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
"Bob Steiner"
** 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
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.
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.
"nospam" Bob Steiner
** The OP never mentioned "mix" at all.His Q relates to summing waves, not multiplying them.
The phenomenon of "beats " is a linear one.
** 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
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
In message , Bob Steiner writes
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.
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.
When the two frequencies are close together in one of the descriptions they are far apart in the other.
Regards,
-- Martin Brown
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