On 7/5/07 12:00 AM, in article ,
"Ron Baker, Pluralitas!" wrote:


"Don Bowey" wrote in message
...
On 7/4/07 8:42 PM, in article ,
"Ron
Baker, Pluralitas!" wrote:


"Don Bowey" wrote in message
...
On 7/4/07 10:16 AM, in article ,
"Ron Baker, Pluralitas!" wrote:


"Don Bowey" wrote in message
...
On 7/4/07 7:52 AM, in article
,
"Ron
Baker, Pluralitas!" wrote:

snip


cos(a) * cos(b) = 0.5 * (cos[a+b] + cos[a-b])

Basically: multiplying two sine waves is
the same as adding the (half amplitude)
sum and difference frequencies.

No, they aren't the same at all, they only appear to be the same
before
they are examined. The two sidebands will not have the correct phase
relationship.

What do you mean? What is the "correct"
relationship?


One could, temporarily, mistake the added combination for a full
carrier
with independent sidebands, however.




(For sines it is
sin(a) * sin(b) = 0.5 * (cos[a-b]-cos[a+b])
= 0.5 * (sin[a-b+90degrees] - sin[a+b+90degrees])
= 0.5 * (sin[a-b+90degrees] + sin[a+b-90degrees])
)

--
rb





When AM is correctly accomplished (a single voiceband signal is
modulated

The questions I posed were not about AM. The
subject could have been viewed as DSB but that
wasn't the specific intent either.

What was the subject of your question?

Copying from my original post:

Suppose you have a 1 MHz sine wave whose amplitude
is multiplied by a 0.1 MHz sine wave.
What would it look like on an oscilloscope?
What would it look like on a spectrum analyzer?

Then suppose you have a 1.1 MHz sine wave added
to a 0.9 MHz sine wave.
What would that look like on an oscilloscope?
What would that look like on a spectrum analyzer?




So the first (1) is an AM question and the second (2) is a non-AM
question......

(1 A) On scope will be a classical envelope showing what appears to be the
carrier amplitude voltage varying from the effects of the sideband phases
and voltages. It's an optical delusion, but is good for viewing linearity
and % modulation.

(1 B) The spectrum analyzer will show a carrier at 1 MHz, a carrier at
999.9 kHz (LSB), and a carrier at 1.1 MHz (USB).

(1 C) Not asked, but needing an answer here, is "if the .1 MHZ modulation
were replaced by a changing signal such as speech or music what would the
analyzer show?" It would show an unchanging Carrier at 1 MHZ with frequency
and amplitude changing sidebands extending above and below the unchanging
carrier.

(2 A) The scope would display a 1.1 MHz sine wave and a .9 MHz sine wave.
They could be free-running or, depending on the scope features, either one
or both could be used to sync a/the trace(s).

(2 B) The spectrum analyzer will show a carrier at 1.1 MHz, and a carrier
at .9 MHz.

Don