Electronics/RCL

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RLC SeriesEdit

An RLC series circuit consists of a resistor, inductor, and capacitor connected in series:


By Kirchhoff's voltage law the differential equation for the circuit is:

 

or

 

Leading to:

 
  ±  

with

  and  

There are three cases to consider, each giving different circuit behavior,   .

  .
  =  
 

Equation above has only one real root

s = -α =  
 


  ,
  >  
 

Equation above has only two real roots

  ±  
 
 


  .
 

Equation above has only two complex roots

  + j 
  - j 
 

Circuit AnalysisEdit

R = 0Edit

If R = 0 then the RLC circuit will reduce to LC series circuit . LC circuit will generate a standing wave when it operates in resonance; At Resonance the conditions rapidly convey in a steady functional method.

 
 
 

R = 0 ZL = ZCEdit

If R = 0 and circuit above operates in resonance then the total impedance of the circuit is Z = R and the current is V / R

At Resonance

  Or  
 
 
 
 

At Frequency

I = 0 . Capacitor opens circuit . I = 0
I = 0 Inductor opens circuit . I = 0

Plot the three value of I at three I above we have a graph I - 0 At Resonance frequency   the value of current is at its maximum   . If the value of current is half then circuit has a stable current  does not change with frequency over a Bandwidth of frequencies É1 - É2 . When increase current above   circuit has stable current over a Narrow Bandwidth . When decrease current below   circuit has stable current over a Wide Bandwidth

Thus the circuit has the capability to select bandwidth that the circuit has a stable current when circuit operates in resonance therefore the circuit can be used as a Resonance Tuned Selected Bandwidth Filter

Further ReadingEdit

  1. RCL circuit analysed in the time domain
  2. RCL circuit analysed in the frequency domain