# RLC resonator to produce beautiful sine wave

Joined Sep 28, 2021
266

Dear all, 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. I hope to get some insights

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Thank you for reading and have a nice day !!

#### Ian0

Joined Aug 7, 2020
9,507

#### Papabravo

Joined Feb 24, 2006
21,013
I'm not aware of any ability for a passive circuit to produce beautiful sine waves. I'm making an assumption that in this context "beautiful" means undistorted with very low harmonic content. This I can tell you:
1. If the damping factor is too low, the sine wave will have a decaying exponential envelope.
2. If the damping factor is too high, sine wave will only last for a few cycles.
3. There is a small range of damping factors where the step response will approach asymptotically without any oscillation at all.
The simulation below looks at the AC response for one selection of values for 150 kHz, which implies:
$$2\pi f\;=\;\omega_{0}\;=\; \cfrac{1}{\sqrt{LC}}$$

So the L and C values produce the resonant peak at 150 kHz. The transient response looks like the following:

Maybe these sine waves are beautiful enough, but the FFT show shows substantial harmonic content. Tell me what you think.

Last edited:

Joined Sep 28, 2021
266
I'm not aware of any ability for a passive circuit to produce beautiful sine waves. I'm making an assumption that in this context "beautiful" means undistorted with very low harmonic content. This I can tell you:
1. If the damping factor is too low, the sine wave will have a decaying exponential envelope.
2. If the damping factor is too high, sine wave will only last for a few cycles.
3. There is a small range of damping factors where the step response will approach asymptotically without any oscillation at all.
The simulation below looks at the AC response for one selection of values for 150 kHz, which implies:
$$2\pi f\;=\;\omega_{0}\;=\; \cfrac{1}{\sqrt{LC}}$$

View attachment 276697
So the L and C values produce the resonant peak at 150 kHz. The transient response looks like the following:
View attachment 276699
Maybe these sine waves are beautiful enough, but the FFT show shows substantial harmonic content. Tell me what you think.
Thank you for your time for the reply sir. I got it

#### k1ng 1337

Joined Sep 11, 2020
911
I'm not aware of any ability for a passive circuit to produce beautiful sine waves. I'm making an assumption that in this context "beautiful" means undistorted with very low harmonic content. This I can tell you:
1. If the damping factor is too low, the sine wave will have a decaying exponential envelope.
2. If the damping factor is too high, sine wave will only last for a few cycles.
3. There is a small range of damping factors where the step response will approach asymptotically without any oscillation at all.
The simulation below looks at the AC response for one selection of values for 150 kHz, which implies:
$$2\pi f\;=\;\omega_{0}\;=\; \cfrac{1}{\sqrt{LC}}$$

View attachment 276697
So the L and C values produce the resonant peak at 150 kHz. The transient response looks like the following:
View attachment 276699
Maybe these sine waves are beautiful enough, but the FFT show shows substantial harmonic content. Tell me what you think.
Where do the harmonics originate? Your simulation is using very near to ideal components no?

#### Papabravo

Joined Feb 24, 2006
21,013
Where do the harmonics originate? Your simulation is using very near to ideal components no?
They come from the square wave input. With non-ideal components there would be an increase in the attenuation and the AC response would have a lower Q.

#### MrChips

Joined Oct 2, 2009
30,497
Where do the harmonics originate? Your simulation is using very near to ideal components no?
If it is not already a beautiful sine wave then it has harmonics. That is the nature of the beast.

#### Papabravo

Joined Feb 24, 2006
21,013
If it is not already a beautiful sine wave then it has harmonics. That is the nature of the beast.
In an actual sine wave generation scheme the source would not be a square wave input, there would usually be some gain from an amplifier, and there would be some filtering to further reduce the harmonics