Author: our resident expert, DonH50
We left Digital Audio Jitter Fundamentals talking about digital signals. However, error correction and design margins mean jitter on the digital bit stream is rarely an issue for the bit rates used for A/V systems. (At 10 Gb/s and above, it is a bigger issue.) When jitter is brought up as an issue in the audio world, we are talking about jitter on the sampling clock. This can happen for all the reasons mentioned before, but once that clock is used to drive your DAC, the jitter goes right to your ears (OK, there are a few steps along the way, but you get the idea).
Clock recovery is a complicated subject beyond the scope of this thread. Let’s just say getting a very clean, low-jitter clock takes some effort. As a result, jitter can run pretty high (several ns or more) in many audio systems. Make it an A/V system with videophiles defining the clocks and not worrying too much about audio, throw in a bunch of various digital signals around the audio bit stream and clock lines, and Bad Things can happen, like signal coupling and excessive jitter.
First, I am going to repeat some information from an earlier post. To see the impact of jitter, let's look at a 16-bit converter sampling at 44.1 kS/s (CD resolution and rate). The DAC is ideal except for the added random timing jitter. A perfect 16-bit ADC has SNR of about 98 dB. I have plotted the SNR vs. jitter for 100 Hz, 1 kHz, 2 kHz, 10 kHz, and 20 kHz signals. You can clearly see how the higher frequencies are much more sensitive to jitter. At 100 Hz, 10 ns of jitter is hardly noticeable, but at just 1 kHz the SNR has decreased by nearly 20 dB (down about 3 bits)! At 20 kHz, we have SNR less than an ideal 10-bit DAC (< 60 dB).
Another way to look at the impact is to plot the SNR lost as jitter increases, as shown below. A perfect 16-bit DAC would lose 0 dB in SNR; as jitter increases, more and more SNR is lost. With 1 ns of random jitter, things don't look too bad through 2 kHz, but at 20 kHz we see that 20 dB SNR loss. To keep the loss to just a few dB at 20 kHz, we need jitter < 100 ps; with just 1 ns of random jitter the upper midrange and high end is getting pretty noisy, with the effective dynamic range reduced by 10 to 20 dB.
I did run a few test cases so we can look at frequency spectrums. (For the geeks: the input frequency is chosen relatively prime and bounded with the sample record to minimize spectral leakage per IEEE Standard 1241.) First, the ideal 16-bit DAC with a full-scale 1 kHz input signal:
Now with 1 lsb (4.9 ns, standard deviation, normal distribution) of added random jitter we’ve lost about 1.5 bits of resolution (from 16 effective number of bits (ENOB) to 14.6 ENOB) and about 8 dB of SNR; spurious-free dynamic range is lower but still very high. Note only the noise floor is raised; random jitter will not generally add discrete tones, just more noise.
Here’s what happens we when double the random jitter:
Lost another bit, but still a very low noise floor (84 dB SNR).
Now look what happens when the signal level is cut in half (-6 dBFS):
Ah, the noise floor drops, too, and ENOB stays about the same. With less signal, ENOB will go down since we are using less of the DAC’s range (reducing the number of bits used). Jitter drops because, as stated in Jitter 101, it is related to the slew rate of the signal. Smaller signal, lower slew rate, at least for a sinusoid. This is not true for something like a square wave that has faster edges (and thus higher frequency components – see the “Building a Square Wave” thread). So, jitter will degrade fast pulses more than a single tone like this test case.
Looking at a 10 kHz tone, 1 lsb of jitter is 1/10th that of the 1 kHz case (0.5 ns vs. 5 ns). As we’d expect, the results are about the same as the 1 kHz test case.
Now, increase the jitter to ~5 ns, equal to 1 lsb at 1 kHz, and performance is markedly lower:
Wow, 70 dB SINAD (signal to noise and distortion), and only a little over 11 bits! Ouch! SFDR is still high, over 100 dB, but the noise level is rising to audibility.
Now let’s return to a 1 kHz input with 5 ns (1 lsb at 1 kHz) jitter, but add 1 lsb of the input to the jitter. That is, nothing fancy, just a simple addition of 1 lsb (in time) modulation of the (formerly) random jitter on the clock. This is the dreaded deterministic jitter term.
Well, ENOB is about as before, but now there’s a 2 kHz tone sticking well above the noise floor. That is second-order distortion, i.e. a second harmonic that wsan’t there before. Probably not really audible at almost 100 dB down, but a very annoying thing to see. Dropping the signal amplitude reduces the distortion spur as well, just as before.
An interesting experiment is to throw in a deterministic term not related to the signal. Below is a plot with the jitter modulated by a 120 Hz signal, such as would come from a typical full-wave power supply, again at the 1-lsb level. Note the ENOB did not change significantly, but now there is a pair of spurs around the 1 kHz signal. Other frequencies, and more complex combinations of deterministic jitter, can generate a series of tones that are not related to the signal. This is important because we can hear non-harmonic distortion much more readily than harmonic distortion.
