# How does increasing the capacitance affect the output voltage for a buck converter and boost converter?

From the formula of charge relating capacitance and voltage, $$Q = CV$$ Capacitance is inversely proportional to voltage.

This is how I got the idea that possibly when increasing the capacitance, the output voltage would decrease for both buck and boost converters.

But I think that idea is invalid because I'm just grasping at straws for the formula because it has a voltage. I have a feeling that the behavior of increasing capacitance might result differently for buck converters and boost converter.

I would like to ask what the answer to this is with an explanation of how it works. I just can't understand what would happen in the given situation of the question.

Thank you.

## 2 Answers

A larger capacitor will decrease the output ripple for a given fixed load.

First, on your equation: your logic isn't right because Q, the charge on the capacitor, isn't fixed. What the equation in fact says instead is that for a given output voltage, a capacitor with more capacitance C will store more charge on its plates. This is related to the reason why more capacitance will decrease the ripple, which we'll talk about next.

Second, for example a boost converter ultimately works by quickly charging something up (say, an ordinary inductor), then connecting the charged thing in series with the power supply in order to increase the output voltage above the supply voltage. Then, after a short time, the converter disconnects the charged thing in order to charge it up again because it will inevitably quickly begin to discharge when it is supplying power to the load.

Putting a smoothing capacitor across the output (i.e. with the other side of the capacitor connected to ground) of such a converter will cause the capacitor itself to charge to the output voltage. Thus, in the periods where the converter cannot itself supply current (i.e. when the converter is charging up the e.g. inductor inside it), the capacitor can supply current to the load instead. Current is charge per unit time, so more current means the smoothing capacitor will discharge faster, and so fail to smooth out the converter output for as long. (Note, your equation says this: as Q decreases for fixed capacitance C, the voltage V must decrease proportionally.) To compensate a capacitor with greater capacitance can be used, since it stores more charge for the same voltage, and thus it will take longer for the output voltage to droop.

Attendum: Of course, eventually after the capacitor has been discharging for some time the switching converter will reconnect and begin to supply to power to charge the capacitor back up as well as supply power to the load. Thus, we don't need an infinitely large capacitor to get acceptable performance: instead, for a given load we are designing the converter for, we only need to use a capacitor which will reduce the output ripple by an acceptable amount for however long the switching converter needs to charge itself back up again.

Also, if you think about it the capacitor will never charge all the way up to the output voltage of the converter when under load, and this is what happens in real life.

• So increasing capacitance decreases the output voltage because it is able to discharge faster? Sorry, I do follow with what you say but when I'm trying to look at my question and make a straight to the point answer my understanding seems to not able to make a clear cut answer. – AndroidV11 Dec 22 '20 at 16:11
• @AndroidV11 If there is no load, the capacitance will essentially not affect the output voltage at all (within limits). See my first point: a bigger capacitor will charge to the same voltage by storing more charge. If there is a significant load, then a bigger capacitor will actually stop the voltage from decreasing as much. This is the meaning of my second point. – Keeley Hoek Dec 22 '20 at 16:14
• How does it stop the voltage from decreasing as much? Because of more charges? Sorry, I'm kinda confused but I think your explanation is actually written clear. I just probably can't seem to understand it at once. – AndroidV11 Dec 22 '20 at 16:22
• That's ok! This is a bit confusing because the capacitor has most of its effect while the whole circuit is supplying power to a load, so you have to imagine current being drawn at the same time. But yes exactly, because more charge is stored on a bigger capacitor, in a given amount of time and with the same load current the bigger capacitor will discharge by a smaller fraction compared to a smaller capacitor. This means the voltage across the bigger capacitor will go down less. (This actually follows from your V = Q/C equation.) – Keeley Hoek Dec 22 '20 at 16:27
• @AndroidV11 A capacitor across a circuit supplies/absorbs charge in an attempt to keep the voltage constant. Putting a bigger capacitor across the output of your converter will therefore cause its output to be less noisy, but it won't usually change the average voltage. – user1850479 Dec 22 '20 at 16:35

In addition to the other answer:

A larger capacitor on the output doesn't decrease the average output voltage if the feedback loop is working properly. It does decrease the ripple on the output voltage (the ESR of the capacitor used also has an influence, and so do the switching frequency and the load).

You can't lower the set output voltage by using a larger capacitor on the output, if that is what you mean. It is the feedback loop that sets the voltage, as long as things are stable.

Because of the ripple the output voltage isn't "flat", and the less ripple, the closer the lowest voltages seen will be to the set voltage; a larger capacitor will make the output voltage smoother, but it will not influence the set/average output voltage.

Note that adding capacity will also affect the frequency response of the feedback loop, and adding too much capacity may make the regulation unstable.

• What do you mean by ripple on the output voltage? I really only am familiar with ripple current but that is associated with the inductor. Is there a formula to represent what you mean about the ripple on the output voltage relating it to the capacitor? If not, at least could you elaborate further and also reiterate what the ripples mean? Only being familiar with ripple current just makes things hard for me to grasp. EDIT: I kind of get what a voltage ripple is after searching a little because I am familiar with rectification but I would love it if you could still explain it. Thanks. – AndroidV11 Dec 22 '20 at 23:40