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#### Wayne A. Pflughaupt

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Okay, here’s a question for you electronics experts. I know a 16-bit A/D converter has 65,536 quantization or amplitude steps, and a 24-bit waveform has 16,777,216. It’s not hard to find that info on the internet, but I can’t find anything on 20-bit A/D converters. I’m working on a review of the Yamaha YDP2006 digital equalizer and it’d be helpful to know that tidbit of information!

Regards,

Wayne A. Pflughaupt

#### stereo2.0

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2 ^ 20 = 1,048,576 steps.

#### Wayne A. Pflughaupt

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Just a matter of knowing the right math I guess, which I don't.
Thank you kind sir!

Regards,

Wayne A. Pflughaupt

#### andyc56

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If you really want to split hairs, for N bits the number of steps is 2 N - 1, while the number of states is 2 N . That is, the number of steps (transitions between states) is one less than the number of states. For instance, draw 4 equally-spaced dots along a line (the states) and there's 3 spaces between them (the steps).

#### DonH50

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For an ideal N-bit converter:
• Number of steps = 2^N - 1
• SNR ~ 6*N + 1.8 dB
• SFDR ~ 9*N dB
• Aperture time = 1/[(2^N)*pi*f] s where pi = 3.141592654 and f = signal frequency (independent of the sampling frequency, for a sine wave input). Note Gaussian (random normal) jitter with standard deviation equal to the aperture time costs about 8 dB in SNR.
• SNR set by jitter tj = 20log(2p*fin*tj)

and so forth... IEEE Standard 1241 deals with ADC specifications.

Wayne A. Pflughaupt

#### arnyk

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Quote:
Originally Posted by DonH50  /t/1522307/how-many-amplitude-steps-quantization-does-a-20-bit-a-d-converter-have#post_24476050

For an ideal N-bit converter:
• Number of steps = 2^N - 1
• SNR ~ 6*N + 1.8 dB
• SFDR ~ 9*N dB
• Aperture time = 1/[(2^N)*pi*f] s where pi = 3.141592654 and f = signal frequency (independent of the sampling frequency, for a sine wave input). Note Gaussian (random normal) jitter with standard deviation equal to the aperture time costs about 8 dB in SNR.
• SNR set by jitter tj = 20log(2p*fin*tj)

and so forth... IEEE Standard 1241 deals with ADC specifications.

The above correct analysis is as it says ideal, but from years of working with him on forums, I'm sure the author also knows the practical perofrmance of converters is almost always far less than the ideal. He left the bad and ugly news for me to bare. ;-)

Most 20 bit converters are called 20 bit converters because they look at or generate 20 bits of unique data.

The first practical exigency is the fact that there are no standard data transmission format with only 20 bits of data. Generally the 20 bits will be padded out to 24 bits to fit into the real world.

The second practical exigency is the fact that manufacturers throw these bit numbers around quite casually, and few if any converters actually have the analog domain performance that their bit designations might suggest.

16 bit converters are lucky to have 14-15 bit performance. 20 bit converters might get to 16 or 17 bits but some only do 15 bits. . 24 or 32 bits might do 18 or 22 bits with maybe 23 bits being the high water mark. Some 24/192 converters are only good for 14-15 bits of analog performance.

The extra data bits are usually noise and distortion. The threshold of hearing is usually around 14 bits at the best, so the excess bits are largely moot, although it generally takes 15 or 16 bit (actual) resolution to deliver 14 or 15 bits to the real world.

#### DonH50

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Yup, I just design 'em, I let you be the heavy in telling folk what the real world is like.

The IEEE committee that did the ADC Standard, among other organizations and many customers, often decries the specsmenship going on. (One of my former bosses is on the committee, and I was the guinea pig for a lot of the reports and proof-reading.) Marketing and engineering debates are not limited to the audio industry! It is very hard to test all conditions, and a lot of times the results are very dependent upon the input signal, so there is always some give and take. At least test conditions are a lot better defined in most datasheets than they were ten years ago.

Glancing at the ADI AD1852, a 24-bit audio DS DAC chip, it lists typical 112 dB SNR and 102 dB THD+N. That is a long ways from the ideal 146 dB ideal number due to quantization noise, and is about 16 - 17 effective bits. My experience has generally been the same as Arny's, with real 16 to 18 bit audio-rate converters losing a bit or two and increasingly more loss as resolution is increased. Just not enough headroom, or low enough noise in distortion, in a real circuit running at only a few volts. Designers often shoot for distortion on the order of the quantization noise floor for a lot of practical circuit reasons, so losing a bit (6 dB) from ideal is pretty common. "Real" 24-bit converters I have seen are very, very slow (integrating or slope converters often operating at a few Hz), may use lots of processing to clean up the output, and/or have much larger (10 - 20 Vpp) input/output swings. Note that for a 2 Vpp swing one lsb of a 24-bit converter is only about 2 uV (microvolts). It is still only 30 uV for a 16-bit converter.