Repeating the plot at 10 kHz with 1 lsb of 10 kHz signal injected puts a spur at 20 kHz at the same level as in the 1 kHz plot, just like the first trials. Using the 1 kHz jitter level as modulated by the 10 kHz signal yields a fairly high (about -76 dBFS) distortion term.
One last series of trials… Here’s a plot using five input tones (1, 2, 3, 5, and 10 kHz) without jitter. Notice the tones are all about 10 dB down; this is because when the all add up (in phase), they drive the DAC to full-scale, even though the average is -10 dB per tone. Music is much more complex thus average values are often -20 dBFS or less to ensure the output doesn’t clip (and sound very, very bad). This eats into your dynamic range pretty quickly, and helps explain why what appears to be low jitter can start to impact the ‘real world” noise floor. It also helps explain why recording systems and studios really like using 24 bits; that extra headroom is a boon when working with everything in the mix before the amplitudes are matched and the signal made to fit back into 16 bits for your CDs.
Here are those same tones but with 5 ns (1 lsb at 1 kHz again) of jitter added, along with 1 lsb of the 1 kHz tone added to the jitter. Note the multiple tones added as the deterministic jitter mixes with the other tones through the sampling process. The effective SFDR is now only about 75 dB from peak signal to peak spur…
My last example is those same five tones, but with the 5 kHz tone reduced 20 dB (about ¼ volume) to emulate what might happen in (very simple) music. I moved the deterministic jitter to 120 Hz, though still at 5 ns (1 lsb at 1 kHz). The distortion spurs are much more numerous and only about 60 dB down (worst-case) from the reduced 5 kHz tone. Would you hear this? I don’t know, but probably not. However, it is clear that as we move toward more complex signals like music, and correspondingly more complex and realistic jitter, we are heading toward something that could be readily audible.
Hopefully this has given you a picture of what jitter can do, and a flavor for the real-world impact it might have. My goal was not a realistic, musical example (readily done but the plots would be very messy), but rather something that helps clearly show what jitter does to DAC performance. Thus, I have not used complicated signals so (hopefully) it is easy to see what happens when jitter is added.
Enjoy! - Don
We left Digital Audio Jitter Fundamentals talking about digital signals. However, error correction and design margins mean jitter on the digital bit stream is rarely an issue for the bit rates used for A/V systems. (At 10 Gb/s and above, it is a bigger issue.) When jitter is brought up as an issue in the audio world, we are talking about jitter on the sampling clock. This can happen for all the reasons mentioned before, but once that clock is used to drive your DAC, the jitter goes right to your ears (OK, there are a few steps along the way, but you get the idea).
Clock recovery is a complicated subject beyond the scope of this thread. Let’s just say getting a very clean, low-jitter clock takes some effort. As a result, jitter can run pretty high (several ns or more) in many audio systems. Make it an A/V system with videophiles defining the clocks and not worrying too much about audio, throw in a bunch of various digital signals around the audio bit stream and clock lines, and Bad Things can happen, like signal coupling and excessive jitter.
First, I am going to repeat some information from an earlier post. To see the impact of jitter, let's look at a 16-bit converter sampling at 44.1 kS/s (CD resolution and rate). The DAC is ideal except for the added random timing jitter. A perfect 16-bit ADC has SNR of about 98 dB. I have plotted the SNR vs. jitter for 100 Hz, 1 kHz, 2 kHz, 10 kHz, and 20 kHz signals. You can clearly see how the higher frequencies are much more sensitive to jitter. At 100 Hz, 10 ns of jitter is hardly noticeable, but at just 1 kHz the SNR has decreased by nearly 20 dB (down about 3 bits)! At 20 kHz, we have SNR less than an ideal 10-bit DAC (< 60 dB).
Another way to look at the impact is to plot the SNR lost as jitter increases, as shown below. A perfect 16-bit DAC would lose 0 dB in SNR; as jitter increases, more and more SNR is lost. With 1 ns of random jitter, things don't look too bad through 2 kHz, but at 20 kHz we see that 20 dB SNR loss. To keep the loss to just a few dB at 20 kHz, we need jitter < 100 ps; with just 1 ns of random jitter the upper midrange and high end is getting pretty noisy, with the effective dynamic range reduced by 10 to 20 dB.
I did run a few test cases so we can look at frequency spectrums. (For the geeks: the input frequency is chosen relatively prime and bounded with the sample record to minimize spectral leakage per IEEE Standard 1241.) First, the ideal 16-bit DAC with a full-scale 1 kHz input signal:
Now with 1 lsb (4.9 ns, standard deviation, normal distribution) of added random jitter we’ve lost about 1.5 bits of resolution (from 16 effective number of bits (ENOB) to 14.6 ENOB) and about 8 dB of SNR; spurious-free dynamic range is lower but still very high. Note only the noise floor is raised; random jitter will not generally add discrete tones, just more noise.
