Return-Path: Received: from post.thorcom.com (post.thorcom.com [195.171.43.25]) by mtain-db01.r1000.mx.aol.com (Internet Inbound) with ESMTP id 24BE238000171; Sun, 9 Jun 2013 07:17:23 -0400 (EDT) Received: from majordom by post.thorcom.com with local (Exim 4.14) id 1UldbO-0002Ge-2x for rs_out_1@blacksheep.org; Sun, 09 Jun 2013 12:16:02 +0100 Received: from [195.171.43.32] (helo=relay1.thorcom.net) by post.thorcom.com with esmtp (Exim 4.14) id 1UldbN-0002GV-2o for rsgb_lf_group@blacksheep.org; Sun, 09 Jun 2013 12:16:01 +0100 Received: from omr-m01.mx.aol.com ([64.12.143.75]) by relay1.thorcom.net with esmtp (Exim 4.77) (envelope-from ) id 1UldbJ-0007of-9n for rsgb_lf_group@blacksheep.org; Sun, 09 Jun 2013 12:15:59 +0100 Received: from mtaout-mb05.r1000.mx.aol.com (mtaout-mb05.r1000.mx.aol.com [172.29.41.69]) by omr-m01.mx.aol.com (Outbound Mail Relay) with ESMTP id 6331A700000AE; Sun, 9 Jun 2013 07:15:55 -0400 (EDT) Received: from White (188-195-246-26-dynip.superkabel.de [188.195.246.26]) by mtaout-mb05.r1000.mx.aol.com (MUA/Third Party Client Interface) with ESMTPA id DDD41E000099; Sun, 9 Jun 2013 07:15:49 -0400 (EDT) Message-ID: <40A4DFBB54EE4044B3B35506177510F3@White> From: "Markus Vester" To: , Date: Sun, 9 Jun 2013 13:15:38 +0200 MIME-Version: 1.0 X-Priority: 3 X-MSMail-Priority: Normal Importance: Normal X-Mailer: Microsoft Windows Live Mail 12.0.1606 X-MimeOLE: Produced By Microsoft MimeOLE V12.0.1606 X-AOL-VSS-INFO: 5400.1158/91304 X-AOL-VSS-CODE: clean DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=mx.aol.com; s=20121107; t=1370776555; bh=2vB77XEPntanUABx27Suoc02m1+NTxh4FJX/B6tDzhQ=; h=From:To:Subject:Message-ID:Date:MIME-Version:Content-Type; b=yDjJSaLizBiAbJSsgh81l9A7gqOIMdKQdevrSHD0LvPDm5mdNZcWONpcs05fIctrq etQjleYxi6+OgMRhnE6D9cH/3yT34D5PhVD1XCrIu7krbc1c7JK8JD3tecNJogyRix yuIMHshVBbM4bI79kS9h8HlUGf0l+RnyFhxBdU7Y= X-AOL-SCOLL-SCORE: 0:2:471723808:93952408 X-AOL-SCOLL-URL_COUNT: 0 X-Spam-Score: -0.1 (/) X-Spam-Report: Spam detection software, running on the system "relay1.thorcom.net", has identified this incoming email as possible spam. The original message has been attached to this so you can view it (if it isn't spam) or label similar future email. If you have any questions, see the administrator of that system for details. Content preview: Roger, attached beneath are a couple of mails on the subject which I had posted on blacksheep in 2010. Here's a summary of the formulas: - An earth antenna forms a magnetic loop antenna between the wire and the subsurface return currents: Aearth = length * effective depth = length * skin depth in ground / sqrt(2). Thus the depth scales inversely with the squareroots of frequency and ground conductivity, and is usually a few tens of meters at VLF. Somewhat surprisingly, this still holds true if the wire length is much shorter than the ground skin depth. [...] Content analysis details: (-0.1 points, 5.0 required) pts rule name description ---- ---------------------- -------------------------------------------------- -0.0 RCVD_IN_DNSWL_NONE RBL: Sender listed at http://www.dnswl.org/, no trust [64.12.143.75 listed in list.dnswl.org] 0.0 FREEMAIL_FROM Sender email is commonly abused enduser mail provider (markusvester[at]aol.com) -0.0 SPF_PASS SPF: sender matches SPF record -0.1 RP_MATCHES_RCVD Envelope sender domain matches handover relay domain 0.0 HTML_MESSAGE BODY: HTML included in message 0.0 T_DKIM_INVALID DKIM-Signature header exists but is not valid X-Scan-Signature: d4c215c7e9a8f7482f4d187e5f30c8ab Subject: LF: Re: ELF antenna ERP calculations - request for resend of information