Explain LC Resonance in a Circuit

[Dracovich]

Hey guys, I'm doing a lab report on an LC resonant circuit, and it's I've kinda hit a speedbump in trying to explain why exactly the resonance is happening.

I don't know if "LC resonant circuit" is a normal thing to call it so i'll explain a bit. You have V_in which goes into a resistor, then the line splits up into V_out on one side, and a capacitor and inductor connected in parallel on the other side.

So this circuit let's through pretty specific frequencies, and i can talk about it mathmatically that when $$\omega$$ is at different values i can see different things. But i was wondering if i could explain it a bit more detailed, trying to explain why physically it happens at those places.

My first thought was trying to think of it in terms of a normal resonance frequency of a standing wave (thinking of a string with two fixed points being vibrated), so if V_out has a much higher impedence then the LC part, then it could be thought of as a fixed point (total reflected wave), but the LC circuit was not, so it just passed through there easily with not much going to V_out, but at certain frequencies (depending on the values of L and C) the impedence of the LC circuit grew so high that it became a fixed point as well and reflected waves completely (although at that point it all goes through V_out i guess since it has a finite impedence, and that would no longer be a fixed point).

But i don't know, my reasoning doesn't seem very solid and i would like to hear from you guys if you had any good thoughts on the matter.

 

[berkeman]

A good way to think about it is in terms of the Z impedance presented to the circuit by the parallel LC. Think about what happens in the LC for a moment -- the energy stored flows back and forth between the voltage across the cap (energy stored in the electric field across the cap) and the current through the inductor (energy stored in the magnetic field of the inductor). The current is max when the voltage across the cap is zero, and the voltage across the cap is max when the current through the inductor is zero. You get a resonance back and forth in the energy storage, and in the transfer of that energy via the voltage and current.

Now, once you get this resonance going, and if there is not much loss in the circuit, then you can disconnect the driving voltage source and let the oscillations continue on their own. So in this state, it takes very little energy input to keep the resonance going, or in other words, the parallel LC circuit has a high input impedance in this state (being driven near resonance). The lower the resistive losses in the parallel LC, the higher the "Q", and the higher the apparent input impedance at resonance.

So, when you have a circuit with an AC voltage source feeding a parallel LC through a resistor, you basically get a voltage divider, and at resonance, you get all of the input voltage carried through to the output, because the LC is in resonance and presents a high impedance to the divider with the input resistance.

Does that make sense? Quiz question -- what if it is a series LC instead of parallel LC? What is different, and what does the output voltage do at resonance?