# LC oscillator and resonance frequency

#### takotak

Feb 20, 2023
5
Hello there,

I'm going back to fundamentals in electronics, and I end up with questions that I can't answer satisfactorily.

The object of my turmoil is the parallel LC circuit, and more especially what happens when it is connected to an AC voltage source that delivers a sine signal at the resonance frequency of the LC circuit.

I'm trying to "get what's happening" without using Kirchhoff's laws, because I want to seize the physical phenomenon instead of proving it mathematically. Showing algebraically that the global impedance of the parallel LC circuit is maximum at resonance frequency does not satisfy me because I want visualize what the charges do in the circuit.

My questions comes from this thinking of mine:

Imagine you connect that AC source to the parallel LC circuit, without having charged the C nor the L before, and neglecting resistive effects. And imagine that the AC source delivers a sine signal at the resonance frequency of the LC circuit.

Now I will describe what I think happens, please correct me if I'm wrong.

During the first quarter cycle of the sine signal, starting with a positive voltage (STEP 1):
- The C (capacitor) gets charged, the current through it going from max value to zero, and the voltage at its ports from zero to max value (following the input AC voltage).
- As for the L (self), the voltage at its ports follows also the input AC voltage, and at the end of the quarter cycle (max positive voltage), the current through it is just about to be positive (the current drags 90 degrees with respect to the voltage at the L ports, as its reactance shows).

Then (STEP 2), the AC voltage starts to decrease (starting the second quarter cycle, just after the max voltage). Therefore, the positive charges accumulated on the positive plate of the C will start to leave the plate as stated by q = Cu (I won't dive into the specifics of drift velocity vs wave velocity, but think in terms of travelling charges instead).

My understanding is as follows:
1) The positive charges leaving the positive plate of the C will go through the L, and the "90 degrees delayed" positive current through the L will correspond to that flow of charges from the C to the L (because at resonance, the modulus of the C-reactance equals the modulus of the L-reactance).
2) As a result, the C is not "asking for" current anymore, and all the current is L is "asking for" comes from the C.
3) As a consequence of 2., the current from the AC source will now be zero, meaning that the impedance of the parallel AC circuit can be considered infinite (open circuit). The voltage between the two ports of the LC circuit will continue oscillating (we neglect the resistive effects), with no current ever delivered by the AC source anymore.

So my questions are:
1. Is what I describe correct ?
2. About point 1), it is correct to assume that it's the electromotive force induced by the L that make the positive charges from the C travel through the L instead of going back to the positive port of the AC source ?

I apologize for not bringing any plots to support my question, but I guess you are familiar enough with the topics to get my point.

With my best regards,
Takotak

#### Delta Prime

Jul 29, 2020
2,214
I apologize for not bringing any plots to support my question, but I guess you are familiar enough with the topics to get my point
I also apologize for not bringing any plots to my answer. But hopefully it'll paint a picture in your mind.
Welcome to Maker Pro.
AC (Alternating Current) this current alternats a particular frequency.
Which is the same as oscillates at a particular frequency.
That's AC power. And that takes energy .So now we're going to say "driven" and
"damped" oscillator,the driving force or driven force feeds energy into the parallel LC circuit.
The parallel LC circuit is a system.
During some parts of the
oscillating system energy is fed or driven and takes energy out during other parts or dampened.
Except when the system is at resonance it does not (dampen or take energy out) it only ( driven or puts energy in.)
Frequency is one of the properties of a wave, regardless of whether the wave is mechanical, electromagnetic, or gravitational.The frequency of the wave is the number of wave oscillations that occur at a point in a length of time, such as a nanosecond, second,or minute.
Resonance allows you to pick out a certain frequency and ignore all the others.
This is how radios,cell phones work.
If you have a radio sitting on your desk, then it is being bombarded by radio waves with all sorts of frequencies.
If you want to pick out a certain frequency, then you can “tune” your radio to that frequency by changing
the radio’s natural frequency or (Resonant frequency) (normally done by changing the capacitance C in the internal circuit). Assuming that the damping
in the circuit is small (this is determined by L), then
there will be a large
oscillation in the circuit, at the radio station’s frequency, but a negligible oscillation at all the other frequencies
The “pipe” of say,a flute has various natural frequencies
(depending on which keys are pressed), and these are the ones that survive when you blow air across the opening.
There is a subtlety about whether some musical instruments function because of resonance
or because of “positive feedback,” .
Millennium Bridge in London: This pedestrian bridge happened to have a lateral resonant frequency on the order of 1 Hz. So when it started to sway (for whatever reason),
people began to walk in phase with it (which is the natural thing to do). This had the effect of driving it
more(positive feedback) and further increasing the amplitude. Dampers where added (taking the energy out), which fixed the problem.
A tall building has a resonant frequency of swaying or actually
couple,depending on the direction and there can be twisting,too.
If the effects from the wind or earthquakes
happen to unfortunately drive the building at this frequency,then the sway
can become noticeable.
“Tuned mass dampers” (large masses connected to damping mechanisms,
in the upper floors) help alleviate this problem.

