AM electromagnetic waves: 20 KHz modulation frequencyonanastronomically-lowcarrier frequency
 

Ron Baker, Pluralitas! wrote:
...
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?




Lots of BS here ...

The signal ends up looking like a 1Mhz signal contained within the walls
of the .1Mhz signal ... and simply said, the 1Mhz signal is enclosed in
the envelope of a .1Mhz signal--the "walls" of this .1Mhz signal being
referred to as "sidebands."

JS

AM electromagnetic waves: 20 KHz modulation frequencyonanastronomically-low carrier frequency
 

"John Fields" wrote in message
...
On Thu, 5 Jul 2007 00:00:45 -0700, "Ron Baker, Pluralitas!"

snip


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

Is there multiplication in DSB? (double sideband)

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,

I think you did
(sin[] + 1) * (sin[] + 1)
not
sin() * sin()

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/

Yes, I have LTSPICE. It is pretty good.



--
JF

AM electromagnetic waves: 20 KHz modulationfrequencyonanastronomically-low carrier frequency
 

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

AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
 

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

"isw" wrote in message
...
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

Please elaborate. I am so eager to hear the
explanation.

The sidebands only show up because there is a rate of change of the
carrier -- amplitude or frequency/phase, depending; they aren't
separate, stand-alone signals. Since the rate of change of the amplitude
of the second harmonic is identical to that of the fundamental, the
sidebands show up the same distance away, not twice as distant.

Isaac

AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
 

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

"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?

I'm sure there's more than one way to do it, but I feel certain that any
competently designed unit will not add any signals of its own to what it
is being used to analyze.

Isaac

AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
 

In article ,
John Fields wrote:

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.

That would suggest that there could be "low IM" instruments which would
be very difficult to tune, since they would produce undetectably small
beats; in fact that does not happen. It would also suggest that it would
be difficult or impossible to create beats between two
very-low-distortion signal generators, which is also not the case.

Other than the nonlinearity of the air (which is very small for
"ordinary" SPL, there's no mechanism to cause IM between two different
instruments, although beats are still generated. The beat is simply a
vector summation of two nearly identical signals; no modulation needs to
take place.

Or consider this: At true "zero beat" with the signals exactly 180
degrees out, no energy is avaliable for any non-linear process to act on.

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

Well, no, mostly they don't, until you get to really high SPL.

and why don't you try being a little less of a pompous ass?

Exposing claims to conditions they have difficulty with is a good way to
understand why those claims are invalid -- so long as the claimant
actually explains what's going on, and doesn't just make up answers that
fit the previously stated beliefs.

Isaac

AM electromagnetic waves: 20 KHz modulation frequencyonanastronomically-low carrier frequency
 

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

"John Fields" wrote in message
...
On Thu, 5 Jul 2007 00:00:45 -0700, "Ron Baker, Pluralitas!"

snip


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

Is there multiplication in DSB? (double sideband)

Yes, and in fact, that multiplication referred to above creates a
DSB-suppressed-carrier signal. To get "real" AM, you need to add back
the carrier *at the proper phase*.

FWIW, if you do the multiplication and then add back a carrier which is
in quadrature (90 degrees) to the one you started with, what you get is
phase modulation, a "close relative" of FM, and indistinguishable from
it for the most part.

A true DSB-suppressed carrier signal is rather difficult to receive
precisely because of the absolute phase requirement; tuning a receiver
to the right frequency isn't sufficient -- the phase has to match, too,
and that's really difficult without some sort of reference.

A SSB-suppressed carrier signal is a lot simpler to detect because an
error in the frequency of the regenerated carrier merely produces a
similar error in the frequency of the detected audio (the well-known
"Donald Duck" effect).

Isaac

AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-lowcarrier frequency
 

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


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

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.

But it is true.

The human ear has a logarithmic amplitude response and the beat note
(the difference frequency) is generated there.

The ear does happen to have a logarithmic amplitude response as a
function of frequency, but that has nothing to do with this
phenomenon. (It relates only to the aural sensitivity of the ear at
different frequencies.) What the ear responds to is the sound pressure
wave that results from the superposition of the two waves. The effect
in air is measurable with a microphone as well as by ear. The same
thing can be seen purely electrically in the time domain on an
oscilloscope, and does appear exactly as Ron Baker described in the
frequency domain on a spectrum analyzer.

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.

The ear does not hear the sum of two waves as the sum of the
frequencies, but rather as the sum of their instantaneous amplitudes.
When the pitches are identical, the instantaneous amplitude varies
with time at the fundamental frequency. When they are identical and
in-phase, the instantaneous amplitude varies at the fundamental
frequency with twice the peak amplitude.

When the two pitches are different, the sum of the instantaneous
amplitudes at a fixed point varies with time at a frequency equal to
the difference between pitches. This does have an envelope-like
effect, but it is a different effect than the case of amplitude
modulation. In this case we actually have two pitches, each with
constant amplitude, whereas with AM we have only one pitch, but with
time varying amplitude.

