This note piqued my interest and I reached the conclusion that the
right answer lies closer to W8JI's claims than K8LV's calculations.
To wit...
K8LV -- Assuming a straightforward construction, my calculations, based upon
standard EM principles, shows that the attenuation constant at 4MHZ for an
IDEAL line (no loss in the spacers or the medium) would be .00012 nepers/m.
(RF units) or .03 db/100feet (ham units.) For 1500 feet, this works out to
.46db of attenuation (about 11% loss). Again, this is a totally optimistic
calculation which assumes absolutely NO losses of any
kind other than the .1ohm/m. of AC ohmic resistance at 4MHZ (properly
corrected for skin-depth). These numbers are chiseled in stone - pure,
basic, electronics.
K9AY -- Frequency-dependent effects, including skin effect, are minimal
at 2 MHz (not much more at 4 MHz), so AC (RF) loss is essentially the
same as DC resistive loss, which is 0.04 dB for 1500 ft. of (2) #8 wires.
(1.90 ohms resistance, 412 ohm load).
K8LV -- Second, the impedance of the line calculates to 412 ohms, which
requires
the noted transformers to get it down to 50 ohms. Broadband transformers, as
stated in the data, would have to be constructed using ferrite cores. It is
not possible to build such transformers, especially at transmitting power
levels, which do not have losses that range from small but noticable, to
overwhelming. If you doubt that, just spend about 10 minutes talking to
anyone who has ever designed a broadband PA. The idea of building these
matching transformers with power losses in the 1% range is just not
thinkable. It would be possible to build transformers using low-loss coax,
which would not be fully broadband, but would have losses that could be kept
down to a few tenths of a db. over a single band.
K9AY -- A properly designed transmission line transformer using the correct
wire size, winding style and core material can have a loss well under 0.1
dB,
as low as 0.03 to 0.5 dB in the frequency range of of optimum performance.
(Ref. "Transmission Line Transformers" by Sevick.)
K8LV -- Third, contrary to popular belief AND statements that I have seen
posted
here, even a perfectly 'balanced' open wire line will radiate some RF ....
...An easier, intuitive way to fathom this phenomenon is as follows. Imagine
taking that 1500 foot by 2 inch loop and stretching it out to a perfect
square (which would be 750 feet on a side.) Such a big loop is obviously
going to do some serious radiating at 4 MHz (or any other frequency for that
matter). Now begin to pull the sides back in while lengthening it, gradually
restoring it to the original line configuration. Is there any basic physical
reason why at some "magic" value of the width of the loop, it should
suddenly stop radiating? Of course not. The radiated field will just
continue to decrease until the width shrinks to zero.
K9AY -- The field intensity from a loop is proportional to the area enclosed
by the loop -- in dB, that's 20 log(Area1/Area2). Applied to the above
analogy, radiation from a 2-inch by 1500 foot loop is -67 dB relative to a
750 by 750 foot loop. -67 dB corresponds to a loss of 0.0000009 dB
(e.g. 0.2 mW out of 1 kW). That's not much radiation.
K8LV -- In conclusion, I do not think an open wire (2) line with a loss of
.005
db/100' is possible in the HF ham bands. I would say that a long line like
this would exhibit at least 1 db. total loss, from one 50ohm port to the
other.
K9AY -- 0.04 dB line loss + (2 x .05 dB) transformer losses = 0.14 dB
For comparison, the loss in 1500 ft. of 7/8" foam dielectric Heliax(R) at
2 MHz is 0.75 dB.
73, Gary
K9AY
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