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

[craigm]

Hi Craig -

Yes, it's pretty consistent alright. It gets even more consistent as
$f1 moves closer to $f2. But you'll note that it gets much less
consistent the further the two frequencies are apart. Which is what
I've been saying. You can also see the periodicity I described.

jk

However, I still do not see anything supporting this statement.

"The period of the 'enveloped' waveform (or the arcane, beat
modulated waveform) then can be seen to vary continuously and
repetitiously over time - from 1/a at one limit to 1/b at the other.
At a particular instant in time the period does in fact equal the
average of the two.  But this is true only for an instant every
1/(a-b) seconds."

 

[isw]

No, that was indeed the claim. As a demonstration, I've
attached a variant of your original LTspice simulation.
Plot Vprod and Vsum. They are on top of each other.
Plot the FFT for each. They are indistinguishable.

-- lots o' snipping goin' on --

OK. I haven't been (had the patience to keep on) following this
discussion, so I apologize if this is totally inappropriate, but

If the statements above refer to creating that set of signals by using a
bunch of signal generators, or alternately by using some sort of actual
"modulation", the answer is, there is a very significant difference.

In the case where the set is created by modulating the "carrier" with
the low frequency, there is a very specific phase relationship between
the signals which would be essentially impossible to achieve if the
signals were to be generated independently. In fact, the only difference
between AM and FM/PM is that the phase relationship between the carrier
and the sideband set differs by 90 degrees between the two.

Isaac

 

[Keith Dysart]

-- lots o' snipping goin' on --

OK. I haven't been (had the patience to keep on) following this
discussion, so I apologize if this is totally inappropriate, but

If the statements above refer to creating that set of signals by using a
bunch of signal generators, or alternately by using some sort of actual
"modulation", the answer is, there is a very significant difference.

In the case where the set is created by modulating the "carrier" with
the low frequency, there is a very specific phase relationship between
the signals which would be essentially impossible to achieve if the
signals were to be generated independently.

All true. The simulation offered previously achieves the
required phase relationship (and more, so that the sum and
product versions can be directly compared).

In fact, the only difference
between AM and FM/PM is that the phase relationship between the carrier
and the sideband set differs by 90 degrees between the two.

I am not convinced. Can you explain? AM modulation with a single
frequency produces a single sum and difference for the sidebands
while FM has an infinite number of frequencies in the sidebands.
This does not seem like a simple phase difference.

....Keith

 

[John Fields]

---
That was my understanding, and is why I was surprised when you made
the claim, above:

"It does not matter how the .9e6, 1.0e6 and 1.1e6 are put into
the resulting signal. One can multiply 1e6 by 1e5 with a DC
offset, or one can add .9e6, 1.0e6 and 1.1e6. The resulting
signal is identical."

which I interpret to mean that three unrelated signals occupying
those spectral positions were identical to three signals occupying
the same spectral locations, but which were created by heterodyning.

Are you now saying that wasn't your claim?
---

No, that was indeed the claim. As a demonstration, I've
attached a variant of your original LTspice simulation.
Plot Vprod and Vsum. They are on top of each other.
Plot the FFT for each. They are indistinguishable.

See the simulation results.

I did not write clearly enough. The three resistors I had
in mind were: one to each voltage source and one to ground.

To get there from your latest schematic, discard the op-amp
and tie the right end of R3 to ground.

That really doesn't change anything, since no real addition will be
occurring. Consider:

f1>---[1000R]--+-->E2
|
f2>---[1000R]--+
|
f3>---[1000R]--+
|
[1000R]
|
GND>-----------+

Note that 0.75V is not equal to 1V + 1V + 1V.

E2 = (V1+V2+V3)/4 -- a scaled sum

Except for scaling, the result is the sum of the inputs.

---
LOL... Except for scaling, Mr. President, the mirror on the Hubble
would have worked the first time out.
---

Oh, yes. And cat whiskers too.

But that was not my point. Because the carrier level was not
high enough, the envelope was no longer a replica of the signal
so an envelope detector would not be able to recover the signal
(no matter how sensitive it was).

---
That's easy enough to make happen, but that's not what this is
about; it's about the out signal from a 3 input adder being
identical to the output signal from a mixer.

