Audiophiles are accustomed to hear jitter values in terms of pico-seconds (psec) RMS, and many oscillators are spec'ed at 1 psec jitter. We know that phase noise is another way to measure jitter, and that jitter RMS values represent the area under the curve. One must realize that the graph is in logarithm scale resulting in large differences even though the curves are sort of close to each other.
Analog Devices has an excellent tutorial on understanding jitter values
You can use the formulas to calculate jitter RMS from phase noise data, but there are easy to use on-line tools that calculate jitter RMS from data you find in datasheets. One such tool is the Phase Noise Calculator from www.jittertime.com (a consultancy on the topic of jitter)
So lets calculate the jitter RMS value for each of the oscillators we compared in the previous post.
Buffalo II oscillator
We find the data points in the graph and enter them in the tool as shown:
The result is 0.446 psec. (if you are wondering why the result is less than the sum of the jitter in each segment, is because they add as Root Sum-of-Squares)
This value agrees with the value is the specification ( typically 0.5 psec). We do the same for the other curves and we find the following:
- Crystek 950 (Buffalo II): 0.446 psec
- Wenzel oscillator: 0.075 psec
- Typical Oscillator (Buffalo I): 29.9 psec
Those are BIG differences when we convert to jitter RMS values. the Wenzel measures 75 femto seconds!. The Crystek 950 measures the expected half a psec; but the typical oscillator measure 30 psec?. But wait a minute, aren't those oscillators spec'ed at 1 psec?.
Lets looks at the specification of the oscillator found in Buffalo I: Crystek c33xx. The spec says: Jitter RMS: 12KHz-80MHz: 0.5 psec. Notice that the jitter is measured after 12 KHz whereas the phase noise plots we see for the better parts starts at 10 Hz. If we instead measure the Jitter RMS for the Crystek 950 shown in the graph with the same scale, of 12 KHz to 80 MHz, we get the value of 0.13 psec.
I used the numbers found in the spec for an 80MHz oscillator and got 0.115 psec for 12KHz to 80MHz. The best spec in the datasheet is for the 100MHz clock with a jitter value of 0.094 psec RMS (12KHz-80MHz). Maybe the custom clock Crystek is making for TPA has better phase noise values than what is stated in the specifications. (Update: according to Brian of TPA, the phase noise specification for their parts is the same as the standard parts)
- Clock for Buffalo I: 0.5 psec RMS (12KHz-80MHz)
- Clock for Buffalo II: 0.115 psec RMS (12KHz-80MHz)
What offset frequency interval is used for audio to calculate jitter? I don't think there are standards in audio, but for other applications there are standards. This article cites two standards:
As an example, SONET uses a frequency offset of 12kHz to 20MHz from the carrier signal to integrate the area under the phase noise plot to measure phase jitter. Fiber Channel uses a frequency offset of 637kHz to 10MHz from the carrier signal to integrate the area under the phase noise plot to measure phase jitter.According to Analog Devices,
It is a little tricky to specify the bandwidth over which phase noise should be integrated in order to calculate the jitter which will actually be observed when that clock signal is used to clock a converter. There are many variables which are seldom known with accuracy – such as the inherent bandwidth of the sample clock circuit on the converter. Also, it is very difficult to actually measure the broadband phase noise of a clock signal beyond an offset of a few MHz. ... For a true "broadband" jitter calculation some assumptions and simplifications must be made. One assumption made by ADIsimCLK, for example, is that the upper offset integration limit is one-half the clock frequency. The lower offset integration limit is assumed to be between 100 Hz and 1 kHz.What frequency interval matters then?
If we take a previous datasheet of the Crystek 950 clock and compare it with the current datasheet, we see that the "close-in" phase noise (closer to the crystal frequency) has increased and that "broad band" phase noise (away from the crystal frequency).
It seems that the engineers at Crystek focused on improving the broadband phase noise values and were willing to tradeoff the close-in phase noise. This implies that broadband phase numbers (or the "noise floor" of the oscillator) is a more important value than close-in noise (at least for the market that this crystal is intended to be used, -which I am sure it is NOT DIY DAC boards :-))
Perhaps it depends on the application
According to tutorial from Analog Devices,
- Close-in phase noise limits the frequency resolution
- Broadband phase noise reduces SNR
YET another data point for frequency interval
A reader alerted me to an excellent AES paper on jitter for audio components, available for free from Wolfson Micro. There, the authors propose a "baseband" value of 100Hz to 40K Hz
If we use these frequency values we obtain (via the handy online jitter calculation tool) the following jitter values:
- 1.6 psec or 1600 fsec for a c33xx class clock (100Hz-40KHz)
- 0.046 psec or 46 fsec for a 950 class clock (100Hz-40KHz)
Unfortunately most of the research on the effect of phase noise revolve around digital telecommunication, where the frequency is in the 100s of MHz. There clock jitter determines the SNR and effectively the bandwidth of the devices, and the phase noise value that is important is the broadband phase noise.
So what is the effect of phase noise in audio?
According to this AES paper by Bruno Putzeys (Hypex, Grimm Audio) it is just noise.
I also took a look at other implementations of the ESS DAC and what kind of clock they use. It seems that only DIY versions can "afford" the high-end clock... Also note that the ESS evaluation board uses a "standard" crystal, rather than a clock (or so it looks like)
Eastern Electric DAC