Re: LF: RE: something for the weekend ??

["Stewart Bryant" <stewart.bryant@virgin.net>]

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.