What is a 1-Bit DAC and How Does it Work?

Рет қаралды 11,986

Iain Explains Signals, Systems, and Digital Comms

2 жыл бұрын

Explains the 1-Bit Digital-to-Analog Converter (DAC) from a signals perspective, and discusses some of the tradeoffs in their performance compared to full resolution DACs.
Related videos: (see iaincollings.com)
• How are Signals Reconstructed from Digital Samples? • How are Signals Recons...
• Sampling Signals • Sampling Signals
• Interpolation of Discrete Time Signals: • Interpolation of Discr...
• Sampling Example • Sampling Example
• How to Understand Convolution • How to Understand Conv...
• Convolution Square with Rectangle • Convolution of Square ...
• Fourier Transform Duality Rect and Sinc Functions • Fourier Transform Dual...
• What is Aliasing? • What is Aliasing?
• What is Negative Frequency? • What is Negative Frequ...
For a full list of Videos and Summary Sheets, goto: iaincollings.com

Пікірлер: 49

@aivyulik 10 ай бұрын

I think it’s the best explanation of how DSD works that I’ve seen. Thank you!

@iain_explains 10 ай бұрын

Glad you liked it.

@sophiacristina Жыл бұрын

Nice to find your channel! It is the kind of resource i was wanting for a while now... Signal processing is kinda underrated and there is not much content. I'm also impressed by the creativity people had to extract information from 1-bit... :)

@iain_explains Жыл бұрын

Welcome aboard!

@looneyburgmusic 3 ай бұрын

@3:10 Was wondering how you were going to recover the waveform between 0 - Ts, since they have the same value, meaning that part of the waveform would have been lost...

@thanhphungtruong119 4 ай бұрын

Thank you very much for your great video. I have a concern about low-resolution converters in a communication system. Could you please help me explain it? Assuming that after precoding, the signal is transmitted via M antennas with low-resolution DACs (say 2-8 bits), can the ADCs at the receivers operate with a different resolution from the DAC at the transmitter?

@iain_explains 3 ай бұрын

Yes, there is no requirement for a DAC at a transmitter to have the same resolution as the ADC at the receiver. Between them, there is a channel with (continuous-valued) gain and amplifier noise, plus potentially interference from other signals. It's not a case of "matching" transmit DAC levels with receive ADC levels.

@user-dc2fw9jd3v Жыл бұрын

Thank you for the great videos. Very informative and enjoyable to watch. I have for years wondered about how a 1-bit ADC worked ever since I saw it advertised for an application back in the late 90’s. Often today 12, 14 or 16-bit Analog to Digital Converters are used to adequately sample and represent a signal. But how in the world to do it with a 1-bit A/D has been a bit of a mystery to me. Would be awesome to see a video about 1-bit ADC if you have knowledge of these and any interest in creating a video. But again, thanks for the great videos!

@user-dc2fw9jd3v Жыл бұрын

By the way, to clarify, I’m not referencing delta-sigma converters, nor comparators. Possibly flip-flops as implemented but I’m uncertain as to whether something like a D flip flop was used in implementation.

@iain_explains Жыл бұрын

A 1-bit ADC works exactly the same as the 1-bit DAC, except in reverse. in other words it also operates at a high rate (ie. sampling rate, in this case) and simply checks to see if the analog signal has gone up or down between samples. It relies on the sampling rate being high enough such that the analog signal changes are small.

@aristotleonassis5792 Жыл бұрын

Could you explain this is all done by the electronic circuits? What equipment holds each voltage level and what syncs the time emission of each? Is it a mixture of hardware and algorithms? For an example analogue represents the audio wave by differences in magnetic displacement and tape speed is the fixed periodicity.

@iain_explains Жыл бұрын

It's a complicated electronic circuit. Too complicated to explain here, sorry.

@kissingfrogs 2 жыл бұрын

Thanks for the video. I watched twice but was still struggling (and always have) with the idea of a CD player using a 1-Bit DAC to convert data that is 16-bit PCM encoded at a 44.1 kHz sampling rate. Intuitively, the data on the CD would need to have been previously 1-bit encoded at (44.1 * 256) kHz. However, you mentioned digital interpolation and finally I think I understand. Thankyou. I am going to watch that video. I always thought it odd that some CD players were proudly claiming to employ 1-Bit DACs which I assumed was either inferior or not possible. Clever marketing I guess.

@iain_explains 2 жыл бұрын

Yes, I've also wondered about the advertising too - ever since I got a portable CD player back in about 1990 when I was an undergraduate student, and I noticed it had "1-Bit DAC" printed on the door/lid/top. It's rather odd to advertise that you're using the cheapest components possible! I've always pictured an advertising person walking into an engineering design lab and asking "what's the latest stuff you're working on?", and then not really understanding the answer, but remembering the phrase "1-Bit DAC", and thinking it sounded catchy!

@pratiraj1 2 жыл бұрын

Great explanation ...very useful :)

@iain_explains 2 жыл бұрын

Thanks. I'm glad you liked it.

@pierreschmidt271 2 жыл бұрын

Thanks for this learnful video. I am still wondering: as the 1 bit DAC finally ends up as PWM+low pass filter based DAC for reproducing the analog signal, what is the benefit for using 1 bit DAC rather than simply considering a 65536 (for 16 bits samples) steps PWM? My guess is that designing such PWM with 65536 increments might be tricky and also the 1 bit DAC "follows closer" to the original signal after doing low pass filtering, but please I would like your confirm.

