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

[isw]

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,

And when the two frequencies are very close to being equal, the spectrum
analyzer will only be able to resolve one frequency, and it will vary
between a maximum of amplitude and zero at a rate which is precisely
related to the difference between the two frequencies. If you get an
analyzer with finer resolution, I can always reduce the difference
frequency sufficiently to produce the described effect, which does not
in any way require a nonlinear process.

---
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.

OK, but off subject. We were discussing whether a "zero beat" while
tuning an instrument requires a non-linear process (i.e. "real"
modulation. It does not.

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

Yup. And since the beat is easily observable using instrumentation of
measurably high linearity, whether or not ears have some IM is of no
matter. In fact, I agree that IM is produced in ears; just not at
significant levels for anything short of pathological SPL -- upwards of
120 dB, say.

Yes. The 180 degree situation is just a special case that very obviously
produces a change in output level in a linear environment. IOW it shows
that a linear combination of two nearly equal tones will cause a "beat"
in amplitude.

---
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.

For your argument to be true, there should be harmonies that can be
shown to "sound better" when played at a lower SPL (or better,
auditioned through a passive acoustical attenuator). Avoiding
pathological sound levels, I am not aware of any such thing ever being
demonstrated. Do you have any examples?

In fact, I believe it is the case that in "musical frequency space"
virtually every IM product of significance, regardless of where it
arises, is considered unpleasant.


And I still don't think you have adequately explained the things I was
referring to.

Do you have any references?

Isaac

 

[isw]

Have you ever actually observed this effect?

Sure. (In a previous life, I designed AM and FM transmitters for RCA).
Just get a short-wave radio, locate yourself fairly close to a standard
AM transmitter, and tune to the harmonics. you'll find, in every case,
that the audio sounds just the same as if you were listening to the
fundamental.

Works for FM, too, but the situation is somewhat more complex.

Isaac

 

[isw]

---
Regardless of the frequency response characteristics of the ear, its
response to amplitude changes _is_ logarithmic.

For instance:

CHANGE APPARENT CHANGE
IN SPL IN LOUDNESS
---------+------------------
3 dB Just noticeable

5 dB Clearly noticeable

10 dB Twice or half as loud

20 dB 4 times or 1/4 as loud

---


---
You missed my point, which was that in a mixer (which the ear is,
since its amplitude response is nonlinear) as the two carriers
approach each other the difference frequency will go to zero and the
sum frequency will go to the second harmonic of either carrier,
making it largely appear to vanish into the fundamental.
---


---
But the resultant waveform will be distorted and contain additional
spectral components if that summation isn't done linearly. This is
precisely what happens in the ear when equal changes in SPL don't
result in equal outputs to the 8th cranial nerve.
---


---
That's not true. In AM we have two pitches, but one is used to
control the amplitude of the other, which generates the sidebands.
---


---
No, it's much simpler since you haven't created the sum and
difference frequencies and placed them in the spectrum.
---


---
"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.

Absolutely correct. And as that "simple algebraic sum" varies with time,
which it will as the phases of the two signals slide past each other, it
produces the tuning "beat" we've been talking about. Totally linear.

Isaac

 

[isw]

Bob M.

(Personal message; sorry, but e-mail wouldn't work.)

Hi, Bob. It's been a long time since we used to correspond on rec.audio.
Nice to hear from you.

Isaac

 

[John Fields]

Hi John -

Given two sources of pure sinusoidal tones whose individual amplitudes
are constant, is it your claim that you have heard the sum of the two
frequencies?

---
I think so.

A year or so ago I did some casual experiments with pure tones being
fed simultaneously into individual loudspeakers to which I listened,
and I recall that I heard tones which were higher pitched than
either of the lower-frequency signals. Subjective, I know, but
still...

A microphone with an amplitude response following that of the human
ear might do better.

Interestingly, this afternoon I did the zero-beat thing with 1kHz
being fed to one loudspeaker and a variable frequency oscillator
being fed to a separate loudspeaker, with me as the detector.

I also connected each oscillator to one channel of a Tektronix
2215A, inverted channel B, set the vertical amps to "ADD", and
adjusted the frequency of the VFO for near zero beat as shown on the
scope.

