Return-Path: Received: from mtain-dj01.r1000.mx.aol.com (mtain-dj01.r1000.mail.aol.com [172.19.187.137]) by air-md05.mail.aol.com (v129.4) with ESMTP id MAILINMD051-8b844c7fdd9f15d; Thu, 02 Sep 2010 13:23:43 -0400 Received: from post.thorcom.com (post.thorcom.com [193.82.116.20]) by mtain-dj01.r1000.mx.aol.com (Internet Inbound) with ESMTP id D1D4238000098; Thu, 2 Sep 2010 13:23:41 -0400 (EDT) Received: from majordom by post.thorcom.com with local (Exim 4.14) id 1OrDUl-0002K4-EO for rs_out_1@blacksheep.org; Thu, 02 Sep 2010 18:22:39 +0100 Received: from [193.82.116.32] (helo=relay1.thorcom.net) by post.thorcom.com with esmtp (Exim 4.14) id 1OrDUk-0002Jv-Ms for rsgb_lf_group@blacksheep.org; Thu, 02 Sep 2010 18:22:38 +0100 Received: from imr-da02.mx.aol.com ([205.188.105.144]) by relay1.thorcom.net with esmtp (Exim 4.63) (envelope-from ) id 1OrDUe-0000gq-El for rsgb_lf_group@blacksheep.org; Thu, 02 Sep 2010 18:22:38 +0100 Received: from imo-ma02.mx.aol.com (imo-ma02.mx.aol.com [64.12.78.137]) by imr-da02.mx.aol.com (8.14.1/8.14.1) with ESMTP id o82HMFQI020077 for ; Thu, 2 Sep 2010 13:22:15 -0400 Received: from MarkusVester@aol.com by imo-ma02.mx.aol.com (mail_out_v42.9.) id l.f15.5fe1db8 (43901) for ; Thu, 2 Sep 2010 13:22:14 -0400 (EDT) Received: from smtprly-da03.mx.aol.com (smtprly-da03.mx.aol.com [205.188.249.146]) by cia-dc06.mx.aol.com (v129.4) with ESMTP id MAILCIADC066-5bbd4c7fdd3f1e5; Thu, 02 Sep 2010 13:22:13 -0400 Received: from webmail-d065 (webmail-d065.sim.aol.com [205.188.59.130]) by smtprly-da03.mx.aol.com (v129.4) with ESMTP id MAILSMTPRLYDA034-5bbd4c7fdd3f1e5; Thu, 02 Sep 2010 13:22:07 -0400 References: <8CD18D91C21534A-1370-2635@Webmail-d118.sysops.aol.com> To: rsgb_lf_group@blacksheep.org Date: Thu, 02 Sep 2010 13:22:07 -0400 In-Reply-To: <8CD18D91C21534A-1370-2635@Webmail-d118.sysops.aol.com> X-MB-Message-Source: WebUI MIME-Version: 1.0 From: Markus Vester X-MB-Message-Type: User X-Mailer: AOL Webmail 32447-STANDARD Received: from 194.138.39.55 by webmail-d065.sysops.aol.com (205.188.59.130) with HTTP (WebMailUI); Thu, 02 Sep 2010 13:22:07 -0400 Message-Id: <8CD18DA80CB913D-1E88-9F@webmail-d065.sysops.aol.com> X-AOL-VSS-CODE: clean X-AOL-VSS-INFO: 5400.1158/0 X-Spam-Flag:NO X-AOL-SENDER: MarkusVester@aol.com X-Spam-Score: 0.3 (/) X-Spam-Report: autolearn=disabled,FORGED_AOL_TAGS=0.281,HTML_MESSAGE=0.001,UNPARSEABLE_RELAY=0.001 Subject: Re: LF: Earth loop depth Content-Type: multipart/mixed; boundary="--------MB_8CD18DA80D9D977_1E88_EA_webmail-d065.sysops.aol.com" X-Spam-Checker-Version: SpamAssassin 2.63 (2004-01-11) on post.thorcom.com X-Spam-Level: X-Spam-Status: No, hits=0.1 required=5.0 tests=FORGED_AOL_TAGS, HTML_FONTCOLOR_UNKNOWN,HTML_MESSAGE autolearn=no version=2.63 X-SA-Exim-Scanned: Yes Sender: owner-rsgb_lf_group@blacksheep.org Precedence: bulk Reply-To: rsgb_lf_group@blacksheep.org X-Listname: rsgb_lf_group X-SA-Exim-Rcpt-To: rs_out_1@blacksheep.org X-SA-Exim-Scanned: No; SAEximRunCond expanded to false x-aol-global-disposition: G X-AOL-VSS-INFO: 5400.1158/62674 X-AOL-VSS-CODE: clean x-aol-sid: 3039cdbc9d054c7fdd9d65e8 X-AOL-IP: 193.82.116.20 X-AOL-SPF: domain : blacksheep.org SPF : none ----------MB_8CD18DA80D9D977_1E88_EA_webmail-d065.sysops.aol.com Content-Type: multipart/alternative; boundary="--------MB_8CD18DA80D9D977_1E88_EB_webmail-d065.sysops.aol.com" ----------MB_8CD18DA80D9D977_1E88_EB_webmail-d065.sysops.aol.com Content-Transfer-Encoding: quoted-printable Content-Type: text/plain; charset="us-ascii" ... here's the attachment as well. Dear LF, =20 I recently discovered that I had a misconception regarding the effective= area of an earth antenna, which may be interesting to other experimenters= as well. It seems that short earth antennas are much more efficient than= I had intuitively anticipated. =20 For small electrode spacing, most of the current returns through the groun= d in the vicinity of the wire. My understanding was that the effective loo= p area would then look similar to the a half-circle beneath the baseline,= as depicted by the red area in the sketch. This means that for small base= lines, effective loop area would scale quadratically with baseline length.= This would hold until the baseline is made so long that penetration becom= es limited by skin effect in the ground, and one enters a regime of linear= scaling of area vs length. =20 Then I tried to calculate the magnetic moment for the non-skin effect case= based on DC current densities in homogeneous halfspace. The curent field= is similar to the electrical nearfield of a dipole. Integrating depth-wei= ghted current densities over the halfspace volume should then give the tot= al magnetic moment. But this integral did not converge to an asymptotic li= mit, but appeared to grow monotonically with integration volume. This impl= ies an infinite effective depth of a DC ground loop! =20 At first I looked for an error in the integral calculations, but then I no= ticed that the divergence can be explained by a simple scaling argument al= ong the following lines. At a distance r from the dipole (current Iq times= length l), current density J in the ground scales as=20 J(r) ~ Iq l r^-3. A large half-shell (green) around the dipole has a perimeter pi r around= its equator, so there the total current would be I(r) ~ Iq l r^-2 dr The contribution to the magnetic moment of the shell is proportional to it= s broadside area A ~ r^2, which gives dM(r) =3D I A ~ Iq l dr ~ constant. This means that each additional shell will add the same amount of magnetic= moment, and the total moment would indeed grow to infinity if r is not bo= unded by skin effect. Even though the outer fieldlines (blue) carry only= a small part of the current, due to their large cross section they still= contribute significantly to the loop area. =20 This reasoning also falls in line with a much easier analysis for the rece= ive case. Vertically polarized groundwaves have transverse magnetic fields= , which must be bounded by radial ground currents (ie in the direction of= wave propagation). The finite surface resistance of the ground creates an= additional radial electric field, which can simply be tapped by the elec= trode baseline. The induced voltage (and thus effective loop area) will de= pend linearly on the baseline length, no matter how short it is. Solving= the equations for equivalent depth is straightforward and gives=20 d_eff =3D (omega mu0 conductivity)^-0.5 =3D skindepth / sqrt(2) . =20 For a crude experimental test, I took a battery operated notebook to the= garden, stuck the two leads of the soundcard input into the soil, and mea= sured the induced voltage from the DHO signal. When going from 1.5 m to 3= m electrode spacing, it went up by 6 dB (and not 12 dB), showing that pic= kup area scaled linearly and not quadratically with baseline. =20 Kind regards, Markus (DF6NM) =20 ----------MB_8CD18DA80D9D977_1E88_EB_webmail-d065.sysops.aol.com Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii"
... here's the attachment as well.
 
