- Thread Starter
- #281
He goes on to say:
Sigh. Seems like he doesn't understand what jitter is. Likely thinks if a device is not a DAC, it can't have jitter. I suggest reading any text on jitter and failing that, Julian Dunn's great AES paper: JITTER AND DIGITAL AUDIO PERFORMANCE MEASUREMENTS
Jitter is a modulation in time of a signal. Mathematically then it would be v'(t) = v(t-delta(t))
Let's assume v(t) is a cosine wave. And delta(t) is our jitter signal and it likewise is a cosine wave. Our equation then becomes:
Looks complicated but it is just the simple equation we started with and simply substituting and expanding.
For small values of jitter we are dealing with we can use this approximation:
And:
Plugging these two into equation (4) we get this:
In plain English, we have our original cosine wave (Acos(wt)). All jitter did was add two sideband cosine waves, one at sum of our signal and that of jitter. And the other, at the difference. We can see this plainly in an example in one of my articles I wrote for WSR Magazine: https://www.audiosciencereview.com/forum/index.php?threads/audibility-of-small-distortions.67/
We took a 10 Khz tone and added sinusoidal jitter at 2.5 kHz. Results are the two sidebands on each side of our signal.
Even if you got lost in all of this , that is OK. The key here is that nothing I have shown so far has anything to do with digital audio! All math was analog in nature. Indeed, the "jitter" shown here is exactly the same as AM modulation used in every AM radio!
Now, change the jitter source to be noise rather than sinusoidal and it causes broadening of our signal tone proportional to PDS of the noise:
That brings us to your gain cell. Your DC input that you are using in Gilbert Cell is a modulator of the audio signal. If it is anything but DC, it will modulate the main signal just like jitter would in a DAC.
In your case, your "DC" signal fed to the Gilbert Cell is polluted with power supply and random noise. The former causes spikes on each side of our tone. The latter causes broadening of the shoulders of our tone. Here it is again:
See the similarity in the way your pre-amp has broadened the bottom of the 1 khz tone and what I showed in my graph above with random jitter. The random noise could be created by the front panel microprocessor for example. Now you see why I call it "jitter like" distortion.
Because you don't measure your designs, and don't understand the fundamentals of the circuit topologies you are using, you are confused by my measurements and terminology. I suggest using this opportunity to learn by instrumenting the signal going into your Gilbert cell. I am pretty sure you will find the noise and power supply spikes riding there. Clean that up and these measurements will improve and will not do anything to deter from the "sound" you think this gain stage has. Lest you want to tell us now all of a sudden that "jitter is good!"
Conclusion
Math, audio science and engineering plus measurements enable us to understand behavior of audio gear. Without it, you are shooting in the dark, producing suboptimal designs. Without scrutiny like we are providing here, you would get away with it much like a restaurant can by not washing their dishes well. But not anymore. Please spend less time being flippant online and more time building better products. Heaven knows I can do other things than being your test and verification shop.
Sigh. Seems like he doesn't understand what jitter is. Likely thinks if a device is not a DAC, it can't have jitter. I suggest reading any text on jitter and failing that, Julian Dunn's great AES paper: JITTER AND DIGITAL AUDIO PERFORMANCE MEASUREMENTS
Jitter is a modulation in time of a signal. Mathematically then it would be v'(t) = v(t-delta(t))
Let's assume v(t) is a cosine wave. And delta(t) is our jitter signal and it likewise is a cosine wave. Our equation then becomes:
Looks complicated but it is just the simple equation we started with and simply substituting and expanding.
For small values of jitter we are dealing with we can use this approximation:
And:
Plugging these two into equation (4) we get this:
In plain English, we have our original cosine wave (Acos(wt)). All jitter did was add two sideband cosine waves, one at sum of our signal and that of jitter. And the other, at the difference. We can see this plainly in an example in one of my articles I wrote for WSR Magazine: https://www.audiosciencereview.com/forum/index.php?threads/audibility-of-small-distortions.67/
We took a 10 Khz tone and added sinusoidal jitter at 2.5 kHz. Results are the two sidebands on each side of our signal.
Even if you got lost in all of this , that is OK. The key here is that nothing I have shown so far has anything to do with digital audio! All math was analog in nature. Indeed, the "jitter" shown here is exactly the same as AM modulation used in every AM radio!
Now, change the jitter source to be noise rather than sinusoidal and it causes broadening of our signal tone proportional to PDS of the noise:
That brings us to your gain cell. Your DC input that you are using in Gilbert Cell is a modulator of the audio signal. If it is anything but DC, it will modulate the main signal just like jitter would in a DAC.
In your case, your "DC" signal fed to the Gilbert Cell is polluted with power supply and random noise. The former causes spikes on each side of our tone. The latter causes broadening of the shoulders of our tone. Here it is again:
See the similarity in the way your pre-amp has broadened the bottom of the 1 khz tone and what I showed in my graph above with random jitter. The random noise could be created by the front panel microprocessor for example. Now you see why I call it "jitter like" distortion.
Because you don't measure your designs, and don't understand the fundamentals of the circuit topologies you are using, you are confused by my measurements and terminology. I suggest using this opportunity to learn by instrumenting the signal going into your Gilbert cell. I am pretty sure you will find the noise and power supply spikes riding there. Clean that up and these measurements will improve and will not do anything to deter from the "sound" you think this gain stage has. Lest you want to tell us now all of a sudden that "jitter is good!"
Conclusion
Math, audio science and engineering plus measurements enable us to understand behavior of audio gear. Without it, you are shooting in the dark, producing suboptimal designs. Without scrutiny like we are providing here, you would get away with it much like a restaurant can by not washing their dishes well. But not anymore. Please spend less time being flippant online and more time building better products. Heaven knows I can do other things than being your test and verification shop.