"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.

onto a carrier via a non-linear process), at an envelope detector the two
sidebands will be additive. But if you independe ntly place a carrier at
frequency ( c ), another carrier at ( c-1 khz) and another carrier at (c+
1
kHz), the composite can look like an AM signal, but it is not, and only by
the most extreme luck will the sidebands be additive at the detector.
They
would probably cycle between additive and subtractive since they have no
real relationship and were not the result of amplitude modulation.

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?


onto a carrier via a non-linear process), at an envelope detector the two
sidebands will be additive. But if you independe ntly place a carrier at
frequency ( c ), another carrier at ( c-1 khz) and another carrier at (c+
1
kHz), the composite can look like an AM signal, but it is not, and only by
the most extreme luck will the sidebands be additive at the detector.
They
would probably cycle between additive and subtractive since they have no
real relationship and were not the result of amplitude modulation.

"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?

In article ,
John Fields wrote:

On Wed, 04 Jul 2007 09:11:58 -0700, isw wrote:

In article ,
"Ron Baker, Pluralitas!" wrote:

You win.

When I conceived the problem I was thinking
cosines actually. In which case there are no
phase shifts to worry about in the result.

I also forgot the half amplitude factor.

While it might not be obvious, the two cases I
described are basically identical. And this
situation occurs in real life, i.e. in radio signals,
oceanography, and guitar tuning.

The beat you hear during guitar tuning is not modulation; there is no
non-linear process involved (i.e. no multiplication).

---
That's not true.

The human ear has a logarithmic amplitude response and the beat note
(the difference frequency) is generated there. The sum frequency is
too, but when unison is achieved it'll be at precisely twice the
frequency of either fundamental and won't be noticed.

Now you get to explain why the beat is measurable with instrumentation,
and can can be viewed in the waveform of a high-quality recording.

Then go on to show why all other multi-frequency-component signals (e.g.
a full orchestra) don't produce similar intermodulation effects in ears
under normal conditions.

Isaac

In article ,
"Ron Baker, Pluralitas!" wrote:

"isw" wrote in message
...
In article ,
"Ron Baker, Pluralitas!" wrote:

"Keith Dysart" wrote in message
ps.com...
On Jul 3, 2:07 pm, Keith Dysart wrote:
On Jul 3, 12:50 pm, John Fields wrote:





On Mon, 2 Jul 2007 23:03:36 -0700, "Ron Baker, Pluralitas!"

wrote:

"John Smith I" wrote in message
...
Radium wrote:

snip

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?

snip

What would it look like on a spectrum analyzer?

| |
| | | |
--------+--------------------+-------+------+----
100kHz 0.9MHz 1MHz 1.1MHz

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?

snip

Tricky!!!

It looks like AM but it isn't, it's just the phases sliding past
each other slowly and algebraically adding which creates the
illusion.

What would that look like on a spectrum analyzer?

| |
| |
-----------------------------+--------------+----
0.9MHz 1.1MHz

--
JF

But if you remove the half volt bias you put on the
100 kHz signal in the multiplier version, the results
look exactly like the summed version, so I suggest
that results are the same when a 4 quadrant multiplier
is used.

And since the original request was for a "1 MHz sine
wave whose amplitude is multiplied by a 0.1 MHz sine
wave" I think a 4 quadrant multiplier is in order.

...Keith-

Ooops. I misspoke. They are not quite the same.

The spectrum is the same, but if you want to get exactly
the same result, the lower frequency needs a 90 degree
offset and the upper frequency needs a -90 degree offset.

And the amplitudes of the the sum and difference
frequencies need to be one half of the amplitude of
the frequencies being multiplied.

...Keith


You win.

When I conceived the problem I was thinking
cosines actually. In which case there are no
phase shifts to worry about in the result.

I also forgot the half amplitude factor.

While it might not be obvious, the two cases I
described are basically identical. And this
situation occurs in real life, i.e. in radio signals,
oceanography, and guitar tuning.

The beat you hear during guitar tuning is not modulation; there is no
non-linear process involved (i.e. no multiplication).

Isaac

In short, the human auditory system is not linear.
It has a finite resolution bandwidth. It can't resolve
two tones separted by a few Hertz as two separate tones.
(But if they are separted by 100 Hz they can easily
be separated without hearing a beat.)

Two tones 100 Hz apart may or may not be perceived separately; depends
on a lot of other factors. MP3 encoding, for example, depends on the
ear's (very predictable) inability to discern tones "nearby" to other,
louder ones.

The same affect can be seen on a spectrum analyzer.
Give it two frequencies separated by 1 Hz. Set the
resolution bandwidth to 10 Hz. You'll see the peak
rise and fall at 1 Hz.

Yup. And the spectrum analyzer is (hopefully) a very linear system,
producing no intermodulation of its own.

Isaac

In article ,
"Ron Baker, Pluralitas!" wrote:

"isw" wrote in message
...

snip


After you get done talking about modulation and sidebands, somebody
might want to take a stab at explaining why, if you tune a receiver to
the second harmonic (or any other harmonic) of a modulated carrier (AM
or FM; makes no difference), the audio comes out sounding exactly as it
does if you tune to the fundamental? That is, while the second harmonic
of the carrier is twice the frequency of the fundamental, the sidebands
of the second harmonic are *not* located at twice the frequencies of the
sidebands of the fundamental, but rather precisely as far from the
second harmonic of the carrier as they are from the fundamental.

