Velocity factor of an air-insulated line

The following discussion about the velocity factor of an air-insulated line took place in the Moon-Net reflector. I found the subject so interesting that I decided to put together all the messages in this page.

On 29-May-2003 OH6XX wrote:
In order to get first stage of my station operational (2*4,2wl yagis) I need to build a power divider for 2m. I will build 1/4wl divider but I have one question. What is a velocity factor for the divider? Is it one or something else?

On 29-May-2003 K1JT wrote:
If you use an air-insulated line (even perhaps with a small number of standoff insulators for mechanical stability) then the velocity factor is essentially 1.0.

On 29-May-2003 OH6XX wrote:
Joe and the rest

I forgot to mention that I will make the outer part of square aluminium tubing and the inner part will be copper or brass (which one is better?). It will be air insulated with N-connectors in each end. After I sent the question I found from W7GJ's web site that he used 0.98 as velocity factor for his 4-way 6 meter divider.

On 29-May-2003 EA3DXU wrote:
0.95 is Air velocity factor.

On 29-May-2003 VE1ALQ wrote:
Wawo, your air is thin (light), Josep, over here air velocity factor is 1 (one), hi hi.

On 29-May-2003 SM5BSZ wrote:
Air velocity factor is 1.00000 exactly.

BUT in real life you have "end effects", stray inductance and stray capacitance that will add a reactive component that you can compensate for by changing the length.

I think you will have a good design if you follow some kind of average of the advice you get - and if you build the connections between the transmission line and the connectors like people usually do.

A stray impedance, L or C at the transmission line end can be compensated for by a length change - but there is also a small change in the transformation ratio. I think you can safely use anything between 0.9 and 1.05 and accept the small SWR that is generated.

I have not measured power dividers, but I assume many vhf/uhf eme-ers have done it and I think common practise will be good. I have no problem with the 0.95 length factor - I just do not like to think of it as a velocity;)

On 29-May-2003 OZ5IQ wrote:
After the production of mni combiners ts my experience that even its AIR you have to use a few percent less than 1.

I use normally 0.98 .

On 29-May-2003 K1JT wrote:
As usual, Leif's advice is very sound and based on fundamental physical principles. My only quibble with his message -- and I emphasize that this is of no practical consequence in the present discussion -- is that (as I'm sure Leif knows) it is the index of refraction of the vacuum, or "free space," that is "exactly" 1.0000. The index for air is approximately 1.000293..., depending slightly on pressure and humidity. The "velocity factor" for air is the inverse of this number, about 0.9997.

End effects and precise geometry matter more than the exact factor you use when drilling holes for the N connectors. Do not agonize over a matter of +/- a few percent of the length.

On 29-May-2003 David wrote:
velocity must have units and in the case of SI units is is metres/second. For a vacuum the velocity of electromagnetic radiation is just under 3x10^8 m/s - I can't be bothered (I've had too many to drink) to look up the right number.

Velocity factor is the ratio of velocity in a medium to that of a vacuum. The velocity factor of air is not 1.00000 exactly, but depends on temperature and pressure. I think an approximate figure at sea level is 1.0006, but maybe wrong on this. Whatever, it is not exactly 1.0000000

In practice the difference between 1.000 and 1.0006 is so small that it's insignificant. But to say the velocity, or even the velocity factor is exactly 1.00000 is incorrect.

On 30-May-2003 OZ5IQ wrote:
Does it matter ????? Combiners are WIDE things !!??

Regarding the Q of how it matters - Torleif I can describe it in this way. Its common knowledge that a 1/4 L combiner do work as well at 3/4 , n/4 in theori BUT a 2M model if you dont take the "shortening factor" into account will resonate abt. 3 MHz too high ! , the returnloss is still better than -20 dB upwards at 70 cm the Q is tribled and the BW is now 1/3 of on 2 M !

Investigating the problem - it shows, that its the lengh from the combiner conductor to the connectors in the end(s) where the female conn. "adds" 5-8 mm of "line" AND this are normally not being taken into account.. So AIR velosity is probaly "1" in the outer space but not where other "shortening factors" do interfear such as : humidity, the prolonging part of thread in the end(s), and surely more.

But now it mattera if this hasen?t been taken into account . It will still be fully usefull but with, lets say 10 dB less Returnloss. ! The Combiner we began with on 2M with a 15 MHz BW do only on 432cm be 5 MHz wide

So - the 1/4L combiner cut the freq of use and I prefer and use a V.factor.

On 30-May-2003 GW4DGU wrote:
Everyone is right! It's just that some people aren't looking at the complete picture.

The propagation speed of a TEM wave (such as propagation in coax lines) in dry air is very close to c (~2.997e8 m/s). However, when you change the dimensions of the transmission line (introduce a discontinuity), stray reactances (strictly immitances) are generated. Depending on the exact nature of the discontinuity, these can usually be compensated-for by shortening the line slightly.

All this has been well covered in the literature, and quasi-exact (and even exact) solutions have been published. It's covered in most basic microwave engineering texts. In practice reducing the length of a power divider matching element by a couple of per-cent for each discontinuity is a good empirical solution at vhf/uhf. On 1.3GHz and up you may need to look more closely at the problem.

I find myself agreeing with Leif! Don't think of a modified velocity factor: think in terms VF = 1.00 for air and reducing the length to compensate for end-effects.

On 30-May-2003 IK2MMB wrote:
Hi Chris an all, I also completely agree to this (your and Leif's) exposure of theory (and facts). I believe that someone here has vy precisely indicated what the relative VF of air (or Er) is and that is is a fact, not an opinion. I do not know if some of you ever tried to build such a coupling device for higher frequencies, say for 1.2 or 2.3 Ghz. At those frequencies the stray reactances become so important, due to the physical dimensions related to lambda (especially around the connector areas), that a simple shortening technique to get proper resonance may lead into much bigger doubts than the ones we are talking about at 2m (much bigger%). In that case it is a common practice to get the coupler back to resonance by compensating the reactances we talked about not by shortening the coupler itself but by adding a 'capacitive hat' (to ground) on the output side (where the output many connectors are). In some cases I've even seen some dielectric discs installed to increase capacitance and therefore insulation ratio (same capacity with more distance between the plates). I believe many or all of you have seen this but I felt it was important to throw it on the table too.

Keep up the good work.

On 30-May-2003 EA3DXU wrote:
Good Darrel

Sure in EA air velocity factor will be also 1 , I have built many power divider for 144 and 432 , " a good practice " is to apply a 0.95 reduction length , or your divider will resonate near 137 / 410 Mhz , still this , is not a big problem.

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