MOTM

Ahh, okay. I'd never thought of it that way before. Probably I've worked
with inferior AC-coupled synthesizers in the past so 0 Hz is basically
"non-existent" because it gets highpass filtered by the coupling capacitors.
So it was never an issue for me. But I see where, at least mathematically,
you're right, and the negative cycle of the waveform would get raised that
way.

-----Original Message-----
From: jhaible@... [mailto:jhaible@...] 
Sent: Thursday, 06 December, 2001 10:09 AM
To: Tkacs, Ken
Cc: motm@yahoogroups.com
Subject: Re: FW: [motm] My failed experiment

Tkacs, Ken schrieb:
> 
> If you feed a sine into both inputs of a ring modulator, 
> you get a sine an 
> octave higher, not a rectified sine. It outputs the sum 
> and difference 
> signals, so the sum of "1" and "1" is "2 (doubled 
> frequency)," and the 
> difference is zero. 

> I'm not sure where you're getting the rectification from. 

Very true. However, "zero" means "zero Hz" (and not "zero voltage").
That is, the difference frequency becomes a DC voltage!
(DC = "AC @ 0Hz" with amplitude = DC voltage). This
adds to the double frequency sine wave, so you get a sine
of 2f that is *raised* above 0V - and here's where the similarity
to "rectification" comes in.

With the old formula (from memory - I hope it's right, and it's
easier with cosinus to write down):

cos(x) * cos(x) = 1/2 + 1/2 * cos(2x) >= 0.

JH.

> Ahh, okay. I'd never thought of it that way before. 
> Probably I've worked 
> with inferior AC-coupled synthesizers in the past so 0 Hz 
> is basically 
> "non-existent" because it gets highpass filtered by the 
> coupling capacitors. 

Nothing bad about AC coupling.

BTW, such circuits have been used as Frequency Doublers for
guitars. AC coupling at the output of course. (AC coupling
at inputs, too.) 
Now the amplitude of the input signal is not constant with
a guitar, so the "DC" voltage at the output is not constant
either. Strictly speaking, it's no more DC then, but a slowly
changing AC. Part of this will go thru the AC coupling, so
you get side effects from "thumping" to "tube like" dynamical 
shift of bias point for the connected circuity - a bug or a 
feature, depending on the application. And the Signal
amplitude at 2*f is the x**2 of the input amplitude, so
the signal becomes more "percussive". There have even been
circuits with a crude compressor at one of the RM inputs to
avoid this ...)

With a fixed input amplitude and AC coupling at the output
you get just the desired frequency doubling. (At half the
input amplitude).

JH.