Content-Type: multipart/mixed; boundary="----=_NextPart_000_001D_01CE6513.6F579D80" X-Spam-Checker-Version: SpamAssassin 2.63 (2004-01-11) on post.thorcom.com X-Spam-Level: X-Spam-Status: No, hits=0.7 required=5.0 tests=HTML_20_30, HTML_FONTCOLOR_UNKNOWN,HTML_MESSAGE,MISSING_OUTLOOK_NAME 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: 5400.1158/91304 X-AOL-VSS-CODE: clean X-AOL-SCOLL-AUTHENTICATION: mtain-db01.r1000.mx.aol.com ; domain : mx.aol.com DKIM : fail x-aol-sid: 3039ac1d405551b4644322d1 X-AOL-IP: 195.171.43.25 X-AOL-SPF: domain : blacksheep.org SPF : none Dies ist eine mehrteilige Nachricht im MIME-Format. ------=_NextPart_000_001D_01CE6513.6F579D80 Content-Type: multipart/alternative; boundary="----=_NextPart_001_001E_01CE6513.6F579D80" ------=_NextPart_001_001E_01CE6513.6F579D80 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Roger, attached beneath are a couple of mails on the subject which I had posted = on blacksheep in 2010. Here's a summary of the formulas: - An earth antenna forms a magnetic loop antenna between the wire and = the subsurface return currents:=20 Aearth =3D length * effective depth =3D length * skin depth in ground / = sqrt(2). Thus the depth scales inversely with the squareroots of frequency and = ground conductivity, and is usually a few tens of meters at VLF. = Somewhat surprisingly, this still holds true if the wire length is much = shorter than the ground skin depth. - The radiation resistance of the loop is=20 Rrad =3D 31171 ohm * area^2 / lambda^4, allowing you to calculate the radiated power in the main lobes as EMRP =3D current^2 * Rrad=20 - The effective area of the earth antenna can be measured simply by = comparing the received voltage from a distant transmitter to that from a = small nonresonant wire loop: Uearth / Uloop =3D Aearth / Aloop Alternatively, using a signal of known fieldstrength E, the loop area = can be calculated by Uearth =3D E * Aearth / (lambda / 2pi) If the loop antenna is not optimally aligned with the wire towards the = other station, a cosine directivity factor should be taken into account. = Best 73, Markus (DF6NM) =20 From: Roger Lapthorn=20 Sent: Saturday, June 08, 2013 6:15 PM To: sub9khz@yahoogroups.com ; rsgb_lf_group@yahoogroups.co.uk ; = rsgb_lf_group@blacksheep.org=20 Subject: LF: ELF antenna ERP calculations - request for resend of = information Some months ago - time flies, so it may have been last year - someone = kindly sent me a copy of a paper, or at least a formula, to work out the = radiated power (as opposed to other forms of signal transmission) from = an earth-electrode pair "antenna" at ELF. I think it was based on some = of the Project Sanguine work at 76Hz back in the 1970s. I thought I'd = saved this, but cannot locate it anywhere. =20 If you remember sending me this data, please would you resend it? Thanks. 73s Roger G3XBM ___________________________________________ From: Markus Vester=20 Sent: Thursday, September 02, 2010 7:22 PM To: rsgb_lf_group@blacksheep.org=20 Subject: Re: LF: Earth loop depth Dear LF, 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. For small electrode spacing, most of the current returns through the = ground in the vicinity of the wire. My understanding was that the = effective loop 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 baselines, effective loop area would scale quadratically with = baseline length. 