how RLC resonant circuit convert square wave to sine wave?

[izzu91]

as i know, to convert square wave to sine wave, we need to find the fundamental frequency of square wave and filter the rest of frequency. so how to calculate that? here i attached the circuit..i wonder how this circuit works?please show me some maths work.

 

[barry]

What you've got there is a low-pass filter. You need to calculate the input/output transfer function of your filter. From that you can determine the appropriate values.

 

[BradtheRad]

The aim is to match impedance of L and C and R. To get values for L and C, use formulas for reactance, impedance, etc.

These simulations compare square waves (left) to sinewaves (right):



Supply current and voltage are in phase. This allows greatest efficiency when powering heavy loads.

Notice the righthand loop produces equal volt levels across all components. Once you have determined the values, they can be used for the lefthand loop.

Or, you can experiment with the lefthand loop, adjusting values until you get a semblance of a sine wave across the load. As it turns out, they will be the same as the values derived from the formulae.

 

[chuckey]

when designing filters you need to know the impedance of the source driving it and the terminating impedance.
Frank

 

[izzu91]

when designing filters you need to know the impedance of the source driving it and the terminating impedance.
Frank

ok, i understand that, but how to calculate it?and how to design the filter?

 

[chuckey]

Read :- https://en.wikipedia.org/wiki/Constant_k_filter
Frank

 

[Georgy]

So with optimal filter.
In table " _RLCF.PDF (220.4 KB)" I can match all- R, C, L, Frequency.
Need only Adobe Acrobat (not only reader) with moving color line, across wanted parametres and get your's choise set.

If you want so match at 50 Hz, yoir's L and C is close optimal for R load = 27 Ohm, it is common optimal case.
With other R load other L and C possible 50 Hz for.

 

[Pulkit Varshney]

a series RLC circuit behaves as a band pass filter..
if your input is a square wave.... you can decompose it into multiple sine waves using Fourier series
therefore, the RLC circuit is selecting only one particular frequency whose value depends upon center frequency and bandwidth of RLC circuit.

 

[barry]

a series RLC circuit behaves as a band pass filter..
if your input is a square wave.... you can decompose it into multiple sine waves using Fourier series
therefore, the RLC circuit is selecting only one particular frequency whose value depends upon center frequency and bandwidth of RLC circuit.

While it's true that a series RLC has a bandpass response, what he's got there has a low-pass (with some peaking) response, not bandpass. Just look at it from this point: at DC, the cap is infinite impedance and the L is zero impedance. At very high frequencies, the C is low impedance and the L is high impedance.

 

[Pulkit Varshney]

@barry,
by calculation the resonating frequency of the circuit comes out to be equal to 50.33 Hz and bandwidth equal to around 43 Hz..
so its like a bandpass filter whose center frequency is at fundamental frequency of square wave and because of its low bandwidth only fundamental is coming out.
resonance frequency = 1/(2*pi*sqrt(L*C))

 

[barry]

Sorry, but that's STILL a low pass function. The transfer function is:

1000/(s^2 + s*270 + 1000)

Plot it!!!

 

[Pulkit Varshney]

yes for voltage that is a low pass filter but for current that is band pass filter.. i think

 

[Georgy]

yes for voltage that is a low pass filter but for current that is band pass filter.. i think

No band pass, only a low pass function for U and I, if we look from sourse to load.