Dear LF,
 
I recently discovered that I had a misconception regarding the effect= ive area of an earth antenna, which may be interesting to other experiment= ers as well. It seems that short earth antennas are much more efficient th= an I had intuitively anticipated.
 
For small electrode spacing, most of the current returns through the= ground in the vicinity of the wire. My understanding was that the effecti= ve loop area would then look similar to the a half-circle beneath the base= line, as depicted by the red area in the sketch. This means that for small= baselines, effective loop area would scale quadratically with baseline le= ngth. This would hold until the baseline is made so long that penetration= becomes limited by skin effect in the ground, and one enters a regime of= linear scaling of area vs length.
 
Then I tried to calculate the magnetic moment for the non-skin effect= case based on DC current densities in homogeneous halfspace. The curent= field is similar to the electrical nearfield of a dipole. Integrating dep= th-weighted current densities over the halfspace volume should then give= the total magnetic moment. But this integral did not converge to an asymp= totic limit, but appeared to grow monotonically with integration volume.= This implies an infinite effective depth of a DC ground loop!
 
At first I looked for an error in the integral calculations, but then= I noticed that the divergence can be explained by a simple scaling argume= nt along the following lines. At a distance r from the dipole (current Iq= times length l), current density J in the ground scales as
 J(r) ~ Iq l r^-3.
A large half-shell (green) around the dipole has a perimeter pi r around= its equator, so there the total current would be
 I(r) ~ Iq l r^-2 dr
The contribution to the magnetic moment of the shell is proportional to it= s broadside area A ~ r^2, which gives
 dM(r) =3D I A ~ Iq l dr ~ constant.
This means that each additional shell will add the same amount of magnetic= moment, and the total moment would indeed grow to infinity if r is not bo= unded by skin effect. Even though the outer fieldlines (blue) carry only= a small part of the current, due to their large cross section they still= contribute significantly to the loop area.
 
This reasoning also falls in line with a much easier analysis for the= receive case. Vertically polarized groundwaves have transverse magnetic= fields, which must be bounded by radial ground currents (ie in the direct= ion of wave propagation). The finite surface resistance of the ground crea= tes an additional radial electric field, which can simply be tapped = by the electrode baseline. The induced voltage (and thus effective loop= area) will depend linearly on the baseline length, no matter how short it= is. Solving the equations for equivalent depth is straightforward and giv= es
 d_eff =3D (omega mu0 conductivity)^-0.5 =3D skindepth / sqrt(2)= .
 
For a crude experimental test, I took a battery operated notebook to= the garden, stuck the two leads of the soundcard input into the soil, and= measured the induced voltage from the DHO signal. When going from 1.5 m= to 3 m electrode spacing, it went up by 6 dB (and not 12 dB), showing tha= t pickup area scaled linearly and not quadratically with baseline.
 
Kind regards,
Markus (DF6NM)
 
 
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