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

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

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.