# How do I calculate the duty cycle range for DC-DC buck converter?

Question: A buck converter supplies power to a microprocessor with a core voltage of 1.2 V and peak power requirement of 2A. The supply for this buck converter is a lithium battery with a nominal voltage of 3.7V (range 4.2 full to 3.0 V flat).

Assuming the converter operates in CCM, what is the duty cycle range as the battery discharges? Both switching devices will be MOSFETs each with less than 30 mOhm on resistance.

• Sounds like homework - what have you uncovered so far? – Andy aka Mar 29 '15 at 15:14
• yeh that's sth to do with modelling and control. It would be great if you could guide me to that question? – palinset Mar 29 '15 at 15:18

Here is a hint: -

Both switching devices will be MOSFETs

This tells me that the buck converter is a synchronous type with a push-pull type switch arrangement - this makes estimating the duty cycle very easy; one switch connects the output to the incoming positive rail then the other switch grounds the output. The average voltage of the switched waveform for an input voltage of 3.7 volts and an output voltage of 1.2 volts is ......? Please fill-in the gap

If you don't quite understand where I'm coming from consider the "proper" output after the inductor and capacitor and think of what the inductor is - it passes DC i.e. if the input voltage has an average value of X then the output voltage also has an average value of X (yes there will be a small volt drop due to current thru the inductor because of the inductor's dc resistance but this can be largely ignored for a decent approximation).

• thanks for explanation. So is the range between 0.286 and 0.4? – palinset Mar 29 '15 at 15:33
• Yes it is but you can go further with it by taking full load current into account and the resistance of the mosfets. The resistance of the mosfets can be seen as being in series with the inductor and hence at 2A there will be an extra volt drop that needs accomodating with a slightly higher duty cycle. – Andy aka Mar 29 '15 at 15:37
• Okay. I want to ask another question if you don't mind? lets say if the operating frequency is 200kHz, how do I select the minimum inductor value in CCM (at 10% load current)? – palinset Mar 29 '15 at 15:43
• The L and C that feed the output should be resonate significantly below 200kHz or you get a series resonant mess and burnt components. The resonance also need to be low to filter the switching waveform i.e. keep the ripple voltage low. Read this: ti.com/lit/an/snva038b/snva038b.pdf – Andy aka Mar 29 '15 at 16:14
• Hi Andy, I can't think of the duty cycle formula when taking full load current and resistance of the mosfets into account. Please help – palinset Apr 5 '15 at 8:12