless lines Stearns, K6OIK Chief Technologist TRW Firestorm Wireless Communication Products Mysteries of the Smith Chart Transmission Lines, Impedance Matching, and Little Known Facts
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