*Half wavelength vertical ground loss*
Let's see if we can quantify the conduction losses of a 1.8 MHz half
wavelength vertical connected to average earth via a ground rod. This paper
by N6LF shows one skin depth at 1.8 MHz to be 6 meters.
http://www.antennasbyn6lf.com/files/ground_skin_depth_and_wavelength.pdf
Let's assume the current magnitude in the ground mirrors that of the
antenna. Driving the antenna at the base such that the current at the
antenna center is 1 amp, the ground current 40 meters away from the antenna
is 1 amp. The 1 amp of ground current passes through a section of earth
having an effective depth of of 6 meters. For a 1 meter radial length and
40 meters from the antenna the section has dimensions of 1 meter X 6 meters
X 250 meters (250 meters is the circumference). Given a resistivity of 200
ohms/meter the resistance of this section is 200/(6 X 250) = 0.13 ohms. The
loss in this section is 0.13 watts. Using NEC we see with the base current
set to give 1 amp at the antenna center the power into the antenna is 100
watts.
Closer to the base of the antenna the effective ground resistance increases
due to the smaller circumference. Closer to the antenna the current
decreases. Roughly Integrating the ground loss from the base to the 80
meters away gives a total ground loss of 4 watts. The no-radial ground loss
is 5 watts and the antenna gain is reduced by 10LOG(100/96) = 0.2 dB from
the full radial case.
How about ground loss due to the induced E-field in the ground? I believe
this is accounted for in the previous calculation. I ran a NEC simulation
to explore this. The two cases were a 266' vertical fed against thirty 3'
radials and thirty 133' radials. The radials are 0.05' above medium ground.
The NEC Average Gain was compared for the two cases and showed a difference
of 0.06 dB.
Dave WX7G
On Sun, Dec 16, 2012 at 6:42 PM, Donald Chester <k4kyv@hotmail.com> wrote:
>
> Then, why do broadcast stations that use vertical towers at approximately
> a half wavelength, purchase valuable real estate and spend thousands of
> dollars for the copper to install from 120 to 240 or more radials, each
> usually a half wave or more in length?
>
> See G. H. Brown: "Ground Systems as a Factor in Antenna Efficiency", IRE
> Proceedings, June 1937 p. 753. Brown demonstrated that the distribution of
> earth currents and ground losses is such that the region of maximum current
> and loss occurs at a distance of about 0.35 wavelengths from the base of a
> ground mounted half wave vertical antenna, which was verified
> experimentally.
>
> There is zero loss at the base of the antenna itself, since there is no
> base current because the antenna a fed at a current node. An rf ammeter
> inserted in the ground lead, as well as one inserted in in the antenna lead
> attached to the insulated base of the radiator will read zero. The ground
> losses occur farther out from the base of the antenna. Low effective earth
> resistance provided by a good ground system is ABSOLUTELY NECESSARY for
> vertical antennas of ANY height if one expects good radiation efficiency.
> The claim that no ground system is needed for a half wave vertical is
> nothing more than a long-standing popular misconception.
>
> This topic prompted me to dig out and review an anecdote I recall reading
> in my decades-old copy of CQ magazine's Vertical Antenna Handbook, by USNR
> Capt. Paul H. Lee, K6TS (1974). He reported receiving mail from a ham who
> had made the "discovery" that he could tune and operate a half wave
> vertical without a ground system, feeding it by a parallel tuned tank
> circuit whose lower end is grounded. Since an rf ammeter in the ground
> lead showed no current, he could dispense with the ground system and its
> loss. He suggested to the Capt. that he should "discover the new world of
> half verticals with no ground system".
>
> Quoting from the text (p. 84):
>
> "The correspondent's claim... is true ONLY IF HE IS CONTENT TO THROW AWAY
> FROM 40 TO 80 PER CENT OF HIS RADIATED POWER IN THE FORM OF EARTH LOSSES.
> (the correspondent) stated, 'The ZL's call ME, when I use my half wave
> vertical!' This is not surprising, in view of the fact that the half wave's
> vertical pattern has a lower main lobe angle than a quarter wave would
> have... However, he would hit the ZL's even harder if he would put in a
> ground system. Of course, the half wave vertical is not dependent on a
> ground plane, however lossy or efficient, for the condition of RESONANCE,
> since it is resonant in itself because of its half wave length. However,
> IT IS DEPENDENT ON A GROUND PLANE FOR ITS EFFICIENCY OF RADIATION, as is
> any vertical antenna...'
>
>
> Don k4kyv
>
>
>
> >Given that a half wave vertical has a base impedance of over 1000 ohms
> and a single ground rod in dirt is 100 ohms at most not a single radial is
> needed to obtain close to 100% radiation >efficiency.
>
> > Dave WX7G
>
>
>
> > And this statement is based on what? Publications, measurements,
> > modeling?
> >
> > I have built a number of 1/2 wave verticals without radials and compared
> > them to 1/4 wave verticals with radials. They are
> > indistinguishable in performance and certainly do not exhibit
> > substantial ground losses AFAIK...
> >
> > Rick N6RK
>
>
> >I can think of NO earthly reason,that makes ANY electromagnetic sense to
> me, as antenna engineer fo placing a radial system under the end of a
> vertical 1/2 wave antenna - "earth-worms" not >withstanding!
>
> >It's CURRENT that "warms the earthworms"! NOT electric field intensity!
>
> >...the ground system does NOT act as a "shield" from the "lossy earth"
> nor protect the "earth-worms"! There is absolutely NO reason to require a
> radial system under a 1/2 wave vertical antenna.
> >Such an antenna will operate just fine on its own in free-space.
>
> >Consider this - to deliver 1000 watts to a 1/4 wave vertical with a
> REALLY GOOD ground system and a driving point impedance of say 40 ohms
> would require 5 amps of RF current delivered to the >antenna system and
> ground. Todeliver that same 1000 watts to an end-fed vertical of 2000-4000
> ohms real would require an antenna current, at the fed endof 0.5 -0.7
> amps! It's the CURRENT >that produces the losses in the "lossy earth" and
> "warms the earth worms". At worst, for the 1/2 wave end fed vertical - a
> simple ground rodshould be just fine, and the earth worms should be >quite
> comfortable, and the antenna will work VERY well!! Of course it will be
> 250-260 feet tall!
>
> >Charlie,K4OTV
>
>
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>
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