Capacitance
F
Inductance
H
Resistance
Ω
Frequency
Hz
Q factor

# RLC Circuit Calculator

By Miłosz Panfil, PhD

With this RLC circuit calculator, you can find the characteristic frequency and the Q-factor of any RLC circuit. Below you will find 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:

• the resistance `R`,
• the impedance `L`,
• and the capacitance `C`.

In its basic form, all three elements are connected in a series. 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;
• 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` and the impedance `L`. The resistance `R` is responsible for losses of energy which are present in every real-world situation. If we try to push through the circuit a signal with a frequency different from the natural, 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` is the resonant frequency.
• `L` is the impedance of the inductor.
• `C` is the capacitance of the capacitor.

If, for example, we assume an impedance `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 value of the capacitance if you need the RLC circuit with resonant frequency `f = 100 MHz` and you have an inductor with impedance `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 is the circuit. If the Q-factor is smaller 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` is the Q-factor
• `R` is the 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`. This value of the Q-factor is rather small. We should redesign the circuit by either decreasing the resistance or increasing the impedance at the cost of decreasing the capacitance (to keep the natural frequency constant). This way we would get a better RLC circuit.

Miłosz Panfil, PhD