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

[Hein ten Horn]

Jim Kelley wrote

Under the stated conditions there is no sine wave oscillating at 222 Hz.
The wave has a complex shape and contains spectral components at two
distinct frequencies (neither of which is 222Hz).

Not a pure sine oscillation (rather than wave), but a near sine
oscillation at an exact period of 1/222 s. The closer the source
frequenties, the better the sine fits a pure sine. Thus if you
wish to get a sufficient near harmonic oscillation, conditions like
"slow changing envelope" are essential.

The particle also does not average the two frequencies.

Hmm, let's examine this.
From the two composing oscillations you get the overall
displacement:
y(t) = sin(2 pi 220 t) + sin(2 pi 224 t)
From the points of intersection of y(t) at the time-axes you
can find the period of the function, so examine when y(t) = 0.
sin(2 pi 220 t) + sin(2 pi 224 t) = 0
(..)
(Assuming you can do the math.)
(..)
The solutions are:
t = k/(220+224) with k = 0, 1, 2, 3, etc.
so the time between two successive intersections is
Dt = 1/(220+224) s.
With two intersections per period, the period is
twice as large, thus
T = 2/(220+224) s,
hence the frequency is
f = (220+224)/2 = 222 Hz,
which is the arithmetic average of both composing
frequencies.

The waveform which results from the sum of two pure sine waves is not a pure
sine wave, and therefore cannot be accurately described at any single
frequency.

As seen above, the particle oscillates (or vibrates) at 222 Hz.
Since the oscillation is non-harmonic (not a pure sine),
it needs several harmonic oscillations (frequencies,
here 220 Hz and 224 Hz) to compose the oscillation at 222 Hz.

Matter would move in the same way the sound pressure wave does,

To be precise, this is nonsense, but I suspect you're trying
to state somewhat else, and since I'm not able to read your
mind today, I skip that part.

the amplitude of which is easily plotted versus time using Mathematica,
Mathcad, Sigma Plot, and even Excel. I think you should still give that a
try.

No peculiarities found.

gr, Hein

 

[Jim Kelley]

Hmm, let's examine this.
From the two composing oscillations you get the overall
displacement:
y(t) = sin(2 pi 220 t) + sin(2 pi 224 t)
From the points of intersection of y(t) at the time-axes you
can find the period of the function, so examine when y(t) = 0.
sin(2 pi 220 t) + sin(2 pi 224 t) = 0
(..)
(Assuming you can do the math.)
(..)
The solutions are:
t = k/(220+224) with k = 0, 1, 2, 3, etc.
so the time between two successive intersections is
Dt = 1/(220+224) s.
With two intersections per period, the period is
twice as large, thus
T = 2/(220+224) s,
hence the frequency is
f = (220+224)/2 = 222 Hz,
which is the arithmetic average of both composing
frequencies.

As I said before, it might be correct to say that the average, or
effective frequency is 222 Hz. But the actual period varies from
cycle to cycle over a period of 1/(224-220).

No peculiarities found.

Perhaps you would agree that a change in period of less than 2% might
be difficult to observe - especially when you're not expecting to see
it. To more easily find the 'peculiarities' I suggest that you try
using more widely spaced frequencies.

gr, Hein

gr right back at ya,

jk

 

[Bob F.]

The fundamental formular Acos(B) + C is all you need to describe angular
modulation.
Changing the value of A over time determines the amplitude of an AM
modulated carrier.
Changing the value of B over time determines the amplitude of an FM
modulated carrier.
The rate of change of A or B changes the modulation frequency respectively.
C is DC, Y axis offset and has not been discussed here.

r, Bob F.

 

[Michael A. Terrell]

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

gr, Hein

I haven't seen the schematics of either model, but most portable SW
recievers suffer from no filtering on the front end, so are susceptible
to overload. A properly designed front end is expensive. Most
manufacturers would rather spend the money on eye candy to make it
attractive to those who don't know what they really need. This is
crossposted to: where the relative merits of
different SW radios are discussed.

