# RLC Circuit Calculator

Created by Miłosz Panfil, PhD
Reviewed by Bogna Szyk and Steven Wooding
Last updated: Jun 26, 2023

With this RLC circuit calculator, you can find the characteristic frequency and the Q-factor of an RLC circuit.

Below you will see the necessary information on RLC circuits and what is the resonant frequency of the RLC circuit, sometimes abbreviated to RLC circuit frequency. You will also find out what's the q of the RLC circuit.

## RLC circuit

The RLC circuit is a fundamental building block of many electronic devices. It consists of the three elements:

• Resistance R;
• Inductance L; and
• Capacitance C.

In its basic form, all three elements are connected in a series (as shown below). Other, more complicated configurations are possible and used for specific purposes. Here, we will look only at the simplest one.

The RLC circuits have many applications. For example, you can encounter them in:

• Tuning circuits – known from analog radios;
• Filters – basic blocks of equalizers in music equipment can also be designed with a simpler RC circuit; and
• Oscillators circuits – converting DC signal to an AC signal, for example, in radio transmitters.

In all these applications, the resonant frequency of the RLC circuit is its chief characteristic. So what is the RLC circuit frequency?

## RLC circuit frequency

The resonant frequency of the RLC circuit is a natural frequency with which the current in the circuit changes in time. This natural frequency is determined by the capacitance C, covered in our capacitance calculator, and the inductance L.

The resistance R is responsible for energy losses present in every real-world situation. If we try to push through the circuit a signal with a frequency different from the natural one, such a signal is damped.

## Formula for the resonant frequency of the RLC circuit

You can compute the resonant frequency of the RLC circuit with the following equation:

f = 1 / [2π × √(L × C)]

where:

• f – Resonant frequency;
• L – Inductance of the inductor; and
• C – Capacitance of the capacitor.

If, for example, we assume an inductance L = 1 µH and the capacitance C = 2 pF, the resulting frequency is f = 112.54 MHz. This frequency is a typical frequency of radio transmissions in the VHF range.

You can also use this RLC circuit calculator to solve the following problem: what should be the capacitance value if you need the RLC circuit with resonant frequency f = 100 MHz and you have an inductor with inductance L = 5 µH?

## Q of the RLC circuit

The first characteristic number of the RLC circuit is the natural frequency. The second is the Q-factor.

Q-factor determines how good the circuit is (how long the oscillations will last). If the Q-factor is less than 1/2, then the oscillations quickly die out.

When designing the RLC circuit, we should aim at getting the Q-factor as large as possible. The formula for the Q-factor of the RLC circuit is:

Q = 1/R × √(L/C)

where the new symbols are:

• Q – Q-factor; and
• R – Resistance.

For the circuit that we considered before with L = 1 µH and C = 2 pF, the resistance R = 1 kΩ leads to the Q-factor Q = 0.7 (try these values in the RLC circuit calculator). This value of the Q-factor is rather small.

We should redesign the circuit by either decreasing the resistance or increasing the inductance at the cost of decreasing the capacitance (to keep the natural frequency constant). This way, we would get a better RLC circuit.

## FAQ

### What is a RLC circuit?

RLC circuits consist of a resistor (R), inductor (L), and capacitor (C) connected in series, parallel, or in a different configuration. The current flows from the capacitor to the inductor causing the capacitor to be cyclically discharged and charged. As there is a resistor in the circuit, this oscillation is damped. The RLC circuit is characterized by its resonant frequency and a quality factor that determines how long the oscillations will last.

### Where can I use a RLC circuit?

You can find RLC circuits for many applications, especially in oscillator circuits and radio and communications engineering. They allow a certain narrow frequency range to be selected from the total spectrum of the surrounding radio waves. For example, an RLC circuit is typically used in radios or television sets to tune a narrow frequency range from a wide spectrum.

### What is the resonant frequency of an RLC circuit?

Each RLC circuit produces a periodic, oscillating electronic signal at its own resonant frequency. The resonant frequency of the series RLC circuit, f = 1 / [2π × √(L × C)], depends on the inductance of the inductor L and the capacitance of the capacitor C. When the RLC circuit is at its resonant frequency, the current reaches its peak.

### How can I find Q-factor of RLC circuit?

To calculate the Q-factor (quality factor) of the RLC circuit, simply complete the steps below:

1. Measure the resistance of the resistor R.
2. Find out the inductance of the inductor L.
3. Determine the capacitance of the capacitor C.
4. Insert the relevant data in the Q-factor equation: Q = 1/R × √(L/C).

### Is there a difference between RLC circuit and LCR circuit?

No, RLC and LCR circuits differ only in the order of the symbol shown in the circuit diagram. Apart from that, they consist of the same elements, and the same formulae can be used to calculate their properties.

### What is the resonant frequency and Q-factor of RLC circuit where R = 30 Ω, L = 25 mH and C = 50 μF?

The resonant frequency f is 142.35 Hz, and Q-factor is 0.75.

Enter the inductance L and capacitance C values to the formula for resonant frequency: f = 1 / [2π × √(L × C)] = 1 / [2π × √(0.025 H × 0.000050 F)] = 142.35 Hz. Then, calculate Q-factor from formula Q = 1/R × √(L/C) = 1/30 Ω × √(0.025 H/0.000050 F) = 0.7454. You can round the Q-factor to 0.75.

Miłosz Panfil, PhD
Capacitance
F
Inductance
H
Resistance
Ω
Frequency
Hz
Q factor
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