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

[Brooke Clarke]

Hi Dave:

I got started looking at low frequency transmission line impedance in 
relation to open wire phone lines.
But for short lengths it's not a transmission line but rather a lumped 
element.
http://www.pacificsites.com/~brooke/Zo.shtml

Have Fun,

Brooke Clarke

w/Java http://www.PRC68.com
w/o Java http://www.pacificsites.com/~brooke/PRC68COM.shtml
http://www.precisionclock.com



Dave Brown wrote:

>----- 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
>
>
>
>
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