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In Reply to: RE: "More DACs"..... posted by Todd Krieger on July 14, 2015 at 16:37:48
"The question I've always had with using multiple DAC chips is *how* it would increase dynamics or lower distortion."
Here are two reasons for increasing signal to noise ratio:
1. Current mode DACs use a fixed resistor in their I/V converter. The Johnson noise (measured as a voltage) depends on the value of this resistor and its temperature. Most DAC chips (especially ones that use CMOS technology such as the SABRE chips) are current sources. If you parallel these you get more current into the same resistor, which means that the signal increases by a factor of N, but the Johnson noise remains the same. This improves the signal to noise ratio.
2. For sigma delta DACs such as the SABRE, the modulator produces noise which is a function of the number of current mode switches per audio channel and the master clock rate. If you parallel chips the signals add coherently, but the noise adds randomly. This also improves the signal to noise ratio.
These is really no different than the situation when comparing the signal to noise ratio of 2 track and 4 track tape. Here the first aspect of wide tape is more signal power to overcome any noise in the receiver amplifier, while the second aspect corresponds to the fact that the tape hiss is uncorrelated.
The situation is more complicated when it comes to distortion and depends more on the details and limitations (design and manufacturing) of the individual DACs. I don't know how to explain this in simple terms, unlike the situation with respect to signal to noise ratio.
Tony Lauck
"Diversity is the law of nature; no two entities in this universe are uniform." - P.R. Sarkar
Follow Ups:
Tony,
your second item is the fundamental reason for an SNR improvement, the signal adds coherently but the noise adds randomly (nicely put), giving a 3dB SNR improvement for every doubling of the number of DAC channels.
Point #1, about a summing resistor, is relevant only where the system noise floor is dominated by the noise of the current-to-voltage converter and not by the DAC chip output.
For distortion, my expectation is that if all the paralleled DACs have the same signal-to-spurious performance then the composite DAC would be the same, but I don't have direct experience of this. Also, my understanding is that most modern DAC chips, SABRE included, are voltage outputs.
Regards
13DoW
I mentioned point one, because some people have argued that the achievable signal to noise ratio of a DAC is limited by Johnson noise. This is not true. If the thermal noise can be made 20 dB below the other sources of noise then it won't have a significant effect on the overall noise floor.
The second method comes from averaging, and if simple methods are used you get a 3 dB gain. You also get a 3 dB gain within a given noise bandwidth by doubling the sampling rate for similar reasons. However, if the sampling rate is increased a much greater gain can be had within a given noise bandwidth by using noise shaping. In addition, if the separate chips are fed different signals it is possible to get more than a 3 dB gain without using noise shaping. (The SABRE chip takes this approach when the number of audio channels is reduced. Halving the number of channels doubles the number of switches available for each channel and this results in a 6 dB gain, not the 3 dB gain one might expect.
One hard limit comes from jitter noise on the master clock. This noise modulates the audio signal and it also modulates the idle audio signal if noise shaping has been used. It may be possible to average out this noise by using separate clocks and get the 3 dB effect, but this will require the clocks to be unsynchronized (random jitter) while still being synchronized (otherwise high frequency response will deteriorate through aperture effect). In the end, the only hard limit is that fixed mathematically by the format. The bit rate of the digital channel provides an upper bound on the possible signal to noise ratio of the analog output of the DAC within a given bandwidth, in accordance with information theory.
Distortion is hard to analyze because it is usually not random. Therefore statistical methods (which gave the 3 dB noise values discussed above) are not properly justified. This is particularly true where the distortion comes from design errors or manufacturing defects (e.g. two DAC chips coming from the same lot may be barely within specification, but their distortion may be highly corellated). Analysis is complex and depends on internal design of the DAC chip and its algorithms and this is likely to be proprietary.
The SABRE chips have two modes of operation, voltage and current. The voltage mode consists of a built in I/V converter and op-amp. This is geared to mid-fi applications of the chip. All high quality applications use the current mode output which requires an external I/V converter. Some DACs such as the PS Audio direct stream DAC takes a single bitstream and uses it to drive high power switches, making it possible to use a transformer to serve as an I/V converter, low pass filter without requiring any output amplifiers. The presumption is that passive components have less distortion than active components. There still will be distortion in this approach. It will come from non-linearities in the sigma-delta modulator. There will also be noise caused by master clock jitter.
