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How to derive cut-off (or center) frequency formula for attached LC filter circuit?

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skarthikbecool

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Hello all,

Could anyone help me how can i drive the cutoff frequency formula for the attached circuit?
 

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Re: How to drive cut of frequencu formula for attached LC filter circuit?

If you're in real life you simulate it and look at the graph (ltspice ac sim)

If you're in academia and want to 'cheat' use 'sapwin' which will solve the circuit for you in the S domain and give you the algebraic expressions for it.
 

Re: How to drive cut of frequencu formula for attached LC filter circuit?

You have no damping, so instead of cutoff frequency, you have a peak that shoots up to infinity at the frequency you would have the cutoff frequency=1/2*Pi*sqrt(L2*C1) of a damped filter.

(no output is shown by the OP, however, the only 2 possible outputs across C1 or C2 have the exact same formula, obviously with alternate "C" and "L" value).
 

Re: How to drive cut of frequencu formula for attached LC filter circuit?

Are you sure that there is no resistor between the signal source and the L1-C2 path?
Otherwise, the circuitry makes no sense.
 

Re: How to drive cut of frequencu formula for attached LC filter circuit?

Hello all,

It is kind of redundancy circuit. The output will be taken across C1 and it would be given as input to one switching regulator.In the same way C2 output will be connected to another Switching regulator.
Hence i would like to theoretically calculate the cut off frequency of this circuit.
 

Re: How to drive cut of frequencu formula for attached LC filter circuit?

You have no damping, so instead of cutoff frequency, you have a peak that shoots up to infinity at the frequency you would have the cutoff frequency=1/2*Pi*sqrt(L2*C1) of a damped filter.

(no output is shown by the OP, however, the only 2 possible outputs across C1 or C2 have the exact same formula, obviously with alternate "C" and "L" value).

I will take output across C1 and C2. In that case could you please guide me how the cut of frequency formula look like ?
 

Re: How to drive cut of frequencu formula for attached LC filter circuit?

I will take output across C1 and C2. In that case could you please guide me how the cut of frequency formula look like ?
Output across C1: freq cutoff=1/2*Π*√(L2*C1)

Output across C2: freq cutoff=1/2*Π*√(L1*C2)
 

Re: How to drive cut of frequencu formula for attached LC filter circuit?

Output across C1: freq cutoff=1/2*Π*√(L2*C1)

Output across C2: freq cutoff=1/2*Π*√(L1*C2)

Thanks for the feedback. I would like to understand how this formula had been arrived. As i know if it single LC low pass filter then the cut off frequency formula can be derived by equating XL=XC and finally we get Fc=1/2*pi*sqrt(LC).. In this same way how the above formulas can be derived?
 

Re: How to drive cut of frequencu formula for attached LC filter circuit?

As LvW pointed out this circuit probably has an error. You have multiple parallel circuits attached to one ideal source. The two LC's therefore have zero interaction with one another. You could delete L1/C2 and it has no impact on the transfer function to C1 (try it). And vise versa.

Hence the math is just the simple formula for a single LC.
 

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