Thanks Hans. Yes, I get the method if the LTspice modulator works as we think it does.
However...
Say we start with a 1kHz sine tone at 0dB. Its spectrum is a single vertical line 1Khz. If we take a high resolution FFT all content drops into the 1Khz bin and sums to 0dB.
If we FM modulate with say at -40dB 10Hz sine tone, the spectrum develops vertical lines at +/- 10Hz, 20Hz etc which are sidebands, and the 1kHz line reduces in amplitude a bit. And if take a high resolution FFT, some of the content appears in sideband bins but the sum of all the bins remains 0dB.
Laws governing sidebands are a bit complex, but at -40dB modulation that's 1% which is small and by account only the 1st sidebands are significant. Apparently it's narrowband FM, and has the same spectrum as AM.
Then if we look in our FFT bins, we should find all of the modulation content in the sideband bins, half each in the + and - sidebands. So that's -46dB in each bin.
Then c -40dB observed level of the 1st sideband means about 1% modulation, not c 0.01%. That's the first thing that troubles me......
Second trouble is that your graph of 1st sideband level versus modulation intercepts 0dB at c 2% - that would mean with only 2% modulation the 1kHz tone and 1st sideband would have the same amplitude, and I struggle that can be right....? From published tables, that intercept should be at a modulation depth of c 75% as far as I can tell so far?
Its sort of interesting, FM modulation and radio has never been on my radar so possible I've misunderstood but I really don't get these anamolies unless what we think the LTspice modulator does is not correct?
LD
The FM modulator is programmed with Space and Mark to give a deviation of +/-5Hz around 1Khz.
So I offerred DC to the modulator at resp 0V and at 1V to check this.
And Yes this was absolutely 100% correct.
So +/-0.5Volt modulates +/-5Hz, that's a fact.
But offering a -40dB 10Hz modulating signal to a 0dB is not the same as 1% modulation. That depends on the gain of the modulator.
In my example +/- 0.5V results in +/-5Hz modulation or 5/1K = 0.5% modulation.
A -40dB modulating signal or +/-10mV, would have resulted in (10m/0.5V)*0,5% = 0,04% modulation.
Had I give the modulator a different gain with Space and Mark, the 10mV would have resulted is a different figure.
But at the end, I would have produced exactly the same image of %modulation versus first sideband in dB, independent of the gain of the modulator.
So your view on the sidebands being at -46dB is not how it is.
I did not try to calculate the sidebands, that's what the FFT did for me. And from experience I know this can be trusted.
With your example with 75% modulation, which to my feeling is 1Khz +/-750Hz (Space=250, Mark=1750), you can see in the image below how the spectrum looks.
All first so many 10Hz sidebands are at the same level, and compared to a non modulated signal you notice what you mentioned as conservation of energy, all spread over the spectrum at a much lower level.
Another proof that the FFT is doing the right job.
On the other hand, there is such a thing as a modulation index, independent of the signal that will be modulated.
This index m is in the 75% case: m = 750Hz/10Hz = 75, just a number, not a percentage.
Maybe the modulation figure and the modulation index got mixed up in your contemplations ?
Maybe you can show the published tables that you mention.
That could give new insights.
Hans
.
So I offerred DC to the modulator at resp 0V and at 1V to check this.
And Yes this was absolutely 100% correct.
So +/-0.5Volt modulates +/-5Hz, that's a fact.
But offering a -40dB 10Hz modulating signal to a 0dB is not the same as 1% modulation. That depends on the gain of the modulator.
In my example +/- 0.5V results in +/-5Hz modulation or 5/1K = 0.5% modulation.
A -40dB modulating signal or +/-10mV, would have resulted in (10m/0.5V)*0,5% = 0,04% modulation.
Had I give the modulator a different gain with Space and Mark, the 10mV would have resulted is a different figure.
But at the end, I would have produced exactly the same image of %modulation versus first sideband in dB, independent of the gain of the modulator.
So your view on the sidebands being at -46dB is not how it is.
I did not try to calculate the sidebands, that's what the FFT did for me. And from experience I know this can be trusted.
With your example with 75% modulation, which to my feeling is 1Khz +/-750Hz (Space=250, Mark=1750), you can see in the image below how the spectrum looks.
All first so many 10Hz sidebands are at the same level, and compared to a non modulated signal you notice what you mentioned as conservation of energy, all spread over the spectrum at a much lower level.
Another proof that the FFT is doing the right job.
On the other hand, there is such a thing as a modulation index, independent of the signal that will be modulated.
This index m is in the 75% case: m = 750Hz/10Hz = 75, just a number, not a percentage.
Maybe the modulation figure and the modulation index got mixed up in your contemplations ?
Maybe you can show the published tables that you mention.
That could give new insights.
Hans
.
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Is anyone running their rig @ a resonance of 15 to 18 hz as recommended here:
http://www.theanalogdept.com/images/spp6_pics/TT_Design/MechanicalResonances.pdf
see the conclusion
Is anyone running their rig @ a resonance of 15 to 18 hz as recommended here:
http://www.theanalogdept.com/images/spp6_pics/TT_Design/MechanicalResonances.pdf
see the conclusion
If you buy this :
BENZ MICRO MC 20 E 2 H (high output) NEW!!! EXTRA RARE!!!
BENZ MICRO MC 20 E 2 H (high output) NEW!!! EXTRA RARE!!! | eBay
4 grams mass
Dynamic Compliance
10 x 10-6cm/Dyne
And used it with one of these :
Moerch UP-4 or DP-6 with a green dot tonearm ( 4 grams eff. mass)
you theoreticaly get a 16.749 resonance frequency if you use this:
Resonance Frequency
(4 gram cartridge plus 1.03 gram soundsmith plastic screws and the dynamic compliance listed above)
Vinylengine specs ,dunno how it would sound
BENZ MICRO MC 20 E 2 H (high output) NEW!!! EXTRA RARE!!!
BENZ MICRO MC 20 E 2 H (high output) NEW!!! EXTRA RARE!!! | eBay
4 grams mass
Dynamic Compliance
10 x 10-6cm/Dyne
And used it with one of these :
Moerch UP-4 or DP-6 with a green dot tonearm ( 4 grams eff. mass)
you theoreticaly get a 16.749 resonance frequency if you use this:
Resonance Frequency
(4 gram cartridge plus 1.03 gram soundsmith plastic screws and the dynamic compliance listed above)
Vinylengine specs ,dunno how it would sound
Although if you used this calculater with post # 87 specs :
Compliance/Effective Mass Calculator
you would have some issues
Compliance/Effective Mass Calculator
you would have some issues
I did actually buy an SME3009SIII with the 30H wand to give me an arm and cartridge effective mass of 4.5g to experiment, but lack of time completely ruined that plan.
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