If you parallel separate sigma-delta DAC chips that are running off separate modulators, if they are fed with the same digital input it is likely the will generate the same digital noise provided they run a deterministic digital algorithm. This is going to create problems, because performance will be better when the multiple DACs are running with unsynchronized modulators. This may or may not happen. The solution is to add randomness into the input of the modulators from time to time. Whether anyone actually does this or not remains to be seen. This os a variation of Murphy's law of clocks, "If a system requires clocks to be synchronized for good performance, then clocks will not remain synchronized. If a system requires clocks to be unsynchronized for good performance, then clocks will remain synchronized.". We found this out at Digital Equipment in the early 80's while designing Ethernet controllers and chips.
Tony Lauck
"Diversity is the law of nature; no two entities in this universe are uniform." - P.R. Sarkar
Tony,
very interesting. My limited exposure to Nyquist rate ADC design dictated trying to get all noise sources low enough so the SNR was dominated by quantization noise.
I knew that the SABRE DAC had both types of output but, somehow, I'd got in my head that the current output was created from the voltage output. Your description makes more sense.
Regarding I/V converters, some people use passive components but that can add distortion as the DAC current output really wants to see a fixed voltage and not a voltage changing with signal level. Hence, an opamp-based virtual earth is often used but that can bring transient problems. Some have used a common-base/gate followed by a resistor that, IMO, is the best of both worlds.
For a bitstream signal the output voltage is all there is, no conversion required, expect for low-pass filtering to remove the shaped quantization noise. For DSD I believe that is quite a complicated filter.
Nice idea about uncorrelating parallel modulators. If no-one is doing this you should file the IP!
Regards
13DoW
If the I/V converter uses a very low value resistor and the current switches are driven off a much higher voltage source then the current contributed by one switch will not be affected very much by the other current sources. The distortion can be made as low as desired simply by lowering the resistor, at least down to the point where output voltage is too low to be amplified with an acceptable signal to noise ratio. This design requires gain downstream of the summing resistor. Another approach is to use a transformer to provide the voltage step up, with similar results.
I haven't said anything that is particularly new, so I don't think there is anything patentable. DSD output filtering can be done by oversampling (as in the SABRE chip) or it can be done by a FIR filter obtained by mixing the output of 1 bit DACs fed with different streams, as in Miksa's design.
Tony Lauck
"Diversity is the law of nature; no two entities in this universe are uniform." - P.R. Sarkar
According to ESS 'specs' the Sabre chip can output in either current or voltage mode depending on the configuration.
From the Spec Sheet:
The default configuration ,in eight channel mode, is that a pair of six bit DACs operating in anti-phase make up each channel. Since the DACs are as described, namely a Thevenin equivalent to a voltage source linearly between AGnd and AVcc having an approximately 800Ω output impedance, you
may choose to connect this output to a voltage mode (non-inverting amplifier) configuration; or you may choose to connect it to a virtual g
round current mode (inverting amplifier) configuration. The highest performance in terms of THD is via the current mode16, but both voltage and current mode provide aboutthe same DNR.
The default configuration for Stereo mode, and the only
configuration that can use the SPDIF input, is to wire four
output channels in parallel. When Stereo mode is enabled in
the configuration registers the same data is sent to all four
channels. Effectively now the DACs become a pair of eight bit
DACs having an output impedance of about 200Ω. This configuration allows
> 132dB of DNR to be typically reached. THD in the Stereo current mode is limited by the external components and measurement equipment. We
recommend using an extremely good op-amp for the highest performance but even an excellent op-amp is the limiting factor in the THD.
Dynobots Audio
Music is the Bridge between Heaven and Earth - 音楽は天国と地球のかけ橋
What I find interesting is that most modern DAC chips have phenomenal dynamic range and signal-to-noise specs. So much so that those numbers can never be achieved in 'real life' products once you surround the DAC chip with it's supporting cast of components. ;-)
Edits: 07/14/15
Even if the supporting cast of components of components is up to the task, few if any digital recordings would utilize it.
Dave
That too! For 99% of my needs, I'm listening to 16/44.1 CD rips and 24/96 uncompressed 'hi-res'. I've played with 24/192 and some DSD but didn't find those resolutions necessary for my overall enjoyment.
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