Last updated: Oct 24, 2024

LC Filter Calculator

Q: What inductor do I need for a 1 kHz LC low pass filter?

Using a standard capacitor of 47 nF , you need an inductor with an inductance of 0.5389 H or 538.9 mH to have a cutoff frequency of 1 kHz. To calculate this answer, follow these steps: Multiply the capacitance with the square of the cutoff frequency : (1×10 3 Hz) 2 × 47×10 -9 F = 47×10 -3 Multiply this result with 4π 2 : 4π 2 × 47×10 -3 ≈ 1.855485 Take the reciprocal of this value to obtain the inductance : 1/1.855485 ≈ 0.5389 H or 538.9 mH

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Table of contents

What are filter circuits?Calculating LC low pass filter Calculating LC high pass filter Calculating LC band-pass filter Using this LC filter calculator Other filter calculators FAQs

Our LC filter calculator will help you calculate an LC filter circuit's cutoff frequency. Whether you're designing a low-pass or a high-pass filter, this calculator will prove helpful. If you know what you're doing, you can calculate an LC band pass filter circuit with this tool!

In the following article, we shall look at what filter circuits are and how to calculate the cutoff frequency of LC filter circuits.

What are filter circuits?

A filter circuit is an electronic circuit designed to "filter" out some frequencies from an input signal. A filter circuit that allows low frequencies to pass while blocking high frequencies is a low-pass filter circuit. On the other hand, a circuit that deters low frequencies and allows high frequencies to pass is a high-pass filter circuit.

Input signals going into a low pass filter, and the filtered output signal. — A low-pass filter blocks high frequencies in the input signals, allowing only low frequencies to pass through.

Input signals entering a high pass filter, and the filtered output signal. — A high-pass filter blocks low frequencies in the input signal, allowing only high frequencies to pass through.

A characteristic of a filter circuit is the cutoff frequency. In a low-pass filter, it is the frequency above which all input signals are blocked. An input signal below this cutoff frequency passes through this circuit.

Bode plot of a low-pass filter. — The Bode plot of a low-pass filter, showing the cutoff frequency above which input signals are blocked.

Theoretically, the transition near the cutoff frequency must be sharp, as shown by the blue line in the plot above. But in practice, this drop in gain is gradual. As such, the cutoff frequency of a filter circuit is defined as the frequency at which the gain has dropped to -3 dB.

Like in a low-pass filter, the cutoff frequency of a high-pass filter is the frequency below which all input signals are blocked. In other words, it is the frequency above which the input signals can pass through a high-pass filter undeterred.

Bode plot of a high-pass filter. — The Bode plot of a high-pass filter, showing the cutoff frequency below which input signals are blocked.

Calculating LC low pass filter

An LC filter is a second-order filter circuit because it has both an inductor and a capacitor, whose impedance depends on the signal's frequency. As such, it reacts faster to a signal frequency and has twice the frequency slope (also known as frequency roll-off) in the Bode plot compared to a passive filter like RC or RL.

A low-pass LC filter circuit has an inductor connected in series with the load and a capacitor connected in parallel. An inductor's impedance is directly proportional to a signal's frequency, while a capacitor's impedance is inversely proportional. So, low frequencies pass through the circuit without hindrance, while high frequencies cannot.

The formula to calculate the LC low-pass filter's cutoff frequency is:

f_c = \frac{1}{2\pi \sqrt{LC}}

where:

$f_c$ — The cutoff frequency of the LC filter circuit;
$L$ — The inductance of the inductor; and
$C$ — The capacitance of the capacitor.

Calculating LC high pass filter

A second-order high-pass LC filter has a capacitor connected in series with the load and the inductor connected in parallel. Because a capacitor's impedance is inversely proportional to the signal frequency, whereas an inductor's impedance is directly proportional to it, the circuit will block low-frequency signals, allowing high-frequencies to pass through it.

The formula to calculate the LC high-pass filter's cutoff frequency:

f_c = \frac{1}{2\pi \sqrt{LC}}

Calculating LC band-pass filter

A band-pass filter is a circuit that allows a desired band of frequencies to pass through, blocking the rest. It is a combination of a low-pass and high-pass filter circuit. So, to calculate an LC band-pass filter, you must:

Calculate an LC low-pass filter that blocks all frequencies below the desired range.
Calculate an LC high-pass filter that blocks all frequencies above the desired range.
Use them in an appropriate combination.

Using this LC filter calculator

This LC filter calculator will be handy when designing either a low-pass or a high-pass filter:

Enter the inductance of the inductor in your desired unit.
Provide the capacitance of the capacitor in a unit of your choice.
The tool will instantly calculate the LC filter's cutoff frequency.

Alternatively, you can use this LC filter calculator to determine the LC filter components required to achieve the desired cutoff frequency:

Input the target cutoff frequency.
Enter either the inductance or the capacitanceand our LC filter calculator will determine the remaining value.

Other filter calculators

Did you find our LC filter calculator helpful? We have more filter calculators for you to try next:

FAQs

How do you calculate the cutoff frequency of an LC filter circuit?

To calculate the cutoff frequency of an LC filter circuit, follow these steps:

Multiply the inductance in Henries (H) with the capacitance in Farads (F).
Take the square root of this product.
Multiply the result with 2π.
Take the reciprocal of this product to obtain the cutoff frequency.

Our LC filter calculator will help you calculate the cutoff frequency of an LC filter without any hassle!

What inductor do I need for a 1 kHz LC low pass filter?

Using a standard capacitor of 47 nF, you need an inductor with an inductance of 0.5389 H or 538.9 mH to have a cutoff frequency of 1 kHz. To calculate this answer, follow these steps:

Multiply the capacitance with the square of the cutoff frequency:

(1×10³ Hz)² × 47×10^-9 F = 47×10^-3
Multiply this result with 4π²:

4π² × 47×10^-3 ≈ 1.855485
Take the reciprocal of this value to obtain the inductance:

1/1.855485 ≈ 0.5389 H or 538.9 mH