How to find coupling and decoupling capacitor values?

Question

I am trying to learn receiver design, one thing I noticed is the use of coupling capacitors and decoupling capacitors and incuctors. There were set of standard values such as 100 pF, 1000 pF or 0.1 uF (at decoup). My doubt is how do we choose those values exactly? I have asked few and they tell about the formula XC=1/2*PIFC but even if I am using that formula, how to know the value of Xc? For example consider I am working on 1 GHz, now how to calculate those values?

Answer 1

The reason for decoupling capacitors is to absorb the current gulps which the IC demands. Without the capacitor, you get lots of high frequency noise between the ground and power. This is the why of decoupling.

There are various methods to apply to select your decoupling capacitors. If they are defined it the datasheet, always follow that. If not, you can either "do the maths" based on the frequencies and work our what you need, or you need to apply the engineering rule-of-thumb. A while ago, there was a strong belief in going for "decade" capacitors, using a 10nf, 100nF and 1uF, to get a good range across the frequency spectrum. These days, after lots of work has been done on it, the rule which gets applied most is "largest capacitor in smallest package". So you get the standard package you're using (say 0603 or 0402) and get the largest capacitance you can find in that package with the required voltage rating. This is usually all you need. If you need more decoupling than that, you will need to "do the maths" which will depend so much on your circumstances that it can't be addressed here.

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For those interested, the reasoning behind largest capacitance in smallest package: the smallest package has the lowest inductance, and therefore will absorb high frequencies easily. Higher capacitor value, will handle higher amplitude noise.

Answer 2

My doubt is how do we choose those values exactly?

We don't! No capacitor is ideal, there is always series resistance and inductance to be considered. To learn more watch this EEVBlog video by Dave Jones. Note that bypass capacitor is just a different word for (supply) decoupling capacitor.

More on the effect of different types of capacitors is demonstrated in this video.

One of the conclusions you should draw after watching the videos linked above is that the choice of (bypass) capacitor depends a lot on the frequencies of the signals you want to decouple your supply for. In the case of (AC) coupling capacitors you want the most optimum capacitor for your signal frequencies.

In practice the actual value of the capacitor does not matter too much as long as it is "enough".

For example, to suppress a supply ripple of 100 Hz, a 10 nF capacitor isn't going to help much. A 100 uF capacitor will help but so will a 47 uF and a 220 uF capacitor.

It depends on the circumstances what a designer will choose. Often if a suitable capacitor is used already elsewhere in the product then that capacitor is chosen to keep the BOM (Bill of materials) shorter.

With experience selecting the components becomes easier as you have seen similar situations before and you will know what to do. Note that on a PCB, if you have enough free area, you can just add footprints for adding (bypass) capacitors. Then if it turns out you didn't make the right choice at the design phase you can easily try out a different capacitor.

Answer 3

You are learning about voltage-dividers. Voltage dividers have a series element and a shunt element.

In a bypass capacitor (lowpass filter), the capacitor is shunting energy to ground. At higher frequencies, the capacitor does a better job of shunting, limited by inductance and resistances (and resonances of the GND system).

In a DC-blocking capacitor, (high pass filter), the capacitor is the series element and at higher frequencies there will be less attenuation.