To: rsgb_lf_group@blacksheep.org
Date: Mon, 08 Mar 2010 09:15:51 -0500
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From: Markus Vester <markusvester@aol.com>
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Subject: LF: Technique for measuring antenna height and noise background
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Dear LF,

in the recent discussion we have basically considered two different method=
s to estimate VLF noise background. One (called "A" here) was directly mea=
suring the noise voltage at an electric antenna of known effective height.=
 The other ("method B") involved transmitting with a known current, calcul=
ating radiated power, and comparing the received signal at a distant locat=
ion to background noise. Both require a priori knowledge of the effective=
 height (h), which is somewhat uncertain.

But it is interesting to note that height uncertainty has an inverse effec=
t on the result of A and B. When h is lower than expected, with A we measu=
re a smaller noise voltage, and will underestimate the noise floor. Howeve=
r with B, we overestimate radiated power and received signal, and thus com=
e up with a higher noise floor result. So in principle a combination of bo=
th methods should enable us to measure h and cancel its effect.

This concept can be generalized. It will allow us to formulate another met=
hod to measure effective height and efficiency, which does not require any=
 kind of calibrated reference antenna, but is only based on reciprocity.

Let's consider a set of three antennas in three different known locations:=
=20

- Antenna A1 will be used only for transmitting. It could be a distant sou=
rce like DCF39 or Alpha, absolute EMRP1 does not have to be known. It coul=
d also be homogeneous background noise,
- A2 is the device under test, whose height h2 we are interested in. It wi=
ll both have to transmit a known current i2, and receive a measurable volt=
age,
- A3 is an uncalibrated receive only antenna, like an active probe, connec=
ted to a receiver which can measure relative voltages.

Then we will do three measurements:

- u12 is the received open-circuit voltage at the output of A2, coming acr=
oss a distance r12 from A1,
- u13 is the receive level caused by A1 at A3,
- u23 is the receive level at A3 when transmitting with current i2 into A2=
.

Assuming 1/r propagation for simplicity, we arrive at

 u12 =3D sqrt (90 ohm * EMRP1) * h2 / r12,
 u13 =3D sqrt (90 ohm * EMRP1) * h3 / r13,
 u23 =3D sqrt (90 ohm * 1589 ohm) * i2 * h2 / lambda * h3 / r23.

We can eliminate EMRP1 and h3 by taking

 u12 * u23 / u13 =3D h2 * h2 * r13 / r12 / r23 * Zo / lambda * i2

with Zo =3D 377 ohms, and finally extract h2

 h2 =3D sqrt ((u12 * r12) / (u13 * r13) * (u23 * r23) / i2 * lambda / Zo)=
 .

Well I have probably reinvented another wheel here... but anyway I think=
 this method can be quite useful for determining our antenna efficiencies.

Kind regards,
MArkus (DF6NM)

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<font color=3D'black' size=3D'2' face=3D'arial'>
<div style=3D"CLEAR: both">Dear LF,</div>


<div style=3D"CLEAR: both">&nbsp;</div>


<div style=3D"CLEAR: both">in the recent discussion we have basically cons=
idered two different methods to estimate VLF noise background. One (called=
 "A" here) was directly measuring the noise voltage at an electric antenna=
 of known effective height. The other ("method B") involved transmitting=
 with a known current, calculating radiated power, and comparing the recei=
ved signal at a distant location to background noise. Both require a prior=
i knowledge of the effective height (h), which is somewhat uncertain.</div=
>


<div style=3D"CLEAR: both">&nbsp;</div>


<div style=3D"CLEAR: both">But it is interesting to note that height uncer=
tainty has an inverse effect on the result of A and B. When h is lower tha=
n expected, with A we measure a smaller noise voltage, and will underestim=
ate the noise floor. However with B, we overestimate radiated power and re=
ceived signal, and thus come up with a higher noise floor result. So in pr=
inciple a combination of both methods should enable us to measure h and ca=
ncel its effect.</div>


<div style=3D"CLEAR: both">&nbsp;</div>


<div style=3D"CLEAR: both">This concept can be generalized. It will allow=
 us to formulate another method to measure effective height and efficiency=
, which does not require any kind of calibrated reference antenna, but is=
 only based on reciprocity.</div>


<div style=3D"CLEAR: both">&nbsp;</div>


<div style=3D"CLEAR: both">Let's consider a set of three antennas in three=
 different known locations: </div>


<div style=3D"CLEAR: both">&nbsp;</div>


<div style=3D"CLEAR: both">- Antenna A1 will be used only for transmitting=
. It could be a distant source like DCF39 or Alpha, absolute EMRP1 does no=
t have to be known. It could also be homogeneous background noise,<br>
- A2 is the device under test, whose height h2 we are interested in. It wi=
ll both have to transmit a known current i2, and receive a measurable volt=
age,<br>
- A3 is an uncalibrated receive only antenna, like an active probe, connec=
ted to a receiver which can measure relative voltages.</div>


<div style=3D"CLEAR: both">&nbsp;</div>


<div style=3D"CLEAR: both">Then we will do three measurements:</div>


<div style=3D"CLEAR: both">&nbsp;</div>


<div style=3D"CLEAR: both">- u12 is the received open-circuit voltage at=
 the output of A2, coming across a distance r12 from A1,<br>
- u13 is the receive level caused by A1 at A3,<br>
- u23 is the receive level at A3 when transmitting with current i2 into A2=
.</div>


<div style=3D"CLEAR: both">&nbsp;</div>


<div style=3D"CLEAR: both">Assuming 1/r propagation for simplicity, we arr=
ive at</div>


<div style=3D"CLEAR: both">&nbsp;</div>


<div style=3D"CLEAR: both">&nbsp;u12 =3D sqrt (90 ohm * EMRP1) * h2 / r12,=
<br>
&nbsp;u13 =3D sqrt (90 ohm * EMRP1) * h3 / r13,<br>
&nbsp;u23 =3D sqrt (90 ohm * 1589 ohm) * i2 * h2 / lambda * h3 / r23.</div=
>


<div style=3D"CLEAR: both">&nbsp;</div>


<div style=3D"CLEAR: both">We can eliminate EMRP1 and h3 by taking</div>


<div style=3D"CLEAR: both">&nbsp;</div>


<div style=3D"CLEAR: both">&nbsp;u12 * u23 / u13 =3D h2 * h2 * r13 / r12=
 / r23 * Zo / lambda * i2</div>


<div style=3D"CLEAR: both">&nbsp;</div>


<div style=3D"CLEAR: both">with Zo =3D 377 ohms, and finally extract h2</d=
iv>


<div style=3D"CLEAR: both">&nbsp;</div>


<div style=3D"CLEAR: both">&nbsp;h2 =3D sqrt ((u12 * r12) / (u13 * r13) *=
 (u23 * r23) / i2 * lambda / Zo) .</div>


<div style=3D"CLEAR: both">&nbsp;</div>


<div style=3D"CLEAR: both">Well I have probably reinvented another wheel=
 here... but anyway I think this method can be quite useful for determinin=
g our antenna efficiencies.</div>


<div style=3D"CLEAR: both">&nbsp;</div>


<div style=3D"CLEAR: both">Kind regards,<br>
MArkus (DF6NM)</div>


<div style=3D"CLEAR: both">&nbsp;</div>
</font>

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