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

[Didier Juges]

It is true is that the impedance of a transmission line is not constant 
with frequency, particularly at the low end (audio).

At the higher end, a lot of things happen, such as impedance, 
attenuation and velocity factor all change (a little) with frequency. 
Also, at the higher end, leakage takes place. The center conductor can 
no longer be considered to be completely enclosed by the shield and some 
of the signal traveling in the cable is radiated out, increasing 
insertion loss (and some outside signals can get in the cable as well). 
Semi rigid cable (where the outer conductor is a solid piece of copper 
tubing) takes care of the leakage issue pretty well, at least far away 
from the connectors.

However, most well designed coax cable exhibit a wide frequency range 
where most of these characteristics are stable enough for practical 
purposes, and the only thing you have to worry about is the increased 
attenuation (or insertion loss) with increased frequency. So from HF to 
VHF (and probably UHF), most coax cable can be considered as having a 
constant impedance. Now, the 1 PPS signal has frequency components as 
low as 1Hz of course, and going well into the higher MHz region, 
depending on the rise and fall times, so you would think the lower 
frequency components must be affected by the change of impedance of the 
cable at the low end.

The characteristic impedance of coax only means anything when the line 
is long enough compared to the signal wavelength (or frequency). With a 
50 feet length of cable, that is about 1 MHz or 2. Below that frequency, 
the characteristic impedance means nothing (that means the line is short 
enough that you can consider the voltage and current to be the same all 
along the line) and the cable is equivalent to a capacitor.

So, unless you deal with very very long transmission lines (like the 
phone companies do), you can ignore the fact that the characteristic 
impedance changes at the low end.

This can be illustrated by the waveform
http://www.ko4bb.com/Test_Equipment/Thunderbolt/PPS_into_50feet_75ohm_cable_1Mohm_load.jpg

You can see the initial reflections are nice and square, and as the 
signal keeps bouncing, the waveform rounds up. This is due to the higher 
order harmonics being attenuated more than the lower harmonics. 
Eventually, the signal looks more and more like a sinewave before it is 
completely attenuated.

I uploaded a couple more pictures:
http://www.ko4bb.com/Test_Equipment/Thunderbolt/2_PPS_into_long_75ohm_cable_thru_500ohm.jpg
and
http://www.ko4bb.com/Test_Equipment/Thunderbolt/2_PPS_into_short_50ohm_cable_thru_500ohm.jpg

These show the waveform at the end of the long (respectively short) coax 
cable when the cable is fed through a approx 500 ohm resistor. The scope 
was set to 1 Mohm input impedance.

You can see that there is no ringing any more, with either cable. The 
dominant feature of the waveform is the attenuation of the leading edge 
due to the capacitance of the cable. The longer the cable (which is 
still very short compared to 1 Hz), the more capacitance. (Please note 
that 75 ohm cable has less capacitance per foot than 50 ohm cable.) Yet, 
when driven by a driver having matched impedance, the leading edge is 
very square, with about 20nS rise time.

Didier KO4BB


Brooke Clarke wrote:
> HI Didier:
>
> It's my understanding that the term impedance can only be applied when 
> sine wave signals are being used.  So for pulse work you might look at 
> the harmonic content and try to match all those frequencies. 
>
> Long ago Bob Grove promoted the idea of using 75 Ohm TV coax for ham 
> antennas at 2 meters and higher frequencies because it had lower loss 
> than 50 Ohm coax and was much lower in cost.  For ham applications the 
> VSWR due to the coax impedance was much smaller than the inherent match 
> (mismatch) of the things on either end.
>
> It's only been in the last few years that I understood that the 
> impedance of a transmission line is only a constant value above some 
> frequency and below that is no longer a constant.  So, for example, 
> audio signals can not be transmitted using "transmission lines" of 
> constant impedance.  For more see: 
> http://www.pacificsites.com/~brooke/Zo.shtml
>
> Have Fun,
>
> Brooke Clarke
>