[time-nuts] 75Z vs 50Z for GPS receivers

[Dave Brown]

----- Original Message ----- 
From: "Arnold Tibus" <Arnold.Tibus at gmx.de>
To: "Discussion of precise time and frequency measurement" 
<time-nuts at febo.com>
Sent: Tuesday, January 30, 2007 4:09 AM
Subject: Re: [time-nuts] 75Z vs 50Z for GPS receivers


> Hi Brooke,
> acc. my understanding, the characteristic impedance of a 
> transmission
> line (ideally losseless) is constant and waveform independant, as
> given by the relation of inductive and capacitive values (muh and 
> epsilon)
> equally distributed over the line.
SNIP**********
> Summarizing my opinion, a 50 Ohm transmission-line does have a Z of 
> 50 Ohms
> on  a l l  frequencies, the charact. impedance remain  c o n s t a n 
> t
> (unless the design or the material fails physically, which occur 
> mainly in the
> microwave region).

Not true.
The characteristic impedance of a transmission
line, in purely general terms, is given by the square root of R plus
jw L divided by G plus jw C, with the usual meaning for symbols used.

In the normal high frequency case, the reactive terms predominate and
we have the usual (but strictly speaking, approximate) relationship,
with the characteristic line impedance given by the square root of L
over C.

 However, at very low frequencies, the reactive terms tend to zero and
we are left with the characteristic impedance being given 
predominantly by the
ratio R over G under the square root sign.

In practice there is a range of low frequencies where both resistive
AND reactive effects contribute to the result.

So the CHARACTERISTIC line impedance DOES change with
frequency and in fact INCREASES at very low frequencies for most real
transmission lines.

 But the impedance SEEN looking into a transmission line is usually of
much more interest.  It is a function of the characteristic impedance,
the line's electrical length AND the termination at the far end of the
line.

Where the electrical length is short, (I prefer 0.1 wavelength, other
definitions of 'short' abound) its effects tend to zero and the
impedance seen is primarily a function of the termination and, to a
far lesser extent, a function of the characteristic impedance.  As
explained above, the increase in characteristic impedance will
contribute more to the result at lower frequencies, but in most
practical cases, the termination will predominate.

Disbelievers may now refer to their favourite transmission line text
where all will be (well... should be) revealed. Problem is, most of
'em gloss over the general case in their undignified hurry to get zed
nought being given by the square root of L over C!  It certainly makes
the math easier!

Regards
DaveB,NZ