Talk:LC circuit

Resonant circuits don't resonate?
The Wikipedia article on resonance defines resonance as:


 * ...the tendency of a system to oscillate with larger amplitude at some frequencies than at others.

This article states:


 * Notice that the LC circuit does not, by itself, resonate. The word resonance refers to a class of phenomena in which a small driving perturbation gives rise to a large effect in the system.

It seems to me that resonant circuits meet the definition of resonance and that the contrary statement in this article is incorrect, including its definition of what resonance really means. If nobody can reconcile this contradiction I am going to remove the statement. Rsduhamel (talk) 12:21, 12 May 2011 (UTC)


 * Agreed, I've removed it. While there is such a thing as a driven resonant frequency, an LC circuit will also resonate (generally at a slightly different frequency) with no driving force applied.  The theoretical LC circuit described here with zero resistance would, in fact, continue to "ring" without decaying indefinitely.  Sp in ni  ng  Spark  17:24, 12 May 2011 (UTC)

I don't like to tread on anyones's toes, and this seems to me to be a rather pedantic point, but I have changed the wording concerning resonance to mean that resonance occurs when the circuit is driven. I am not happy with the definition of resonance as a tendency; to me it is an occurrence which either happens or does not. It happens when the circuit is driven at an appropriate frequency; this is consistent with the etymology of 'resonance' - to resound. Resonance is not an intrinsic quality of a circuit - it is a phenomenon - something that the circuit does; it resonates. In the theory of LCR circuits, a distinction is made between the natural oscillatory frequency (to which Spinningspark refers), and the resonant frequency at which the amplitude response is greatest when the circuit is driven. There is also the question of the frequency at which the terminal impedance is entirely real (resistive). In some LCR circuits all of these are at slightly different frequencies. I would like to suggest that the necessary distinction is made between natural oscillation and resonance. Spinningspark refers to it; I have added it to the text. G4oep (talk) 10:47, 13 January 2015 (UTC)
 * I believe it is usual to call them resonant circuits anyway. OK, if you take an LC circuit and add an amplifier, then it will resonate. Or it might be used as a filter, in which case the input is driving it. The active region of a laser is called a resonator (for the same reason) even when it is turned off. Quartz crystals are called resonators even when turned off. It might be easier to consider the mechanical analog, such as tuned air columns of a pipe organ. They are commonly considered resonators, and will resonate with appropriate ambient sound. Gah4 (talk) 02:05, 15 February 2023 (UTC)
 * I believe it is usual to call them resonant circuits anyway. OK, if you take an LC circuit and add an amplifier, then it will resonate. Or it might be used as a filter, in which case the input is driving it. The active region of a laser is called a resonator (for the same reason) even when it is turned off. Quartz crystals are called resonators even when turned off. It might be easier to consider the mechanical analog, such as tuned air columns of a pipe organ. They are commonly considered resonators, and will resonate with appropriate ambient sound. Gah4 (talk) 02:05, 15 February 2023 (UTC)

"Second order" LC circuit?
Is it necessary to have the confusing term "second order" in the introduction? Is it really correct to call the circuit a "second order LC circuit"? It is a "second order circuit", because it has one inductance and one capacitance and is represented by a 2nd order differential equation. But it is never called "second order LC circuit". This is going to be confusing to general readers, they are going to ask "What then is a first order LC circuit?" I understand the reason it was added, to distinguish this circuit from LC circuits with more reactances. But I think that could be relegated to another section, or at least put at the end of the introduction, to avoid confusing readers. -- Chetvorno TALK 00:26, 10 October 2014 (UTC)


