RLC Resonant Frequency Calculator [Series/Parallel]

RLC resonant frequency calculator is used to calculate the resonant frequency of series/parallel circuits. It also calculates series and parallel damping factor.

RLC Resonant frequency Formula

RLC Resonance is a special frequency at which the electrical circuit resonates. The value of RLC frequency is determined by the inductance and capacitance of the circuit. Resonance occurs in series as well as in parallel circuits. Although the basic formula to calculate series and the resonant frequency is same, However, there are certain differences which governs the resonant frequency.

Series Resonant Frequency

The resonance of a series circuit occurs when the inductive reactance is exactly equal to capacitive reactance. However, the necessary condition is a phase difference of 180 degrees at which they should cancel each other. A series resonance circuit has a minimum impedance at resonance. The series resonance circuit and its formula are:

series-resonant-frequency

 

Parallel Resonant Frequency

While parallel resonant frequency is more common in electronic circuits, it is equally complex. We can define parallel resonance as the condition of zero phase difference or a unity power factor. A parallel resonance circuit has maximum impedance.

parallel-resonance-frequency

Damping factor

The damping factor of a circuit is defined as the ratio between bandwidth and center frequency. The damping factor of circuit determines the bandwidth frequency. A higher damping factor means the wider bandwidth and a lower damping factor indicates that bandwidth will be lower. The damping factor of a series circuit is directly related to the resistance by the formula:

series-damping-factor

Whereas the parallel damping factor is inversely related to the resistance:

parallel-damping-factor

Practical Applications

Practically series and parallel RLC, and LC, resonant circuits are used in electronic design applications and modeling of circuits.

Desing of Filter Circuits

Frequency filters such as low pass, high pass, band stop, and bandpass filters utilize the concepts of band frequency and resonant frequency in their design.

Tuning of analog radio set

The tuning of analog radio is done by using a parallel plate variable capacitor whose value is changed to tune the radio with frequencies coming from radio sat.

Example Numerical Problems

Example # 1: A series resonant circuit has an inductance of 50 mH and a capacitance of 20 µF which connect to a 10 kΩ resistor. Find the resonance frequency and damping factor.

Solution:

Given values: L = 50 mH, and C = 20 µF

From the formula:

resonance-frequency-formula

= 1/(50 * 0.001 * 20 * 0.000001) = 1000 Hz or 1 kHz

Series damping factor can be calculated from:

series-damping-factor

= (5 kΩ) √((20*0.000001)/(50*0.001) = 100

Example # 2: A parallel resonant circuit has 1 MΩ resistor, a 20 pF capacitor and 500 µH inductor. Find the resonant frequency and parallel damping factor.

Solution:

Given values: L = 500 µH, C = 20 pF

From

resonance-frequency-formula

= 1/√(500 µH * 20 pF) = 10 MHz

To calculate Parallel damping use the equation:

parallel-damping-factor

= 1/(2 * 1 MΩ) √(500 µH / 20 pF)

Electrical Calculators © 2018