[TenTec] 75 Ohm twin velocity factor ?

[Jim FitzSimons]

characteristic impedance is 120 cosh^-1 b/a  

This is a quote from the help for DERIVE which is a product of TI.

"ACOSH(z) is the inverse hyperbolic cosine of z.  
ACOSH(z) simplifies to  2*LN(SQRT(z - 1) + SQRT(z + 1)) - LN(2)"

120*ACOSH(b/a)=120*(2*LN(SQRT(b/a-1)+SQRT(b/a+1))-LN(2))
This is not very simple, but you can calculate the impedance 
on most calculators using this formula.

Here is the reverse formula to calculate b/a from impedance z.
b/a=e^(z/120)/2+e^(-z/120)/2

Here is a link to DERIVE http://www.derive.com

Jim FitzSimons W7ANF


-----Original Message-----
From: tentec-bounces at contesting.com [mailto:tentec-bounces at contesting.com]
On Behalf Of Dr. Gerald N. Johnson
Sent: Friday, January 26, 2007 3:26 PM
To: tentec at contesting.com
Subject: Re: [TenTec] 75 Ohm twin velocity factor ?

On Fri, 2007-01-26 at 21:35 +0000, Steve Hunt wrote:
> Folks,
> 
> Thanks for all the responses on the Velocity Factor issue.
> 
> I would expect 75 Ohm twin to have a lower VF than 300 Ohm or 450 Ohm
line. With nothing but air between the conductors the limit on
characteristic impedance is 83 Ohms, so to achieve 75 Ohm the line must have
a significant amount of dielectric material as a separator; this will tend
to lower the VF.

That 83 ohm limit is untrue. Its where the conductors would have to overlap
if you use the log formula which is only accurate above 200 ohms. The proper
formula for all impedances and spacings that works down to .01 ohm
characteristic impedance is 120 cosh^-1 b/a  (that's the inverse hyperbolic
cosine, not often in a calculator or set of tables) as I recall. That shows
curved lines on a log log chart.