<html><head><style type='text/css'>p { margin: 0; }</style></head><body><div style='font-family: Times New Roman; font-size: 14pt; color: #000000'><P>I thought this was simply an elaborate explanation of Norton's reference to "audio."</P>
<P> </P>
<P><BR>----- Original Message -----<BR>From: "George Andrews" <gandrews@ntplx.net><BR>To: "144.450 Mailing List" <450@lists.vhfwiki.com><BR>Sent: Thursday, November 25, 2010 6:25:52 AM<BR>Subject: [450] Happy Thanksgiving to All!<BR><BR></P>
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<DIV><FONT size=2 face=Arial>Hope no one strained brain on this. Just BS. (Not really it applies to radar and particle accelerator applications of RF (MWatt and up))</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>George</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
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<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV style="FONT: 10pt arial; BACKGROUND: #e4e4e4; font-color: black"><B>From:</B> <A title=gandrews@ntplx.net href="mailto:gandrews@ntplx.net" target=_blank>George Andrews</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A title=450@lists.vhfwiki.com href="mailto:450@lists.vhfwiki.com" target=_blank>144.450 Mailing List</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Wednesday, November 24, 2010 9:44 PM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> Re: [450] the wound! (i mean wind)</DIV>
<DIV><BR></DIV>
<DIV><FONT size=2 face=Arial>Bob,</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>I get it,but this is what I was talking about:</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><SPAN id=Range_resolution class=mw-headline>Range resolution</SPAN>
<P>Let us determine the range resolution which can be obtained with such a signal. The return signal, written <IMG class=tex alt="\scriptstyle r(t)" src="http://upload.wikimedia.org/math/7/8/9/789b5d76808fc838cb7149608672b52a.png" dfsrc="http://upload.wikimedia.org/math/7/8/9/789b5d76808fc838cb7149608672b52a.png">, is an attenuated and time-shifted copy of the original transmitted signal (in reality, <A title="Doppler effect" href="http://en.wikipedia.org/wiki/Doppler_effect" target=_blank>Doppler effect</A> can play a role too, but this is not important here.) There is also noise in the incoming signal, both on the imaginary and the real channel, which we will assume to be <A title="White noise" href="http://en.wikipedia.org/wiki/White_noise" target=_blank>white</A> and <A title="Normal distribution" href="http://en.wikipedia.org/wiki/Normal_distribution" target=_blank>Gaussian</A> (this generally holds in reality); we write <IMG class=tex alt="\scriptstyle B(t)" src="http://upload.wikimedia.org/math/e/1/6/e16e0fa6f211c8a395b2edeecc505f00.png" dfsrc="http://upload.wikimedia.org/math/e/1/6/e16e0fa6f211c8a395b2edeecc505f00.png"> to denote that noise. To detect the incoming signal, <A title="Matched filter" href="http://en.wikipedia.org/wiki/Matched_filter" target=_blank>matched filtering</A> is commonly used. This method is optimal when a known signal is to be detected among an additive white Gaussian noise.</P>
<P>In other words, the <A title=Cross-correlation href="http://en.wikipedia.org/wiki/Cross-correlation" target=_blank>cross-correlation</A> of the received signal with the transmitted signal is computed. This is achieved by <A title=Convolution href="http://en.wikipedia.org/wiki/Convolution" target=_blank>convolving</A> the incoming signal with a <A title="Complex conjugate" href="http://en.wikipedia.org/wiki/Complex_conjugate" target=_blank>conjugated</A> and time-reversed version of the transmitted signal. This operation can be done either in software or with hardware. We write <IMG class=tex alt="\scriptstyle <s,\,r>(t)" src="http://upload.wikimedia.org/math/f/3/2/f327416432346a6004db72c32e9ecf39.png" dfsrc="http://upload.wikimedia.org/math/f/3/2/f327416432346a6004db72c32e9ecf39.png"> for this cross-correlation. We have:</P>
<DL>
<DD><IMG class=tex alt="<s,r>(t) = \int_{t'\,=\,0}^{+\infty} s^\star(t')r(t+t') dt'" src="http://upload.wikimedia.org/math/f/6/5/f65d32014632b71286bf28c900ea737e.png" dfsrc="http://upload.wikimedia.org/math/f/6/5/f65d32014632b71286bf28c900ea737e.png"> </DD></DL>
