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