Sure enough, I heard the beat even though it came from different
sources, but I couldn't quite get it down to DC even with the
scope's trace at 0V.

Close, though, and as it turned out it wasn't the zero output
amplitude as shown by the scope which made the difference, it was
the amplitude of the signals which got to my ear(s). As fate would
have it, I have two ears, with some distance between them, so
perfect cancellation in one left some uncancelled signal in the
other, obviating what otherwise might have been perfect silence.
Except, perhaps, for the heterodynes.

Anyway, I'm off to the 75th reunion of the Panama Canal Society and
the 50th reunion of the Cristobal High School Class of '57 in
Orlando, so I'll see y'all when I get back on Sunday, GLW.

 

[Ron Baker, Pluralitas!]

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

That doesn't explain why the effect would
come and go.
But once again you have surprised me.
Your explanation of the non-multiplied sidebands,
while qualitative and incomplete, is sound.
It looks to me that the tripple frequency sidebands
are there but the basic sidebands dominate.
Especially at lower modulation indexes.

 

[Ron Baker, Pluralitas!]

I'm sure there's more than one way to do it, but I feel certain that any

Which of them is linear?

 

[John Fields]

Sorry, John - while the ear's amplitude response IS nonlinear, it
does not act as a mixer.

---
Sorry, Bob, If the ear's amplitude response is nonlinear, it has no
choice _but_ to act as a mixer.
---

"Mixing" (multiplication) occurs when
a given nonlinear element (in electronics, a diode or transistor, for
example) is presented with two signals of different frequencies.
But the human ear doesn't work in that manner - there is no single
nonlinear element which is receiving more than one signal.

---
Not true.

Just look at the tympanic membrane, for example.

Consider it a drumhead stretched across a restraining ring and it
becomes obvious that the excursion of its center with respect to the
pressure exerted on its surface won't be constant for _any_ range of
sound pressure levels it experiences.

Consequently, when it's hit with two different frequencies, its
displacement will vary non-linearly with the pressures they exert
and sidebands will be generated.

 

[Ron Baker, Pluralitas!]

On 7/4/07 8:42 PM, in article [email protected],
"Ron


On 7/4/07 10:16 AM, in article
[email protected],


On 7/4/07 7:52 AM, in article
[email protected],
"Ron

<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......

What is the difference between AM and DSB?

 

[Ron Baker, Pluralitas!]

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."

Is that for both cases?

Where did the 1 MHz component in your
result come from?

 

[John Smith I]

Where did the 1 MHz component in your
result come from?

From your original question; hell to get old and experience
Alzheimers', huh?

What, you have never seen rf in a modulation envelope before?

JS

 

[John Smith I]

Where did the 1 MHz component in your
result come from?

From your original question; hell to get old and experience
Alzheimers', huh?

What, you have never seen rf in a modulation envelope before?

JS

 

[Ron Baker, Pluralitas!]

From your original question; hell to get old and experience Alzheimers',
huh?

Says the fellow who hit the send button twice.

What, you have never seen rf in a modulation envelope before?

JS

What is the difference between AM and DSB?

 

[Brenda Ann]

Says the fellow who hit the send button twice.


What is the difference between AM and DSB?

Both are AM.

Standard AM is DSB with full carrier

SSB with and without carrier/reduced carrier are also both AM.

 

[Ian Jackson]

Sure. (In a previous life, I designed AM and FM transmitters for RCA).
Just get a short-wave radio, locate yourself fairly close to a standard
AM transmitter, and tune to the harmonics. you'll find, in every case,
that the audio sounds just the same as if you were listening to the
fundamental.

Works for FM, too, but the situation is somewhat more complex.

Isaac

Yes, I think I'm missing something obvious here. Let me have another
think (aloud)....

If you FM modulate a 1MHz carrier with a 1kHz tone, you get a spectrum
consisting of a 1MHz carrier in the middle, plus a family of sidebands
harmonically spaced at 1kHz, 2kHz, 3kHz etc (to infinity).