<P>If the reflected signal comes back to the receiver at time <IMG class=tex alt="\scriptstyle t_r" src="http://upload.wikimedia.org/math/7/2/1/72127434c2bcee0664bce7c4f71d0e3f.png" dfsrc="http://upload.wikimedia.org/math/7/2/1/72127434c2bcee0664bce7c4f71d0e3f.png"> and is attenuated by factor <IMG class=tex alt="\scriptstyle K" src="http://upload.wikimedia.org/math/5/8/a/58a0d43f50180ea2c46c506e745f0e8d.png" dfsrc="http://upload.wikimedia.org/math/5/8/a/58a0d43f50180ea2c46c506e745f0e8d.png">, this yields:</P>
<DL>
<DD><IMG class=tex alt="r(t)= \left\{ \begin{array}{ll} K A e^{2 i \pi f_0 (t\,-\,t_r)} +B(t) &\mbox{if} \; t_r \leq t < t_r+T \\ B(t) &\mbox{otherwise}\end{array}\right." src="http://upload.wikimedia.org/math/7/8/8/788254b01315c6f67c4c73aa6a28ab03.png" dfsrc="http://upload.wikimedia.org/math/7/8/8/788254b01315c6f67c4c73aa6a28ab03.png"> </DD></DL>
<P>Since we know the transmitted signal, we obtain:</P>
<DL>
<DD><IMG class=tex alt="<s,r>(t) = KA^2\Lambda\left (\frac{t-t_r}{T} \right)e^{2 i \pi f_0 (t\,-\,t_r)} + B'(t)" src="http://upload.wikimedia.org/math/f/0/5/f05ca50901a6feb08a74f468f547d14f.png" dfsrc="http://upload.wikimedia.org/math/f/0/5/f05ca50901a6feb08a74f468f547d14f.png"> </DD></DL>
<P>where <IMG class=tex alt="\scriptstyle B'(t)" src="http://upload.wikimedia.org/math/2/2/c/22c8e0ca89de0a991eb80ba8e4909788.png" dfsrc="http://upload.wikimedia.org/math/2/2/c/22c8e0ca89de0a991eb80ba8e4909788.png">, the result of the intercorrelation between the noise and the transmitted signal, remains a white noise of same characteristics as <IMG class=tex alt="\scriptstyle B(t)" src="http://upload.wikimedia.org/math/e/1/6/e16e0fa6f211c8a395b2edeecc505f00.png" dfsrc="http://upload.wikimedia.org/math/e/1/6/e16e0fa6f211c8a395b2edeecc505f00.png"> since it is not correlated to the transmitted signal. Function <SPAN class=texhtml>Λ</SPAN> is the triangle function, its value is 0 on <IMG class=tex alt="\scriptstyle [-\infty,\, -\frac{1}{2}] \,\cup\, [\frac{1}{2}, \,+\infty]" src="http://upload.wikimedia.org/math/9/7/2/97263a46e2f4f20f80df63bb91803b9b.png" dfsrc="http://upload.wikimedia.org/math/9/7/2/97263a46e2f4f20f80df63bb91803b9b.png">, it augments linearly on <IMG class=tex alt="\scriptstyle [-\frac{1}{2},\, 0]" src="http://upload.wikimedia.org/math/5/3/0/530a876a05ff66e0d4dbf1aceba64c30.png" dfsrc="http://upload.wikimedia.org/math/5/3/0/530a876a05ff66e0d4dbf1aceba64c30.png"> where it reaches its maximum 1, and it decreases linearly on <IMG class=tex alt="\scriptstyle [0,\,\frac{1}{2}]" src="http://upload.wikimedia.org/math/a/f/f/aff8ada40777aac77a57230f93253d76.png" dfsrc="http://upload.wikimedia.org/math/a/f/f/aff8ada40777aac77a57230f93253d76.png"> until it reaches 0 again. Figures at the end of this paragraph show the shape of the intercorrelation for a sample signal (in red), in this case a real truncated sine, of duration <IMG class=tex alt="\scriptstyle T\,=\,1" src="http://upload.wikimedia.org/math/f/f/9/ff9568de6e3b9e89d7ee59c5c4a4e4db.png" dfsrc="http://upload.wikimedia.org/math/f/f/9/ff9568de6e3b9e89d7ee59c5c4a4e4db.png"> seconds, of unit amplitude, and frequency <IMG class=tex alt="\scriptstyle f_0\,=\,10" src="http://upload.wikimedia.org/math/d/2/f/d2f9076bd410e9042ff4f94844dc0774.png" dfsrc="http://upload.wikimedia.org/math/d/2/f/d2f9076bd410e9042ff4f94844dc0774.png"> hertz. Two echoes (in blue) come back with a delay of 3 and 5 seconds, respectively, and have an amplitude equal to 0.5 and 0.3; those are just random values for the sake of the example. Since the signal is real, the intercorrelation is weighted by an additional <SPAN class=frac><SUP>1</SUP>⁄<SUB>2</SUB></SPAN> factor.</P>
<P><FONT size=2 face=Arial>This is why you get more for less. On VHF and up this works fine. On HF you can expect over 1000 miles per watt, particularly on 40 and 20 M. There is tremendous gain above 30 GHz also but one must allow for pathway attenuation in microwave frequencies. But that kind of RF is not for the wimpy folk. Don't strain the brain, just try it and see for yourself!</FONT></P>
<P><FONT size=2 face=Arial>George</FONT></P>
<P><FONT size=2 face=Arial>N1YAE</FONT></P>
<P><FONT size=2 face=Arial></FONT> </P>
<P><FONT size=2 face=Arial></FONT> </P></DIV>
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<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV style="FONT: 10pt arial; BACKGROUND: #e4e4e4; font-color: black"><B>From:</B> <A title=n1ujs@toast.net href="mailto:n1ujs@toast.net" target=_blank>Bob</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A title=450@lists.vhfwiki.com href="mailto:450@lists.vhfwiki.com" target=_blank>144.450 Mailing List</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Wednesday, November 24, 2010 7:35 PM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> Re: [450] the wound! (i mean wind)</DIV>