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#### Delta Prime

Jul 29, 2020
2,214
What is the load?the circuit requires to be closed all these things the capacitor the inductor obviously the AC source must be connected to something and that is part of the circuit as well.
the reactance releases energy in the form of a magnetic field, it is called inductive reactance XL whereas if the reactance releases energy in the form of an electric field, it is called capacitive reactance XC

Question? I know you have to start somewhere but why one quarter of the cycle.
You can't discount resistance and you've never mentioned or capacitive reactants or inductive reactants.

impedance is only used in AC systems and does not have any use in DC diagrams. Another considerable difference for identifying resistance vs. impedance is that impedance can be combined with inductive reactance, resistance, or capacitance reactance. While resistance only means the resistance of an instrument. We must know their application in AC and DC circuits before understanding the resistance vs. impedance term
When values of inductive reactance and capacitive reactance become equal, they are said to be resonant.
It has been proven that the resonance is obtained when the capacitive impedance and the inductive impedance values are equal.

#### Delta Prime

Jul 29, 2020
2,214
I'm going back to fundamentals in electronics, and I end up with questions that I can't answer satisfactorily.
I myself frequently must revisit the fundamentals in electronics it never hurts to reinforce the fundamentals.
As for your other questions I really don't know how to answer those. Apologies.

#### hevans1944

##### Hop - AC8NS
Jun 21, 2012
4,891
1. Is what I describe correct ?
Lessee... you reject circuit analysis using algebra and well-known mathematical formulas that describe how capacitive and inductive reactance vary inversely with each other as a function of frequency. Then you postulate that when these reactances are equal (same modulus in your words) the parallel LC circuit is at resonance and no energy is drawn from the AC excitation source. You then jump to the conclusion that if no energy is taken from the AC source, then the impedance of the parallel LC circuit must be infinite.

So, IMHO, the answer to your question is NO. Hand waving, which is what you are doing, is not a substitute for science, engineering, or mathematics.

You talk about "positive charges" as if these really occur in a parallel LC circuit. They do not. In a parallel LC circuit there are NO positive charges that participate in circuit operation. Everything that occurs is a result of the flow of electron current. Electrons are point-like particles that exhibit mass and a unit of negative charge. The valence electrons of the atoms in the wire are responsible for any current or voltages you observe.

The "charge" on a capacitor is neither positive nor negative. It simply represents the physical separation of numerous electrons between the two plates of the capacitor: Q (charge separation in coulombs) = C (capacitance in farads) x V (voltage measured between the two capacitor plates). Since there are two terminals on a capacitor, the polarity of the voltage will depend on how you measure it. If a "charged" capacitor has a positive voltage measured from one plate with respect to the other plate, then it will have a negative voltage if measured from the "other" plate to the first plate. The charge has not changed.

Charging a capacitor means you take electrons from one plate and move them to the other plate, by whatever means. There are no positive charges moving between the capacitor plates.

I'm going back to fundamentals in electronics
If only that were a true statement. The fundamentals of electronics were established in the 19th century by people like Michael Faraday and James Clerk Maxwell and many others. Math is essential to quantitatively describing electronics circuits. You start with atomic theory and move on up from there.

Atomic theory states that matter is composed of small entities called atoms that consist of a nucleus with protons that have a +1 charge and possibly also several neutrons that have no charge at all. The nucleus contains most of the mass of the atom. One or more "shells" of electrons, each electron having a -1 charge, surround the nucleus. The mass of an electron is about 1/1000th the mass of a either a proton or a neutron, so most of the mass of an atom is in the nucleus. The total negative charge, which is the sum of the charges of all the shell electrons, exactly cancels the positive charge of the nucleus, rendering the atom as a whole neutral when viewed at a distance.