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 current = field is similar to the electrical nearfield of a dipole. Integrating = depth-weighted current densities over the halfspace volume should then = give the total magnetic moment. But this integral did not converge to an = asymptotic 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 = argument along 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 = its 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 bounded 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 = direction of wave propagation). The finite surface resistance of the = ground creates 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 gives=20 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 = that pickup area scaled linearly and not quadratically with baseline. Kind regards, Markus (DF6NM) =20 From: Markus Vester=20 Sent: Thursday, September 02, 2010 7:07 PM To: rsgb_lf_group@blacksheep.org=20 Subject: Re: LF: ERP calculation (revised) Dear Roger, thanks for sharing your results!=20 The directional dependence should be a simple cosine law, so going from = 45=B0 to 0=B0 would give you another 3 dB, or 3.8 uW ERP. Thus your = total radiated power was 2.0 uW (EMRP). At 62 km, this gives -14 dBuV/m, = which should indeed be well readable in QRSS 3 under quiet conditions.=20 Taking a loss resistance of 60 ohms, 4 watts would have given you an = antenna current of 0.26 A. The radiation resistance is then=20 Rrad =3D EMRP / Iq^2 =3D 30 microohms.=20 A standard formula for loops is=20 Rrad =3D 31171 ohm * A^2 / lambda^4, resulting in an effective loop area A =3D 155m^2. Note this is using the radiation resistance for a loop in free space, as = the effect of ground is already included in the earth antenna picture. = For an above-ground loop with a mirror image beneath it, radiation = resistance would be doubled.=20 Best wishes, Markus (DF6NM) -----Urspr=FCngliche Mitteilung-----=20 Von: Roger Lapthorn An: rsgb_lf_group@blacksheep.org Verschickt: Mi., 1. Sept. 2010, 13:41 Thema: LF: ERP calculation (revised) Today I managed, I believe, for the first time to accurately measure the = ERP of my QRPp system on 137kHz. This is the method used: a.. Using the E-field probe, FT817 (AGC off, gain backed off as far as = possible and a 10dB pad between the EFP and the FT817) and Spectran I = went to my usual test site 1.5km away from the QTH, 45 degrees off the = main lobe of the TX loop/earth electrode antenna.=20 b.. Measured the signal level of DCF39 on 138.83kHz c.. Measured the signal level of G3XBM on 137.675kHz d.. Repeated this three times to reduce errors.=20 e.. Noted the difference in FS level. Difference in signal level =3D 44dB . I feel pretty confident this is an = accurate figure now and not effected by AGC and overload. Assuming DCF39 = is 1mV/m here (info from Alan Melia) then my FS at the test site is = 6.4uV/m. Using the formula ERP =3D (E*d)^2/49 where E =3D 6.4*10E-6 and = d=3D1.5*10E3 gives an ERP =3D 1.9uW giving an antenna efficiency of = -63dB using the earth electrode antenna with the elevated feed and 4W = from the PA. =20 The test site is about 45 degrees off the main line of fire of the = antenna, so in the best direction it could be 10dB (?) stronger, i.e. = 20uW ERP giving an antenna efficiency of -53dB in the best directions. = Frankly I'm amazed that anyone can copy this signal at any distance, so = full marks to G3XIZ (48km) and G3XDV (62km). Next stage is to try this arrangement for a few more days using QRSS3 = and WSPR before swapping to a full "in the air" loop and repeating these = tests. Great fun and I'm leaning as I go, which is the whole point of ham = radio. 73s Roger G3XBM ------=_NextPart_001_001E_01CE6513.6F579D80 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Roger,
 