I tend to use older, rack mounted equipment that I've restored and
when I have the time, I like to design my own equipment. I only have
one portable receiver, the RS DX-375, which is kept in my hurricane
emergency kit. It was bought on price, alone when it was discontinued
for $50, about eight or nine years ago. The power line and ignition
noise is so high around here that a portable is almost useless. After
the last hurricane, the nearest electricity was over 5 miles away for
about two weeks, and I was picking up stations from all over the world.
It reminded me of visits to my grandparent's farm back in the early
'60s, when their farm was the last one on their road with electricity.
They had nothing that generated noise, other that a few light switches,
when they were flipped on or off. I didn't have a shortwave radio, but
I could pick up AM DX from all over the country, late at night.


--
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

 

[craigm]

As I said before, it might be correct to say that the average, or
effective frequency is 222 Hz. But the actual period varies from
cycle to cycle over a period of 1/(224-220).

How about showing us your math or data supporting this?

Perhaps you would agree that a change in period of less than 2% might
be difficult to observe - especially when you're not expecting to see
it. To more easily find the 'peculiarities' I suggest that you try
using more widely spaced frequencies.

An example showing this would be appreciated.

 

[msg]

I only have > one portable receiver, the RS DX-375, which is kept in
my hurricane emergency kit. It was bought on price, alone...

I had one and was quite disappointed by its image response (even in
the absence of strong signal IMD, overloading, etc.). For example,
WWV on 10 Mhz was equally strong on 9545 kHz. I never saw the
schematic so I know nothing about its front end and evidently
it is single conversion but one would have hoped for a varactor
tuned preselector

How is image rejection on yours?

Cross-posts limited to sci.electronics.basics and rec.radio.shortwave

Regards,

Michael

 

[Michael A. Terrell]

I had one and was quite disappointed by its image response (even in
the absence of strong signal IMD, overloading, etc.). For example,
WWV on 10 Mhz was equally strong on 9545 kHz. I never saw the
schematic so I know nothing about its front end and evidently
it is single conversion but one would have hoped for a varactor
tuned preselector

How is image rejection on yours?

Its acceptable for emergency, but not what I'd want for daily use.
I have a 50 KW FM transmitter and multiple cell sites within a mile
Right now I'm restoring a 1950's era national NC183R with a properly
designed front end, with two tuned RF preamp stages.

http://bama.edebris.com/download/national/nc183/nc183.pdf See page 16
for the front end circuitry. (855 KB (876,468 bytes))


I also have a HP 312B frequency selective voltmeter:

http://bama.edebris.com/download/hp/312bd/hp312bd.pdf (106 MB download).


--
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]

An example showing this would be appreciated.

http://webphysics.davidson.edu/applets/Superposition/GroupVelocity.html

(change 8.0 to 7.7 (for example) in one of the functions and examine
the number of zero crossings in each division on the horizontal axis.)

Hope that helps.

jk

 

[craigm]

http://webphysics.davidson.edu/applets/Superposition/GroupVelocity.html

(change 8.0 to 7.7 (for example) in one of the functions and examine
the number of zero crossings in each division on the horizontal axis.)

Hope that helps.

jk

Yes it shows very consistent spacings. Nothing like what you suggest I
should see. Of course, a numerical, rather than graphical example would be
much clearer.

 

[Hein ten Horn]

As I said before, it might be correct to say that the average, or effective
frequency is 222 Hz. But the actual period varies from cycle to cycle over
a period of 1/(224-220).


Perhaps you would agree that a change in period of less than 2% might be
difficult to observe - especially when you're not expecting to see it. To
more easily find the 'peculiarities' I suggest that you try using more
widely spaced frequencies.

Before we go any further I'd like to exclude
that we are talking at cross-purposes.
Are you pointing at the irregularities which
can occur when the envelope passes zero?
(That phenomenon has already been
mentioned in this thread.)

gr right back at ya,

"gr" is not customary, but, when writing it satisfies
in several languages: German (gruß, grüße),
Dutch (groet, groeten) and English.

Adieu, Hein