I found the circuit below for a Bluetooth sudio module that included a 100 mH inductor in series and then a 10 uF capacitor in parallel to the power input.
Image source: Iranian electronics seller called ECA
What is the function of the inductor? Is it necessary for the module to work smoothly? Is it necessary for it to be 100mH or can it be lower, 30/60mH in my case?
It's meant for filtering the supply power, though I'm not convinced it's a good idea to use an inductor here. If you have a dirty supply, or if you need to keep noise from the bluetooth module out of your supply, it would probably be better to use a ferrite bead.
A ferrite bead is something rather similar to an inductor, but instead of being designed for storing energy with low losses, they're specifically designed to have high loss at high frequencies. Where a low-loss inductor would just act as a barrier to noise energy, bouncing it back where it came from, a ferrite bead actually dissipates noise energy, removing it from the circuit entirely. The reason you'd use a ferrite over a resistor (which would also work) is that the loss in a ferrite is frequency-dependent: the loss at low frequencies and DC--where a power supply line normally operates--is very low, while the loss at high frequencies--which are undesirable on a power line--is high. A resistor would have similar losses at all frequencies.
A suitable ferrite bead would also have much lower inductance than a suitable filter inductor, meaning fewer problems with voltage spikes that could potentially damage your bluetooth module.
The inductor is not mandatory for the operation of the module, however it is recommended to prevent noise in audio and stability issues with Bluetooth. It serves the purpose of filtering the power provided to the module.
The inductor does not let the AC component of the input voltage to pass leaving only the DC component, thus making the input voltage cleaner and more stable.
You can learn more about this and other types of filters by googling “inductor input filter”
Edit: After reading few articles I wanted to add a bit more on the topic. This is an L-type LC filter with a cutout frequency of ~160Hz, so if assumed that the capacitor and the inductor are perfect it will attenuate all frequencies more than 160Hz.
