Electronics Handbook/Components/RLC Network

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  
   

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