Re: NEC-LIST: coax line with strip centre conductor?

In nec-list, <Stanley> wrote:
>
> Does anyone know if there is a formula for the characteristic
> impedance of a coax line having a symmetrically placed infinitely thin
> strip as its centre conductor?

Suppose it consists of a cylinder with radius R, and a centered strip
with width w (which means w should be less than 2R to fit in). I would
use (in Mathematica notation) the conformal mapping:

  t = EllipticF[ ArcSin[(z/R+R/z)/2], m ]

  m = 4 / (w/(2R)+2R/w)^2

which maps one quarter of the cross section to [0,K(m)] x [0,K(1-m)],
where K(m) is the complete elliptic integral. You get:

  Cline = eps0 * epsr * (4 EllipticK[m] / EllipticK[1-m])

  Zline = Z0 Sqrt[mur/epsr] * EllipticK[1-m] / (4 EllipticK[m])

Example: R=5; w=8; epsr=1; mur=1 (value for air) will give:

  In[7]:= N[Zline]
  Out[7]= 0.135865 Z0 (characteristic impedance)

  In[8]:= N[Cline]
  Out[8]= 7.36022 eps0 (capacitance per unit length)

Greetings,
Jos

--
  Dr. Jozef R. Bergervoet                      Electromagnetism and EMC
  Philips Research Laboratories,             Eindhoven, The Netherlands
  Building WS01                                     FAX: +31-40-2742224
  E-mail: bergervo_at_natlab.research.philips.com    Phone: +31-40-2742403