Understanding coupled LC circuit

[toyonline]

Hi, I am recently working on a coupled LC resonance circuit as attached. What I know is this circuit will introduce two resonant frequency. But I do want to understand more, i.e. why there are two resonance frequency? Is there any physical explanation of this two frequencies? Is there any connection between simple LC circuit (both series and parallel) and coupled LC circuit?

I have try to figure this out, and my explanation is like: the circuit is composed of a series and a parallel LC circuit. The series LC will inherently possess a resonant frequency f1. After the introduction of a parallel LC part, there will be another frequency f2. Impose these two gives a production of two frequencies. But since the combination will affect both series and parallel part, the overall new frequency will be different from original f1 and f2.

I know my explanation seems to simple, but currently I have no idea of physical picture of a coupled LC circuit. Would anyone help me to show the right way to understand this? Thank you guys!

[JackOfVA]

Think of it as two independent tuned circuits with energy transferred from one to the other via the common impedance, i.e., the 75 pF shunt capacitor. That's somewhat of a simplification, but it's a useful aid in understanding how the two interact.

It will become clearer if you redraw the circuit as a two loop mesh with the 75 pF being the common element and it will become clearer.

Try a Google search with the terms "under coupled" "critical coupled" and "over coupled" tuned circuit for the classic treatment of coupled tuned circuits.  These are also known as "double tuned" networks.

This has the look of a homework problem to me so I will limit my observations to these comments.

[toyonline]

Thanks very much.

These circuit could be considered as two independent LC circuit, coupled with 78pF capacitor. A combination of these two LC will produce two overall circuit oscillations. One is both oscillation at the same phase, the other is at a 180 phase difference. That could be somehow interpreted as two 'normal mode oscillation'. I could only reach this explanation.

More generally, if more LC circuit are coupled, in order to predict its possible numbers of frequencies, it is better to first find out how many numbers of 'normal mode oscillation' exist. So, I take a 3 LC coupled circuit to test. But the hypothesis doesnot work! There should be 3 frequencies, but what I observed is only 2. Could you please help point out what's wrong with my explanation?

Actually I am a chemist try to build such a circuit for research purpose. I know through mathematics, one could deduce those two frequencies. But what I more interested in is to figure out a more qualitatively way to understand that circuit rather than complicated formula.

Think of it as two independent tuned circuits with energy transferred from one to the other via the common impedance, i.e., the 75 pF shunt capacitor. That's somewhat of a simplification, but it's a useful aid in understanding how the two interact.

It will become clearer if you redraw the circuit as a two loop mesh with the 75 pF being the common element and it will become clearer.

Try a Google search with the terms "under coupled" "critical coupled" and "over coupled" tuned circuit for the classic treatment of coupled tuned circuits.  These are also known as "double tuned" networks.

This has the look of a homework problem to me so I will limit my observations to these comments.

[IonizedGears]

You could build the circuit, then have a sweep function gen on the input and a spectrum analyzer on the output to find these two resonant frequencies. If you don't have the equipment you could use a simulation program for this.