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RE: Bits of Resolution!

Posted by Thorsten (M) on October 19, 2015 at 07:36:33

In Reply to: Bits of Resolution! posted by Bromo33333 on October 18, 2015 at 09:11:11:

Hi,

Let us define first Resolution in digital systems and related terms...

Resolution (technically) means the difference between the smallest and largest signal signal the device can convert.

THD & N = Distortion plus noise compared to a signal level, audio specification typically stated at a given level, commonly 0dBFS which is always the worst case. Retest at -6dBFS and pretty much all digital audio parts improve significantly.

DR = Dynamic Range, audio specification typically stated at -60dBFS/997Hz signal and A-Weighted

ENOB = Effective Number of Bits - states how many "Bit's" the analogue performance allows, disregarding how many bits in a technical sense are used (1, 4, 8 32 etc.), ENOB can be misleading, because while commonly it is calculated on SINAD it is equally valid to calculate it on SFDR.

SFDR = Spuriae Free Dynamic Range, industrial measurement of the difference between full scale level for a ADC/DAC and the highest harmonics, it is quite similar to THD & N but in prectice values may differ a little

SINAD = Signal-to-Noise Ratio Distortion Ratio is an industrial/RF measurement of the ratio between noise and distortion and a given (stated) signal. It is somewhat parallel to the audio dynamic range, but no a-weighting is employed and the reference level may be different from -60dBF.

> 1. Commercial "Delta-Sigma" DAC chips - typically have under
> 20 bits of resolution. The absolute state of the art is 21bits.

I do noot think there is a single pure delta sigma chip that goes past 18 Bit ENOB at 96kHz, but I am happy to stand corrected. Note "pure delta sigma" implies strictly a system with two output states, 0 & 1...

> 2. Programmable discrete logic/DSP/FPGA/etc.:

Is irrelevant to actual conversion, it simply contains digital processing, such as digital filters and moduators. The actual conversion does happen outside the programmable logic.

In practice the principles differ zero from standard filters and modulators integrated on chip for generic modern audio ADC/DAC, but the precise implementation may be able to diverge from the set of compromises applied by the Chip Maker and may suit a specific designer better.

We are starting to see more DAC and ADC chip's that included programmable filters, I predict that in the not too far future you run off the mill 1 buck chuck ADC/DAC chip will allow you to load different filter coefficients, effectively giving similar flexibility as using a FPGA.

> 3. Ladder Networks: Problems with loss of linearity towards the LSB
> due to unavoidable error stack-up.

There are many ways to deal with that. The long discontinued PCM63 and AD1862 both offered 20 Bit ENOB.

Certain Burr Brown (now TI) DAC's used a set number of multibit "bits" for the upper (Most Significant Bits - MSB's), between 6 - 10 Bit worth, with lower bits handled by a separate DS modulator. This kind of hybrid DAC has many advantages in practice over pure multibit systems as well as over pure delta sigma systems, but costs are relatively high for a given level of objective performance.

And the higher cost is the only argument against "ladders" - performance was never the issue, if we are truthful.

There is a reason however why the "mediocre" BB PCM1704 multibit DAC (without any integrated digital processing and for a single channel) costs more than a highly configurable 8-Channel hybrid DAC Chip that you can even load your filters into and where each of the 8 Channels knocks the PCM1704 clean out of it's socks (never mind shoes) and nevertheless has remained in production.

As TI/BB have defended their IP for this type of multibit plus DS hybrid DAC vigerously and still hold valid patents all other had to find different ways. Most common (and now used by BB/TI for lower end parts as Cirrus Logis's patents have run out) are switched capacitor filters, which add usually around 8 - 16 Levels (so 3-4 Bit worth of "multibit") with agressive noiseshaping. It is very cheap to make.

In fact, those switched capacitor filter parts are what you referred to above as "delta sigma DAC's", which is not completely correct, they are hybrid types which is why they can get past the 16...18bit realistic limits of pure DS systems.

> 4. Conversion from PCM to PWM/DSD: It is growing in popularity,
> but does require some digital noise shaping.

Actually, it requires a truckload of noise shaping.

In reality standard DSD struggles to exceed 18 Bit equivalent noise levels 20Hz-20kHz under loopback conditions and to get this it requires a 7th order modulator at 64 X Oversampling. And the 7th order noise floor rise starting in the audio range is one of the big problems there.

Now, let me get back to bits... Allow me an analogy.

We have five experts evaluating mixed signal conversion parts. They may be AD/DA or possibly even DD or AA converters...

Expert A comments on Part A: "It is a 24 Bit/192kHz audio part that delivers a fine analogue performance for this kind of part with a 114dB dynamic Range."

Expert B comments on Part B: "It offers over 16 Bit ENOB based on SINAD at -60dB and has a usable signal bandwidth of up to 100kHz."

Expert C comments on Part C: "The poor linearity at full scale means that this part is equivalent to no more than 14 Bit and performance suffers further if we increase the bandwith to the 100kHz theoretically available."

Experd D comments on Part D: "Offering a hardware resolution of merely 128 Levels or 7 Bit for a 21uS timeframe it is unsuited to any task that requires high instanious precision, such as fast and unpredictably changing transient signals."

Do you think they are talking about four different parts? Nope, they are talking about the same exact part. One might think that of these guys three must be deluded and only one can be right, but they are, in a specific sense all correct.

The part is an ADC or DAC based single bit (Delta Sigma) operation at appx. 6MHz regardless of input/output sample rate. It offers 0.005% THD & N at digital full scale and 114dB Dynamic range (audio style), accepts and processes without truncation (before the DS modulator anyway) 24 Bit audio data and accepts sample rates of up to 216kHz.

In the year 2015 this is hardly world beating stuff but it is solid performance given the tech employed and it is bound to be so cheap, it ain't funny.

Now here is the final clincher. Of all the experts talking about this part, no-one offered us anything that can be related to sound quality. Neither does the manufacturers datasheet contain anything that would allow us to evalute the possible sound signature.

I have come across parts with very similar fundamental specifications (THD & N, DR, SFDR, SINAD, ENOB) within one or two dB. Some sounded so awful, it was "turn it off - make it go away", others sounded quite excellent, often better than much more expensive and higher spec parts.

Conclusion, if we do industrial measurements, RF Work like RADAR and so on, SDFR, SINAD and ENOB are important. For audio they have surprisingly little meaning and their Audio Kissing Cousins like THD & N and DR are equally useless in determining sound quality, once the basic performance exceeds certain minimum levels.

Thor

At 20 bits, you are on the verge of dynamic range covering fly-farts-at-20-feet to intolerable pain. Really, what more could we need?

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