The simplest atom, hydrogen, has a single proton for the nucleus and a single electron in the one and only shell. Every other atom has a nucleus composed of a various number of protons bound to a number of neutrons by the strong nuclear force, but the number of protons is always the same as the number of shell electrons. The number of protons in an atom determines which element of the Periodic Table of Elements the atom belongs to.

Showing algebraically that the global impedance of the parallel LC circuit is maximum at resonance frequency does not satisfy me because I want visualize what the charges do in the circuit
Visualize all you want, but that doesn't make it so. Charge is an invisible electrical property, so even if you squint really hard, you will never "see" to visualize charge. You can see the effects of charge, but electrical charge cannot be visualized meaningfully. J.J. Thomson is credited as being the first person to "discover" the electron by observing the effect of magnetic and electrical fields on the behavior of light emitted from the phosphor of a cathode-ray tube (CRT) by a beam of electrons. However, it was the American physicist Robert Andrews Millikan (1868-1953) who first determined the charge on an electron using the motion of charged oil drops in a gravitational and electrical field.

Therefore, the positive charges accumulated on the positive plate of the C will start to leave the plate as stated by q = Cu (I won't dive into the specifics of drift velocity vs wave velocity, but think in terms of travelling charges instead).
There are NO net positive charges in a capacitor because that would require that protons (atoms) be moved along the wires connected to the capacitor. What actually happens in a capacitor is an external electrical field causes loosely bound and mobile valence electrons in the atoms of one capacitor plate to migrate and accumulate on the other plate. Thus one plate loses electrons and becomes positively charged, because the nucleus of atoms losing electrons is positvely charged, relative to the other plate. The "other" plate gains electrons and becomes negatively charged relative to the first plate. The overall charge of the capacitor is zero because the surplus of electrons on one plate is exactly balanced by the absence of electrons on the other plate. The only way you can determine if a capacitor is "charged" is to measure the voltage between the two capacitor plates, or you can determine that an electrical field exists between the two plates by using a device that measures the presence of electrical fields.

2) As a result, the C is not "asking for" current anymore, and all the current is L is "asking for" comes from the C.
Please do not attribute anthropomorphic qualities to inanimate, non-living, objects. Electronic components are not "asking for" anything. Electronic components obey "physical laws" that are expressed by mathematical relations and functions. Hand waving explanations may "feel good," but they are seldom good analogies in their ability to predict circuit behavior. You need math and electronics theory for that... or you could just call yourself a "maker" and throw stuff together until you get the results you want. The end result my resemble electronics, but it is not electrical engineering.

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#### Delta Prime

Jul 29, 2020
2,214
The end result my resemble electronics, but it is not electrical engineering

#### takotak

Feb 20, 2023
5
Lessee... you reject circuit analysis using algebra and well-known mathematical formulas that describe how capacitive and inductive reactance vary inversely with each other as a function of frequency. Then you postulate that when these reactances are equal (same modulus in your words) the parallel LC circuit is at resonance and no energy is drawn from the AC excitation source. You then jump to the conclusion that if no energy is taken from the AC source, then the impedance of the parallel LC circuit must be infinite.

So, IMHO, the answer to your question is NO. Hand waving, which is what you are doing, is not a substitute for science, engineering, or mathematics.

You talk about "positive charges" as if these really occur in a parallel LC circuit. They do not. In a parallel LC circuit there are NO positive charges that participate in circuit operation. Everything that occurs is a result of the flow of electron current. Electrons are point-like particles that exhibit mass and a unit of negative charge. The valence electrons of the atoms in the wire are responsible for any current or voltages you observe.

The "charge" on a capacitor is neither positive nor negative. It simply represents the physical separation of numerous electrons between the two plates of the capacitor: Q (charge separation in coulombs) = C (capacitance in farads) x V (voltage measured between the two capacitor plates). Since there are two terminals on a capacitor, the polarity of the voltage will depend on how you measure it. If a "charged" capacitor has a positive voltage measured from one plate with respect to the other plate, then it will have a negative voltage if measured from the "other" plate to the first plate. The charge has not changed.

