Re: Plane wave antenna thoughts

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Original poster: "Gerry  Reynolds" <gerryreynolds@xxxxxxxxxxxxx>

Hi Terry,

I hoped you would respond.

> Original poster: Terry Fritz <vardin@xxxxxxxxxxxxxxxxxxxxxxx>
>
> Hi,
>
> I have been sort of quiet on this, but now I will speak :o))
>
> The plane wave antenna was originally designed with spice.  Been 
> there, done that...  The only reason the 50 ohm resistor is in there 
> is to match and damp out the 50 ohm coax cable.  The scope end is 
> pretty much "open load" so the resistor gives that magic .7071 "Q" 
> value to prevent ringing in the cable system to the scope.  One 
> could eliminate all that if the scope were right at the 
> antenna...  Dmitry asked why the "Q" was not "1" but a Q of one 
> still rings a little bit...  I used to design speakers too ;-))

Certainly a matching resistor will kill the reflections.  I'm not 
sure that LCR analogies are appropriate here but they may be, given 
Zo = sqrt(L/C) where L and C are the distributed parameters of the 
coax (sounds like a good homework assignment).  If R = Zo (matched 
case), then Q = 1.0  using sqrt[L/C] / R.


> With a six foot cable and assuming a propagation of 1 foot / nS, 
> pure cable reflections start at 6nS or about 170MHz.  But the 
> cable's propagation velocity is really 66% so we can really get a 
> value of  1/ (6 x 0.66 / (186282.397 x 5280)) = 248MHz...  That is 
> afar above what the antenna is "speced" at...  So, I would refer 
> those that worry about the cable and attenuation things to page "one" here:...
>
> http://hot-streamer.com/temp/PlaneWave.pdf

I think with a velocity factor of 66%, the prop time is ~1.5ns/ft  or 
9ns not 6 x 0.66, otherwise it would exceed the speed of light and 
you would get the nobel prize and then we could all share in the 
profits :o))  Given 9ns to propagate one length of the cable, the 
corresponding frequency would be 109 MHz.  Of course the length of 
the coax would load up as a 1/4 wave antenna at a lower frequency and 
only if the currents in it were unbalanced. 1/4 wave would be 27 
MHz.  Ah, the length of a CB (27 MHz) 1/4 wave antenna is about 108 
inches or 9 ft where the velocity factor about 0.95.

If the currents in the coax are balanced, there are no fields outside 
the coax and if properly terminated the length would not be important 
(other that for losses).  Otherwise, how could I use 75 feet of coax 
for a 400+ MHz transmitter (the operative word here is properly terminated).

The physical dimensions of the copper plate could also determine the 
upper frequency limit since currents in the plate are unbalanced and 
the plate will will probably load up as a 1/4 wave antenna at around 
490 MHz (assumptions:  length from the center tap to the edge of 5.5 
inches and a velocity factor in copper of about 0.9).  For the 
frequencies of interest, the antenna is not resonating and acts only 
as part of a capacitor divider. The self resonance of the 20nf 
capacitor could also limit the upper frequency (due to what this may 
do the the termination).


> But if the 50 ohm resistor and cable match right (not all that 
> easy!!) then the cable reflections will be damped too.  If the 
> resistor is say 45 ohms, then the higher frequencies start to ring 
> up very dramatically. Thus the note about trying to get the resistor 
> "just right".  But all that really is at only the super high 
> frequencies which really "don't matter" anyway...  I know that most 
> 50 ohm cable systems deliver "power" where a 50 ohm "load" is needed 
> too.  But we don't care about "power" in this case...  We just care 
> about delivering an accurate voltage to the scope's vertical voltage 
> amplifiers...

YES, but even with 45 ohm termination, there will only be several 
down and back reflections before the energy gets absorbed and 
antenuated,  probably dies out by the "next transition" (pulse 
analysis). You could use a smith chart to figure the impedance at the 
antenna end of the coax that the open circuit scope end presents to 
the capacitor divider and series resister for a given 
frequency.  This might determine the limiting BW as well. Just thoughts


> The frequency response comes out to 7.9Hz to 245MHz...  At say 
> 250MHz, eddy currents and other effects can start to "matter", thus 
> the funny etched pattern...

I question the 245 MHz, but I also dont think it matters.  Also, to 
have eddy currents, the H field must have a component normal to the 
surface.  I believe most H field contributors (currents) will result 
in tangental H field components (assuming no streamers that will 
result in H field components dependent on its path).  I'm having a 
hard time envisioning a source of H field that would be normal to the 
surface if the antenna was pointed directly at the coil.


