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" <[EMAIL PROTECTED]> >To: "Discussion of precise time and frequency measurement" ><time-nuts@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 > > > > >_______________________________________________ >time-nuts mailing list >time-nuts@febo.com >https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts > > > _______________________________________________ time-nuts mailing list time-nuts@febo.com https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts