How to calculate inductor value for Buck Converter

RaghuRaj's picture

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How to calculate inductor value for Buck Converter
October 25, 2018 - 1:00pm

I am building a simple buck converter to regulate a 5V form my 9.6V battery. The battery is a pack of 3 18650 cells (3S) and the output is supposed to power my MCU (PIC) a couple of sensors and a servo motor.

Initially I thought I could get away with a simple Linear regulator like 7805, but the efficiency of these devices are very bad. Also, since I am running on battries I hae limited juice and have to use a switched power supply like a Buck Converter. I went though the basics of the converter and now I am stuck at a place where I have to decide the value of the inductor for my circuit which is shown below

 

So far I have decided to use the IRFZ44N MOSFET as a switch and the controller will be an Arduino so make things easy for my first run. Can some one please explain me how to calculate the value Inductor? A direct formulae will be more helpful.

 

John_Kripto's picture

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Formula to calculate Inductor value for Buck converters
October 25, 2018 - 1:16pm

Hi Raj, welcome to CircuitDigest Forums...

The value of an Inductor in a Buck converter is decided by considering a lot of factors. Before we get into that you should know that the buck converter can operate in 3 different modes based on the value of the Inductor you are using and you have specified nothing about it. The three modes are 

  • CCM - Continues Conduction Mode
  • BCM - Boundary Conduction Mode
  • DCM - Dis-continues Conduction Mode

Most converters operate in the CCM mode, but to keep calculations simple people normally calculate the Inductor value for BCM. This Inductor value is called the Critical Inductor Value. Once we get this Critical inductor value we can slightly increase it to work in CCM mode ot decrease it to operate in the DCM mode based on the required ripple voltage.

You can read the application guide by ROHM Semicondutors to know more on how the formula is derived, but since you have asked for a direct answer you can use the formula 

L = ((Vi-Vo)/(2<io>) * DT

This formula will help you in calculating the value of Inductor in Henry, it gives a rough figure, but it should work fine for your application. Here Vi is the Input Voltage, Vo is the Output Voltage <io> is the average current through your load and DT is the switching frequency of your MOSFET in ton/ton+toff. 

RaghuRaj's picture

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what is <io> in the formula
October 26, 2018 - 11:03am

Thanks for the reply john. But I am still confused here on how to find the value of <io>. 

You have mentioned <io> to be average load current, my load should not consume anywhere more than 1A so is my <io> just equal to 1?

Also the value of my input voltage Vi and duty cycle DT is not fixed how to I substitute these values in the formulae ? 

John_Kripto's picture

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Finding Vi, ,io, and DT for buck converter
October 26, 2018 - 11:09am

Yes Raj, since your load comprises only of digital IC's and sensors you need not worry much about the peak or ripple current. Assuming it to be 1A will work fine. 

The value of Vi and DT are variable as you said, you can calculate the L value for minimum and maximum value of Vi. DT is controlled through program. If you PWM can be from 0% to 100% then you can play with the formulae in such a way that for all values of Vi you should be able to get the desired output voltage Vo for your value of L by simply varying the duty cycle.

Hope you get the point here

RaghuRaj's picture

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100uH is my required value, now where to buy them?
October 26, 2018 - 11:15am

Hi, that did clear up my doubts. I roughly approximated my inductor value to be 100uH, with this value of L I should be able to get a constant 5V by varing by duty cycle between 40% to 90% for an input voltage varying from 7V to 13V.

Now I where to buy this 100uH, is it a good idea to find my own inductor I have a toroid core with me. My local electronics shop only has color ring type inductors which I thin is not suitable for this circuit. 

John_Kripto's picture

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Try mouser, digikey or RS components
October 26, 2018 - 11:16am

I am not sure where you are from, but normally people like mouser and digikey will help you to find the materials you need. If you are from asian countries also try tanotis