physical explanation of phenomenon of resonance

physical explanation of rlc circuit

From circuit point of view, a series RLC circuit resonance is easy to understand, but I want to explore it for more details: the voltage and current at the inductor is out of phase, the voltage and current at the capacitor is also out of phase, but the voltage and current at the resistor is in phase, and the overall input voltage and current is in phase when it resonant.
Now we consider a resonante cavity(it can be closed metal cavity or dielectric cavity withoout any metal coating), from electromagnetic theory we know that this kind of structure have resonant frequency and corresponding resonant mode. I understand that the energy stored in both E field and H field inside this structure, when it is resonant, the engery storage is from E field to H field and reverse(assuming no any loss). and it can be strictly derived from Maxwell's equations. but my confusion comes: :?:
1. EM wave is too abstract to understand, is there any explanation of resonance phenomenon in terms of energy (just like the formation of standing wave)? For example, the total internal reflection (TIR) theory for fiber analysis.
In another word, the resonant structure is there, I have some EM wave to excite this structure, only thing I know is that some part of energy will go in this structure, and only specific mode will exist inside this structure, How can we descibe and explain this phenomenon in physics? sry for my poor description of this problem, because I did not clearly formulated my problem, just blablabla ... here. ^_^
2. When whole strcutre is resonant, I believe the E/H field intensity maxium is out of phase, am I right? And we can try to relate it to circuit theory, E corresponding to voltage, H corresponding to current, we can conclude that the equivalent current and voltage should be out of phase. It seems that there is discrepence with circuit theory. so I am more confused now.


Welcome for any comment!


Best Regards,

explanation of resonance

EM wave is the picture Maxwell and Hertz molded to interpret the "electric" and "magnetic" ENERGY flow so that we can calculate and design the flow of ENERGY. The Newton force is abstract to my kid at KG. In fact we "think" we understand the more we train our brain to "abstract" a phenomenon in terms of some words.
Building on what you "undersatand"="abstract" from circuit the electric field in a resonator (either metal cavity or dielectric) forms astanding wave so it is practically like stored electric energy in a capacitor only you cannot recognize which are the plates that face each other (all facing metal walls are practically equivalent to parallel capacitors and all reflecting dielectric-air interface are practically as high in reflection as the metal) so here lays the electric energy storage. Needless to say that the magnetic field stored crosses any areay you like "inside" the resonator produces flux linkage and meanwhile its circulation within the resonator volume is equivalent to current so you can recognize inductors across the capacitor plates shunting them, (the inductors face the hard imagination problem like the dielectric reflector.)
Oh I guess you wionder about the resistor there are two types of it ... think a littele the answer is coming

phenomenon of resonance

Well if there is some conductivity inside the resonator then the dissipated power will give you shunt resistor. if the resonator some how open to the outer "environment" the power radiation loss will give series resistor

Oh you got a second confusion point:
As I recall from the cavity lectures the elelctric and magnetic fields (transverse to each other) of the resonant mode developed a complex basis factor i (or j) so that they were interpreted that they will carry NO POWER along any direction of the resonator. The fields are said to be orthogonal in the phase space (Not out of phase).
Yet you are comparing the property of the capacitor's voltage to the capacitor's current and the inductor's voltage to the inductor's current and want to reflect the capacitor's voltage to the electric field and the inductor's current to the magnetic field! unfortunately ther is no equivelance between feild and circuit quiantities here.
If you know well the waveguide impedance would you tell me how the real impedance means no dissipation while a carbon resistor have real resistance dissipates the electric power?!
Best of luck with waves

sifeddin said:

EM wave is the picture Maxwell and Hertz molded to interpret the "electric" and "magnetic" ENERGY flow so that we can calculate and design the flow of ENERGY. The Newton force is abstract to my kid at KG. In fact we "think" we understand the more we train our brain to "abstract" a phenomenon in terms of some words.
Building on what you "undersatand"="abstract" from circuit the electric field in a resonator (either metal cavity or dielectric) forms astanding wave so it is practically like stored electric energy in a capacitor only you cannot recognize which are the plates that face each other (all facing metal walls are practically equivalent to parallel capacitors and all reflecting dielectric-air interface are practically as high in reflection as the metal) so here lays the electric energy storage. Needless to say that the magnetic field stored crosses any areay you like "inside" the resonator produces flux linkage and meanwhile its circulation within the resonator volume is equivalent to current so you can recognize inductors across the capacitor plates shunting them, (the inductors face the hard imagination problem like the dielectric reflector.)
Oh I guess you wionder about the resistor there are two types of it ... think a littele the answer is coming

Click to expand...

Thanks for your response, I can not agree more with you about the electric energy and magnetic energy together formed the EM wave.
Let's come back to resonance, this physical phenomenon. The first time I learn this word is from physics fundamentals, from the standingwave. The pure standing wave can not transfer energy. The same principle for TEM vertical hitting PEC wall, pure standing wave we got, no enrgy at the direction of wave propagation. But, there is still EM wave, still have electric and magnetic field. Definitely the direction of E filed and H field are perpendicular, my concern is that when energy sotre inside E field is maxium, then the energy store inside H field is minimum, and vice versa. So in this point of view, I call it "out of phase".

sifeddin said:

Oh you got a second confusion point:
As I recall from the cavity lectures the elelctric and magnetic fields (transverse to each other) of the resonant mode developed a complex basis factor i (or j) so that they were interpreted that they will carry NO POWER along any direction of the resonator. The fields are said to be orthogonal in the phase space (Not out of phase).
Yet you are comparing the property of the capacitor's voltage to the capacitor's current and the inductor's voltage to the inductor's current and want to reflect the capacitor's voltage to the electric field and the inductor's current to the magnetic field! unfortunately ther is no equivelance between feild and circuit quiantities here.
If you know well the waveguide impedance would you tell me how the real impedance means no dissipation while a carbon resistor have real resistance dissipates the electric power?!
Best of luck with waves

Click to expand...

I didnt understand "The fields are said to be orthogonal in the phase space (Not out of phase)". I dont know what is waveguide impedance, I know what is wave impedance.
The EM wave can propagate, because of inter-changing of E field and H fied, and hence the energy was moving at the direction of wave propagation direction, but for the case of resonance, what happened?

I think I need further clarify my question:

The resonant phenomenon is easy to understand like the example of spring, RLC circuit. But how about EM wave? and How resonance happened for EM wave?

Yes, standing wave should be the best example to understand EM wave resonance.
So for parallel metal plane as capacitor, we can still use standing wave to explain resonanse, same principle we can use to cavity model, But all my understanding of resonant structure come from strictly Maxwell Equation, (for waveguild, for metal cavity), I can not relate it to any knowledge from physics. ALL my understanding come from the eigen matrix equation, the eigen value, eigen vector.
I wonder all those numbers,vectors mean what in physic.

Let's consider an example first, just a ideal metal cavity, no any loss, once I excite some energy into this cavity, what will happen?


Give me more time to clearly formulate myself, I am very messy now.

Best Regards,

There are many ways to view the resonance phenomena. But the simplest off all is energy. Does anyone remember some resonance examples from simple classical mechanics?

asdfaaa said:

I didnt understand "The fields are said to be orthogonal in the phase space (Not out of phase)". I dont know what is waveguide impedance, I know what is wave impedance.

Click to expand...

Orthogonal in phase space means not in phase in time space!

Maybe you think about a little wire it has an impedance so what is a waveguide impedance?

Kuehnsen said:

asdfaaa said:

I didnt understand "The fields are said to be orthogonal in the phase space (Not out of phase)". I dont know what is waveguide impedance, I know what is wave impedance.

Click to expand...

Orthogonal in phase space means not in phase in time space!

Maybe you think about a little wire it has an impedance so what is a waveguide impedance?

Click to expand...

HI, Can give more hints?

Best Regards