<DIV><BR></DIV>
<DIV><FONT size=2 face=Arial>In the tradition of "Siskel & Ebert" (or Saturday Night Live's point/counterpoint skit with "Jane you ignorant slut!").............</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>Oh hush George you namby pamby pantywaist!</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>"My stuff is not as effective..." Hah!! That should read "....while no one can hear my puny signal....".....</FONT></DIV>
<DIV><FONT size=2 face=Arial>Noone has heard you in at least 10 years!!</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>This is no time to succumb! This is the time to stand up and say I will not be beaten! Take that bitch!</FONT></DIV>
<DIV> </DIV>
<DIV><FONT size=2 face=Arial>This is the time for larger diameters! Sleeve it inside and out at the stress points! Then ADD 10 feet!!!</FONT></DIV>
<DIV> </DIV>
<DIV><FONT size=2 face=Arial>Hee hee.....</FONT> <FONT size=2 face=Arial>George....you know I respect your great scientific mind and your keen understanding of physics and such......I'm sure you can appreciate this in the spirit intended.....</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV>----- Original Message ----- </DIV>
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<DIV style="FONT: 10pt arial; BACKGROUND: #e4e4e4; font-color: black"><B>From:</B> <A title=gandrews@ntplx.net href="mailto:gandrews@ntplx.net" target=_blank>George Andrews</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A title=450@lists.vhfwiki.com href="mailto:450@lists.vhfwiki.com" target=_blank>144.450 Mailing List</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Wednesday, November 24, 2010 6:44 PM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> Re: [450] the wound! (i mean wind)</DIV>
<DIV><BR></DIV>
<DIV><FONT size=2 face=Arial>Dave,</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>Give thought to what happened. I know 42 inches probably probably means a lot to you and I can understand that. You have determined the weak point in the system. If your mast was steel, continued flexing softens the metal at the flex point. Aluminum becomes brittle with flexing (work hardens). If you leave it where it is, you may not have to worry about wind. Model the antennae to see what the decreased gain is. Maybe you don't want to go back to the full 42 inch difference. There is a gain to be achieved in never having to worry about wind and ice load and wind. My antennae are not as high as they could be, but ice and windload or wind have never been a worry. My three element 6 M beam is set up with a very crude slipping clutch so that all the mast and rotor rotate if the wind really gets a hold of it. This way a component of the energy that might bend the mast or damage the antenna gets translated to a rotational component. I have to rezero rotor every so often, but that is trivial. Over the years, I have heard some strange creaking and groaning, but have not lost an antenna or had damage since I have been licensed. On the flip side, my stuff is not as effective as if I pushed the envelope. But physics and gravity will always win!</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>George</FONT></DIV>
<DIV><FONT size=2 face=Arial>N1YAE</FONT></DIV>
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<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV style="FONT: 10pt arial; BACKGROUND: #e4e4e4; font-color: black"><B>From:</B> <A title=k1fsy@vhfwiki.com href="mailto:k1fsy@vhfwiki.com" target=_blank>David McKenzie</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A title=450@lists.vhfwiki.com href="mailto:450@lists.vhfwiki.com" target=_blank>144.450 Mailing List</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Wednesday, November 24, 2010 12:23 PM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> [450] the wound! (i mean wind)</DIV>
<DIV><BR></DIV>The mast on the HF tower bent just above the thrust bearing in last night's wind. I dropped it down and cut the mast just above the bend. The HF beam and loops are now 42 inches lower until I can replace it.<BR><BR>The bend was very slight but was more than enough to bring the top about 30 degrees off vertical.<BR><BR>No other damage here.<BR>
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