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

[Ron Baker, Pluralitas!]

Hint: Modulation is a "rate effect".

Isaac

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

 

[Ron Baker, Pluralitas!]

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.

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?

 

[John Fields]

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?

---
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/

 

[John Fields]

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.

 

[Keith Dysart]

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?

---
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/

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

 

[John Smith I]

...
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

 

[Ron Baker, Pluralitas!]

On Thu, 5 Jul 2007 00:00:45 -0700, "Ron Baker, Pluralitas!"

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.

 

[Don Bowey]

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......

(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

 

[torbjorn.ekstrom]

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




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

modern Spectrum analyzer have different measurement methode, peak, min
peak, max peak, averange, RMS and nowday using DSP to analyze complex
modulation as WCDMA, GSM etc.


depend of model and how much money you vill spend, linerarity is around
75 to 95 dBc between carrier and intermodulation in two carrier test.


High linearity is a importent factor in using of spectum analyser.

 

[isw]

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

 

[isw]

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


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

 

[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; 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.

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

 

[isw]

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

 

[Jim Kelley]

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

 

[John Fields]

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?
---

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.

 

[John Fields]

But it is true.


The ear does happen to have a logarithmic amplitude response as a
function of frequency, but that has nothing to do with this
phenomenon.

---
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

---

(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 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.

---
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.
---

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.

---
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.
---

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.

---
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.
---

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.

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

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.

---
"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.

 

[Rich Grise]

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.

Have you ever actually observed this effect?

Thanks,
Rich

 

[Jim Kelley]

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.

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?

ac6xg

 

[Keith Dysart]

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

 

[Bob Myers]

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.

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

Frequency discrimination in the ear occurs through the resonant
frequencies of the 20-30,000 fibers which make up the basilar
membrane within the cochlea. Each fiber responds only to those
tones which are at or very near its resonant frequency. While
the response of each fiber to the amplitude of the signal is nonliner,
no mixing occurs because each responds, in essence, only to a
single tone. A model for the hearing process might be 30,000 or
so non-linear meters, each seeing the output of a very narrow-band
bandpass filter covering a specific frequency within the audio
range. There is clearly no mixing, at least as the term is commonly
used in electronics, going on in such a situation, even though there
is non-linearity in some aspect of the system's response.

Audible "beats" are perceived not because there is mixing going on
within the ear, but instead are due to cycles of constructive and
destructive
interference going on in the air between the two original tones.

Bob M.