Wayne A. Pflughaupt

#### Wayne A. Pflughaupt

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
Quote:
Originally Posted by arnyk  /t/1522307/how-many-amplitude-steps-quantization-does-a-20-bit-a-d-converter-have#post_24476434

The second practical exigency is the fact that manufacturers throw these bit numbers around quite casually, and few if any converters actually have the analog domain performance that their bit designations might suggest.

16 bit converters are lucky to have 14-15 bit performance. 20 bit converters might get to 16 or 17 bits but some only do 15 bits...
Quote:
Originally Posted by DonH50  /t/1522307/how-many-amplitude-steps-quantization-does-a-20-bit-a-d-converter-have#post_24478006

Glancing at the ADI AD1852, a 24-bit audio DS DAC chip, it lists typical 112 dB SNR and 102 dB THD+N. That is a long ways from the ideal 146 dB ideal number due to quantization noise, and is about 16 - 17 effective bits. My experience has generally been the same as Arny's, with real 16 to 18 bit audio-rate converters losing a bit or two and increasingly more loss as resolution is increased. Just not enough headroom, or low enough noise in distortion, in a real circuit running at only a few volts.

Are we talking about bit “loss” and distortion due to deficiencies in accompanying electronics, such as the power supplies? Or deficiencies in the actual converters themselves?

Regards,

Wayne A. Pflughaupt

#### Ethan Winer

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
Quote:
Originally Posted by Wayne A. Pflughaupt  /t/1522307/how-many-amplitude-steps-quantization-does-a-20-bit-a-d-converter-have#post_24475186

I know a 16-bit A/D converter has 65,536 quantization or amplitude steps, and a 24-bit waveform has 16,777,216.

I think "steps" is the wrong word because audio doesn't emit from a D/A converter with steps. The better term is "noise floor" because that's what is actually determined by the number of bits. Wayne, I assume you've seen this wonderful video, but just in case:

Monty Montgomery explains digital audio

--Ethan

#### arnyk

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
Quote:
Originally Posted by Wayne A. Pflughaupt  /t/1522307/how-many-amplitude-steps-quantization-does-a-20-bit-a-d-converter-have#post_24478310

Quote:
Originally Posted by arnyk  /t/1522307/how-many-amplitude-steps-quantization-does-a-20-bit-a-d-converter-have#post_24476434

The second practical exigency is the fact that manufacturers throw these bit numbers around quite casually, and few if any converters actually have the analog domain performance that their bit designations might suggest.

16 bit converters are lucky to have 14-15 bit performance. 20 bit converters might get to 16 or 17 bits but some only do 15 bits...
Quote:
Originally Posted by DonH50  /t/1522307/how-many-amplitude-steps-quantization-does-a-20-bit-a-d-converter-have#post_24478006

Glancing at the ADI AD1852, a 24-bit audio DS DAC chip, it lists typical 112 dB SNR and 102 dB THD+N. That is a long ways from the ideal 146 dB ideal number due to quantization noise, and is about 16 - 17 effective bits. My experience has generally been the same as Arny's, with real 16 to 18 bit audio-rate converters losing a bit or two and increasingly more loss as resolution is increased. Just not enough headroom, or low enough noise in distortion, in a real circuit running at only a few volts.

Are we talking about bit “loss” and distortion due to deficiencies in accompanying electronics, such as the power supplies? Or deficiencies in the actual converters themselves?

Power supplies and accompanying electronics are a minor issue, not nearly what some make them out to be.

These numbers are primarily related to the limitations of the DAC chips themselves.

For example this is a link to the preferred evaluation board for this part:

Obviously it is designed to show the DAC chip at its best.

Its contents are normal commercial grade parts. For example the dual OP275 op amp runs less than \$1.50 in small quantities

#### Wayne A. Pflughaupt

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Hey Ethan, long time! Believe it or not I was just thinking about you yesterday, that we haven’t crossed paths in quite a while! No, haven’t seen that video, I’ll check it out.

Regards,

Wayne A. Pflughaupt

#### Wayne A. Pflughaupt

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This has been very helpful, guys, thank you very much! Hope you don’t mind if I plagiarize/paraphrase some of this in the review.

Regards,

Wayne A. Pflughaupt

#### DonH50

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Hey Wayne,

I was speaking of distortion and noise in the data converter itself. Buffer amplifiers at the output of DACs is usually the next major contributor, and as you might imagine can easily contribute as much as the DAC itself if not well designed. To this gets added power supply noise (to the extent above the PSRR floor), coupled noise/EMI/RFI, any other system noise, etc. The DAC and buffer amplifier are normally the dominant players in THD+N, and over most of the output range it's the DAC itself.

Similar arguments can be made on the ADC side, which requires an input buffer and anti-alias filter.

In an audio system, normally the distortion is (by far) limited by the speakers.

On the steps, any DAC requires an anti-image filter that suppresses images of the output that occur at multiples of one-half the sampling rate. This filters the steps seen at the output of a conventional (Nyquist) DAC but they are still there. However, most audio DACs are delta-sigma designs, and they do not generates steps in the normal sense of the word. The output of a delta-sigma DAC is a "digital" pulse stream that is filtered so you do not see any steps.

HTH - Don

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