[TowerTalk] RG-149: 50 ohm/70 ohm - does it matter?

[Jim Lux]

On 12/15/13 4:21 PM, Richard (Rick) Karlquist wrote:
>
>
> On 12/13/2013 3:32 PM, kr2q at optimum.net wrote:
>
>> Contributor B says, "What if the impedance at the antenna is only 33
>> ohms....
>> and you have a quarter wavelength of 75 coax."  Then...Oh horrors.
>>
>> Well, don't look now, but if the feedpoint is 33 and the coax is 50, I
>> calculate that to be the
>> same VSWR as if the feedpoint were 50 and the coax were 75.  No?
>> Nobody worries about
>> the former, do they?
>
> Let me clarify this.  If you have a 50 ohm transmitter and use 50 ohm
> coax to drive a 75 ohm load, the SWR is indeed 1.5:1.  OTOH, if you
> have a 50 ohm transmitter and use 75 ohm coax to drive a 50 ohm load,
> the transmission line mismatch is 1.5:1, but the SWR as far as the
> 50 ohm transmitter is concerned is 2.25:1 in the worst case of an odd
> multiple of 1/4 wl.  Thus a load mismatch is not as bad as a coax
> impedance mismatch.
>>
>> How likely is it to get your coax to be in odd multiples of quarter
>> lambda?  I am guessing, "Not too likely."
>> And if it is, well, just add some more coax (if you care about SWR).
>> Would that not work?
>
> If you are driving a multiband antenna, it is actually
> quite likely to have near a 1/4 wl on some frequency especially
> if you have a few hundred feet of coax.
>
> Remember, the original poster asked "does it matter"?
> In general it might matter, but you might be able to work
> around it.  But you shouldn't just assume it doesn't
> matter at all and ignore it.  The one case where it
> doesn't matter is when the coax is close to a multiple
> of a half wave.  Everyone knows that principle.
> I highly recommend that, if you are able to implement it.
>
> Also to clarify some questions about directional couplers:
> the concept would appear to be associated with
> traveling waves in transmission lines, but
> it is possible to make audio directional couplers
> out of ordinary transformers, such as in legacy
> phone patches.  Everything is essentially of
> zero size relative to a wavelength.  You can
> also make a directional coupler entirely from resistors.
> The bandwidth of such a coupler is essentially
> "DC to daylight" if you use very small resistors.
> "directivity" is just a mathematical concept.
>


I think the real question is whether a  such a hybrid/coupler/line 
sampler would have a characteristic impedance? That is, if I have a 75 
ohm source and a 75 ohm load and I put a line sampler (designed for 50 
ohm systems) in between, will the 50 ohm source see a mismatch.  I think 
not.

Taking the telephone hybrid for example.. the nominal impedance of the 
1:1 transformers is 600 ohms (which, obviously is only at one 
frequency), but the impedance that a source on one side of the 
transformer sees is pretty much the impedance that is connected to the 
other side.

looking at it another way, such a measurement system can be a series 
current sensor with a parallel voltage sensor, and by measuring the 
phase difference between the current sample and voltage sample (and 
their levels) you can tell which way power is flowing.

I suppose such a widget will have some series R (probably pretty small), 
and some shunt R (probably pretty large), and you can pick the values so 
that when you hook a 50 ohm resistor on one side, you measure 50 ohms 
from the other.

50 = Rseries + (Rshunt || 50)

And, were you to hook up 75 or 100 ohm resistors, this relationship 
wouldn't hold.