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Provide any two of \( f_0 \), \( L \), \( C \) — the third is solved. The angular resonant frequency \( \omega_0 \) is always shown as an additional output.
An LC circuit consists of an inductor \( L \) and a capacitor \( C \) connected together. At the resonant frequency, the energy oscillates between the electric field of the capacitor and the magnetic field of the inductor. The resonant frequency is: \[ f_0 = \frac{1}{2\pi\sqrt{LC}} \] Where:
Given any two of the three variables, the calculator solves for the third. The rearranged formulas are:
The angular frequency \( \omega_0 \) is often more convenient in circuit analysis and filter design: \[ \omega_0 = 2\pi f_0 = \frac{1}{\sqrt{LC}} \] It is expressed in radians per second (rad/s). Many filter and impedance formulas use \( \omega_0 \) directly, avoiding the repeated \( 2\pi \) factor.
LC circuits are used as tuned filters, oscillators, and impedance matching networks. In radio receivers, a variable capacitor is tuned to set \( f_0 \) equal to the desired station frequency. In switching power supplies, the LC output filter is designed so that \( f_0 \) is well below the switching frequency, attenuating the ripple. In RF design, LC tanks set the operating frequency of oscillators and amplifiers.
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