[Antennas] Balanced line optimum conductor spacing?

2002年1月05日 07:32:41 -0500

Gene Mason wrote:
>> Comment.. Is this a case of the 'proof is left up to the student' ?
> btw, the last time I checked, Maxwells equations didn't discriminate
> between positive and negative currents.

You are correct in that Maxwell's Equations don't discriminate based on
current polarity; but, the resulting EM fields are vectors that have
magnitude and direction [a 100 V/M field at 0 degrees at a point and a
100V/M field at the same point from near the same source but at -180
degrees relative phase shift produce a 0 V/M field.
>> In a transmission line, frequency doesn't enter into the
> calculations, until the line losses become excessive at the upper
> frequency limit. 

Disagree. Attenuation in a transmission line is present at all
frequencies. It is measured in Nepers/Wavelength. Frequency is very much
part of all transmission line calculations [reciprocal/wavelength].
Current is not constant in the transmission line. It decreases along the
length of the line as e^-((alpha + jBeta)*L) where alpha is the
attenuation in Nepers/wavelength and Beta is the phase velocity in
radians/unit-length and L is line length. So, from the point of Physics
the vector sum of the fields from an open wire line, using a method of
moments calculation, contains more energy from the source portion of the
line than the load portion of the line. From an engineering perspective
line losses are part of the system power budget.
> The technical data on designing and constructing open
> wire feeders, suggests that the wire is not insulated and low loss
> spreaders are used. To do otherwise will produce undesireable
> results. 

Agree. But the question dealt with line to line spacing in open wire
line and trying to determine 'optimum' spacing. If you are a Physicist
the optimum spacing is as close as you can make it to minimize pattern
distortions from the collinear axis of the line. If you are an engineer,
a small variation in a pattern is accepted as the result of a series of
compromises including wire strength, wind loads, ice loads, practical
characteristic impedance levels, construction details such as spreader
losses, precipitation effects, etc.
Driven antenna arrays, Collinear or Broadside, are examples of open
transmission lines, 1/4 to 1/2 WL long, where the line to line spacing
is a significant portion of a wavelength producing relative phase angles
in the resulting EM fields to achieve gain! This gain is the
'distortion' I'm trying to address. As long as the relative spacing
between the wires is a small percentage of a wavelength the
'distortion', radiation from the line, is minimal.
> At very high frequencies, there exist alternative
> transmission devices, these are called waveguide at microwave
> frequencies.

Agree, but it was not a question of waveguides! It was about spacing of
the wires in open line construction. Propagation in waveguides is a
totally different mode from transmission lines. In waveguides the energy
is contained in the fields within the guides, not the conducting
surfaces. In a TL the energy is contained in the conductors.
[BTW, my center fed doublet uses #16 stranded and insulated wire at a
nominal 600 ohms characteristic impedance.]
Let's let it end here before this becomes an honest dispute between
Physics and Engineering.
73, Dave, W1MCE, BSEE
Manager, Textron Antenna Range, retired
PS
W8JK, John Kraus, has written extensively, McGraw-Hill Publishing, in
his University Text Books on Electromagnetics and Antennas on this
subject. It's been 43 years since I plowed through the math, but I
really learned the lesson!