Reply-To: "Kevin Aylward"
From: "Kevin Aylward"
References: <email@example.com> <2ltr9.338$cV6.firstname.lastname@example.org> <3DAED797.email@example.com>
Subject: Re: How does a mixer work?
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Date: Thu, 17 Oct 2002 16:47:30 +0100
NNTP-Posting-Date: Thu, 17 Oct 2002 16:47:31 BST
"Fred Bloggs" wrote in message
> Kevin Aylward wrote:
> > "Asa Cannell" wrote in message
> > news:firstname.lastname@example.org...
> >>How does a mixer work? I don't understand why it needs a non-linear
> >>element. I think examples of why a linear element (resistor) wont
> >>would help illustrate why a non-linear element (diode) will. Also,
> >>what does 'mutiply' mean in terms of mixing? What if two DC signals
> >>are applied to a mixer, like 2V and 4V? Will the output be 8V?
> > The basic reason is based on a standard trigonometric result.
> > Sin(A)*Sin(B)= 0.5*(Cos(A-B) + cos(A+B))
> Huh? And which alternative reality is this?
This one. In what universe is this not true?
I am somewhat bemused by all the posts in this thread "explaining" mixer
action, yet no one seems to be really explaining it at all, imo.
*The* *fundamental* reason a mixer works, i.e. it generates sum and
difference frequencies is because of the above trigonometric relation,
Sin(W1.t)*Sin(W2.t)= 0.5*(Cos(W1.t-W2.t) + cos(W1.t+W2.t))
That is, multiplying sine waves generates sum and difference sinewaves.
Therefore to create a mixer, you need to generate a multiplication term.
You can do that directly, e.g., in a Gilbert cell, or indirectly, by
e.g. square (V1.Sin(W1.t) + V1.Sin(Ws.t)), as I explained in my post.
Simple stating that you are multiplying signals, does not explain why,
hence the bit of high school trig.
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