Talk:LC circuit

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Request for photos

The article needs more pictures of tuned circuits. High Q tank circuits in radio transmitters should be easy for general readers to understand because they usually consist of a coil suspended in air and a variable capacitor with exposed plates. I added a photo of a tank circuit from a transmitter, but Commons had almost none so I had to use a black & white one from a 1938 book. I'd like to request any radio amateurs out there that would like to help, open the case of your transmitter (and/or antenna tuner) and see if you can get a good shot of the tank circuit. Also military radio equipment or transmitters of AM radio stations would be good sources. If you are unfamiliar with the process of uploading a photo to Commons I can help. Thanks! --Chetvorno^TALK 20:49, 20 June 2023 (UTC)

Laplace solution : verify correctness of full demonstration

Hi, I followed this very well written article completely and found the same formulas... EXCEPT for the very last one for the case of a sinusoidal function as input. After careful examination, I perform the same transform and arrive to the conclusion that certain factors in front of the sinusoidal functions in the time domain expression namely 1/omega0 and 1/omegaf are there only if we replace the nominator of the summands 1 by omega_0/omega_0 and omega_f/omega_f in order to be able to perform the Laplace transform. Is that correct ?

$\operatorname {\mathcal {L}} ^{-1}\left[\ \omega _{0}^{2}\ U\ \omega _{\mathrm {f} }{\frac {\frac {1}{(\omega _{\mathrm {f} }^{2}\ -\omega _{0}^{2})}}{\ s^{2}+\omega _{0}^{2}\ }}\ +{\frac {-{\frac {1}{(\omega _{\mathrm {f} }^{2}\ -\omega _{0}^{2})}}}{\ s^{2}+\omega _{\mathrm {f} }^{2}\ }}\ \right]$

Isolating the constant and adjusting for lack of numerator:

${\frac {\ \omega _{0}^{2}\ U\omega _{\mathrm {f} }\ }{\ \omega _{\mathrm {f} }^{2}-\omega _{0}^{2}\ }}\operatorname {\mathcal {L}} ^{-1}\left[\ \left({\frac {\omega _{0}}{\omega _{0}(s^{2}+\omega _{0}^{2})}}-{\frac {\omega _{0}}{\omega _{0}(s^{2}+\omega _{f}^{2})}}\right)\ \right]\,$

Performing the reverse Laplace transform on each summands:

${\frac {\ \omega _{0}^{2}\ U\omega _{\mathrm {f} }\ }{\ \omega _{\mathrm {f} }^{2}-\omega _{0}^{2}\ }}\ \left(\operatorname {\mathcal {L}} ^{-1}\left[\ {\frac {1}{\omega _{0}}}{\frac {\omega _{0}}{(s^{2}+\omega _{0}^{2})}}\right]\ -\operatorname {\mathcal {L}} ^{-1}\left[{\frac {1}{\omega _{\mathrm {f} }\ }}{\frac {\omega _{\mathrm {f} }\ }{(s^{2}+\omega _{f}^{2})}}\right]\right)\,$

${\frac {\ \omega _{0}^{2}\ U\omega _{\mathrm {f} }\ }{\ \omega _{\mathrm {f} }^{2}-\omega _{0}^{2}\ }}\ \left(\ {\frac {1}{\omega _{0}}}\operatorname {\mathcal {L}} ^{-1}\left[{\frac {\omega _{0}}{(s^{2}+\omega _{0}^{2})}}\right]\ -{\frac {1}{\omega _{\mathrm {f} }\ }}\operatorname {\mathcal {L}} ^{-1}\left[{\frac {\omega _{\mathrm {f} }\ }{(s^{2}+\omega _{f}^{2})}}\right]\right)\,$

$v_{\mathrm {in} }(t)={\frac {\ \omega _{0}^{2}\ U\ \omega _{\mathrm {f} }\ }{\omega _{\mathrm {f} }^{2}-\omega _{0}^{2}}}\ \left({\frac {1}{\omega _{0}}}\ \sin(\omega _{0}\ t)-{\frac {1}{\ \omega _{\mathrm {f} }\ }}\ \sin(\omega _{\mathrm {f} }\ t)\right)\;,$

Furthermore, there seems to be a step to simplify the expression of v(t) that has not be taken as b/b = 1 and not b should appear in the last formula in the time domain. Instead of this:

$v(t)=v_{0}\cos(\omega _{0}\ t)+{\frac {v'_{0}\ b}{\ b\ \omega _{0}\ }}\ \sin(\omega _{0}\ t)+{\frac {\omega _{0}^{2}\ U\ \omega _{\mathrm {f} }}{\ \omega _{\mathrm {f} }^{2}-\omega _{0}^{2}\ }}\left({\frac {1}{\omega _{0}}}\ \sin(\omega _{0}\ t)-{\frac {1}{\ \omega _{\mathrm {f} }\ }}\ \sin(\omega _{\mathrm {f} }\ t)\right)\;.$

Should we not have the following ?

$v(t)=v_{0}\cos(\omega _{0}\ t)+{\frac {v'_{0}}{\omega _{0}\ }}\ \sin(\omega _{0}\ t)+{\frac {\omega _{0}^{2}\ U\ \omega _{\mathrm {f} }}{\ \omega _{\mathrm {f} }^{2}-\omega _{0}^{2}\ }}\left({\frac {1}{\omega _{0}}}\ \sin(\omega _{0}\ t)-{\frac {1}{\ \omega _{\mathrm {f} }\ }}\ \sin(\omega _{\mathrm {f} }\ t)\right)\;.$

Cordially yours, Temnothorax (talk) 23:22, 24 October 2023 (UTC)