Isaac

Whoa. I thought you were smoking something but
my curiosity is piqued.
I tried shortwave stations and heard no harmonics.
But that could be blamed on propagation.
There is an AM station here at 1.21 MHz that is s9+20dB.
Tuned to 2.42 MHz. Nothing. Generally the lowest
harmonics should be strongest. Then I remembered
that many types of non-linearity favor odd harmonics.
Tuned to 3.63 MHz. Holy harmonics, batman.
There it was and the modulation was not multiplied!
Voices sounded normal pitch. When music was
played the pitch was the same on the original and
the harmonic.

One clue is that the effect comes and goes rather
abruptly. It seems to switch in and out rather
than fade in an out. Maybe the coming and going
is from switching the audio material source?

This is strange. If a signal is multiplied then the sidebands
should be multiplied too.
Maybe the carrier generator is generating a
harmonic and the harmonic is also being modulated
with the normal audio in the modulator.
But then that signal would have to make it through
the power amp and the antenna. Possible, but
why would it come and go?
Strange.

Hint: Modulation is a "rate effect".

Isaac

"isw" wrote in message
...
In article ,
"Ron Baker, Pluralitas!" wrote:

snip


While it might not be obvious, the two cases I
described are basically identical. And this
situation occurs in real life, i.e. in radio signals,
oceanography, and guitar tuning.

The beat you hear during guitar tuning is not modulation; there is no
non-linear process involved (i.e. no multiplication).

Isaac

In short, the human auditory system is not linear.
It has a finite resolution bandwidth. It can't resolve
two tones separted by a few Hertz as two separate tones.
(But if they are separted by 100 Hz they can easily
be separated without hearing a beat.)

Two tones 100 Hz apart may or may not be perceived separately; depends
on a lot of other factors. MP3 encoding, for example, depends on the
ear's (very predictable) inability to discern tones "nearby" to other,
louder ones.

I'll remember that the next time I'm tuning
an MP3 guitar.


The same affect can be seen on a spectrum analyzer.
Give it two frequencies separated by 1 Hz. Set the
resolution bandwidth to 10 Hz. You'll see the peak
rise and fall at 1 Hz.

Yup. And the spectrum analyzer is (hopefully) a very linear system,
producing no intermodulation of its own.

Isaac

What does a spectrum analyzer use to arive at
amplitude values? An envelope detector?
Is that linear?

On Thu, 5 Jul 2007 00:00:45 -0700, "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?

---
The first example is amplitude modulation precisely _because_ of the
multiplication, while the second is merely the algebraic summation
of the instantaneous amplitudes of two waveforms.

The circuit lists I posted earlier will, when run using LTSPICE,
show exactly what the signals will look like using an oscilloscope
and, using the "FFT" option on the "VIEW" menu, give you a pretty
good approximation of what they'll look like using a spectrum
analyzer.

If you don't have LTSPICE it's available free at:

http://www.linear.com/designtools/software/


--
JF

On Thu, 05 Jul 2007 00:06:02 -0700, isw wrote:

In article ,
John Fields wrote:

On Wed, 04 Jul 2007 09:11:58 -0700, isw wrote:

In article ,
"Ron Baker, Pluralitas!" wrote:

You win.

When I conceived the problem I was thinking
cosines actually. In which case there are no
phase shifts to worry about in the result.

I also forgot the half amplitude factor.

While it might not be obvious, the two cases I
described are basically identical. And this
situation occurs in real life, i.e. in radio signals,
oceanography, and guitar tuning.

The beat you hear during guitar tuning is not modulation; there is no
non-linear process involved (i.e. no multiplication).

---
That's not true.

The human ear has a logarithmic amplitude response and the beat note
(the difference frequency) is generated there. The sum frequency is
too, but when unison is achieved it'll be at precisely twice the
frequency of either fundamental and won't be noticed.

Now you get to explain why the beat is measurable with instrumentation,
and can can be viewed in the waveform of a high-quality recording.

---
Simple. The process isn't totally linear, starting with the musical
instrument itself, so some heterodyning will inevitably occur which
will be detected by the measuring instrumentation.
---

Then go on to show why all other multi-frequency-component signals (e.g.
a full orchestra) don't produce similar intermodulation effects in ears
under normal conditions.

---
They do, and why don't you try being a little less of a pompous ass?


--
JF

On Jul 5, 10:01 am, John Fields wrote:
On Thu, 5 Jul 2007 00:00:45 -0700, "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?

---
The first example is amplitude modulation precisely _because_ of the
multiplication, while the second is merely the algebraic summation
of the instantaneous amplitudes of two waveforms.

The circuit lists I posted earlier will, when run using LTSPICE,
show exactly what the signals will look like using an oscilloscope
and, using the "FFT" option on the "VIEW" menu, give you a pretty
good approximation of what they'll look like using a spectrum
analyzer.

If you don't have LTSPICE it's available free at:

http://www.linear.com/designtools/software/

--
JF

Since your modulator version has a DC offset applied to
the 1e5 signal, some of the 1e6 signal is present in the
output, so your spectrum has components at .9e6, 1e6 and
1.1e6.

To generate the same signal with the summing version you
need to add in some 1e6 along with the .9e6 and 1.1e6.

The results will be identical and the results of summing
will be quite detectable using an envelope detector just
as they would be from the modulator version.

Alternatively, remove the bias from the .1e6 signal on
the modulator version. The spectrum will have only
components at .9e6 and 1.1e6. Of course, an envelope
detector will not be able to recover this signal,
whether generated by the modulator or summing.

....Keith