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This is a pretty simple question, I'm guessing its a not so simple answer.

Basically I want to know if I have two chips on my board, and on each of their data sheets it calls for a 0.1uF capacitor to be connected to the Vdd and Vss, do I need to add two 0.1uF capacitors?

what if they are far apart on the board?

Also what if one calls for a 4.7uF and the other calls for a 0.1uF on VDD then what do I do?

UPDATE: I feel I need to include more information to help guide the answers.
I have several components all connected to either AVDD or DVDD and they all call for various capacitors, such as several needing 0.1uF, several needing a 10uF, another needing a 4.6uF and a few needing a 0.1uF and a 1uF all connected to AVDD. all within an inch or two of each other.

What approach should I take?

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1  
You're right, this is a question that can lead down a rabbit hole, but generally speaking, give each component the decoupling it asks for. A 0.1uF capacitor near a component several inches away from another component isn't going to do much. – Krunal Desai Feb 26 at 22:46
    
I had this same exact question when I got started. @pipe answered correctly. The closeness of the cap to the power input pin prevents voltage sag to the device during switching on of transistors/etc inside when an inrush current is required – Pugz Feb 27 at 2:02
up vote 1 down vote accepted

There are plenty of very good bulk/bypass/decoupling capacitor answers on this site:

For rather simple boards, I like to think of it two ways: I need bulk capacitance for power supply integrity and I need bypass capacitance for EMI/Noise/Signal Integrity, and I attack them separately.

Each IC will be like a (literal and figurative) island where you decouple according to datasheets and keep everything nice and tight. Each IC can generate its own noise, so it should have a bypass capacitor to keep that noise within the island. 0.1uF, 0.01uF, etc. caps keep the higher frequency stuff contained and should be dealt with first. Laid out closest to the pins that need them and laid out first for the shortest distance. Many times you'll see these caps called out on a datasheet and explained in detail.

Secondly, you can consider what you'd call "bulk" capacitance for power bus ripple. These are typically your larger capacitors that will be most helpful for slower, stronger switching currents. These are usually called out on datasheets for individual ICs like MCUs, opamps, etc. but will also be called out on your power management ICs. Those 10 uF caps you see called out (like below) are more like those bulk capacitors

You end up with a lot of duplication of capacitors as you add more ICs to the board and as you get more savvy you'll get a feel for which ones can be removed or changed safely. As a starter, I would place every single capacitor recommended and see what you end up with. In your case, for example, it MAY be possible to take that 4.7uF cap and change it to a 10uF cap to save a line on your BOM. Or remove a few 1uF and 4.7uF caps and replace them with a lower number of 10uF or 47uF caps. Steps like that should be either simulated beforehand and/or tested on the bench to see their impact.

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Yes. The idea is to place these capacitors as close to the device as you can, in order to create a "local" reservoir capacitance, isolating the instantaneous current draw from loading down the rest of the PCB.

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Every IC should have a 0.1µF decoupling capacitor as close to it's VCC and VSS as possible. Don't skimp. The 4.7µF is a beefier filtering cap, and should be in addition to the 0.1µF cap.

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In some applications, you may need to go a step further and place one capacitor per power pin. The schematic would look something like this:

Decoupling

Then in the layout, you would try to place each cap as close to the particular pin as possible.

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