@iain_explains 2 жыл бұрын

It depends on what you mean by a 65536 step PWM.

@pierreschmidt271 2 жыл бұрын

@@iain_explains A PWM with 65536 different high/low ratios. It might not be difficult to design such PWM with a 16 bit counter followed by comparator whose output toggles upon detecting equality between counter and incoming 16bits sample value. So the question is what benefit has 1-bit DAC over simple PWM based DAC?

@iain_explains 2 жыл бұрын

A PWM that has 2^16 different pulse widths is not the same as a 1-bit PWM running at 2^16 times the rate. For example, the high rate 1-bit PWM can produce waveforms that toggle between values multiple times, within the same period that the PWM can only change values once.

@pierreschmidt271 2 жыл бұрын

@@iain_explains Thanks, my understanding is that toggling multiple times instead of only once within the same period of time, will shape the signal closer to the original (analog) one after the output is integrated (filtered).

@sc0or Жыл бұрын

Just multiply, and you will find a PWM counter speed about 2.5GHz for 16/44.1. That’s why math helps to reduce this number to reasonable 100 times smaller values inside modern DACs

@emadibnalyaman8073 2 жыл бұрын

Sir, first, Thank you ... your videos are beneficial for us; can you please make a series of videos to talk about beamforming algorithms like the MVDR algorithm.

@iain_explains 2 жыл бұрын

Thanks for the suggestion. I'll add it to my "to do" list.

@salmonsandwich3183 10 ай бұрын

let's say I'm looking at portable cd players on ebay. One player is 1bit dac. the other is 8 times oversampling. Which one sounds better? I watched your video, but I'll probably have to re-watch a few more times to really get it. From what I understand after my first watch, the 8x oversampling is the better sounding (more detailed and accurate) unit, right?

@iain_explains 10 ай бұрын

It depends on the amplitude resolution of the "8 times oversampled" DAC. If they don't say what it is, then it's probably low resolution. Maybe not as low as 1-bit, but the 1-bit DAC probably oversamples by much more than 8 times.

@alexanderwolfe8782 2 жыл бұрын

great video!

@iain_explains 2 жыл бұрын

Glad you liked it.

@eliesgrau7487 Жыл бұрын

My DAC is a 1995 Philips 1549T/N1. I found some information about the 1549 and other versions too but not about my specific N1 version. I'm new and confused with this about DACs. Can you tell me if my DAC is good/normal/bad quality? what potential does it have if I combine it with other components? I can't find much information on the internet. Thanks

@iain_explains Жыл бұрын

Sorry, I'm not familiar with specific chip sets.

@eliesgrau7487 Жыл бұрын

@@iain_explains thanks

@attilabpc542 Жыл бұрын

Amazing engineering.

@iain_explains Жыл бұрын

I'm glad you liked the video.

@shovon3091 2 жыл бұрын

How did you get the 1.166 as a factor for twice the sampling rate?

@iain_explains 2 жыл бұрын

Ah yes, well the full range has 8 levels, but only 7 gaps between those levels. So with double rate sampling, there are 4 levels, with 3 gaps between them, that need to span a range of 7/2 = 3.5. So, 3.5/3 = 1.16666.

@shovon3091 2 жыл бұрын

@@iain_explains thanks

@jaybrodnax 11 ай бұрын

Some companies seem to market 1 bit DACs as if they are an interesting or beneficial quality...are there any potential advantages besides lower cost?

@iain_explains 11 ай бұрын

I'm not a hardware expert, but there may be advantages in power consumption, since the circuitry is most likely simpler with fewer components, even though it's operating at a much higher clock rate. I really don't know - but am interested to find out myself.

@pierreschmidt271 2 жыл бұрын

One more question: due to avaibility of the analog pencil drawn waveform, it becomes easy to draw the red dots, which simplifies the interpolation process. What about real world where on a CD there are consecutive samples with nothing between them? There is no other choice than drawing a straight line between the samples as any other waveform might be further from the original analog waveform.

@iain_explains 2 жыл бұрын

Perhaps this video will help: "How are Signals Reconstructed from Digital Samples?" kzfaq.info/get/bejne/mqppe6ZirLrMio0.html

@dscrimager 5 ай бұрын

You are correct; two samples at the same level provide no information between those points and the level output is constant. The solution is sampling (Nyquist) at a high enough rate that the 'missing' samples are not audible.

@tuongnguyen9391 2 жыл бұрын

This is quite strange but can you do a tutorial on how to read and write research paper :D

@iain_explains 2 жыл бұрын

Interesting question. Thanks for the suggestion. I'll give it some thought.

@tuongnguyen9391 Жыл бұрын

Do people actually use 1 bit adc in mobiphone or this is just some basic research concept that does not serve a practical design ?

@iain_explains Жыл бұрын

My first portable CD player (back in the late 1980's) used a 1-bit DAC, and even advertised the fact with a sticker on the front! I remember it clearly because I used to wonder why they were advertising that they were using the cheapest DAC they could. I still wonder about this. Anyway, yes, they're still widely used.

@dlarge6502 Жыл бұрын

Practically everything uses a 1 bit DAC, now when they DONT use one they advertise it as a marketing point and increase the price of the product.

@stevengross4113 Жыл бұрын

Don't follow this. One bit would mean 0 or 1 only, 0 or full scale. Don't get how you move in such a small increment.

@iain_explains Жыл бұрын

No it doesn't have to be "0 or full scale". The key is that the sampling rate is so high that the signal doesn't change much between samples. So all you need to do is encode whether the signal went up or down relative to the previous sample.