# Second Order LC Low Pass Filter Calculator

Calculate resonant frequency(fr)
Inputs:

Theoretical Results:

Calculate L:
Inputs:

Theoretical Results:
Formula Used:
$$L =\frac{1}{4 \pi^2 f_{r}^2 C}$$
Calculate C:
Inputs:

Theoretical Results:

Formula Used:
$$C =\frac{1}{4 \pi^2 f_{r}^2 L}$$

## About LC Parallel Resonant Circuit Calculator

The above online calculator for second order LC low pass filter calculates the cutoff frequency and Q from given inductor, capacitor and load resistor values or calculate inductor, capacitor values from given cutoff frequency.

### Notes on Second Order LC Low Pass Filter Calculator

The Q of the filter is given by,$Q=\frac{R}{X_L}$where, the inductor reactance $$X_L$$ is calculated at the resonant frequency. When Q is high the gain will increase and in frequency response graph we will see peak. The following graph illustrates frequency response of LPF when Q is high.

To get maximally flat response(Butterworth Response), Q should be 0.707 and at this Q=0.707 value the frequency response of the LC low pass filter will be like the following,
Higher order LC LPF

The quality factor Q of the LC parallel tank is given by the following equation:

$$Q=\frac{Energy \space stored \space in \space Reactive \space component}{Energy \space dissipated}$$

or, $$Q=\frac{X_C}{R_w}=\frac{X_L}{R_w}$$

Some example usage of this online LC parallel resonant circuit calculator are as follows.

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