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| To: | [email protected] |
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| Subject: | Re: LF: RE: something for the weekend ?? |
| From: | [email protected] |
| Date: | Fri, 25 Apr 2003 11:48:02 EDT |
| Reply-to: | [email protected] |
| Sender: | <[email protected]> |
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Think I got it...
The output from the upper mixer branch is: sin(a+b) - sin(a-b) The assumption "delayed this by 90 degrees" should give cos(a+b) - cos(a-b) does not look right in my opinion. Instead, do the "90° phase shift" from the upper mixer's output in the term where all trigonometric functions have only a single argument. Upper mixer branch sin(a+b)-sin(a-b) = 2*cos(a)*sin(b) [ go figure ...] Now only one argument in each trig function, looks safe to do the 90 degree phase shift by adding 90 degrees in the argumens: Upper mixer branch, delayed by 90°: 2*cos(a+90°)*sin(b+90°) = - 2*sin(a)*cos(b) = - sin(a-b) - sin(a+b) So this is the delayed output from the upper mixer branch. Now add upper and lower branch (without the phase shifters): Lower branch : sin(a+b)-sin(a-b) Upper branch : -sin(a+b)-sin(a+b) Add both: sin(a+b)-sin(a-b)-sin(a-b)-sin(a+b) = -2sin(a-b) Et volia, the upper sideband has been cancelled (should have subtracted for USB ;) Hope this is not totally wrong.. Regards, Wolf DL4YHF. |
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