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I'm currently studying designs for a pulse oximeter for use with Arduino, I have seen two Schematic designs form the same company, https://www.protocentral.com/sensors/1113-protocentral-afe4490-pulse-oximeter-shield-for-arduino-v2-642078949425.html and https://www.protocentral.com/open-source-health/1252-healthypi-v3-basic-hat-kit-for-raspberry-pi.html . Both of them are identical and are base around the AFE4490RHAT IC from Texas Instruments. Both designs have 4 inductors : L1, L2, L3 , L4.

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1) What are these inductors used for in the design?

2) In one of the designs they are using 4 CIG22L100MNE and in the other 4 LPS3010 (they don't specify the full part number) but the Samsung one seems to be discontinued and the other one seems to be not recommended for new designs, I'm trying to choose and equivalent I have compared the specifications between the two parts and a part from the inductance they seem to have very different properties regarding current rating, DC resistance and inductance frequency, what specifications are more important when choosing a replacement part?

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1) The inductors are used to filter noise from supply voltage. As each supply node has its own inductor, noise caused by periodic gulping of current on one supply node cannot pass on to other supply nodes and cause problems taking the sensitive measurements.

2) That is a good question and there may not be an answer. It seems that the evaluation kit for the pulseoximeter chip used a 10uH inductor LPS3010-103MLB everywhere, most likely to reduce cost by using same part for everything, and that reference design got copied everywhere. So as long as the parameters are reasonably same almost any inductor could be used.

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1) What are these inductors used for in the design?

Each inductor forms a LC low pass filter (L1 & C19, etc), to filter out noise originating from the 3V3 source to which they are connected to.
The cutoff frequency is determined by

$$ f_c = \frac{1}{2 \pi \sqrt{LC} } \approx 16 \text{ kHz} $$

2) […] what specifications are more important when choosing a replacement part?

If you don't know the current requirements of the loads (labelled as LED_DRV_SUP, etc) I would just pick the same current rating (or higher).
As shown above, the value of inductance is determining the cutoff frequency of a LC filter. As I don't expect it needs to be exactly 16 kHz, you can change the value: 8.2 uH or 12 uH will probably do as well.

It can be useful looking at distributor's websites for alternatives for an obsolete component. E.g. Arrow gives as (one of the ) alternatives to the CIG22L100MNE the CB2518T100KV which also has a 10 uH inductance, a 0.6A current rating, but just a smaller package shape

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As others have noted, the inductors are part of the noise filtering.

They are extremely non critical - within reason "some inductance of about the right value" is liable to be suitable. Pulse oximeters are liable to be moderately sensitive to noise but not immensely so - the signal levels involved are small but not (usually) in the microvolt range. Good layout and design - (PCB tracks, capacitor locations and quantity, ...) are liable to be as important as inductance values.

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