It seems, you want to try to prove that multiplication is tha same
as addition, with:

Version 4
SHEET 1 980 680
WIRE -1312 -512 -1552 -512
WIRE -1200 -512 -1232 -512
WIRE -1552 -496 -1552 -512
WIRE -1312 -400 -1440 -400
WIRE -1200 -400 -1200 -512
WIRE -1200 -400 -1232 -400
WIRE -768 -384 -976 -384
WIRE -976 -368 -976 -384
WIRE -1440 -352 -1440 -400
WIRE -544 -352 -624 -352
WIRE -1200 -336 -1200 -400
WIRE -1136 -336 -1200 -336
WIRE -544 -336 -544 -352
WIRE -768 -320 -912 -320
WIRE -1312 -304 -1344 -304
WIRE -1200 -304 -1200 -336
WIRE -1200 -304 -1232 -304
WIRE -1200 -288 -1200 -304
WIRE -1344 -256 -1344 -304
WIRE -912 -256 -912 -320
WIRE -544 -240 -544 -256
WIRE -464 -240 -544 -240
WIRE -544 -224 -544 -240
WIRE -1552 -144 -1552 -416
WIRE -1440 -144 -1440 -272
WIRE -1440 -144 -1552 -144
WIRE -1344 -144 -1344 -176
WIRE -1344 -144 -1440 -144
WIRE -1200 -144 -1200 -208
WIRE -1200 -144 -1344 -144
WIRE -1552 -128 -1552 -144
WIRE -912 -128 -912 -176
WIRE -544 -128 -544 -144
FLAG -1552 -128 0
FLAG -1136 -336 Vsum
FLAG -976 -368 0
FLAG -912 -128 0
FLAG -544 -128 0
FLAG -464 -240 Vprod
SYMBOL voltage -1552 -512 R0
WINDOW 3 -216 102 Left 0
WINDOW 123 0 0 Left 0
WINDOW 39 0 0 Left 0
SYMATTR Value SINE(0 .5 900 0 0 90)
SYMATTR InstName Vs1
SYMBOL voltage -1344 -272 R0
WINDOW 3 -228 104 Left 0
WINDOW 123 0 0 Left 0
WINDOW 39 0 0 Left 0
SYMATTR Value SINE(0 .5 1100 0 0 -90)
SYMATTR InstName Vs3
SYMBOL res -1216 -320 R90
WINDOW 0 -26 57 VBottom 0
WINDOW 3 -25 58 VTop 0
SYMATTR InstName Rs3
SYMATTR Value 1000
SYMBOL res -1184 -192 R180
WINDOW 0 -48 76 Left 0
WINDOW 3 -52 34 Left 0
SYMATTR InstName Rs4
SYMATTR Value 1000
SYMBOL res -1216 -416 R90
WINDOW 0 -28 61 VBottom 0
WINDOW 3 -30 62 VTop 0
SYMATTR InstName Rs2
SYMATTR Value 1000
SYMBOL res -1216 -528 R90
WINDOW 0 -32 59 VBottom 0
WINDOW 3 -30 62 VTop 0
SYMATTR InstName Rs1
SYMATTR Value 1000
SYMBOL voltage -1440 -368 R0
WINDOW 3 -210 108 Left 0
WINDOW 123 0 0 Left 0
WINDOW 39 0 0 Left 0
SYMATTR Value SINE(0 1 1000 0 0 0)
SYMATTR InstName Vs2
SYMBOL SpecialFunctions\\modulate -768 -384 R0
WINDOW 3 -66 -80 Left 0
SYMATTR InstName A1
SYMATTR Value space=1000 mark=1000
SYMBOL voltage -912 -272 R0
WINDOW 3 14 106 Left 0
WINDOW 123 0 0 Left 0
WINDOW 39 0 0 Left 0
SYMATTR InstName Vp1
SYMATTR Value SINE(1 1 100)
SYMBOL res -560 -240 R0
SYMATTR InstName Rp2
SYMATTR Value 1000
SYMBOL res -560 -352 R0
SYMATTR InstName Rp1
SYMATTR Value 3000
TEXT -1592 -560 Left 0 !.tran 0 .02 0 .3e-7

---
But, using the adder, if you change the amplitude and/or the
frequency of any input what happens to the output? The spectral
line corresponding to the changed input will change, but the lines
corresponding to the other inputs will not.

