# Subtleties of Boost Conver (Step-up Converter)

simulate this circuit – Schematic created using CircuitLab

Generally Boost Converter fault happens in my workplace and difficult to find the problem of converter. So I try to understand the logic of the boost conventer. I would be glad if you answer a few questions that be on my head.

1- How to determine the volt of the condenser at the output. Is the volt of the condenser at the output equal to the maximum induced voltage in the inductance? What will happen if I use smaller or bigger condenser?

2- How many Henry the inductance should be? In addition, some companies make thin wire with a lot of winding (48 Henry), while in some companies they combine 3 thick wire, and make little winding (4.8 Henry). Which is correct? What should be the wire thickness, what should we choose the number of turns (so Henry)?

3- As far as I understand, the factors that affect the output voltage "Vout" are: the input voltage "Vin", Inductan "L", Mosfet gate frequency "HzGate" and the Duty Cycle of the Mosfet Gate leg "λ". What is the formula of the output voltage according to these parameters.

• 48 or 4.8 henries? Neither is correct and how can they be when you show 1 uH in your circuit? – Andy aka Feb 2 at 9:43
• @Andyaka well circuit is a sample dc boost converter. values are default. – mehmet Feb 2 at 12:48

1) The output voltage at Cout is a function of duty-cycle (turn-on time) of the transistor M1. The size of the capacitor does not have an influence on the steady-state output voltage, but it influences the remaining ripple (AC) value of Vout.

2) The size (in Henry) of the inductance depends on the switching frequency, output current and driving mode of the boost converter. So I can't say without more info. Most converters seen today have an inductance somewhere in the range of 1uH to 100uH.

3) There is not a single formula. Lets start with the ideal transfer function Vout=Vin*(1/(1-DutyCycle)).

How many Henry the inductance should be?

Here are some pointers but, bear in mind this is a big topic and I can’t cover all the subtleties.

1. Start by defining the maximum power and the regulated voltage on the load. This should be easy. Let’s say it’s 10 watts and 10 volts just as an example.
2. Think about the switching frequency to be used. A pretty common frequency is 100 kHz but anything up to and beyond a couple of MHz might be contemplated. I assume 100 kHz for this answer.
3. The maximum power divided by the switching frequency equals the energy to be liberated from the inductor during each switching cycle on full load. Controlling the PWM duty cycle ensures that the output voltage remains constant on lighter loads. For this example, energy per cycle (W or work) is 100 uJ maximum.
4. Now think about the input voltage and how low it might drop before the converter stops operating. It might be nominally designed to be powered from 5 volts and you might choose 4 volts as the bottom limit.
5. So, at 4 volts on the input you want to store at least 100 uJ of energy in the inductor. Because we want to have a sensible duty cycle range, we know that the duty cycle will be close to the maximum in this scenario but, let’s not be greedy; choose 90%.
6. Armed with knowledge of the input voltage and the on-time (determined by duty and frequency) and, how much energy we wish to store, we can calculate the inductance value.
7. The important formulas that determine this are

$$V=L\dfrac{di}{dt}$$

$$W=\dfrac{L i^2}{2}$$

I have to say at this point that I’m assuming the converter is what is known as operating in DCM. DCM stands for discontinuous current mode and it is underpinned by all the energy that was stored in the inductor being fully used in each switching cycle. It’s probably more intuitive to help beginners understand what happens and how the interactions play out in DCM.

The other mode (CCM) I’ll leave for the OP to investigate.

What is the formula of the output voltage according to these parameters.

Better to understand what happens and derive it yourself. I never really have a formula; I always do the mental thinking about stuff first because it reminds you what are the important things to consider.

• @mehmet are you satisifed you have your answer now? If not please do say because it's good to formally close a question down by accepting an answer. – Andy aka Apr 14 at 13:28