Line of Sight Antenna Range Vs Frequency?

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Richard Fry:
Quote from: KB9WIS on July 27, 2010, 02:32:54 PM

...Say you have a 6 meter, 2 meter, and a 440 omni ground plane on a 100' tower, what is the range difference?

The FCC has an on-line calculator that may be helpful here (link below).  The calculator is based on measured data for the value of space wave field intensity present at an elevation 30 feet above the earth for a given frequency, radiated power and transmit antenna height above "average terrain."

Using that program to calculate the distance to the 5 µV/m F(50,50) field for 50, 144 and 440 MHz when the radiated power is 100 watts and the transmit antenna height is 100 feet above average terrain gives these results:

 Freq (MHz)      Distance (miles)
     50                        43.7
   144                        42.5
   440                        33.2

More specific answers are possible using Longley-Rice calculations for the field at the exact height of the receive antenna, and the terrain contour for that point-point propagation path (as well as the other variables).

FCC link:  http://www.fcc.gov/mb/audio/bickel/curves.html

RF http://rfry.org

DAVE CUTHBERT:
Quote

Using that program to calculate the distance to the 5 µV/m F(50,50) field for 50, 144 and 440 MHz when the radiated power is 100 watts and the transmit antenna height is 100 feet above average terrain gives these results:

 Freq (MHz)      Distance (miles)
     50                        43.7
   144                        42.5
   440                        33.2


Given a field strength of 5 uV/m what voltage does this induce in the receiver? For that we can use something called AF (Antenna Factor). The AF for a dipole at 36 MHz is 1 = 0 dB. What that means is the antenna terminal voltage into 50 ohms is equal to the field strengh in V/m.

At 50 MHz the antenna factor is 30MHz/50MHz = 0.72 = -(-2.9 dB) = 2.9 dB. At 50 MHz in a field of 5 uV/m the terminal voltage of a dipole terminated into 50 ohms is 36MHz/50MHz(5uV) = 3.6 uV
The AF is 3 dB

At 144 MHz: 36MHz/144MHz(5uV) = 1.3 uV
The AF is 12 dB. To obtain an antenna terminal voltage of 5 uV we need an antenna having a gain of 12 dBD.

At 440 MHz: 36MHz/440MHz(5uV) = 0.4 uV
The AF is 22 dB. To obtain an antenna terminal voltage of 5 uV we need an antenna having a gain of 22 dBD.

We need a high gain receive antenna at 440 MHz (19 dBD) to do what a dipole can do at 50 MHz.

A quicker way to determine how much more receive antenna gain is needed at 440 MHz, to obtain the same receiver voltage as at 50 MHz, for a given field strength is 20LOG(440/50) = 19 dB


Richard Fry:
Quote

We need a high gain receive antenna at 440 MHz (19 dBD) to do what a dipole can do at 50 MHz.

Or another way to look at this is that for a receiver with fixed input sensitivity using a matched 1/2-wave dipole receive antenna, for equivalent system performance it takes about 19 dB more radiated power on 440 MHz as on 50 MHz.

This is the reason why the FCC permitted up to 5 megawatts ERP for UHF analog TV stations compared to the 100 kilowatts it permitted for analog Ch 2-6 VHF TV stations.

That ERP difference is only 17 dB, but then the gain of typical UHF TV receive antenna systems typically was/is several dB higher than for VHF.

UHF broadcast TV transmit antennas also tended to be installed on taller towers, which improved the fields within their coverage area (other things equal).
//

Dale Hunt:
Some of these differences are because a half wave dipole, for example, is smaller at 440 than for 6m and
thus has a smaller capture area.  The difference is less if you compare antennas of similar physical sizes.
For example, for the same physical length an omnidirectional vertical for 440 can have about 3dB gain over
one for 2m, and similarly for 2m and 6m.  This still isn't a precise comparison, however, as the capture area
is WIDER on the lower band.  A better comparison would be a 3-dimensional volume.  For example, in a
box 10' square you can stack a pair of 6m yagis, or a larger number of higher gain (longer in wavelengths)
yagis for the higher bands.  If properly designed these should have about the same capture area, and by
using one at each end of the path you should get closer to the same signal strengths on each band.


However, if you are talking about repeater coverage, there are a number of issues.  The theoretical
coverage formulas for antennas at a particular height above ground apply to flat terrain with no
obstructions, and presume that the signal grazes the surface of the Earth at some point on the path.
The characteristics of the terrain at that intermediate point where the signal is close to the ground
have a large bearing on whether the path actually works.  A pasture with short grass would offer
minimal attenuation, but a field of growing corn of resonant length might have a lot more loss.  A cow
walking across the pasture at the wrong spot could change the path characteristics.  Buildings and
hills at that point will have more effect than if they are closer to either end.  I've watched signal
strengths on 2m bounce up and down on a path that crosses an elevated freeway - dropping when
a car goes by (or especially a large truck), and coming back up between vehicles.


But LOS paths are rarely the problem for repeater coverage.  That's when you have rubber duck
coverage from an HT, and I can't test a radio on a dummy load without keying the repeater.  It's
the paths that are beyond LOS that make more of a difference in the coverage area for a repeater.
For SSB and other weak signal modes these may be tropo scatter, as Steve suggests.  For a strong
signal mode like FM in hilly terrain they often are reflections or diffraction.  I can work simplex across
a range of 500' hills due to signals reflecting off the hillsides and up the valleys.  Knife-edge diffraction
over a sharp ridge also allows coverage of longer paths - in some cases 220MHz may be better for this
than the adjacent bands.

As you go higher in frequency the characteristics of the RF paths change.  On 6m signals tend to
be better in rolling hills than on the higher bands, while in a city 440 (or higher) is often better as it
tends to bounce off buildings better where the lower bands would be absorbed more.  (900 MHz is
often better inside a building as it follows hallways and elevator shafts better.)

So the question of actual coverage area is very complex - it depends on the terrain, number and
height of buildings at various points on the path between the two stations, etc. 

Stephen L Crook:
But VHF/UHF "line-of-site" is *slightly* longer than the straight line geometric LoS due to *slight* curvature of the RF beam, regardless of power or antenna gain, assuming flat (actually spherical) terrain & no tropospheric ducting, Es, edge refraction, multi-path, etc.

I think his question was: what's the increase in radio horizon distance as a function of frequency, e.g. does 440 MHz have a larger (or smaller) theoretical radio horizon than 50 MHz and if so by how much?

Granted the real world of rough terrain, tall buildings, etc. clutters the theoretical case of an antenna over a perfect sphere of large radius compared to the antenna height(s)

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