 # Sommerfeld, Goubau & Coax TM0 Calculator Parameters

May 26, 2014

• k1, ki, k2       bulk propogation constants       k2 = ω2εμ + jσωμ
• δ1       skin depth of conductor 1      δ = 1/Sqrt(πfμσ)
• η1, ηi, η2       intrinsic (wave) impedances for polarized plane wave: Ex/Hy      η = ωμ/k
• β       propogation constant expj(β*z - ωt)
• α       power attenuation coefficient 2β_im
• u, v       radial function parameters: u = Sqrt(λ1*a1) v=Sqrt(λ2*a1) in Stratton (1941) notation
• Pz       total axial power, per unit current-squared, outside of wire (bare or coated)
• P(ρ)       percentage of total external axial power flow contained in external radius ρ (coated wire only)
• Zo       coax characteristic impedance      Zo = Sqrt(Z/Y)
• Z       coax series impedance per unit length (Ω/m)    Z = Zsi + Zso + Zsext
• Zsi       series (surface) impedance of INNER conductor per unit length (Ω/m)
• Zso       series (surface) impedance of OUTER conductor per unit length (Ω/m)
• Zsext     series impedance due to magnetic field BETWEEN conductors per unit length (Ω/m)
• Y       coax shunt admittance per unit length (mho/m)
exp(+jωt) engineering sign convention used for Zo, Z, Zsi, Zso, Zsext and Y impedance values (e.g. Schelkunoff, 1934) .
Reference:
• Sommerfeld TM0 Wire Wave
• Goubau TM0 Wire Wave
• Goubau F(γ'ρ) Function
• Coaxial Cable Characteristic Impedance vs Frequency
• Zenneck TM0 Surface Wave
• Electromagnetic Theory, J. Stratton, 1941, McGraw Hill, pp. 524-536
• The Electromagnetic Theory of Coaxial Transmission Lines, S. Schelkunoff, 1934, Bell System Technical Journal, p. 532
• Electrodynamics, A. Sommerfeld, Lectures on Theoretical Physics, 1952, VIII Academic Press, pp 177-185
• Surface Waves and Their Application to Transmission Lines, G. Goubau, J. Appl. Phys, V21, 1950, p.1119
• Field Theory of Guided Waves, R. E. Collin, 1991, IEEE Press, pp.697-700
• Fields and Waves in Communication Electronics, S. Ramo, J. Whinnery, T. Van Duzer, 1984, J. Wiley & Sons. pp. 279-283