 * Changed lead paragraph. -- Chetvorno TALK 00:06, 20 November 2014 (UTC)
 * I've tried to clarify that a bit, it is ambiguous which term is "occasionally applied to more complicated LC networks" and could wrongly be read to mean that is "second order LC circuit". I agree with your original comment on this.  I think the discussion of order could be moved out of the lead altogether.  It can then be treated in a bit more detail with an explanation of what the order actually means. SpinningSpark 00:48, 20 November 2014 (UTC)
 * By the way, second order LC circuit does not redirect to this article (it does not exist at all) so there is no need to have it as a bolded term and thus even less need for it to be in the lead. SpinningSpark 00:52, 20 November 2014 (UTC)
 * Yes, that is better. I'll move it down into the article then.  Don't know just where it should go, though. -- Chetvorno TALK 03:01, 20 November 2014 (UTC)
 * Create a terminology section? Some of the other clutter in the lead could then also be moved there. Spinning<b style="color:#4840A0">Spark</b> 11:27, 20 November 2014 (UTC)
 * Sounds good. Thanks for clarifying my text, it was confusing. -- Chetvorno <i style="color:purple; font-size:smaller;">TALK</i> 15:06, 27 November 2014 (UTC)
 * Yes. RC and RL filters are first order, and LC filters second order.  Somewhat like you get with an RC and RL filter, with R going to zero (or infinity). But the reason I am reading this today is to find where in Wikipedia filter order is discussed. It should be somewhere! Gah4 (talk) 01:36, 26 April 2021 (UTC)
 * Agree. I suggest Electronic filter.  Actually it is already mentioned obscurely in the "Transfer function" section: "The order of the transfer function will be the highest power of s encountered in either the numerator or the denominator."  I think this section could be expanded to include the relationship between the order of a filter, the number of poles and zeros, the number of reactive components.  (capacitors and inductors) in the circuit (greater than or equal to the order), and the maximum slope of the Bode gain plot (20dB/decade times the order).  This is kind of an important relationship for classifying filters.  --Chetvorno<i style="color: Purple;">TALK</i> 23:04, 5 April 2023 (UTC)
 * Theoretically, filter order and transfer function order could have different definitions. In any case, all that I know give the slope in dB/octave. Gah4 (talk) 20:31, 6 April 2023 (UTC)
 * Theoretically, filter order and transfer function order could have different definitions. In any case, all that I know give the slope in dB/octave. Gah4 (talk) 20:31, 6 April 2023 (UTC)
 * Theoretically, filter order and transfer function order could have different definitions. In any case, all that I know give the slope in dB/octave. Gah4 (talk) 20:31, 6 April 2023 (UTC)

Tank circuit - non-transistor amplifiers - request for article / section
Between LC circuit being redirected from Tank circuit, and Amplifier being mostly in regard transistor amplifiers we seem to be missing an entire Tank circuit article dealing with non-transistor amplifiers. The Tank circuit was entirely the amplifier pre-transistor apart from various inductive amplification. At least include a full section under either the aforementioned and reference to either both. Thank-you KING (talk) 07:36, 24 December 2015 (UTC)


 * I'm not sure what you are referring to. By "tank circuit" do you mean a tuned radio frequency (RF) amplifier that uses a tank circuit?  If so, that is briefly covered in the stub RF power amplifier, although it certainly needs to be expanded.   I agree that type of amplifier seems to be missing from the Amplifier article. -- Chetvorno <i style="color:purple; font-size:smaller;">TALK</i> 11:54, 24 December 2015 (UTC)
 * A tank circuit is not called an amplifier in modern terminology. Amplifier usually implies an increase in power in electronics usage.  An LC circuit used to increase voltage or current is more correctly called a (voltage or current) multiplier.  This is not the case for an analogous mechanical passive resonator, where it can be called a mechanical amplifier.  Same goes for acoustics.  But I agree that this seems to be missing from Wikipedia.  It could be described here, at voltage multiplier, or in a new article.  I don't think that tank circuit would be a good home for it though, that's not my understanding of what tank circuits are for. <b style="background:#FAFAD2;color:#C08000">Spinning</b><b style="color:#4840A0">Spark</b> 13:34, 24 December 2015 (UTC)
 * Hmm. Consider the horns used in early phonographs, which aren't amplifiers, but impedance matching. Impedance matching doesn't increase power, but makes better use of the power you have. Driving a circuit (or mechanical system) at resonance can generate a large amplitude with a small input power. Gah4 (talk) 02:14, 15 February 2023 (UTC)
 * Hmm. Consider the horns used in early phonographs, which aren't amplifiers, but impedance matching. Impedance matching doesn't increase power, but makes better use of the power you have. Driving a circuit (or mechanical system) at resonance can generate a large amplitude with a small input power. Gah4 (talk) 02:14, 15 February 2023 (UTC)

