From: pcdhSpamMeSenseless@electrooptical.net   
      
   Liz Tuddenham  wrote:   
   > What physical properties determine the velocity factor of co-ax?  Most   
   > of the amateur radio books give around 60% as the velocity factor for   
   > 'common' types of 50-ohm co-ax.   
   >   
   > I recently bought a drum of fairly cheap 50-ohm co-ax with the screen   
   > made from a metallised plastic tape and a loosely-woven copper braid.   
   > Using a VNA I measured the reflected impedance of a known length (about   
   > 6 metres), open circuit at the far end, and found the frequency at which   
   > its reactance first swung through purely resistive.   From this I   
   > calculated its effective electrical length and the velocity factor,   
   > which turned out to be 78%.   
   >   
   > This seems so different from the 'conventional' value that I am   
   > suspicious of my measurements - but this type of screen construction was   
   > not in common use when the original 'words of wisdom' were written.   
   >   
   > Are there any physical properties of the co-ax could I check, which   
   > might explain my measured velocity factor?   
   >   
      
   There are two leading-order effects that change the phase velocity in a   
   transmission line.   
      
   One is the shape of the lowest-order normal mode.  Without going into   
   higher (but very pretty) math, there’s only so much curvature that the   
   field plot can have. (It doesn’t mean that the field direction necessarily   
   changes—it’s the second derivatives that are in view.)   
      
   If the boundary conditions force the transverse variation to have   
   curvature, as in a metal waveguide, there’s less curvature available for   
   the longitudinal variation—k_z is lower than the free space value. Since   
   v_p = omega/k_z, the phase velocity exceeds c in the material, and can   
   exceed c in vacuum.   
      
   As the waveguide cross-section decreases, there’s less and less for k_z,   
   until cutoff, where k_z is 0, the phase velocity diverges, and the wave   
   can’t propagate.   
      
   In a coaxial geometry, there’s no transverse curvature, so k_Z gets it all,   
   and the phase velocity is c.   
      
   Which brings us to the second first-order effect, namely the dielectric.   
   In free space, c is reduced by a factor of 1/sqrt(mu epsilon), which is   
   about 1.5 for solid polyethylene, leading to a velocity factor of 0.65-0.7.   
      
      
   Foam and spiral dielectric spacers have lower effective epsilon, and thus   
   higher velocity factors.   
      
   Cheers   
      
   Phil Hobbs   
      
   --   
   Dr Philip C D Hobbs  Principal Consultant  ElectroOptical Innovations LLC /   
   Hobbs ElectroOptics  Optics, Electro-optics, Photonics, Analog Electronics   
      
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