Charging a capacitor means you take electrons from one plate and move them to the other plate, by whatever means. There are no positive charges moving between the capacitor plates.

If only that were a true statement. The fundamentals of electronics were established in the 19th century by people like Michael Faraday and James Clerk Maxwell and many others. Math is essential to quantitatively describing electronics circuits. You start with atomic theory and move on up from there.

Atomic theory states that matter is composed of small entities called atoms that consist of a nucleus with protons that have a +1 charge and possibly also several neutrons that have no charge at all. The nucleus contains most of the mass of the atom. One or more "shells" of electrons, each electron having a -1 charge, surround the nucleus. The mass of an electron is about 1/1000th the mass of a either a proton or a neutron, so most of the mass of an atom is in the nucleus. The total negative charge, which is the sum of the charges of all the shell electrons, exactly cancels the positive charge of the nucleus, rendering the atom as a whole neutral when viewed at a distance.

The simplest atom, hydrogen, has a single proton for the nucleus and a single electron in the one and only shell. Every other atom has a nucleus composed of a various number of protons bound to a number of neutrons by the strong nuclear force, but the number of protons is always the same as the number of shell electrons. The number of protons in an atom determines which element of the Periodic Table of Elements the atom belongs to.

Visualize all you want, but that doesn't make it so. Charge is an invisible electrical property, so even if you squint really hard, you will never "see" to visualize charge. You can see the effects of charge, but electrical charge cannot be visualized meaningfully. J.J. Thomson is credited as being the first person to "discover" the electron by observing the effect of magnetic and electrical fields on the behavior of light emitted from the phosphor of a cathode-ray tube (CRT) by a beam of electrons. However, it was the American physicist Robert Andrews Millikan (1868-1953) who first determined the charge on an electron using the motion of charged oil drops in a gravitational and electrical field.

There are NO net positive charges in a capacitor because that would require that protons (atoms) be moved along the wires connected to the capacitor. What actually happens in a capacitor is an external electrical field causes loosely bound and mobile valence electrons in the atoms of one capacitor plate to migrate and accumulate on the other plate. Thus one plate loses electrons and becomes positively charged, because the nucleus of atoms losing electrons is positvely charged, relative to the other plate. The "other" plate gains electrons and becomes negatively charged relative to the first plate. The overall charge of the capacitor is zero because the surplus of electrons on one plate is exactly balanced by the absence of electrons on the other plate. The only way you can determine if a capacitor is "charged" is to measure the voltage between the two capacitor plates, or you can determine that an electrical field exists between the two plates by using a device that measures the presence of electrical fields.

Please do not attribute anthropomorphic qualities to inanimate, non-living, objects. Electronic components are not "asking for" anything. Electronic components obey "physical laws" that are expressed by mathematical relations and functions. Hand waving explanations may "feel good," but they are seldom good analogies in their ability to predict circuit behavior. You need math and electronics theory for that... or you could just call yourself a "maker" and throw stuff together until you get the results you want. The end result my resemble electronics, but it is not electrical engineering.

Thank you very much for your replies. I appreciate you took the time for them.

I must say however that they do not address the issue as I expected, but it is entirely my fault.
I should have stated my background, that would have helped you getting what I was asking for.
I've got a degree in electrical & telecommunication engineering, and a Ph.D. in physics, as well as a college degree in mathematics.

So, I'm pretty familiar with Rutherford-Bohr's atomic model and Maxwell's theory, including the electromagnetic theorems derived from them (even if empirically found before, such as Faraday/Lenz induction law). And I'm not rejecting mathematics to address physics and electrical problems, to say the least...

What I'm trying to do is to set a thought experiment to get a qualitative and intuitive way to think about LC electrical resonance. Using this kind of thought experiment is actually pretty standard in physics, Einstein used a lot of them, and Maxwell himself used this kind of approach in his founding paper "A Dynamical Theory of the Electromagnetic Field" (1865) [see the section about "Coefficients of Induction for Two Circuits, for instance", for instance]. So using analogies to better understand phenomena is pretty standard, it's a matter of understanding the limits of them with respect to the original problem.

