Message-ID: <3EAA3D7D.9040802@virgin.net>
Date: Sat, 26 Apr 2003 09:04:13 +0100
From: "Stewart Bryant" <stewart.bryant@virgin.net>
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References: <1e5.78b8a15.2bdab2b2@aol.com> <3EAA3857.5020400@virgin.net>
Subject: Re: LF: RE: something for the weekend ??
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Just thinking about this a little more, if you could
generate the right dispersion characteristics in the
IF phase shifter, can't you do the whole thing
with a single mixer and IF processing?

Stewart


Stewart Bryant wrote:
> 
> I am not sure about the physics of this.
> 
> The 90deg phase shifter has to be some sort of dispersion
> device (propagation time varies with frequency), and this
> will operate on the fourier components of the waveform.
> 
> The fourier components present are sin(a+b) and sin(a-b),
> not the complex waveform cos(a)*sin(b).
> 
> Therefore the phaseshift will apply individually to
> sin(a+b) and to sin(a-b).
> 
> Can we go back to the physical device itself, and confirm
> that the IF phase shifter is shifting by 90deg (as opposed to
> say 270deg) and that you can select both sidebands
> properly with the add/subtract?
> 
> Stewart G3YSX
> 
> 
> DL4YHF@aol.com wrote:
> 
>> 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.
> 
> 
> 
> 
>