Use the multiplier and what happens if you change either the carrier
or the LO? The output lines will _all_ change even though only one
input has been changed.

On top of that, even if the output spectrum of the adder is made to
look like the output spectrum of the mixer, the phase relationship
between the outputs of the two will be different unless
extraordinary care is taken to make them the same and, even then, if
information is impressed on the adder's center frequency it will not
convey to the "sidebands".

 

[[email protected]]

Beats are actually a well known phenomenon in physics and actually they
require no mixing at all. In fact all that is required is a very linear
operation of addition. A quick check of google turns up many
explanations of how two aubible frequencies can interfere in a very
linear fashion and result in beats. In fact beats don't require a human
head involvement in any way. Wikipedia has a pretty good description
with a trig identity for the math hungry.

As the identity shows, when two sin waves are added (linearly) the
result is equivalent to the average of the two tones with an amplitude
that varies at the frequency of the difference between the two tones.

About the amplitude warble, this can easily be demonstrated by anyone
with an actual volume knob ( surprisingly rare these days ). It's
possible to vary the volume at frequencies well under 20hz and hearing
the changes even with a human ear that can't hear a tone at frequencies
under 20hz.

okay, gentleman

i just spent 15 minutes typing my most recent response just to lose it
somehow?

condensed and summarized

high/low frecency cell phones will be the next frontier

correct me so we can define further, the limits of our existance

lets form a group called good, goood, goooooood, vibrations

anyone willing to bank on this?

 

[Jim Kelley]

However, I still do not see anything supporting this statement.

"The period of the 'enveloped' waveform (or the arcane, beat
modulated waveform) then can be seen to vary continuously and
repetitiously over time - from 1/a at one limit to 1/b at the other.
At a particular instant in time the period does in fact equal the
average of the two. But this is true only for an instant every
1/(a-b) seconds."

'You can lead a horse to water, but you can't make him drink.'

jk

 

[Hein ten Horn]

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.

I've once listened to the first five harmonics of a
powerful medium wave transmitter (400 kW) at
a distance of some 300 m.
All harmonics gave normal audio; no strange
switching effects (Sony ICF-7600D).

What I'd like to know is if in such an 'experiment'
it can be excluded that (some of) these signals are
generated by the receiver itself.

gr, Hein

 

[Hein ten Horn]

I suppose so; I've spent over fifteen years poking around in the
entrails of MPEG...

Ever learned, unfortunately seldom used.
What can radio hobbyists do with Fourier transforms
nowadays? (Nowadays, for aids and appliances like
software and spectrum analysers take over some work.)
If somebody could provide some examples I'd be grateful.
Thanks.

gr, Hein

 

[Hein ten Horn]

I've posted nothing like that, so if you have graphics which support
your position I'm sure we'd all be happy to see them.

Oops, I'm sorry Keith!
http://keith.dysart.googlepages.com/radio5

Retrospectively viewed: not the term "linear".

gr, Hein

 

[Hein ten Horn]

So where did you apply the laws of physics?
You said, "It's just a matter of applying the laws of
physics." Then you did that for the single sine case. Where
is your physics calculation for the two sine case?
Where is the expression for 'f' as in your first
example? Put x(t) = 2 * cos(2pi 2 t) * sin(2pi 222 t)
in your calculations and tell me what you get
for 'f'.

And how do you get 222 Hz out of
cos(2pi 2 t) * sin(2pi 222 t)
Why don't you say it is 2 Hz? What is your
law of physics here? Always pick the bigger
number? Always pick the frequency of the
second term? Always pick the frequency of
the sine?
What is "the frequency" of
cos(2pi 410 t) * cos(2pi 400 t)


What is "the frequency" of
cos(2pi 200 t) + cos(2pi 210 t) + cos(2pi 1200 t) + cos(2pi 1207 t)



How do you determine amplitude?
What's the math (or physics) to derive
amplitude?

