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

Dr Bruce Griffiths bruce.griffiths at xtra.co.nz
Sun Jan 28 18:25:30 EST 2007


Didier Juges wrote:
> 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
>   

Didier

The effect of reflections from the source and load are still evident 
particularly if the timebase speed is increased.
However the transitions are monotonic albeit with small step treads 
evident for the duration of the cable round trip delay.

If the load is a time interval counter or similar device, setting the 
trigger threshold about halfway up the first step ensures that the 
reflections have little or no effect on measurement accuracy.
Bruce



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