Free LC Filter Calculator

LC Filter Calculator – Understanding Cutoff Frequency

The LC filter calculator is an interactive online tool that serves as both a low pass filter calculator and a high pass filter calculator for inductor‑capacitor (LC) circuits. It quickly returns the cutoff frequency when you provide the inductance and capacitance, or it can determine a missing component when given a target cutoff frequency. This utility also simplifies the design of band‑pass filters by allowing you to calculate the required stages separately.

Basic Concepts of Filter Circuits

Filter circuits are electronic networks that selectively allow signals within a certain frequency range to pass while attenuating others. A low‑pass filter transmits signals with frequencies below a chosen threshold—the cutoff frequency—and blocks higher frequencies. A high‑pass filter does the opposite, passing frequencies above the cutoff and blocking those below. In practical circuits the transition at the cutoff is not perfectly sharp; therefore engineers conventionally define the cutoff frequency as the point where the output power has dropped by half (i.e., –3 dB relative to the passband gain). This corresponds to a voltage drop to approximately 70.7 % of the passband level.

Why LC Filters Are Different

An LC filter is a second‑order circuit because it contains an inductive element $L$ and a capacitive element $C$. Their impedances depend on frequency: inductive reactance $X_L = 2\pi f L$ increases with frequency, while capacitive reactance $X_C = 1/(2\pi f C)$ decreases. This complementary behavior gives the LC filter a roll‑off slope of –40 dB per decade in the stopband—twice as steep as first‑order RC or RL filters. Consequently, LC filters provide sharper frequency separation and greater out‑of‑band rejection, making them popular in audio crossovers, power‑supply filtering, and RF circuits.

Low‑Pass LC Filter

In a low‑pass LC filter, the inductor is connected in series with the load and the capacitor is placed in parallel. At low frequencies, the inductor offers low impedance and the capacitor offers high impedance, so the signal passes through with little loss. At high frequencies, the inductor becomes high‑impedance and the capacitor low‑impedance, shorting the signal to ground. The cutoff frequency is given by the standard formula:

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

where $f_c$ is in hertz, $L$ in henries, and $C$ in farads.

High‑Pass LC Filter

For the high‑pass configuration, the capacitor is placed in series with the load and the inductor is shunted across the load. Low frequencies are blocked because the capacitor presents high impedance while the inductor provides a low‑impedance path to ground; high frequencies pass because the capacitor’s impedance drops and the inductor’s impedance rises. Remarkably, the cutoff frequency formula is identical to that of the low‑pass filter:

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

Thus the same component values can be used for either a low‑pass or a high‑pass filter simply by rearranging the components.

Designing a Band‑Pass Filter

A band‑pass filter can be constructed by connecting a low‑pass filter and a high‑pass filter in series. The high‑pass section sets the lower cutoff frequency, and the low‑pass section sets the upper cutoff frequency. To design such a filter, determine the desired band limits and compute the required $L$ and $C$ for each stage individually using the formula above. The LC filter calculator handles each stage separately, making the process straightforward and reducing manual calculation errors.

Putting the Calculator to Work

The online tool offers two primary modes:

• Cutoff frequency calculation: Enter the known inductance and capacitance in any convenient units (e.g., µH, nF, mH, µF). The calculator instantly displays the corresponding cutoff frequency.
• Component value finding: If you have a target cutoff frequency and know one of the component values, input those numbers, and the calculator will determine the missing inductance or capacitance.

As an illustration, consider a filter that uses $L = 1\ \text{mH}$ and $C = 1\ \mu\text{F}$. The product $LC = 10^{-3} \times 10^{-6} = 10^{-9}\ \text{H·F}$, its square root is $3.162\times10^{-5}$, and $2\pi\sqrt{LC} \approx 1.987\times10^{-4}$. The reciprocal yields $f_c \approx 5.03\ \text{kHz}$. Similarly, if a cutoff of $10\ \text{kHz}$ is needed and a $470\ \text{nF}$ capacitor is available, the calculator returns an inductance of roughly $0.539\ \text{mH}$. This dual‑functionality accelerates both analysis and prototyping.

The calculator automatically handles unit conversions, so you can work with the values you have on hand without manual scaling. When translating the ideal result to a real circuit, always consider that practical inductors have series resistance and self‑resonance, and capacitors have equivalent series resistance (ESR). These parasitics can shift the effective cutoff, so the calculator’s output should be used as a starting point and then verified with a network analyzer or simulation.