That being said, I'm aware that the description I propose has limits. But the limits you raise are not relevant in my opinion:

1. Using positive charges instead of negative charges to describe current has been widely used for decades in electrical engineering, as positive chages can be considered as lack of electrons or, as stated in semiconductors theory, "holes". So there's nothing wrong in using this approach, as far as a particles-based description is concerned. And saying that the current is actually made of moving electrons (in that case) your are not bringing anything new to me Actually, if you really want to stress the limit of that approach, it's more that electrical phenomena in variable configurations should be described by waves of voltage/current induced by waves of electromagnetic fields determined by Maxwell's equations, instead of a flow of charged particles. You are indeed making a mistake saying "What actually happens in a capacitor is an external electrical field causes loosely bound and mobile valence electrons in the atoms of one capacitor plate to migrate and accumulate on the other plate." The drift velocity of electrons in a conductor is very very small. So it's not the electrons from one plate that goes to the other plate, but rather the wave of electromotive force that decreases the electron accumulation on one plate and increases it at the other plate.

2. "Then you postulate that when these reactances are equal (same modulus in your words) the parallel LC circuit is at resonance and no energy is drawn from the AC excitation source. You then jump to the conclusion that if no energy is taken from the AC source, then the impedance of the parallel LC circuit must be infinite." No. I'm not assuming the LC circuit is already at resonance, because I'm assuming that the LC circuit is uncharged at t=0. So there is energy taken from the AC source to charge the LC circuit. Saying that infinite impedance leads to no energy is wrong. It's POWER that is null (because current is null), but electrical energy get stored.

3. "Electronic components obey "physical laws" that are expressed by mathematical relations and functions. Hand waving explanations may "feel good," but they are seldom good analogies in their ability to predict circuit behavior. You need math and electronics theory for that... or you could just call yourself a "maker" and throw stuff together until you get the results you want. The end result my resemble electronics, but it is not electrical engineering." As already stated, I'm not rejecting maths to study electrical engineering. I want to support the mathematically demonstrated resonance of the LC circuit with a thought experiment. Physics do not derive from maths, but maths is used to put in from, in a domain of validity, what happens in the physical world. You can be satisfied by just using Kirchhoff's laws and finding the frequency that leads to maximum impedance of the parallel LC circuit. But I'm not.

I ended up finding about the circuit simulator Falstad, and it seems to support the description of my original post. But I don't know the reliability of that simulator, maybe you do.
So, as Einstein said, "If you can't explain it to a six year old, you don't understand it". If you think I'm wrong, maybe you can describe what happens like you would do for a six year old
I always find this way of thinking particularly stimulating.

With my best regards,
Takotak

#### Delta Prime

Jul 29, 2020
2,214
I always find this way of thinking particularly stimulating.
Agreed. I believe we're not here to see through one another but see one another through...

Feb 19, 2021
824
@takotak

I am a EE, and a wannabe but not capable or competent physicist.

Looking for critical comment on my understanding.

I used to think of current flow as an e- moving from A thru a loop of
conductivity back to A.

Now I think its an e- in a statistical state, moving from an outer
valence band to inner, and releasing a wave of EMF, light, in the
process, that then affects other e-'s. But how many other e-'s
can it affect, just one more ? If more than 1 than there is gain that
appeared out of nothing. That means there is a gain in mass so is
the mass of the universe increasing ? And that e-gets re-affected
by its own or another e- wave of EMF, that then jumps it back to outer
valence band. But that band is even statistical, what band is it in ?
Nobody knows. And then we have if e- releases E, that is same as
releasing mass, and a hard little ball is the manifestation of E. But
the hard little balls shape is virtual, a cloud, a probability that its
there, might be, maybe not. So its not hard, maybe not even there....
So if its not then it never existed in the first place. So I too may not
exist, there is a finite probability I never was, or I appeared virtual
for a moment and then gone until the next rainy day.

And if an e- drops from an outer band to inner, releasing E, hence mass,
(light as well, more mass) are all our wires shrinking ?

And this is where I need a strong drink.

Regards, Dana.

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#### Delta Prime

Jul 29, 2020
2,214
It's always the quiet ones.
That was both barrels double ought shell's.

#### takotak

Feb 20, 2023
5
Nice poetical irony
Does my original question seems stupid / poorly formulated to you ?