low frequency
Recent edit summary suggests that LC circuits don't go to low frequencies. It seems that LC filters in power supplies are rare these days, but not so rare in the vacuum tube days. So, yes, you can build and LC filter with electrolytic capacitor and iron core inductor, below 60Hz. Probably to 0.42Hz if you really want one. But yes, the common use is for radio receivers at RF. Gah4 (talk) 23:25, 13 February 2023 (UTC)
 * I don't think user:Chetvorno was saying low-frequency filters do not exist. Just that 0.42 Hz is a highly improbable and misleading example.  By the way, not that it makes any difference to this discussion, the filtering following a full-wave rectifier and reservoir capacitor needed to have a cut-off below 120 Hz (for a 60 Hz supply) not 60 Hz.  That applied to both vacuum tube and transistor power supplies.  I'd also note that LC circuits were never used for this purpose.  A filter might consist of a pi circuit, or just a series choke.  As we moved into the cheap transistor era, filtering was often dispensed with altogether – much better results could be achieved with just a large enough reservoir capacitor to stop the voltage dipping too low followed by a stabiliser circuit clipping the voltage to a reference value (such as from a Zener diode). <b style="background:#FAFAD2;color:#C08000">Spinning</b><b style="color:#4840A0">Spark</b> 14:39, 14 February 2023 (UTC)
 * As the Q probably isn't all that high, it should probably be below 60Hz, but yes the component is at 120Hz. I suppose pi circuit might be usual, but with at least one L and one C, LC doesn't seem so far off. I think I remember them from vacuum tube amplifiers, and not from transistor amplifiers. It isn't completely obvious why. One is the different voltage, means different size L and C. Well, also the IV characteristic of vacuum tube rectifiers is different. Gah4 (talk) 01:57, 15 February 2023 (UTC)
 * I was recently looking at the manual for the Heathkit W-3AM amplifier that I used to have. (After my dad got a Heathkit transistorized amplifier.) It seems to have a 10uF capacitor, 10Hy inductor, and 25uF capacitor. The capacitors are actually two 20uF and 50uF, 350V, in series to get high enough voltage. 10Hy and 25uF gives about 10Hz resonant frequency. I suspect this was usual for tube amplifier power supplies. Gah4 (talk) 06:12, 5 April 2023 (UTC)
 * As the Q probably isn't all that high, it should probably be below 60Hz, but yes the component is at 120Hz. I suppose pi circuit might be usual, but with at least one L and one C, LC doesn't seem so far off. I think I remember them from vacuum tube amplifiers, and not from transistor amplifiers. It isn't completely obvious why. One is the different voltage, means different size L and C. Well, also the IV characteristic of vacuum tube rectifiers is different. Gah4 (talk) 01:57, 15 February 2023 (UTC)
 * I was recently looking at the manual for the Heathkit W-3AM amplifier that I used to have. (After my dad got a Heathkit transistorized amplifier.) It seems to have a 10uF capacitor, 10Hy inductor, and 25uF capacitor. The capacitors are actually two 20uF and 50uF, 350V, in series to get high enough voltage. 10Hy and 25uF gives about 10Hz resonant frequency. I suspect this was usual for tube amplifier power supplies. Gah4 (talk) 06:12, 5 April 2023 (UTC)
 * I was recently looking at the manual for the Heathkit W-3AM amplifier that I used to have. (After my dad got a Heathkit transistorized amplifier.) It seems to have a 10uF capacitor, 10Hy inductor, and 25uF capacitor. The capacitors are actually two 20uF and 50uF, 350V, in series to get high enough voltage. 10Hy and 25uF gives about 10Hz resonant frequency. I suspect this was usual for tube amplifier power supplies. Gah4 (talk) 06:12, 5 April 2023 (UTC)

order, again
It seems that I already have a section on order. As a recent undo notes, LC filters have even order. There are RC and RL filters, starting with first order. Or, as noted in the edit summary, it comes from the order of the differential equation. The not very many, and not necessarily WP:RS that I searched, all say LC starts at 2. Gah4 (talk) 05:15, 5 April 2023 (UTC)

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<i style="color: Purple;">TALK</i> 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)