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Electronics Handbook/Components/RLC Network

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Series RLC

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Circuit of three components R, L, C connected in series







Differential Equation of the circuit

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At equilibrium the total voltage of the circuit is zero

±

With

.

When

  • .
=

The equation has only one real root

s = -α =


  • ,
=

The equation has two real roots


  • .

The equation has two complex roots

+

Resonance

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Resonance occurs when the frequencies components cancels out . Therefore, at resonance

. .
  • At
  • At .
  • At

Impedance

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Summary

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  • The resonance response is in the type of Tuned Resonance Band Pass Filter
  • The natural response is a wave of decreasing magnitude
. One real root .
. Two real roots .
. Two complex roots .
Circuit Series RLC
Configuration
Impedance
Differential Equation
General Differential Equation
Natural Equation


.



.



.

A