what criteria you use to choose a smoothing capacitor?

[hanhan]

Hi,
I want to ask about smoothing capacitor.

I am wondering what criteria you use to choose a smoothing capacitor?

I think there are two criteria:
1. High capacitance
2. Low ESR
However, I can't see any capacitors met both criteria.
For example, with electrolytic capacitor, it has very high capacitance but it also posseses a large ESR.

 

[Jony130]

I use this equation
C = Q/V ----> (I * t)/V

where
I - load current
t - discharge time 1/50Hz (20ms) for half wave rectifier and 1/100Hz (10ms) full wave rectifier or 1/60Hz and 1/120Hz for countries with 60Hz mains.
V - capacitor ripple voltage.

And next we add a voltage regulator circuit. And I think that you worry too much about this capacitors. The value is not all that critical in most applications.

 

[misterT]

Hi,
I think there are two criteria:
1. High capacitance
2. Low ESR
However, I can't see any capacitors met both criteria.
For example, with electrolytic capacitor, it has very high capacitance but it also posseses a large ESR.

Low ESR is very important in switching power supplies. In this case that is not that importan.. Of course high ESR wastes power and heats up the capacitor.
If you want low ESR, then you can put two or more capacitors in parallel.

 

[MrAl]

Hi,

The ESR is not that high in some good quality electrolytics. It can however get higher over time. But usually for a new design the ESR for a power supply like this wont be that important. You can however evaluate to find out for sure.

But first, the approximations already given are based on the approximation that the ripple voltage is small so it appears as a straight line that slants down and runs from the time of one peak (of the rectified wave) to the time of the next peak. The approximation in simple terms is:
dv=I*dt/C
where I is the load current and dt is the time between peaks. This also assumes no ESR and no input series resistance or inductance which means it can be way off. But we'll use this as a starting point because it greatly simplifies things.
So to start with you can calculate the capacitance from that.

Next, we can evaluate the effect of the cap ESR with a slight modification to that formula:
dv=I*dt/C+(I+i)*ESR

So we see already we get more ripple voltage (dv) because of that ESR, but if the ESR is small then we dont have to worry too much because the ripple due to the capacitance alone will still be higher than that across the ESR.
The current 'i' is a little difficult to evaluate unless you know the input series resistance and inductance so we'll have to approximate that or else leave it as an unknown. If we do approximate it as 4*I then we get:
dv=5*I*ESR

as the ripple due to the capacitor ESR. But also part of that dv is a short hump not over the entire discharge cycle.
So with this in mind, if we have 1 amp of current and 0.010 ohms ESR then we end up with 0.05 volts of ripple due to the ESR of the cap. If we have 10 amps, then we get 0.5 volts due to the ESR. We can then compare that to the ripple due to the capacitor itself (repeated here):
dv=I*dt/C

and see how it weighs in. Very often we'll see this last voltage surpass the ESR ripple so we dont worry too much about the ESR unless of course it is too high (poor cap quality) to begin with, but it can also help us select a cap without over specifying it (and increasing the cost too much).