[One obvious difference between the FM spectrum and that of an AM signal
is that the AM spectrum only has sidebands at 1kHz, and the amplitude of
the carrier does not vary with modulation depth. With the FM signal, the
amplitudes of the carrier and each pair of sideband do vary with the
amount of modulation.]

So, if you FM modulate a 1MHz carrier with a 1kHz tone, you get a 1Mhz
carrier and the family of 1kHz 'harmonic' sidebands. Demodulated it, and
you hear a 1kHz tone.

Now double the signal to 2MHz. You might expect the sidebands to appear
at 2, 4, 6kHz etc. However, if you demodulated the signal, you still
hear the original 1kHz tone (which should now be double the amplitude of
the original 1MHz signal). You definitely don't hear 2kHz. This at least
proves that the original 1kHz FM modulation is preserved during the
doubling process.

So, would it be simplistically correct to consider that, during the
doubling process, the original family of 1kHz sidebands also mix with
the new 2MHz carrier, and create a family of 1kHz sidebands centred on
2MHz?

Or, alternatively, does the original family of 1kHz sidebands (on the
1MHz signal) mix with the original 1MHz carrier to produce a family of
baseband 1kHz 'harmonic' signals, and these then mix with the new 2MHz
carrier to create the family of 1kHz sidebands centred on 2MHz?

Or are both equally valid (invalid)?

A possible flaw in my simplistic 'explanations' is that I would have
thought that, while the doubling process occurs as a result of 2nd-order
intermodulation, surely the two-step process in both 'explanations' is
really 4th-order intermodulation?

However, my explanations work equally well (?) for FM and AM.

Am I wrong, or am I wrong?

Ian.
--

 

[Don Bowey]

On 7/4/07 8:42 PM, in article [email protected],
"Ron


On 7/4/07 10:16 AM, in article
[email protected],


On 7/4/07 7:52 AM, in article
[email protected],
"Ron

<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......

What is the difference between AM and DSB?

AM is a process. DSB (double sideband), with carrier, is it's most simple
result. DSB without carrier (suppressed carrier dsb) requires using, at
least, a balanced mixer as the AM multiplier.

 

[Don Bowey]

(snip)

What is the difference between AM and DSB?

You asked this identical question in another post, and it was answered.

 

[John Smith I]

...
What is the difference between AM and DSB?

This is your last question of 1001 questions:

Since the information (modulation/voice) is repeated in both sides of
the modulation envelope in am, ssb "chops off" one half of the envelope.
The receiver is responsible for "mirroring" the other and reproducing
the information on that end--this allows for almost doubling the
effective range of am.

Get off the drugs, get a job and become a productive citizen!

JS

 

[isw]

On 7/5/07 12:00 AM, in article [email protected],


On 7/4/07 8:42 PM, in article [email protected],
"Ron


On 7/4/07 10:16 AM, in article
[email protected],


On 7/4/07 7:52 AM, in article
[email protected],
"Ron

<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......

What is the difference between AM and DSB?

AM is a process. DSB (double sideband), with carrier, is it's most simple
result. DSB without carrier (suppressed carrier dsb) requires using, at
least, a balanced mixer as the AM multiplier.

And requires, for proper reception, that a carrier be recreated at the
receiver which has not only the amplitude of the original, but also its
exact phase. Absent some sort of "pilot" to get things synchronized,
this makes reception very difficult.

Isaac

 

[Don Bowey]

On 7/5/07 12:00 AM, in article [email protected],


On 7/4/07 8:42 PM, in article [email protected],
"Ron


On 7/4/07 10:16 AM, in article
[email protected],


On 7/4/07 7:52 AM, in article
[email protected],
"Ron

<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......

What is the difference between AM and DSB?

AM is a process. DSB (double sideband), with carrier, is it's most simple
result. DSB without carrier (suppressed carrier dsb) requires using, at
least, a balanced mixer as the AM multiplier.

And requires, for proper reception, that a carrier be recreated at the
receiver which has not only the amplitude of the original,

There is no need at all to match the carrier amplitude of the original
signal. You can use an excessively high carrier injection amplitude with no
detrimental affect, but if the injected carrier is too little, the
demodulated signal will be over modulated and sound distorted.

but also its exact phase.

Exact, not required. The closer the better, however.