# Why LC tank only oscillates at resonant frequency?

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1. Nov 30, 2015

### anhnha

I am wondering why LC tank only oscillates at resonant frequency not other frequencies?
Is there a physics explanation for that?

2. Dec 1, 2015

### Jarrodmccarthy

"resonance" is achieved when the inductive and Capacative reactance's are equal in magnitude.

What does this mean physically?

It means that if you apply a time-varying voltage that has a frequency equal to the resonant frequency of the circuit, the energy you give the circuit by applying the voltage will be passed back and forth by the capacitive and inductive components based on the frequency.

So why not other frequencies?

If you applied a frequency other than the resonant frequency when the energy of the circuit was being passed to/from the components the applied voltage would be having some interferring affect on the circuit voltage. So the nice, resonant voltage that the capacitor and inductor would have made would be interrupted by the applied voltage's frequency. Which may disturb the 'rhythm' of the resonance.

Not sure if that was the explanation you were looking for but hopefully it helps to some degree.

3. Dec 1, 2015

### Svein

Yes. If you write down the equation for the current and voltage, you get a second-order differential equation with the resonant frequency as the solution (see https://en.wikipedia.org/wiki/LC_circuit for the explanation of the derivation).

4. Dec 1, 2015

### anhnha

Thanks a lot!
I have one more question. Assume I have an ideal parallel LC and it is connected permanently with an ideal constant voltage source. Does the LC tank oscillate with a sinusoidal waveform? I am confused because it is connected with a constant voltage source?

Last edited: Dec 1, 2015
5. Dec 1, 2015

Staff Emeritus
That's not true. It will oscillate at whatever frequency you drive it at.

6. Dec 1, 2015

### Jarrodmccarthy

If the signal isn't time varying there will be no oscillation.

7. Dec 1, 2015

### anhnha

So, could you explain why this cross coupled oscillator below oscillate? It is only connected with a DC voltage source.

#### Attached Files:

• ###### Cross coupled Oscillator.png
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8. Dec 1, 2015

Staff Emeritus
That's not an LC circuit. That's not even an RLC circuit.

9. Dec 1, 2015

### anhnha

Hi, I read that that circuit can be converted to LC tank circuit using negative resistance of these mos transistors.
So I think they are equivalent.

10. Dec 1, 2015

### Jarrodmccarthy

I'm not familiar with the symbols but they might be transistors.

In that case the transistors could be used to cut the DC voltage to make a time varying voltage. If the transistors were capable of switching pretty frequently it may resemble a regular AC circuits characteristics.

11. Dec 1, 2015

Staff Emeritus
They're MOSFETs. And circuits with transistors are not simple LC circuits.

12. Dec 1, 2015

### Svein

Oscillation - it is possible. It looks like a Flip-Flop with tuned drain circuits to me. Since the LC combination has no phase shift at resonance, it does not help any. What helps, is that the MOSFET that is "on" only has a given amount of current (current source at the bottom of the figure) and after some time the current through the inductance does not increase and the voltage across it will decrease. This will make the other MOSFET start conducting, sending a current through its drain circuit and "stealing " current from the first MOSFET. This behavior will "kick" the drain circuit into oscillation mode and couple this oscillation to the other MOSFET.

There are several variants of LC tank oscillator, and this is not one of the most used. The dominant circuits are the Colpitts oscillator (https://en.wikipedia.org/wiki/Colpitts_oscillator) and the Hartley oscillator (https://en.wikipedia.org/wiki/Hartley_oscillator).

13. Dec 1, 2015

### Jarrodmccarthy

I guessed they were transistors so thanks for specifying MOSFE.
Seems like Svein said a more sophisticated version of what I said to me.

14. Dec 1, 2015

### anhnha

I have some problems understanding the oscillator. The first one relating to the boldfaced part above. I don't get what you meant here.
Second problem is that how can the oscillation start up? Two transistors are exactly the same, so which one will be ON first? Will both transistors be OFF permanently?

15. Dec 1, 2015

### Jarrodmccarthy

I think those resistances are different so there would be a potential difference giving preference to one MOSFET or the other.

16. Dec 1, 2015

### anhnha

Hi, the resistances are same (not exactly because tolerance)

17. Dec 1, 2015

### Svein

If both start OFF, they will not draw current, which makes the drain HIGH, turning the other one ON. If both start ON, they will pull the drain low, turning the other one OFF. Which one? Random.

18. Dec 1, 2015

### anhnha

I simulated the oscillator. If Vdd is step voltage then the oscillator oscillates but if Vdd is constant then it doesn't oscillate. Could you explain why?

19. Dec 1, 2015

### Svein

As I remarked above:
Such a circuit will usually only oscillate when you do not want it to (cf. Murphy's law). Try this circuit instead:
(copied from http://www.datasheetdir.com/Nanopower-Lc-colpitts-Oscillator-Circuit+Application-Notes, you can find component values there).