[TenTec] 75 Ohm twin velocity factor ?

[Jim FitzSimons]

The TI-83 has cosh^(-1) function built-in.
I did not check but I assume all the TI graphing calculators 
have the inverse hyperbolic cosine cosh^(-1). 

Jim FitzSimons


-----Original Message-----
From: tentec-bounces at contesting.com [mailto:tentec-bounces at contesting.com]
On Behalf Of Dr. Gerald N. Johnson
Sent: Saturday, January 27, 2007 10:00 AM
To: tentec at contesting.com
Subject: Re: [TenTec] 75 Ohm twin velocity factor ?

On Sat, 2007-01-27 at 09:07 +0000, Steve Hunt wrote:
> Jerry,
> 
> Despite using the wrong formula I guess I came to the right conclusion
.... you can't get down to 75 Ohms without some "non-air" dielectric.
> 
> I have three HP41C calculators (one in the house, one in the shack, and a
spare) and was surprised something so sophisticated doesn't have hyperbolic
functions; but I believe they were available on one of the plug-in math
modules.
> 
> 73,
> Steve

How do you get that? I tried 0.1" diameter conductors 0.11" center to
center and it comes up 53.2 ohms impedance. That's 0.010" gap, fairly
closely spaced. Same conductors 0.105" center to center (0.005" gap) is
37.79 ohms impedance. Cut that gap to 0.001", 0.101 gives 16.96 ohms
impedance. That's 120 arccosh (S/d). S is center to center spacing, d is
conductor diameter. Working closer, 0.0001" gap for 0.1001" center to
center gives 5.37 ohms. So lower impedances are possible, maybe not
practical, but possible. 10 millionths gap makes 1.7 ohms, 1 millionth
gap makes half ohm impedance. But yet the conductors don't quite
intersect or touch unless the gap gets all the way to nothing. And then
the impedance is zero.

-- 
73, Jerry, K0CQ,
All content copyright Dr. Gerald N. Johnson, electrical engineer