Well, I think I've had it. A 'never' ending story.
Too much to straighten out. Too much comment
needed. Questions moving away from the subject.
No more indistinguishable close frequencies.
No audible beat, no slow changing envelopes.

Take a plot, use a high speed camera or whatever
else and see for yourself the particle is vibrating at a
period in accordance with 222 Hz. In my view I've
sufficiently underpinned the 222 Hz frequency.
If you disagree, then do the job. Show your
frequencies and elucidate them. (No hint needed,
I guess.)

gr, Hein

 

[Michael A. Terrell]

'You can lead a horse to water, but you can't make him drink.'

"You can lead a troll to information, but you can't make him think."


--
Service to my country? Been there, Done that, and I've got my DD214 to
prove it.
Member of DAV #85.

Michael A. Terrell
Central Florida

 

[John Fields]

Indeed. We would hear f3 and f4 if they were in fact there.


The term is commonly used in describing the results of interference in
time, as well as for mixing.


Perhaps you're confusing log(sin(a)+sin(b)) with
log(sin(a))+log(sin(b)).

---
Perhaps, but I don't think either of those is correct, since for
mixing to occur (AIUI, for sidebands to be generated) the sine waves
themselves must be multiplied at the lowest level of the equation
instead of added.

That is, the solution of


log(sin(a)+sin(b))


will describe the numerical value of the logarithm of the vector sum
of two sine waves, and since the addition created no sidebands, the
output of the circuitry providing the logarithmic transfer function
will only be the instantaneous value of the logarithm of the vector
sum of the amplitudes of both signals.

Similarly,


log(sin(a))+log(sin(b))


describes the addition of the logarithm of the amplitude of sin(a)
to the logarithm of the amplitude of sin(b), which still produces
only a sum.

That is, no sidebands.
---

If you don't mind me asking, where did you get this notion about the
ears creating sidebands?

---
Well, whether I mind or not it seems you've asked anyway, so your
concern for my sensitivity is feigned.

That, coupled with your relegating it to being a "notion", seems to
be designed to discredit the hypothesis, offhandedly, and make me
work against a headwind in order to prove it valid, with you being
the negative authoritarian blowhard detractor.

If you're really interested in the subject I'll be happy to discuss
it with you if you can keep your end of the discussion objective and
free from pejorative comments.

Otherwise, piss off. ;^) <-- Note tongue-in-cheek smiley,

 

[Michael A. Terrell]

I've once listened to the first five harmonics of a
powerful medium wave transmitter (400 kW) at
a distance of some 300 m.
All harmonics gave normal audio; no strange
switching effects (Sony ICF-7600D).

What I'd like to know is if in such an 'experiment'
it can be excluded that (some of) these signals are
generated by the receiver itself.

That much power that close to the receiver? Its a wonder you didn't
destroy the receiver's frontend.


--
Service to my country? Been there, Done that, and I've got my DD214 to
prove it.
Member of DAV #85.

Michael A. Terrell
Central Florida

 

[Ron Baker, Pluralitas!]

---
Well, I'm just back from the Panama Canal Society's 75th reunion and
I haven't read through the rest of the thread, but it case someone
else hasn't already pointed it out to you, it seems you've missed
the point that a non-linear detector, (the human ear, for example)
when presented with two sinusoidal carriers, will pass the two
carrier frequencies through, as outputs, as well as two frequencies
(sidebands) which are the sum and difference of the carriers.

The human auditory system has many components,
some linear and some not. One must consider which
component is in play when considering whether there
is mixing.
As a first order approximation: the cochlea is a continous
array of resonators that separates the frequency components
the incoming signal. That is pretty linear.
Then the system assesses the amplitudes of the
various separated components. Assessing amplitude
is a nonlinear process.

The cochlea's ability to separate frequencies is not perfect.
If two frequency components are too close the
cochlea is not able to separate them before determining
amplitude. In which case intermodulation occurs in
detecting amplitude and thus there is a 'beat'.

If a 300 Hz tone and a 400 Hz tone are coming in then
the cochlea can separate them into independent areas
and assess their amplitudes independently. No beat.
If the two tones are too close, say 400 Hz and 410
Hz the cochlea can't separate them into separate
areas and assesses the amplitude of the sum of the
two tones. Since amplitude detection is nonlinear
there is intermodulation in that case and thus a beat.

