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## FW: Re: Ant Gain is NOT subjective

 Subject: FW: Re: Ant Gain is NOT subjective aa2du@netcom.com (aa2du@netcom.com) Fri Aug 11 17:50:54 1995
 ```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. > > > > > > >-- >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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