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I have two questions in one:

I have collected some schematic from datasheet from manufacturer of chip. Inside the datasheet there are the following circuit shown below.

1./ The manufacturer don't provide the BOM, so I don't have part number for all those small passive components. How to decide which one to use in terms of tolerance, X5R/X7R, Voltage, package ?

2./ On some schematic there are some polarized capacit, typically some round cylinder space consumming. By what type of SMD can I replace those big cylinder to make the circuit smaller ?

While answering this question, please explain it so I can understand what logical methodology you are using

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You must use general knowledge from understanding circuit design. In fact the exact make and model of capacitor or resistor are very rarely critical to the proper operation of the circuit.

For example, in the case of C1201, you probably would NOT want to use a capacitor of significantly LOWER value than is shown because that will reduce the ability of the circuit to smooth whatever ripple there may be on the incoming source. And if you used a capacitor significantly larger than the specified value, you may risk of a current surge during power-up cycle.

And you certainly want to select a capacitor (in any part of the circuit) that has sufficient voltage rating for that point in the circuit. For C1201, for example, if you know FOR SURE that the incoming "+5V" is already regulated or otherwise reliable stable, you might get away with a 6.3V rated capacitor. But you may want a higher voltage rating if the source is the very common raw output of a mains-supplied transformer, rectifier, capacitor arrangement. Or some other source with a wider range of expected voltages.

C1203 may be more critical as it provides some stability for U1200. Recommend studying the MIC29302 data sheet to learn about the special role of the input (C1202) and output (C1203) capacitors in voltage regulator chips.

Bypass capacitors like C500 and C501 are added as needed ("season to taste") to maintain quiet power into chips like U500. Bypass filtering is partly an "art" and sometimes a pragmatic exercise of trial and error.

With rare exceptions, the exact KIND of capacitor is not a critical factor. A chip ceramic or SMD electrolytic or even tantalum would likely be equally effective, so it is a matter for the product/board designer to select the proper component that meets not only the requirements of the electronic circuit, but also the space available on the board and the budget for the project, etc.

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    \$\begingroup\$ Good answer. I'd just like to point out that it's very important to check the datasheet of voltage regulators when picking input and output capacitors. There are two families here: Those regulators who need a low ESR capacitor and those regulators who must not be buffered with a low ESR. For old jellybean parts such as 780x and LM317 it won't make a difference, but these modern LDO regulators are very demanding. \$\endgroup\$ – Nils Pipenbrinck Jun 5 '16 at 5:23
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On the small decoupling caps: X5R/X7R only differ in the rated temperature range and a few minor properties that don't matter much, and the tolerances are non-critical either, with 5% or 10% being typical for such capacitors. 25-50V ceramic capacitors in that value range are typical for the case sizes normally used, while the actual case size/package depends on what you or your assembler are comfortable handling and the amount of PCB real estate you have to play with.

On the large bulk decouplers: SMT tantalums or polymer electrolytics can be used instead of aluminum electrolytic "cans" if you wish to save some space. Another option these days is are large value multilayer ceramic capacitors, although they generally are only available in larger SMT case sizes.

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