LC Tank Oscillation

4:57 AM

1. Away from the tank's resonance, the tank shorts the op-amp's noninverting input to ground. Either through the inductor for low frequencies, or through the capacitor for high frequencies.

2. At resonance, the impedance of the tank is high, so the output of the op-amp is effectively tied directly back to the noninverting input.

Allenph

So, in your circuit, R1 prevents the shorting of the op-amps output.

But how would I know which resistor to use in that case? The output will need to feed the Tank Circuit eventually.

I'm also confused on how the circuit would gain power at all. Upon connecting the power source, it seems that both inputs would be at 0v, and therefore there would be no gain, resulting in a loop which keeps the circuit from having any power at all.

The Photon

Sorry, got called away..

As for the dc operating point, since it's a '741 circuit, they're probably assuming +/- 15 V supplies. Having an operating point at 0 V doesn't mean it can't oscillate.

I'll have to think about how to modify the circuit for single-supply operation.

Allenph

I apologize, but that went right over my head. I'm new to electrical engineering. If I understand correctly, your circuit would only work if I provided alternating current to the circuit, rather than direct current.

The Photon

5:13 AM

@Allenph The point of an oscillator is that it is self-sustaining once it gets started. And there is "always" a little bit of noise in the circuit to get it started.

Allenph

So just connecting the battery will start a chain reaction because of minute in-perfections in the components?

The Photon

@Allenph More or less.

Allenph

Okay. The next question is about the reference point. If both of the inputs are connected to feedback, then how will the circuit "know" that it's supposed to attain a certain voltage, without having a constant application of that voltage to compare against?

The Photon

First look at DC. There's no feedback to the noninverting input, because it's shorted through the inductor. There's only negative feedback.

Then with the negative feedback set up you get v_out * (R3)/(R2+R3) = 0. So you get v_out = 0 V.

At other frequencies where the tank isn't resonant, same story: v_out = 0.

Allenph

I'm not sure what you mean by "isn't resonant." Does that mean it isn't oscillating? Although I'm not sure how to calculate it, or what it's called, shouldn't the length of time it takes the capacitor to charge and discharge dictate the frequency?

The Photon

5:23 AM

At resonance, you basically have the difference of two feedback paths. For the negative path V- = v_out * R3 / (R2+R3). But V+ = V_out. So the difference between the two inputs is [1 - R3/(R2+R3)]*v_out.

The tank has a resonant frequency.

At any other frequency it isn't resonant.

Resonance is when Y_L + Y_C = 0

LC circuit

An LC circuit, also called a resonant circuit, tank circuit, or tuned circuit, is an electric circuit consisting of an inductor, represented by the letter L, and a capacitor, represented by the letter C, connected together. The circuit can act as an electrical resonator, an electrical analogue of a tuning fork, storing energy oscillating at the circuit's resonant frequency. LC circuits are used either for generating signals at a particular frequency, or picking out a signal at a particular frequency from a more complex signal. They are key components in many electronic devices, particularly radio...

Allenph

I was actually just on that page.

$user image$

This is the equation for resonance, but I'm not sure exactly what resonance is. Is it a preferred frequency, or simply any frequency?

The Photon

@Allenph Which is also the condition where the admittances cancel, giving a net high impedance.

@Allenph It's called the natural frequency of the circuit.

Allenph

That equation is 1 over the square-root of inductance * capacitance, yes?

The Photon

For the parallel tank circuit, the net impedance is high at resonance and low at any other frequency.

Allenph

Ahh, so because the resonance is low at any other frequency, the circuit will tend to graduate to the resonant frequency eventually, correct?

(Impedance is the equivalent of resistance in DC circuits, but for AC circuits if I understand correctly. )

The Photon

5:35 AM

The impedance is low at all frequencies except the resonant frequeny.

In the circuit in my answer, that means the noninverting input is shorted to ground, so there's no positive feedback.

At resonance, the tank circuit's impedance is high, so the signal from the op-amp output is connected to the noninverting input.

That gives positive feedback (loop phase approximately 0), satisfying point 2 of the Barkhausen criterion

...

Sorry, time to go for me.

Allenph

Thank you very much Photon. I have a lot to chew on.

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