ERP derivation? - RF Cafe Forums

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Mr.Whatever

Post subject: ERP derivation?

Posted: Tue Sep 05, 2006 4:08 pm

Captain

Joined: Fri Apr 07, 2006 6:10 pm
Posts: 18

I was reading the Electronics Engineers' Handbook and they have the following formula:

E = [7 * sqrt(pt)] / d

where E is the field strength in V/m, d is the distance in meters, and pt is the effective radiated power (ERP), which includes the transmitter gain with respect to a half-wave dipole.

How was this formula derived?

Thanks!

Mr.Whatever

Post subject:

Posted: Wed Sep 20, 2006 11:59 pm

Captain

Joined: Fri Apr 07, 2006 6:10 pm
Posts: 18

I found the answer to this question after reading some more wave propagation stuff. I thought I'd share it.

power: (V^2) / R = P

power flux density: s = P / (4*pi*r^2), where pi = 3.14 and r = distance

field strength: e = sqrt (120 * pi * s) = sqrt(30 * P) / r

A half-wave dipole has a 1.64 gain in its equatorial plane, therefore:

e = sqrt(1.64*30*P) /r = 7*sqrt(p) / r

Pretty simple, but I hate it when other books try to make me memorize a formula. I prefer finding out how its derive, so I can start from "scratch" whenever I forget the formula.

Posted 11/12/2012