In the following, I put a photo taken from capacitor current and output voltage of a buck converter.

As I know when the capacitor current is positive, the voltage should be increasing.
Can anybody tell me why in the photo, the ripple of current and voltage are almost in negative of each other?

 

Which direction of capacitor current is "positive"?

 

Any sensible answer not dependent on guessing would require you to POST THE SCHEMATIC of this mystery converter.

That includes your measurement points and method.

 

The hall effect sensor is in series with Cout
A 20 ohm resistor is in output

 

When I use a small capacitance like 470nF, the problem is solved ! But the ripple is very high. I should use a 100uF capacitance.

 

You can using 470nF in parallel with 220uf, and measure the ripple again, if the ripple still there and a lot, then it could be the current not enough to offering for 20 Ohm Load as I = 10V/20 ohm = 500mA, show the waveform for ripple.

How is the spec of L1? (current,henry)

 

The current in the figure is the -ic
L in a toroid with about 2 cm diameter and with a winding with about 20 turns
the nominal current of L is 5A

 

...
Can anybody tell me why in the photo, the ripple of current and voltage are almost in negative of each other?

Because you are measuring current coming OUT of the capacitor. As the buck turns off the output voltage drops, and the capacitor sources current to the load.

Basically it depends how you connect the "current" sensing probes to the cap. (As others have said).

The best current diagnostic on a buck is to monitor the inductor current.

 

the ripples are the same in the following two cases and i is not equal to Cdv/dt:
1) C=100uf
2) C=100uf + 470 nF
but with C=470nF the ripple in output voltage is very high and the relation i=Cdv/dt is satisfied

 

Because you are measuring current coming OUT of the capacitor. As the buck turns off the output voltage drops, and the capacitor sources current to the load.

Basically it depends how you connect the "current" sensing probes to the cap. (As others have said).

The best current diagnostic on a buck is to monitor the inductor current.

The inductor current has the same wave but with a dc value.

 

Even when I short circuit the current sensor, the waveforms exist but with very lower amplitudes !

 

You can calculate the output current I=V/20 ohm, how is the V?
You can calculate the V and ignore the ripple temporary.

 

The inductor current has the same wave but with a dc value.

Are you arguing with my point that the best current waveform to monitor is the inductor current?

It does not have the "same wave". It CAN have a similar looking wave shape under certain operating conditions. It can also have a very different wave shape. However it will always show you the very critical buck loop current.