attached beneath are a couple of mails = on the=20 subject which I had posted on blacksheep in 2010. Here's a summary of = the=20 formulas:
 
- An earth = antenna forms a magnetic=20 loop antenna between the wire and the subsurface return=20 currents: 
 Aearth =3D length * effective = depth =3D length * skin depth in ground / = sqrt(2).
Thus the depth scales inversely = with the=20 squareroots of frequency and ground conductivity, and is usually a = few tens=20 of meters at VLF. Somewhat=20 surprisingly, this still holds true if the wire length is=20 much shorter than the ground skin depth.
 
- The radiation resistance of the loop = is=20
 Rrad =3D 31171 ohm * area^2 /=20 lambda^4,
allowing you to calculate the radiated = power in the=20 main lobes as
 EMRP =3D current^2 * Rrad =
 
- The effective area of the = earth=20 antenna can be measured simply by comparing the received = voltage=20 from a distant transmitter to that from a small nonresonant = wire=20 loop:
 Uearth / Uloop =3D Aearth / = Aloop
Alternatively, using a signal of = known=20 fieldstrength E, the loop area can be calculated by
  Uearth =3D E * Aearth / (lambda = /=20 2pi)
If the loop antenna is not = optimally aligned=20 with the wire towards the other station, a cosine=20 directivity factor should be taken into account. 
 
Best 73,
Markus (DF6NM)
 
   
From:=20 Roger Lapthorn=20
Sent: Saturday, June 08, = 2013 6:15=20 PM
Subject: LF: ELF antenna = ERP=20 calculations - request for resend of information

Some months ago - time flies, = so it may=20 have been last year - someone kindly sent me a copy of a paper, or at = least a=20 formula, to work out the radiated power (as opposed to other forms of = signal=20 transmission) from an earth-electrode pair "antenna" at ELF. I think it = was=20 based on some of the Project Sanguine work at 76Hz back in the 1970s. I = thought=20 I'd saved this, but cannot locate it anywhere.

 
If you remember sending me = this data,=20 please would you resend it?

Thanks.

73s
Roger G3XBM
___________________________________________
=
From: Markus Vester
Sent: Thursday, September 02, 2010 7:22 PM
To: rsgb_lf_group@blacksheep.org= =20
Subject: Re: LF: Earth loop depth

Dear LF,
 
I recently discovered that I had a misconception regarding the = effective=20 area of an earth antenna, which may be interesting to other = experimenters as=20 well. It seems that short earth antennas are much more efficient than I = had=20 intuitively anticipated.
 
For small electrode spacing, most of the current returns through = the ground=20 in the vicinity of the wire. My understanding was that the effective = loop area=20 would then look similar to the a half-circle beneath the baseline, as = depicted=20 by the red area in the sketch. This means that for small baselines, = effective=20 loop area would scale quadratically with baseline length. This would = hold until=20 the baseline is made so long that penetration becomes limited by skin = effect in=20 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=20 based on DC current densities in homogeneous halfspace. The current = field is=20 similar to the electrical nearfield of a dipole. Integrating = depth-weighted=20 current densities over the halfspace volume should then give the total = magnetic=20 moment. But this integral did not converge to an asymptotic limit, but = appeared=20 to grow monotonically with integration volume. This implies an infinite=20 effective depth of a DC ground loop!
 
At first I looked for an error in the integral calculations, but = then I=20 noticed that the divergence can be explained by a simple scaling = argument along=20 the following lines. At a distance r from the dipole (current Iq times = length=20 l), current density J in the ground scales as
 J(r) ~ Iq l = r^-3.
A=20 large half-shell (green) around the dipole has a perimeter pi r around = its=20 equator, so there the total current would be
 I(r) ~ Iq l r^-2 = dr
The=20 contribution to the magnetic moment of the shell is proportional to its=20 broadside area A ~ r^2, which gives
 dM(r) =3D I A ~ Iq l dr ~=20 constant.
This means that each additional shell will add the same = amount of=20 magnetic moment, and the total moment would indeed grow to infinity if r = is not=20 bounded by skin effect. Even though the outer fieldlines (blue) carry = only a=20 small part of the current, due to their large cross section they still=20 contribute significantly to the loop area.
 
