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# Buck (in CCM) equation adjust for voltage sag

#### ACharnley

##### Member
Hi all,
I've a voltage-mode buck controlled by a MCU and it's a large enough inductor etc to ensure it almost always operates in CCM. I set the duty by knowing what input voltage I want to drive to (it's MPPT) and the output is fixed at 5V.

duty = output / input * 100
At high loads and when the output voltage is slower there is a sag in the actual output voltage, I figure due to losses in the FET and inductor.

Should I make the 5V dynamic based on an actual read of the output rather than the expected? Say it's 4.75V, that would slightly decrease the duty which would make the output drop further. I think I've semi answered my own question but thought I'd seek some clarity!

Cheers, A.

#### Papabravo

##### Well-Known Member
Hi all,
I've a voltage-mode buck controlled by a MCU and it's a large enough inductor etc to ensure it almost always operates in CCM. I set the duty by knowing what input voltage I want to drive to (it's MPPT) and the output is fixed at 5V.

duty = output / input * 100
At high loads and when the output voltage is slower there is a sag in the actual output voltage, I figure due to losses in the FET and inductor.

Should I make the 5V dynamic based on an actual read of the output rather than the expected? Say it's 4.75V, that would slightly decrease the duty which would make the output drop further. I think I've semi answered my own question but thought I'd seek some clarity!

Cheers, A.
At high loads the voltage will sag because the duty cycle does not allow enough time for the inductor to transfer enough charge to the output capacitor. The solution is to increase the duty cycle to compensate for this. The usual approximations do not account for losses in the switches (MOSFETS or MOSFET and Diode), DC resistance of the inductor, and ESR of the capacitor, so in a closed loop system the duty cycle will actually be a few percent higher than the equation would suggest.

#### ACharnley

##### Member
This is what I'd expect, up the duty to maintain the voltage level under load, however doing so would reduce the input voltage - and I'm tracking it for MPPT purposes.

My thinking for doing the opposite would worsen the voltage level but continue tracking the correct input voltage.

ie. 5/30 > 4.7/30
But I also think this smells - I read 4.7v at the output because of losses in the fets/inductor at higher current. Perhaps it's correct to use the fixed voltage output regardless?

#### Papabravo

##### Well-Known Member
This is what I'd expect, up the duty to maintain the voltage level under load, however doing so would reduce the input voltage - and I'm tracking it for MPPT purposes.

My thinking for doing the opposite would worsen the voltage level but continue tracking the correct input voltage.

ie. 5/30 > 4.7/30
But I also think this smells - I read 4.7v at the output because of losses in the fets/inductor at higher current. Perhaps it's correct to use the fixed voltage output regardless?
What is your reason for thinking a change in duty cycle would necessarily lower the input voltage? As long as the power available from the input source is adequate to supply the required power to the output there should not be a problem. If it is a problem, then maybe operating at the MPPT point is not in your best interest.

#### ACharnley

##### Member
The input is high impedance, it will sag. Increase the duty past the optimal and it will deliver less power. If it were low impedance I'd not be bothering with MPPT at all and would optimise the output voltage using the method you mention.

Getting back to it, for the equation output/input, should output be the ideal voltage (5v, the point where regulation occurs) or the actual voltage once losses are considered (using an adc to determine it)?

( I'm assuming the buck and the feedback loop using the adc is slow, large capacitors required etc. )

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