[sdiy] Dual Frequency Shifter update

[Magnus Danielson]

From: Grant Richter <grichter at asapnet.net>
Subject: Re: [sdiy] Dual Frequency Shifter update
Date: Tue, 18 Jul 2006 15:47:26 -0500
Message-ID: <63D7BA13-C499-4C03-BC40-3DA9DF08CF34 at asapnet.net>

> The Raytheon RC4200 used the Log-Antilog scheme for multiplying as  
> the sum of logs. That is x * y = antilog((log x) + (log y)) They have  
> to be DC biased for single quadrant. It had the lowest rated  
> distortion (0.1%) of the commercial multipliers (vs. 1% for AD633).
> 
> I always wanted to try using RC4200s since fooling around with the  
> Bode and Buchla FS units gave me the impression that the multipliers  
> are the weak point for sideband suppression (perhaps more audible  
> than dome filter errors, because the sideband bleed through has  
> harmonics produce by the multiplier errors?).
> 
> Is is possible you could use summers instead of multipliers using a  
> sum of logs trick on a SYSTEM basis?
> That could save parts, and possibly improve performance.
> 
> Let's see, you would need the log of all 4 quadratures, but then  
> summing is the same as multiplying if you take the anti-logs  
> afterwards. That is what you would get if you used RC4200s for the  
> multipliers.
> 
> What if you used a single log conversion BEFORE the dome filters,  
> then summers, then anti-log, then sum and differential addition. Dome  
> filters should be DC linear, so logging before won't matter? It would  
> replace the multipliers with linear summers, possibly improving  
> sideband suppression and S/N ratio.
> 
> I have not it given any rigorous thought. Just thought I would toss  
> it out for possible discussion.

I don't feel like spoiling the party (here it comes)... BUT.

If you log your signal down, filter it (you always need to toss it through
a filter, "dome" or whatever) and exp it back you have a run into a pair of
problems:

1) Signal is inherently bi-polar, log and exp is inherently operating on
positive at one side of their respective function and bi-polar on the other
side. Unfortunatly the bi-polar side is "inside" where as the positive is on
the outside.

2) We have moved the non-linear to the wrong side of the filter, so it is
treating the now distorted signal by a linear filtering process and then apply
the reverse function of the non-linearity will *NOT* get the right signal back.
It's FUBAR by now. You guys of any should know this by heart and use it into
deep dangerous and nasty areas ... you know....

Exercise: Take a sine, toss it through an logarithm (see all the nice overtones
at different amplitudes and phases), phase shift them differently and put them
back together again through the exponential function. Do we have an undistored
sine? Oh, how did you do that and maintained the sign?

I think you are out for a fishingtour on dark waters chasing a red herring!

Cheers,
Magnus