Second-order circuit that can be over-, critically or under-damped.
Series RLC: s²+(R/L)s+1/LC=0. Damping ratio ζ=(R/2)√(C/L). Over-damped, critically damped or under-damped with ringing frequency ω_d. Natural frequency ω₀=1/√(LC). Models filters, resonators and power system oscillation.
R=10 Ω, L=1 mH, C=1 µF rings at about 5 kHz.
Second-order circuits behave like mechanical oscillators, so their damping and resonance decide filter shape and transient response.
Second-order circuit that can be over-, critically or under-damped.
Second-order circuits behave like mechanical oscillators, so their damping and resonance decide filter shape and transient response.
The ratio of resistance to the characteristic impedance. Low resistance gives underdamped ringing, and high resistance gives overdamped response.
Energy swaps between the capacitor and inductor, and the resistor dissipates it, so oscillation appears when the swap is faster than the loss.
Typical applications include analysing the ringing of an RLC filter after a switching event, selecting components for a critically damped power supply response and designing a resonant tank circuit for a radio receiver.
Study "RL circuit transient" first (topic 35 of 106 in Electrical Engineering). It covers the groundwork this topic builds on.
Settling time ~4/(ζω₀). Overshoot depends on ζ. Parallel RLC is dual.
R=10 Ω, L=1 mH, C=1 µF rings at about 5 kHz.
The next topic is "Sinusoidal AC", which builds directly on this one.
It is classed as Beginner in Electrical Engineering (topic 36 of 106). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.
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