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Gap in beat freqs.

B

Bob Steiner

Jan 1, 1970
0
Can anyone tell me if there is a qualitative difference in the sum
frequency waveform when using two beat frequencies that are
realtively close in frequency as opposed to distant?

For example, producing a 1MHz beat from 10MHz plus 9MHz vs. from
1.000010MHz and 10Hz.

PS: I am not referring to stability of the oscillator.

Bob Steiner
 
P

Phil Allison

Jan 1, 1970
0
"Bob Steiner"
Can anyone tell me if there is a qualitative difference in the sum
frequency waveform when using two beat frequencies that are
realtively close in frequency as opposed to distant?

For example, producing a 1MHz beat from 10MHz plus 9MHz vs. from
1.000010MHz and 10Hz.


** In the former case - the wave consists of a two frequencies with their
combined amplitude ( ie envelope) varying at the rate of 1MHz.

In the latter case, the wave is two frequencies, a 1MHz wave riding on a
10 Hz one.


........ Phil
 
N

nospam

Jan 1, 1970
0
Bob Steiner said:
Can anyone tell me if there is a qualitative difference in the sum
frequency waveform when using two beat frequencies that are
realtively close in frequency as opposed to distant?

When you mix two frequencies there is no 'sum frequency waveform'. There
one waveform which contains the sum, difference and depending on how
carefully you mixed both starting frequencies.
For example, producing a 1MHz beat from 10MHz plus 9MHz vs. from
1.000010MHz and 10Hz.

If you wanted to filter *the* waveform to obtain only the difference it is
a lot easier when the closest other frequency is 8MHz rather than 10Hz
away.
--
 
P

Phil Allison

Jan 1, 1970
0
"nospam"
Bob Steiner
When you mix two frequencies


** The OP never mentioned "mix" at all.

His Q relates to summing waves, not multiplying them.

The phenomenon of "beats " is a linear one.


If you wanted to filter *the* waveform to obtain only the difference...


** There just ain't one to be had.

There are only the two original frequencies.

The "envelope" is not of fixed amplitude, that is all.



....... Phil
 
B

BobW

Jan 1, 1970
0
Bob Steiner said:
Can anyone tell me if there is a qualitative difference in the sum
frequency waveform when using two beat frequencies that are
realtively close in frequency as opposed to distant?

For example, producing a 1MHz beat from 10MHz plus 9MHz vs. from
1.000010MHz and 10Hz.

PS: I am not referring to stability of the oscillator.

Bob Steiner

Are you talking about a "beat" frequency that occurs when two sinusoids are
passed through a linear system, or "sum and difference" frequencies that
occur when two sinusoids are passed through a non-linear system?

The so-called beat frequency is an apparent modulation due to phase
cancellation, but there is no sum and/or difference frequency generated.
That is, only the two original sinusoids remain at the output of the linear
system.

Bob
 
M

Martin Brown

Jan 1, 1970
0
Bob Steiner said:
Can anyone tell me if there is a qualitative difference in the sum
frequency waveform when using two beat frequencies that are
realtively close in frequency as opposed to distant?

If you assume linear mixing at equal amplitude and pure sine waves then
you can use the trig identity to work out what the equivalent
multiplicative description would be.

Sin(X) + Sin(Y) = 2 Sin((X+Y)/2).Cos((X-Y)/2)

You don't actually create any real new frequencies by linear mixing.
Whereas combining in a multiplier will generate new frequencies.
For example, producing a 1MHz beat from 10MHz plus 9MHz vs. from
1.000010MHz and 10Hz.

So 10MHz + 9MHz equal mixed is equivalent to 9.5MHz carrier frequency
with a multiplicative envelope modulation of 0.5MHz.

And 1.00001 MHz + 10Hz equally mixed is equivalent to having
0.50001MHz multiplied by 0.5MHz.

In this case the nearly 1MHz wobbling up and down on a slowly changing
baseline is probably the more intuitive description to work with.
PS: I am not referring to stability of the oscillator.

When the two frequencies are close together in one of the descriptions
they are far apart in the other.

Regards,
 
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