RLC resonant frequency calculator is used to calculate the resonant frequency of series/parallel circuits. It also calculates series and parallel damping factor.
List of Contents
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:
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.
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:
Whereas the parallel damping factor is inversely related to the resistance:
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:
= 1/(50 * 0.001 * 20 * 0.000001) = 1000 Hz or 1 kHz
Series damping factor can be calculated from:
= (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
= 1/√(500 µH * 20 pF) = 10 MHz
To calculate Parallel damping use the equation:
= 1/(2 * 1 MΩ) √(500 µH / 20 pF)