More on Antenna Gain:
On Thu, 10 Aug 1995 09:44:18 -0400 Rob Hummel WS1A wrote:
>>Rob-
>>Perhaps you would be kind enough to supply us with the formulae
>>for the three-antenna gain measurements?
>>-Tony, K1KP, fisher@hp-and.an.hp.com
>>
>
>Sure. Here's how you'd calibrate your CONTEST antennas.
>
>We start with the basic antenna measurement circuit:
>
> / \
>Po ---< <----R-----> >--- Pr
> \ /
> antenna antenna
> A B
>
>Po = power level at the input terminals of the transmit antenna
>Pr = power level at the output terminals of the receive antenna
>R = separation distance
>
>The power transfer between the two is written as:
>
>Pr = Po * Ga * Gb * (W/(4*PI*R))^2
>
>Where W = wavelength. All values are assumed to be in linear terms (watts,
>feet, etc). The same equation written in logrithmic form is:
>
>Lr = Lo + ga(r) + gb(r) - 20 log(4*PI*R/W)
>
>Lr = power level at the input terminals of the transmit antenna relative to a
> convenient reference such as 1 milliwatt (dBm)
>Lo = power level at the output terminals of the receive antenna (dBm)
>ga(r) = gain of antenna A in dB
>gb(r) = gain of antenna B in dB
>W = wavelength
>
>In the two-antenna measurement method, the two antennas must be identical. Thus
>
>ga(r) = gb(r) = 0.5 (Lr - Lo - 20 * log (4*PI*R/W))
>
>and you're done! Once you've calibrated your antennas this way, they can be
>used as standards to gauge other antennas in relative gain measurements.
>
>The three-antenna method doesn't assume that any of the antennas being
>tested are identical. Three measurements are performed between pairs of
>antennas: A vs B, A vs C, and B vs C. All three measurements produce an
>equation similar to:
>
>Lr = Lo + g1(r) + g2(r) - 20 log(4*PI*R/W)
>
>or, equivalently,
>
>g1(r) + g2(r) = Lr - Lo - 20 log(4*PI*R/W)
> = E(1,2)
>
>So the three equations for antennas A, B, and C are:
>
>ga(r) + gb(r) = E(a,b) [equation 1]
>ga(r) + gc(r) = E(a,c) [eq 2]
>gb(r) + gc(r) = E(b,c) [eq 3]
>
>Which can be solved simultaneously for ga, gb, and gc. For example. To solve
>for gc, subtract [eq 2] from [eq 1]:
>
> ga(r) + gb(r) = E(a,b)
> -[ga(r) + gc(r) = E(a,c)]
>-------------------------
> gb(r) - gc(r) = E(a,b) - E(a,c) [eq 4]
>
>Now solve [eq 4] for gb in terms of gc:
>
> gb(r) = E(a,b) - E(a,c) + gc(r)
>
>Substitute into [eq 3] in place of gb(r):
>
> E(a,b) - E(a,c) + gc(r) + gc(r) = E(b,c)
>
>Solve for gc(r):
>
> gc(r) = (E(b,c) + E(a,c) - E(a,b)) / 2
>
>Knowing gc(r), you can now solve [eq 2] for ga(r). Knowing ga(r), you can
>then solve [eq 1] for gb(r).
>
>Now, one word of caution. This method will determine the absolute gain of
>the antennas at the point in their patterns where they are pointed at each
>other. To find the peak gain, you need to first find the peak of each
>pattern by rotating the antennas in both azimuth and elevation. At HF,
>ground effects and reflections will have a substantial, although not
>insurmountable, affect on this. At sufficient height, this isn't a problem
>at VHF/UHF and above.
>
>Finally, remember that I'm not suggesting every amateur should equipe his
>shack to make these measurements. I am saying that any antenna company
>worthy of the name should. To publish gain and pattern data without actual
>measurements to back them up and without indicating that this is the case is
>just short of fraud and certainly deceptive.
>
> <Rob Hummel>
> <Internet: rhummel@top.monad.net>
> <MCI: 371-5998>
>
>
>--
>Submissions: yccc@eng.pko.dec.com
>Administrative requests: yccc-request@eng.pko.dec.com
>Problems: reisert@eng.pko.dec.com
>
J.P. Kleinhaus, AA2DU ARRL CAC hudson Div. Rep.
E-mail: aa2du@netcom.com
Compu$erve: 74660,2606
It's not a bug...It's a feature!
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