From: DL4YHF@aol.com
Message-ID: <1e5.78b8a15.2bdab2b2@aol.com>
Date: Fri, 25 Apr 2003 11:48:02 EDT
To: rsgb_lf_group@blacksheep.org
MIME-Version: 1.0
Subject: Re: LF: RE: something for the weekend ??
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<HTML><FONT FACE=arial,helvetica><FONT  SIZE=2>Think I got it...
<BR>
<BR>The output from the upper mixer branch is:
<BR> &nbsp;sin(a+b) - sin(a-b) &nbsp;
<BR>
<BR>The assumption "delayed this by 90 degrees" should give
<BR> &nbsp;cos(a+b) - cos(a-b) 
<BR>does not look right in my opinion.
<BR>
<BR>
<BR>Instead, do the "90° phase shift" from the upper mixer's output in the term where all trigonometric functions have only a single argument. 
<BR>Upper mixer branch
<BR>sin(a+b)-sin(a-b) = 2*cos(a)*sin(b) &nbsp;[ go figure ...]
<BR>Now only one argument in each trig function, looks safe to do the 90 degree phase shift by adding 90 degrees in the argumens:
<BR>Upper mixer branch, delayed by 90°:
<BR>2*cos(a+90°)*sin(b+90°) = - 2*sin(a)*cos(b) = - sin(a-b) - sin(a+b)
<BR>
<BR>So this is the delayed output from the upper mixer branch. Now add upper and lower branch (without the phase shifters):
<BR>Lower branch : sin(a+b)-sin(a-b)
<BR>Upper branch : -sin(a+b)-sin(a+b)
<BR>Add both: &nbsp;&nbsp;&nbsp;sin(a+b)-sin(a-b)-sin(a-b)-sin(a+b) = -2sin(a-b)
<BR>Et volia, the upper sideband has been cancelled (should have subtracted for USB ;)
<BR>
<BR>
<BR>Hope this is not totally wrong..
<BR>
<BR>Regards,
<BR> Wolf DL4YHF.
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