#### hevans1944

##### Hop - AC8NS
Jun 21, 2012
4,891
And this is where I need a strong drink.
Mind-altering drugs, whether that be a single-malt Scotch whisky, or a fine bourbon aged in charred oak barrels, or perhaps a fine wine, or perhaps something prescribed by a medical doctor, for example medical marijuana, are some of the ways of coping with this fascinating world we get to (temporarily) live in. That doesn't mean our minds have to be permanently altered, but over a sufficient period of time, and with some reflection on what it all means, perhaps that is inevitable. A mind is a terrible thing to waste! My mind continues to grow and embrace new things.

Does my original question seems stupid / poorly formulated to you ?
Yes. It came across as if you know NOTHING about electronics, which is what this forum is usually all about.

For example, trying to describe what happens in the frequency domain by describing what you THINK happens (so-called thought experiment) in the time domain is just not the way LC circuits operate... the parallel resonant LC circuit is called a "tank circuit" because it stores electromagnetic energy, which by analogy is what a conventional (non-electronic) tank does with a liquid. But the analogy is specious because a non-electronic tank is also a non-leaking, static, reservoir of some liquid (water, oil, gasoline, whatever) whereas the LC tank must be continuously replenished with electromagnetic energy from an external source. Resistance is always present (except for superconductors) in practical LC tank circuits. Because of the skin effect, silver is often electroplated onto the inductor conductors (usually copper tubing or copper solid wires) to minimize resistive losses, but these losses always exist and they cause undesirable heating of the LC tank components, especially at higher power levels.

If you want to explain something and have someone accept your explanation as truth, you should take into consideration everything that affects what you are trying to explain. That is clearly impossible, which is the reason NO theory can ever be proven true: there is always the possibility that a single counter-example will demonstrate the theory to be flawed. Reasoning by analogy is always suspect. There is an old cartography saying: "The map is not the territory." If you understand that statement, you may be aware of the severe limitations of analogy to "explain" anything.

I've got a degree in electrical & telecommunication engineering, and a Ph.D. in physics, as well as a college degree in mathematics.
Congratulations! Has the Biden administration forgiven your student loans yet? Or did you serve in the military and receive Government funding for your education? Maybe you were blessed with wealth? I am generally not impressed with people having advanced degrees, not that anyone here in these forums (or anywhere else) cares much about whether I am impressed or not.

IMHO, colleges today crank out advanced degrees like they are jelly beans. Even a few engineers, who if successful tend to be very practical, have been seduced into formal enhancements of their undergraduate education. I started down that track, but soon decided that there were some things that I didn't really need to pay to know. Graduate education is mainly an expensive and useless effort if you want to earn a living, but it is generally a requirement if you want to get paid to work in academia. Colleges and universities promote the notion that an advanced degree will guarantee success in the real world. Nonsense! Some of the best electrical engineers I have personally known did not bother, after graduating college, to continue their formal education. College taught them how to continue learning "on their own" by reading published literature and interacting with their professional colleagues.

Of course our civilization "needs" not just engineers, physicists, mathematicians, chemists, biologists, ministers and priests, and a bunch of other professions that need something more than a high-school diploma to participate. It also needs technicians, mechanics, miners and plain old laborers to get things done. We live in a world of conflicting ideology, so we probably need soldiers, sailors, marines, and airmen too. And lots of bigger and better weapons to wage war with.

Two-year community colleges and trade schools use to fuel the skilled labor market, but now most high-school graduates eschew that. These people are told by "guidance counselors" that they need a college degree to be successful. And they want nothing to do with military service, much less an entire career.

Einstein said, "If you can't explain it to a six year old, you don't understand it". If you think I'm wrong, maybe you can describe what happens like you would do for a six year old
I believe Einstein was a great thinker, but I do not agree that even he could explain everything to a six year old. The mind does not fully develop until much later in life, and there are many things that are beyond the comprehension of even an adult twenty-five year old, much less someone who is only six. Einstein did use "thought experiments" to try to understand and explain things, for example his Special Relativity Theory. However, if you want to really understand Einstein's General Relativity, and use its principles to make corrections to the data that satellite constellations forming our Global Positioning System (GPS) produce for navigation, then you had better understand the math that describes it.

Thought experiments are never guaranteed to lead to understanding. Unlike real experiments, thought experiments do not create or confirm real theories. No one has yet offered a tested theory, or even demonstrated the existence, of quantum gravity. This is despite gazillions of taxpayer dollars spent on two LIGOs (Laser Interferometer Gravitational-Wave Observatory) in the United States, and others in places worldwide, to test Einstein's conjecture that gravitational waves should exist. The LIGO is a REAL experiment, not just a thought. And so is ITER, and other nuclear fusion experiments. They all did just begin with a thought experiment.

