# How to design LC filter for smoothing out sine wave from sine PWM?

I am making an inverter to convert 12 DC to AC(~8.5Vrms) @50Hz. Later i will do the same for 400V DC to 250Vrms. I am using IRF540N and IRF9540 mosfets as switch. And IR2110 mosfer driver for gate control. I get SinePWM from arduino with carrier frequency of 15kHz. And the whole project work successfully till this stage.

But now i am confuse about how to filter this PWM to pure sine wave. I know i can use low pass filter but how to choose value of L and C? And is there more than one topologies to make filter?(i read on internet but i am not sure) Also does this L and C's value depends on how much load i have connected?

• On top of what Andy already wrote, please keep in mind and/or simulate the difference between running your “L” in continuous versus discontinuous conduction mode. You may require forced CCM or minimum load to make output stable sine wave. – winny Feb 17 '18 at 10:34

Normally, a good starting point for the LC filter is choosing the cut-off frequency and that can be found by finding the logarithmic half-point between 50 Hz and 15 kHz (in your example). Numerically it is $\sqrt{50 \cdot 15000}$ = 866 Hz. It's not a hard rule but something to get you started.

So this constrains L and C somewhat but loading effects can reduce the Q of the LC circuit and this is probably best done using a simulator like micro-cap 11 or LTSpice (both free). Just model the circuit with with highest and lowest loads and see what happens to the shape of the sine wave and its amplitude.

I'd consider starting with L = 10 mH and C = 3.3 uF (876 Hz) with a little series resistance with the inductor to avoid Q factor rising too high on low output currents.

You first focus on the PWM gate driving. The output current should already match the 50Hz sine close enough. Your LC filter will never filter at 50HZ to make your output a pure sine.

Your output LC filter is there to filter the PWM enough so you achieve the ripple current or voltage that you want. So you need a spec for the ripple. If you do not have a spec, then there are some rules of thumb as in ripple current is 10% of peak current. I talk about current as you can, even without load. Your LC filter will make output current (from the FET bridge) possible.

From there it's only calculus. -3db freq of LC filter is at 1/(2.pi.sqrt(L.C)). From there it rolls of at 40db/decade. Start with an easy to find capacitor that can handle the ripple current and calculate the inductor. Might be an iterative process to find a realistic inductor. The actual -3db point also does not have to be precise. If you calculated for 10% ripple, it's no bug deal if it ends up to be 5% or 20%.

Other filtering you will most certainly need are snubbers at the FET's.

Use an Ott filter to convert your PWM output waveform to a sine wave. The Ott filter input will always be capacitive which your inverter can tolerate. Other low pass filters allow an inductive input impedance which can damage your inverter.