# RLC resonator to produce beautiful sine wave

simulate this circuit – Schematic created using CircuitLab

I have read about the RLC tank which can help to resonate a pulse wave of a certain frequency so that it will produce a beautiful sine wave. What would be the values of R , L and C if a 150kHz pulse square wave is used to produce a beautiful 150kHz sine wave? From what I simulated, I learnt that there is a sweet spot of value ratio between these components to produce the nicest sine wave possible.

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• There is no one answer. You'll never eliminate all of the harmonics, so it'll never be a perfect sine wave. And which values you choose are affected by what circuits you're attached to, by size, and by economics. You either need to narrow your question down to one specific problem (including, in technical terms, what is "beautiful enough"), or you pretty much need to learn basic circuit theory, and maybe go component shopping -- these days, if you want a beautiful sine wave at 150kHz, the least expensive way to get it involves highly integrated digital logic and, possibly, no coils at all. Sep 21 at 14:43
• @TimWescott, hi sir, this is just for my learning and I just want to experiment it. Beautiful sine wave means it looks like a sine wave haha :) Sep 21 at 14:45
• I came across a sinusoidal signal which was like a $e^{-t}$ function in some RLC circuit. I have it somewhere. It was a nice experience. Sep 21 at 14:49
• You can produce a sine wave with DC voltage. Sep 21 at 15:01
• @AmitM You'll get that as an impulse response from any RLC circuit, as can be simply seen from the Laplace transform of the circuit. Sep 21 at 15:01

The resonant frequency is:

$$\f = \frac{1}{2\pi\sqrt{LC}}\$$

To get a good sine wave out, you want the Q of the filter to be as high as possible (you want the resonant frequency to be amplified a lot). This means that you want the resistance to be as low as possible. My frequency generator has 50 $$\\Omega\$$ output impedance. Don't add any more resistors. Choose an inductor with low ESR. I have a 330 $$\\mu\$$H in my stash (< 1 $$\\Omega\$$ ESR), so I used it with a 2200 pF cap. The calculated resonant frequency is 187 kHz.

I put a 1 V p-p square wave in (I set the function generator to half this since it assumes a 50 $$\\Omega\$$ load). I found the frequency at which the output was the greatest, it was 192 kHz, slightly different than the calculation due to component tolerances. I get a 7.8 V p-p sine wave out. The sine wave looks really good, the FFT function on my scope indicates that the 3rd harmonic is -44 dB less than the fundamental.

To get exactly 150 kHz, you will need to adjust the values.

The simulation matches, although you need to watch out for how it measures waves, it appears that it measures peak to DC.

simulate this circuit – Schematic created using CircuitLab

Any repetitive waveform is made up of sine waves, one at the fundamental frequency, and zero or more at harmonics of the fundamental. To get a sine wave at the fundamental you just need to filter out the harmonics. Since all of the harmonics are above the fundamental you can use a low pass filter.

To properly design a filter you need to know the input and output impedances. You then need to choose a type of filter, and what order the filter will be (higher order, better filtering). I won't go into the types of filters, that's a rather involved subject that you can research on your own.

To design the filter the easiest thing to do is use a filter calculator such as this one. Enter the filter properties you want and run the program, then take the resulting circuit and enter it into your simulator to test it.

Here's one I did for 50$$\\Omega\$$ input and output impedances. I set it for lowpass, 5th order Chebyshev, series first (determines the orientation of the first filter element) and 0.10 dB passband ripple. I added C3 to remove any DC offset.

Any passive filter is going to have loss, so the output level is lower than the input. Generally, the higher order the filter the more loss, it's the price you pay for a tighter filter. If you want to keep the level the same or higher you need to use an active filter with transistors or opamps. You should be able to find reference material on those if that sounds like something you'll need.