Of course negative results, or even no results, do not "prove" a theory is wrong, just as positive results confirming a theory do not "prove" the theory is correct, or even complete. We do tend to trust theories, like Newton's laws of gravity, when those theories yield predictable results, without counter-examples negating the theory, over long periods of time. It is only when astronomers looked closer into perturbations in the orbit of Mercury around the Sun, that it was discovered that Newton wasn't exactly correct. Einstein proposed a new theory that accounted for the discrepancy, but there is no guarantee that is the end of the discussion about gravity.

I ended up finding about the circuit simulator Falstad, and it seems to support the description of my original post. But I don't know the reliability of that simulator, maybe you do.
If you want to see what Falstad "can do" in the hands of someone who is clueless, just look up most of the inane posts presented by @dragon. Use "Falstad" and "dragon" as your key words for the search because trying to look up @dragon will yield nothing. Dragon has limited the ability of members to learn more about his MakerPro persona.

I have never used, and know nothing about, Falstad. I have over the years used other circuit simulation software, beginning in college with the Runge-Kutta method of solving differential equations describing real circuits. You have to know the limitations of the simulation, and the limitations of the component models the simulation uses, if you want believable results. This is a hobbyist forum, so real circuits assembled with real components are the usual end result, not simulated results. There is nothing wrong with using simulation to develop real circuits, but simulation should not be the goal of all your endeavors. Maybe you fancy yourself to be a teacher... teachers teach and doers do. Seldom will you find both in the same room.

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Jul 29, 2020
2,214

#### takotak

Feb 20, 2023
5
Hello,

I agree with many of your points. Especially with respect to degrees and their limitations. I did not mention them in order to try to impress or anything of course, just to support that I was aware of the elements that you provided in your detailed first answer (atomic theory, flow of electrons, how a capacitor works, etc.). And I'm european so no student loan needed !

I think the question I asked is relevant, in order to catch what happens during the transient phase of a parallel LC circuit; ie. when the switch connecting the LC circuit and the AC source gets closed. It is true that the dichotomy time analysis vs harmonic analysis is traditionally used, and the latter to study electrical resonance more particularly. However, there is a transient phase that is not described using complex harmonic analysis, and that's precisely what I'm intrigued about.

I kept browsing to see if I could find something addressing that particular question, and I found this:

I find the content very interesting, maybe you will too. I will take the time to read it in details, I think it provides what I'm looking for.

Kind regards,
Takotak

#### Delta Prime

Jul 29, 2020
2,214
You kicked off my own though experiment . I am the six year old.
Try to make a coloration between what I experienced at that age & resonance (hindsight being 20/20)
If your explaining to a six year old then naturally you think as such .
Monkey Bars? Those looked dangerous, over concrete.
The swings sets at the park.
Pretending to cry so my big sister would push me
a couple times.
Swing my legs felt natural if I wanted to swing higher. Only at the right moment (The natural frequency of the swing) amplification
would take place. "Resonance"!

#### hevans1944

##### Hop - AC8NS
Jun 21, 2012
4,891
What I'm trying to do is to set a thought experiment to get a qualitative and intuitive way to think about LC electrical resonance.
Nothing wrong with that. I had problems "visualizing" reactance, much less understanding it, when I was growing up. Grandfather got me started learning about DC electricity by describing Ohm's Law, but that wasn't enough to even begin to explain what happens when you try to force current (the flow of electrons) through the two terminals of a capacitor or inductor. It was many years later, while attending college, that I began to get a glimmer of understanding. Things that I learned as an adult simply were not possible for me to learn as a teenager... or younger. I will continue to try to learn until I die, because I think that is what we are here to do.

