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From: Fred Bloggs
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Subject: Re: How does a mixer work?
References: <firstname.lastname@example.org> <3DB2E3CE.email@example.com> <firstname.lastname@example.org> <email@example.com> <3DB34C15.5203CF0@webaccess.net> <3DB37C55.6F63@Spam.Bots> <3DB36A58.4E49CEAC@webaccess.net>
Date: Tue, 22 Oct 2002 11:11:40 GMT
NNTP-Posting-Date: Tue, 22 Oct 2002 04:11:40 PDT
Organization: EarthLink Inc. -- http://www.EarthLink.net
Chuck Simmons wrote:
> At this point I take a stand against the hidebound conventionalism that
> is the application of mathematics to engineering. I am very sensitive to
> this because I have no engineering education whatever and ALL
> mathematical statements engineers make can be considered suspect because
> of the hidebound conventionalism.
> Consider the equation:
> This is really an identity. The left hand side says that the carrier
> varies in amplitude according the the operations on the field of real
> numbers. The second says that, fully equivalently, there are three
> constant frequencies and amplitudes.
> It is pure hidebound conventionalism that says that though the two sides
> of the equation are correct, the right hand side is more correct. Pure
> mathematical hogwash. There can be no justification for that sort of
> narrow thinking.
If the early developers adopted your perspective, there would be no
sideband communication. The left hand side of the equation is deceiving,
it is the time domain description of the modulated waveform and is
easily interpreted as instantaneous variation of the carrier amplitude.
The right hand side of the equation reveals much more. It shows that the
effect of the modulation is to produce sideband power offset from the
carrier in frequency. It also points up the fact that the information is
duplicated in each sideband and that the carrier itself conveys nothing.
The carrier is no longer defined by voltage variation of the sin(Wct)
term of the time-domain waveform, it is defined by the power level at
frequency Wc. For purposes of actually constructing transmitters and
receivers, the right hand side of the equation is by far the more
useful. That equation defines the spectral bandwidth required as well as
the power handling capability of the transmitter and power supplies. So
now I ask you, so what if the time-domain display looks like a carrier
amplitude variation,? What does this get you? The answer is - nothing.
Anyone planning such a system better plan on supporting the power
demands of a *constant amplitude* carrier transmission, and this is what
it boils down to.
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