Here’s what happens we when double the random jitter:
Lost another bit, but still a very low noise floor (84 dB SNR).
Now look what happens when the signal level is cut in half (-6 dBFS):
Ah, the noise floor drops, too, and ENOB stays about the same. With less signal, ENOB will go down since we are using less of the DAC’s range (reducing the number of bits used). Jitter drops because, as stated in Jitter 101, it is related to the slew rate of the signal. Smaller signal, lower slew rate, at least for a sinusoid. This is not true for something like a square wave that has faster edges (and thus higher frequency components – see the “Building a Square Wave” thread). So, jitter will degrade fast pulses more than a single tone like this test case.
Looking at a 10 kHz tone, 1 lsb of jitter is 1/10th that of the 1 kHz case (0.5 ns vs. 5 ns). As we’d expect, the results are about the same as the 1 kHz test case.
Now, increase the jitter to ~5 ns, equal to 1 lsb at 1 kHz, and performance is markedly lower:
Wow, 70 dB SINAD (signal to noise and distortion), and only a little over 11 bits! Ouch! SFDR is still high, over 100 dB, but the noise level is rising to audibility.
Now let’s return to a 1 kHz input with 5 ns (1 lsb at 1 kHz) jitter, but add 1 lsb of the input to the jitter. That is, nothing fancy, just a simple addition of 1 lsb (in time) modulation of the (formerly) random jitter on the clock. This is the dreaded deterministic jitter term.
Well, ENOB is about as before, but now there’s a 2 kHz tone sticking well above the noise floor. That is second-order distortion, i.e. a second harmonic that wsan’t there before. Probably not really audible at almost 100 dB down, but a very annoying thing to see. Dropping the signal amplitude reduces the distortion spur as well, just as before.
An interesting experiment is to throw in a deterministic term not related to the signal. Below is a plot with the jitter modulated by a 120 Hz signal, such as would come from a typical full-wave power supply, again at the 1-lsb level. Note the ENOB did not change significantly, but now there is a pair of spurs around the 1 kHz signal. Other frequencies, and more complex combinations of deterministic jitter, can generate a series of tones that are not related to the signal. This is important because we can hear non-harmonic distortion much more readily than harmonic distortion.
Repeating the plot at 10 kHz with 1 lsb of 10 kHz signal injected puts a spur at 20 kHz at the same level as in the 1 kHz plot, just like the first trials. Using the 1 kHz jitter level as modulated by the 10 kHz signal yields a fairly high (about -76 dBFS) distortion term.
One last series of trials… Here’s a plot using five input tones (1, 2, 3, 5, and 10 kHz) without jitter. Notice the tones are all about 10 dB down; this is because when the all add up (in phase), they drive the DAC to full-scale, even though the average is -10 dB per tone. Music is much more complex thus average values are often -20 dBFS or less to ensure the output doesn’t clip (and sound very, very bad). This eats into your dynamic range pretty quickly, and helps explain why what appears to be low jitter can start to impact the ‘real world” noise floor. It also helps explain why recording systems and studios really like using 24 bits; that extra headroom is a boon when working with everything in the mix before the amplitudes are matched and the signal made to fit back into 16 bits for your CDs.
Here are those same tones but with 5 ns (1 lsb at 1 kHz again) of jitter added, along with 1 lsb of the 1 kHz tone added to the jitter. Note the multiple tones added as the deterministic jitter mixes with the other tones through the sampling process. The effective SFDR is now only about 75 dB from peak signal to peak spur…
My last example is those same five tones, but with the 5 kHz tone reduced 20 dB (about ¼ volume) to emulate what might happen in (very simple) music. I moved the deterministic jitter to 120 Hz, though still at 5 ns (1 lsb at 1 kHz). The distortion spurs are much more numerous and only about 60 dB down (worst-case) from the reduced 5 kHz tone. Would you hear this? I don’t know, but probably not. However, it is clear that as we move toward more complex signals like music, and correspondingly more complex and realistic jitter, we are heading toward something that could be readily audible.
Hopefully this has given you a picture of what jitter can do, and a flavor for the real-world impact it might have. My goal was not a realistic, musical example (readily done but the plots would be very messy), but rather something that helps clearly show what jitter does to DAC performance. Thus, I have not used complicated signals so (hopefully) it is easy to see what happens when jitter is added.
Enjoy! - Don
) systems, there is one clock next to the DAC, and it doesn't need to be recovered. Again, anyone but an expert would walk away thinking that digital audio is (a) really difficult and (b) just another form of analogue, where every stage in the 'signal' path contributes to a build-up of jitter and noise - which isn't true. The beauty of the concept becomes lost in the technical details.