> At below 1MHz, the pattern is not important at all...  I can and 
> have tested the thing with a signal generator to 15MHz and it is 
> "really flat" over that range.  I am real confident that the 
> frequency response is flat over say the 1kHz to 10MHz range and am 
> very unconvinced to the arguments otherwise...

> My good pal Gerry talks of a problem at 80Khz...  "Show me"... ;-))

I never said that there is a problem at 80Kz (at least I dont think I 
did). 80Kz is where the 20nf cap has an impedance of 100 ohms 
(matches the 50 ohms coax plus 50 ohms resister).  Maybe 160 KHz 
should be the frequency (where the capacitor impedance becomes 50 
ohms).  Anyway, the termination starts to become reactive and 
imperfect at these frequencies and more so at lower 
frequencies.  Reflections start to have a longer settling time as the 
frequency gets lower.  Neglecting the 1 Mohm input impedance of the 
scope, the settling time becomes infinite at DC for a lossless cable 
(no energy absorption).  Also, as the frequency gets lower than 80Kz, 
the signal that is forward propagating toward the scope becomes smaller.

Thevenize the capacitor divider into a source and series 
capacitance.  Then do a voltage division from this thevenin source 
using the series coax inpedance (50 ohms) as one side of the divider 
and the 50 ohm resister in series with the thevenin capacitor as the 
other side of the divider.  As the forward propagating voltage gets 
smaller, it will take more trips down and back for the voltage at the 
scope end to reach the value of the thevenin source.  Also, the lower 
the frequency, the more time there is for this to settle so it may 
not be a problem.  I just worry about things like this until it can 
be proven that it is not a problem.  The spice simulation I did 
showed a steady state AC voltage that was accurate but had a low 
frequency drift to it.  This is what made me think about transient 
response.  The artifact could also be a problem in the transmission 
line modeling of the simulator and would therefore have no real significance.

The one way I know of the find out for sure is to put a unity gain 
high BW amplifier at the antenna end to buffer the coax from the 
capacitor divider. This amp would have a 50 ohm source impedance so 
source termination would be constant over the frequencies of interest 
and down to DC.  The amp would be battery powered.  Both the amp and 
battery would be totally shielded with an RF feed thru capacitor to 
get the signal into the box and a BNC connector to get the buffered 
signal out of the box.


> Streamer effects - worst case - streamer hits the antenna 
> =:O  Massive errors are noted!!!  Don't do that!! :o))

Yeh, especially if you care for your scope :-))

> Streamers are dynamic and sort on unpredictable "noise" in the 
> antenna's pickup.  Perhaps one could simply do digital averaging to 
> "eliminate" their effects.  But "I" think if you have sort of small 
> streamers directed far away from the antenna, it is not a "big 
> deal".  I also thing "streamer loading (to the air) is not a "great" 
> load on the coil anyway...  Or spice coil models would fail 
> drastically if they were that far off...  It really depends on how 
> accurate you are trying to be...  In many cases, like 50% if really good ;-))

I think the effect that a streamer has on the coil is small (maybe 
5%) compared to the top load capacitance.  However, when you have a 
capacitive divider that has only 0.047 pf between the toroid and 
antenna,  It seems like it wont take much streamer toward the antenna 
to significantly change this.  Digital averaging may very well be the answer.

> Backplane - It is supposed to block stray signals.  In retrospect, 
> there are NO stray signals within like 5 orders of magnitude 
> :o)))  I stoled the idea from ones that measured 5V computer noise 
> signals :o)))  It does help to "direct" the antenna's sensitivity 
> zone.  That might be useful...  But you probably don't need any back 
> plane at all...  The 20nF cap provides all the divider load 
> needed...  So you can use just a single sided PC board or metal plate...

The backplane may also cause unbalanced currents in the coax causing 
it to "load up".  I just dont know about this one.


> The plane wave antenna things was really just meant to be better 
> than the "wire off a scope probe" thing...  It really is MUCH 
> better!!  But it is not perfect and you can trick it if you try 
> easily enough...  But really, even a wire antenna with the cable 
> loading and matching "tricks" added would really do very 
> well!!!!  Maybe that is the best solution in the long run...  I am a 
> little intrigued by using an "array" of them to see a "bigger picture"...
>
> All things considered, I think we can figure out top voltages darn 
> well now-a-days... :D

And I too believe it is a great, low cost, and easy to make addition 
to our tool box.  Cant really talk "bad" about it when there is 
nothing within our reach that is better.  I do think the discussion 
has been positive in that it suggests certain areas for exploration 
and verification, and perhaps improves the awarness of what can go 
wrong :o))  Thankyou Terry for this invention.

Gerry R