The terms in the trig identity are open to a bit of misinterpretation.
At first glance it does look as though we have a wave sin(a+b) which
is being modulated by a wave sin(a-b). But what we have is a more
complex waveform than a pure sine wave with a modulated amplitude.
There exists no sine wave with a frequency of a+b in the frequency
spectrum of beat modulated sine waves a and b. As has been noted
previously, this is the sum of two waves not the product. I think it
can also help not to inadvertantly switch back and forth from time
domain to frequency domain when thinking about these things.

ac6xg

AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
 

On Thu, 05 Jul 2007 10:00:33 -0700, isw wrote:

In article ,
John Fields wrote:

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.

That would suggest that there could be "low IM" instruments which would
be very difficult to tune, since they would produce undetectably small
beats;

---
Not at all. Since tuning is the act of comparing the acoustic
output of a musical instrument to a reference, the "IM" of the
instrument would be relatively unimportant, with a totally linear
device giving the best output. For tuning, anyway. Then, the
output of the instrument and the reference would be mixed, in the
ear, with zero beat indicating when the instrument's output matched
the reference.
---

in fact that does not happen. It would also suggest that it would
be difficult or impossible to create beats between two
very-low-distortion signal generators, which is also not the case.

---
That is precisely the case. Connect the outputs of two zero
distortion signal generators so they add, like this, in a perfect
opamp, (View in Courier)


+-----+ +--------+ +---------+ +-----+
| SG1 |---[R]--+----[R]---+--| POWER |--| SPEAKER |--| EAR |
+-----+ | | | AMP | +---------+ +-----+
| +V | +--------+
+-----+ | | |
| SG2 |---[R]--+----|-\ | +----------+
+-----+ | --+--| SPECTRUM |
+----|+/ | ANALYZER |
| | +----------+
GND -V

and the spectrum analyzer will resolve the signals as two separate
spectral lines, while the ear will hear all four signals, if f1 + f2
is within the range of audibility.
---

Other than the nonlinearity of the air (which is very small for
"ordinary" SPL, there's no mechanism to cause IM between two different
instruments, although beats are still generated. The beat is simply a
vector summation of two nearly identical signals; no modulation needs to
take place.

---
I understand your point and, while it may be true, the
incontrovertible fact remains that the ear is a non-linear detector
and will generate sidebands when it's presented with multiple
frequencies.

What remains to be done then, is the determination of whether the
beat effect is due to heterodyning, or vector summation, or both.
---

Or consider this: At true "zero beat" with the signals exactly 180
degrees out, no energy is avaliable for any non-linear process to act on.

---
Or any other process for that matter, except the conversion of that
acoustic energy into heat. That is, with the signals 180° out of
phase and precisely the same amplitude, didn't you mean?
---


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

Well, no, mostly they don't, until you get to really high SPL.

---
That's not true. Why do you think some harmonies sound better than
others? Because the heterodyning occurring at those frequencies
causes complementary sidebands to be generated which sound good, and
that happens at most SPL's because of the ear's nonlinear
characteristics.
---

and why don't you try being a little less of a pompous ass?

Exposing claims to conditions they have difficulty with is a good way to
understand why those claims are invalid -- so long as the claimant
actually explains what's going on, and doesn't just make up answers that
fit the previously stated beliefs.

---
I wasn't talking about making and/or debating claims, I was talking
about your smartass "Now you get to explain" and "Then go on to show
why" cracks.


--
JF

AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
 

On Jul 5, 7:15 pm, John Fields wrote:
Regardless of the frequency response characteristics of the ear, its
response to amplitude changes _is_ logarithmic.

It seems clear that the brain's perception of amplitude changes
is logarithmic. It is not so obvious that this means there
exists a non-linear amplitude response in the ear such that
harmonics are generated.

I suggest the following alternative explanations:
- the nerve signals from the ear to the brain could have a
linear response but the low level driver in the brain
converts it to a logarithmic response for later processing.
- the nerves from the ear could have a logarithmic response
- the AGC which limits the signal applied to the detectors in
the ear by tightening muscles in the bones, could have a
logarithmic response. The cycle by cycle response in the
ear could be linear.

The actual detector (if I recall my physiology correctly)
consists of little hairs that actually detect different
frequencies so that what is presented to the low level
drivers is actually a spectrum, not the sound waveform.

A non-linear amplitude response in these hairs would not
produce inter-mod but would be preceived as non-linear.

It is possible that the eardrum and bones connecting to
the cochlea exhibit a non-linear response and are
capable of generating inter-mod, but this is not
proven just because the system has an apparent logarithmic
response at the point of perception.

Is there other evidence that the ear is non-linear before
separating the signal into its component frequencies and
therefore can generate inter-mod?

"Beat modulated" ??? LOL, if you're talking about the linear
summation of a couple of sine waves, then there is _no_ modulation
of any type taking place and the instantaneous voltage (or whatever)
out of the system will be the simple algebraic sum of the inputs
times whatever _linear_ gain there is in the system at that instant.

Real modulation requires multiplication, which can be done by mixing
two signals in a nonlinear device and will result in the output of
the original signals and their sum and difference frequencies.

A 4 quadrant multiplier will leave no trace of the original
two frequencies, only the sum and difference will be present
in the spectrum. This could equally well have been generated
by adding the two frequencies present in the spectrum. If
the two frequencies in the spectrum are close, there will
be an observable envelope that will be perceived as the
sound rising and falling in amplitude. There is no need
for a non-linear response for this to occur.

Not that this proves there is not one, but the existence
of the effect does not prove that there is one.

....Keith