# A curious challenge on series resonance.

Discussion in 'Homework Help' started by t_n_k, Feb 17, 2012.

1. ### t_n_k Thread Starter AAC Fanatic!

Mar 6, 2009
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Not sure if this shouldn't be in the Maths Forum but I'll try here first. I've been thinking around some issues on resonance.

For a challenge with a curious outcome - find the transient voltages for time = 0 to 25 milliseconds at each probe position. Or just simulate the circuit and explain what's happening. Does this offer any insights on the meaning of resonance?

C1 is initially charged to 50V at t=0 and the current is zero. C2 & L2 have no initial condition.

F1 is a current controlled current source with transfer factor -0.01.

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2. ### Vahe Member

Mar 3, 2011
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I simulated it in LTspice and can also derive the analytical expressions -- is there something out of the ordinary that you are observing with this system. Maybe I need to take a closer look at the details of the waveform.

Vahe

3. ### t_n_k Thread Starter AAC Fanatic!

Mar 6, 2009
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After providing some input on another thread I was re-visiting the concept of resonance in relation to a series LCR circuit. One of my old textbooks suggests one has resonance in a circuit [or any physical system for that matter] when the driving function has the same form as the natural response of the system. So I was attempting to set up the circuit conditions where the driving current has the same form as the natural response [i.e. a damped sinusoid]. While the two LCR circuits in my schematic have different component values they have exactly the same natural response. So I have ensured the forcing function arises from different circuit values as those in the driven circuit - only the driving form has to be identical.

I note that at 'resonance' the response at the right hand probe is a pure step response - a rather interesting result. Is this what you observed?

The concept of resonance has therefore been somewhat challenged in my mind. Why would my old text discuss resonance in these terms, when everyone 'knows' resonance occurs when one equally well drives a system into resonance with a suitable source whose output is of type simple sinusoidal function of the right [resonant] frequency.

The writer of the text - Ronald E. Scott - was one of the most highly regarded university professors of his time. He clearly thought the distinction was worth making.

Last edited: Feb 21, 2012
4. ### Wendy Moderator

Mar 24, 2008
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If you are talking about what I think you are talking about, it was something i worked on first year of college.

Are you talking the extreme voltages generated with resonance?

It would be an interesting application to try to use this voltage, but the problem is the moment you tap into it you destroy the resonance. A pretty problem.

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5. ### steveb Senior Member

Jul 3, 2008
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I'm very confused about what is being asked here. The series RLC circuit on the output side is being driven by a dependent current source. Normally, a series RLC circuit is driven by a voltage source, even if that voltage source has zero value, as it does in the input side of the given circuit.

A current source driving a series RLC circuit forces the same current through the coil and the capacitor, which effectively decouples the interaction between these two components. Hence, the output side circuit has a current that just mirrors the input side current. The input side has a true resonance, but there can be no resonance on the output side.

I guess I'm just missing the point?

6. ### t_n_k Thread Starter AAC Fanatic!

Mar 6, 2009
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I am also confused.....

According to the learned professor Scott's proposition on resonance, if I drive the current in the second circuit as a damped sinusoid of the same form as the natural [decaying] current response of an RLC circuit with equivalent damped frequency and damping factor, I have a resonant condition in the driven circuit.

Why does he write this?

7. ### steveb Senior Member

Jul 3, 2008
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I don't know why he says this. I guess it's true from a particular point of view. If the current source is replaced by a short circuit, then the natural response of the right side RLC circuit (once excited by the correct initial conditions) would have a current that mimics the left side RLC circuit.

But, my view is that the right side RLC circuit is not even a resonant circuit, unless the current source is shorted. If the current source is set to zero to give a condition for natural response only, then no current can flow and there is no coupling between the coil and capacitor. If the current source is not zero, then then cap, coil and resistor independently develop the necessary voltage for that current source, and still there is no coupling between components. Hence, resonance is not possible in either case.

I'm not sure if this view is helpful at all, but that's how I see it right now?

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8. ### Ron H AAC Fanatic!

Apr 14, 2005
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I tried to simulate this on LTspice, but it blows up. The sim runs, but probing currents through series components yields totally different values, and some node voltages approach 1 teravolt.
Vahe, can you post the .asc file for your simulation? I would post mine now, but I failed to save it before closing LTspice.

9. ### Wendy Moderator

Mar 24, 2008
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As I understand it, and I could be wrong, a Tesla Coil is a good example of the extreme voltages generated. You have a massive coil and high voltage capacitors being driven at resonance with a really low resistance. Let there be light!

Of course, any resistance at all lowers the Q of the circuit. It also limits the current, which also lowers the extreme voltages, since there is a type of current to voltage conversion going on. The voltages on the coil and the cap are equal and opposite (180° out of phase), so they cancel on the total circuit.