I am not a fanboy of simplification or "intuitive" understanding or qualitative learning of anything:

"When you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind: it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science, whatever the matter may be." -- Lord Kelvin (1824 - 1907)

Some things are best explained, not with written words, but with math. Demonstration can also be a way to learn about something, and that does not necessarily have to be just a qualitative learning experience, although it often is. Talk about and try to explain the experience of riding in the front car of a really high and fast roller coaster. Words fail to describe the experience. The rigorous explanation of some things remains still incomprehensible to me, because I have already reached my maximum level of incompetence when it comes to math. When I was growing up in the 1940s, my elders were fond of telling me that only a half-dozen or fewer people understood Einstein's Theory of Relativity. Apparently a lot of people have become a whole lot smarter since then, because scientists and engineers associated with the space program use the principles of relativity every day. Alas, I am not among them.

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#### crutschow

May 7, 2021
863
'm trying to "get what's happening" without using Kirchhoff's laws, because I want to seize the physical phenomenon instead of proving it mathematically.
The operation of an LC tank circuit is not complicated conceptually if you look at it from an energy point-of-view (which does require a little simple math).
Once there is energy stored in an ideal tank, the energy is simply transferred back and forth between the capacitor (all the energy when its voltage is maximum, E = 1/2 CV², and the inductor current is zero) to the inductor (all the energy when its current is maximum, E=1/2LI², and the capacitor voltage is zero).
This happens because there is no stable state, once there is any energy in the tank system.
The time it takes for a full energy transfer from L to C, or C to L, as determined by the values of L and C, is 1/4 cycle of the resonant frequency.

An applied voltage at the resonant frequency just serves to apply energy to start the tank and/or top off the energy in the tank due to any real circuit losses.
An ideal tank with no losses would continue oscillate forever, once there is energy stored in the tank.

Below is the simulation of an ideal 1F, 1H tank circuit, starting with 1V on the capacitor (green trace):
The yellow trace shows the tank current, the red trace shows the instantaneous inductor energy, and the blue trace show the instantaneous capacitor energy.
It should now be apparent why the tank inductor current and capacitor voltage must be 90° out of phase.

Does that help any?

#### takotak

Feb 20, 2023
5
The operation of an LC tank circuit is not complicated conceptually if you look at it from an energy point-of-view (which does require a little simple math).
Once there is energy stored in an ideal tank, the energy is simply transferred back and forth between the capacitor (all the energy when its voltage is maximum, E = 1/2 CV², and the inductor current is zero) to the inductor (all the energy when its current is maximum, E=1/2LI², and the capacitor voltage is zero).
This happens because there is no stable state, once there is any energy in the tank system.
The time it takes for a full energy transfer from L to C, or C to L, as determined by the values of L and C, is 1/4 cycle of the resonant frequency.

An applied voltage at the resonant frequency just serves to apply energy to start the tank and/or top off the energy in the tank due to any real circuit losses.
An ideal tank with no losses would continue oscillate forever, once there is energy stored in the tank.

Below is the simulation of an ideal 1F, 1H tank circuit, starting with 1V on the capacitor (green trace):
The yellow trace shows the tank current, the red trace shows the instantaneous inductor energy, and the blue trace show the instantaneous capacitor energy.
It should now be apparent why the tank inductor current and capacitor voltage must be 90° out of phase.

Does that help any?

View attachment 59561

Hello Crutschow,

Thanks for your reply. Yes, the energy point of view is interesting to get the picture.
What I was really questioning myself about is the transient phase.
I recommend to have a look at the website I mentioned in my previous post (www.rfinsights.com). It addresses specifically that point, and pedagogically so in my opinion.

Kind regards
Takotak

#### crutschow

May 7, 2021
863
Here's the sim when applying a 1Vpk sinewave to the tank for 1 1/4 cycles at its resonant frequency.

#### hevans1944

##### Hop - AC8NS
Jun 21, 2012
4,891
I find the content very interesting, maybe you will too.
I did find it interesting, especially since the author included graphs with the written explanations. What I didn't like was the anthropomorphism attributed to inanimate capacitors and inductors. I must confess that, while interesting to read, the article did not improve or correct my understanding of parallel resonance as it applies to inductors, capacitors, and resistive losses. My understanding may not be as intuitive as yours, but it has served my electrical engineering career and continues to be an important part of my amateur radio hobby.

For those of you out there who don't believe that the motion of electrons is responsible for separating equal positive and negative charges on the plates of a capacitor, I invite you to investigate what happens during electroplating. Or very closely examine what is going on in a Van de Graaff generator, or a Cockroft-Walton voltage multiplier. There is more happening than just electromagnetic waves propagating.

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