In this thread I'm going to show you that the cutoff frequency of an LC low pass filter is not
as always people and even teachers says, I want to see your comments.

I'm going to start by finding the transfer function of the filter with a resistive load

From the previous equation you can see that if R is too big, then the equation simplifies to the transfer function of an LC filter without load

Therefore the resonance frequency of the filter happens when the amplitude is maximum, and denominator becomes zero and R is too big.

One thing is the resonance frequency and another is the cutoff frequency, so in order to find the cutoff frequency of the filter, the first thing to do is find the magnitude of the transfer function:

Then by definition the cutoff frequency is reached when there is a drop of -3dB from the maximum gain, in this case 0dB.

So the angular cutoff frequency w is given by the next equation

This is too hard to solve by hand so I use Matlab to find the angular cuttoff frequency w, and this is what I found:

I did a couple of simulations using matlab to see if it is true, so L=100mH, C=10nF and R=1kΩ replacing these values in the equation I get a cuttoff frequency of f=1.7659kHz, and the same in the simulation look:

But when R is too big there is resonance and the formula doesn't work anymore, look at the simulation for L=100mH, C=10nF and R=10MΩ , fres=5kHz

As I have shown, the cutoff frequency of a LC low pass filter is not
that expression is the resonance frequency. The cutoff frequency is much more complicated and is given by
.

I'm going to start by finding the transfer function of the filter with a resistive load

From the previous equation you can see that if R is too big, then the equation simplifies to the transfer function of an LC filter without load

Therefore the resonance frequency of the filter happens when the amplitude is maximum, and denominator becomes zero and R is too big.

One thing is the resonance frequency and another is the cutoff frequency, so in order to find the cutoff frequency of the filter, the first thing to do is find the magnitude of the transfer function:

Then by definition the cutoff frequency is reached when there is a drop of -3dB from the maximum gain, in this case 0dB.

So the angular cutoff frequency w is given by the next equation

This is too hard to solve by hand so I use Matlab to find the angular cuttoff frequency w, and this is what I found:

I did a couple of simulations using matlab to see if it is true, so L=100mH, C=10nF and R=1kΩ replacing these values in the equation I get a cuttoff frequency of f=1.7659kHz, and the same in the simulation look:

But when R is too big there is resonance and the formula doesn't work anymore, look at the simulation for L=100mH, C=10nF and R=10MΩ , fres=5kHz

As I have shown, the cutoff frequency of a LC low pass filter is not

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