This is my limited understanding, please feel free to add or correct anything.
Some of the capacitors uses related to all zishan models that come to mind are:
- Power supply reserve/storage/smoothing: Caps can be used as _local_ power reserve. As the word says they are used as local power reserve and to supply smooth stable voltage, to try to keep voltage as stable as possible. They are used in parallel with the power supply lines and ground.
You need them near the opamps power supply pins, connected in parallel with the power supply pins and ground. They try to supply a steady smooth power to the opamp. One upgrade possible is to add (where missing) or increase the capacity.
They are also used in stm32 power supply pins, stm32 datasheet recommends more capacitance than zishan uses, so one of the upgrades is increase the stm32 power supply pins caps capacitance. This is important, not only to stm32 operation, but to the rest of the circuit. If the cpu needs current fast and we don't have these, it can make power fluctuations in the rest of the circuit.
They are also used in the DACs power supply lines, there are a lot of them in z1, z2, z3 and DSD around the DAC, we can read the dac datasheet and implement the recommended capacitance and cap type in the circuit, this is one of the possible zishan upgrades.
- Coupling capacitors: In series with the signal path, capacitors pass AC, but block DC signals, so they can be used to separate these components, to pass the music (AC) and block DC. To do this they are connected in series with the audio signal path.
These are the electrolytic capacitor that people usually change in zishan.
The DC component we want to block (a DC voltage), displaces the speaker cone from it's central position, it can cause distortion or even kill the speaker.
When this caps are used they "spoil" sound to some extent, so people change them to change sound color to personal taste or to try to minimize changes.
Also this signal couple caps, have a side effect of acting as freq. filters, so their capacitance must be calculated not to filter the audio freq. band.
In sum, in some circuits they are needed to block DC in audio path, but they "change/degrade" sound and act like a frequency filter.
Their capacitance must be calculated not to filter the audio band and people change them to minimize their effect in sound or to color sound to personal preference.
- High pass and low pass filters:
Here caps are used to make filters and selected the audio freq. band that will be amplified and heard.
- Bypass capacitors:
In parallel with power supply lines and ground, a capacitor is used to short AC signals to ground, they filter/remove interference. This way AC noise present in DC can be removed and we have a cleaner power supply. In zishan we can see 0.1uF ceramic bypass capacitors in parallel with some, but not all of power reserve caps. One upgrade can be to add some more bypass caps where needed. They need to be located very close (ideally at the legs) to the power supply legs of the opamps, dac, cpu, etc.