How digital data converted to analogue sound

 
A converter circuit should be used, named DAC (Digital to Analogue Converter). In essence it is a reversed process of the conversion from analogue to digital. It translates a binary audio data signal to analogue oscillating/ alternating electrical signal, essentially continuous voltages instead of an on/off signal. 

The binary code is like coordinates for the original analogue voltage values. The code is linked to a voltage range between zero and the maximum voltage level of the binary signal  

The three most common DAC systems: 

 
Summing Amplifier: 

The simplest (but the least practical) of all . An op-amp connected to weighted (increasing in resistance) several resistors. A signal enters at a solo input and goes through of the different resistors. At the end a summing amplifier combines the divided signal into one. It has to have carefully selected resistor. As the bit depth is increasing the number of required resistors are multiplying, it is not a practical solution for high resolution conversions 

 
R-2R Ladder: 

This is not the droid you are looking for. This based on the principles of connected resistors in series and parallel, acting as voltage dividers. Each leg of the ladder will let through one half of the reference level, that can be passed by the previous step (or the maximum V(r) for the first step. Then each step are being switch on/off depending on the binary code’s individual bits. At the end of the ladder, the values summed up to a single analogue output. 

 
PWM DAC: 

Most modern DACs are using this technology. PWM (pulse width modulation) signal is essentially a more complex binary signal with a time element. It has to be used with an RC (resistor-capacitor) filter, which separates the DC and AC elements of the signal (keeping the AC only).  

Jitter in DAC 

Jitter in DAC is a discrepancy between the timing of samples during ADC and DAC. It occurs during reconstruction and the root cause usually an inferior clock signal either at ADC or DAC, or a binary signal noise usually introduced by a faulty or unsuitable DC transformer close to the clock. It manifests in a form of audible distortion as the given voltage values appear at the wrong time thus the signal is distorted compared to the original one. 

Avoid jitter by using reliable word-clock during both the ADC and DAC and eliminate DC noise in the binary signal 

What is a reconstruction filter?

It is a low pass filter (only allows to get through frequencies which are below a certain threshold. It meant to filter out unwanted non-linear high frequencies which was introduced during the DAC process as a result of insufficient data (too much guesswork)  

Oversampling 

Oversampling is a process when we increase the sampling rate above the minimum requirement, determined by the Nyquist theorem. With more samples taken, the accuracy of the binary representation of the analogue wave can be increased. 

Why we need that? Mathematically we do not need oversampling as in theoretical calculation we assume that perfect components are being used, such as a brick limit low pass filter, which doesn’t exist in reality because of technical limitations. Oversampling is also assuring that we capture the whole desired frequency response in practice. Covering everything which would be missed because of the lag of certain electrical components. 

References:

https://components101.com/articles/digital-to-analog-converters-dac
https://www.arrow.com/en/research-and-events/articles/dac-buying-guide-find-the-best-digital-to-analog-converter https://www.electronics-tutorials.ws/combination/r-2r-dac.html
https://www.electronics-tutorials.ws/combination/digital-to-analogue-converter.html
https://headfonics.com/what-is-jitter-in-audio/
https://hifigo.com/blogs/guide/what-is-digital-jitter-and-how-to-avoid-jitter-dac-101-part-3 https://www.sciencedirect.com/topics/engineering/reconstruction-filter
https://www.thebroadcastbridge.com/content/entry/15904/digital-audio-part-5-oversampling