To do amplitude detection the ear does something
like take only the positive half of the
signal, or take the positive absolute value of the
signal or square the signal. Then it
averages it (or otherwise lowpass it).
The first step is nonlinear. It produces intermodulation
if there is more than one frequency component
present in the band of interest.

With a single sine wave input the nonlinear
part of the amplitude detection gives a DC term and
various harmonics of the sine wave. The averaging
filter filters out all the harmonics and leaves
the DC 'amplitude' value.

If there are two frequencies close enough that they
both get into the same amplitude detector
then the nonlinearity of amplitude detection
results in intermodulation.
That gives a DC and a sum and a difference
frequency and harmonics. The averaging lets only
the DC and the difference frequency through. The
difference frequency is the beat.

Thus two tones separated sufficiently in frequency
produce no beat. Two tones within 20 Hz or
so produce a difference frequency beat but no
sum frequency tone.

---
No, it doesn't.

Since the response of the ear is non-linear in amplitude it has no
choice _but_ to be a mixer and create sidebands.

Only if the tones are not separated in frequency
by the cochlea first.

What you see on an oscilloscope are the time-varying amplitude
variations caused by the linear vector summation of two signals
walking through each other in time, and what you see on a spectrum
analyzer is the two spectral lines caused by two signals adding, not
mixing. If you want to see what happens when the two signals hit
the ear, run them through a non-linear amp before they get to the
spectrum analyzer and you'll see at least the two original signals
plus their two sidebands.

Actually the nonlinear part is in the amplitude detection
which is present toward the end of the chain in both human
hearing and in spectrum analyzers.

<snip>

 

[Ron Baker, Pluralitas!]

Well, I think I've had it. A 'never' ending story.
Too much to straighten out. Too much comment
needed. Questions moving away from the subject.
No more indistinguishable close frequencies.
No audible beat, no slow changing envelopes.

Take a plot, use a high speed camera or whatever
else and see for yourself the particle is vibrating at a
period in accordance with 222 Hz. In my view I've
sufficiently underpinned the 222 Hz frequency.
If you disagree, then do the job. Show your
frequencies and elucidate them. (No hint needed,
I guess.)

gr, Hein

Bravo. Well done. What an impressive
display of applying the laws of physics.
Newton, Euler, Gauss, and Fourier have nothing
on you.

 

[isw]

That much power that close to the receiver? Its a wonder you didn't
destroy the receiver's frontend.

That particular receiver doesn't have much of a "front end"; diodes
(with protection) and straight into the first mixer. No RF stage, tuned
or otherwise.

Isaac

 

[Michael A. Terrell]

That particular receiver doesn't have much of a "front end"; diodes
(with protection) and straight into the first mixer. No RF stage, tuned
or otherwise.

It can exceed the PIV of the protection diodes and cause them to
short, or explode. That crappy Sony design is where the harmonics came
from. The diodes, (or any other semiconductor) with enough RF can
generate a lot of spurious signals. It can even come from a rusty joint
in the area.


--
Service to my country? Been there, Done that, and I've got my DD214 to
prove it.
Member of DAV #85.

Michael A. Terrell
Central Florida

 

[Jim Kelley]

log(sin(a))+log(sin(b))


describes the addition of the logarithm of the amplitude of sin(a)
to the logarithm of the amplitude of sin(b), which still produces
only a sum.

That is, no sidebands.

log(x)+log(y)=log(x*y)

jk

 

[Hein ten Horn]

It can exceed the PIV of the protection diodes and cause them to
short, or explode. That crappy Sony design is where the harmonics came
from. The diodes, (or any other semiconductor) with enough RF can
generate a lot of spurious signals. It can even come from a rusty joint
in the area.

Is the ICF-SW7600GR significantly better performing
than the ICF-7600D on this?

gr, Hein

 

[Hein ten Horn]

Bravo. Well done. What an impressive
display of applying the laws of physics.
Newton, Euler, Gauss, and Fourier have nothing
on you.

Thanks for your constructive contributions.

gr, Hein