This reasoning also falls in line with a much easier analysis for = the=20 receive case. Vertically polarized groundwaves have transverse magnetic = fields,=20 which must be bounded by radial ground currents (ie in the direction of = wave=20 propagation). The finite surface resistance of the ground creates an = additional=20 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=20 equations for equivalent depth is straightforward and gives
 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=20 garden, stuck the two leads of the soundcard input into the soil, and = measured=20 the induced voltage from the DHO signal. When going from 1.5 m to 3 m = electrode=20 spacing, it went up by 6 dB (and not 12 dB), showing that pickup area = scaled=20 linearly and not quadratically with baseline.
 
Kind regards,
Markus (DF6NM)
 
 =20
Sent: Thursday, September 02, 2010 7:07 PM
To: rsgb_lf_group@blacksheep.org
Subject: Re: LF: ERP calculation (revised)

Dear Roger,
 
thanks for sharing your results!
 
The directional dependence should be a simple cosine law, so going = from 45=B0=20 to 0=B0 would give you another 3 dB, or 3.8 uW ERP. Thus your total = radiated power=20 was 2.0 uW (EMRP). At 62 km, this gives -14 dBuV/m, which should indeed = be well=20 readable in QRSS 3 under quiet conditions.
 
Taking a loss resistance of 60 ohms, 4 watts would have given you = an=20 antenna current of 0.26 A. The radiation resistance is then =
 Rrad =3D=20 EMRP / Iq^2 =3D 30 microohms.
A standard formula for loops is =
 Rrad =3D=20 31171 ohm * A^2 / lambda^4,
resulting in an effective loop = area
 A =3D=20 155m^2.
Note this is using the radiation resistance for a loop in free = space, as=20 the effect of ground is already included in the earth antenna picture. = For an=20 above-ground loop with a mirror image beneath it, radiation resistance = would be=20 doubled.
 
Best wishes,
Markus (DF6NM)
 


-----Urspr=FCngliche=20 Mitteilung-----
Von: Roger Lapthorn = <rogerlapthorn@gmail.com>
An:=20 rsgb_lf_group@blacksheep.org
Verschickt: Mi., 1. Sept. 2010, = 13:41
Thema:=20 LF: ERP calculation (revised)

Today I = managed, I=20 believe, for the first time to accurately measure the ERP of my = QRPp=20 system on 137kHz.

This is the method used:
  • Using the E-field probe, FT817 (AGC off, gain backed off as far as = possible and a 10dB pad between the EFP and the FT817) and Spectran I = went to=20 my usual test site 1.5km away from the QTH, 45 degrees off the main = lobe of=20 the TX loop/earth electrode antenna.=20
  • Measured the signal level of DCF39 on 138.83kHz
  • Measured the signal level of G3XBM on 137.675kHz
  • Repeated this three times to reduce errors.=20
  • Noted the difference in FS level.
Difference in = signal level =3D=20 44dB . I feel pretty confident this is an accurate figure now and = not effected by AGC and overload. Assuming DCF39 is 1mV/m here = (info from=20 Alan Melia)  then my FS at the test site is 6.4uV/m.  = Using the=20 formula ERP =3D (E*d)^2/49 where E =3D 6.4*10E-6 and d=3D1.5*10E3 gives = an ERP =3D=20 1.9uW giving an antenna efficiency of -63dB using the earth = electrode=20 antenna with the elevated feed and 4W from the PA. 

The = test site=20 is about 45 degrees off the main line of fire of the antenna, so in the = best=20 direction it could be 10dB (?) stronger, i.e. 20uW ERP giving an = antenna=20 efficiency of -53dB in the best directions. Frankly I'm amazed = that=20 anyone can copy this signal at any distance, so full marks to G3XIZ = (48km) and=20 G3XDV (62km).

Next stage is to try this arrangement for a few = more days=20 using QRSS3 and WSPR before swapping to a full "in the air" loop and = repeating=20 these tests.

Great fun and I'm leaning as I go, which is the = whole point=20 of ham radio.

73s
Roger=20 G3XBM

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