 
 
 
  
  
  
  
  
  
  
 
  
  
  
 
  
  
  
 
 8.5
 Step-Response Parallel 
  RLC Circuits (2)
 
 The solution of the equation should have two
 components:
 the transient
 response vt(t) & the steady-state response vss(t):
  
 
  
  
   
   
   
   
   
   
   
   
   
   
   
   
  
  
  
 
  
 
  
  
  
  
  
 
  
  
  
 
  
  
  
 
 ·The transient response it is the same as that for source-free case
 
 ·The steady-state response is the final value of i(t). 
 Ø    iss(t) =  i(∞) = Is 
 ·The values of A1 and A2 are obtained from the initial
 conditions:
 Ø    i(0) and di(0)/dt. 
  
   
 
  
 
  
 
  
   
  
   
   
   
  
  
   
  
   
   
   
  
  
   
  
   
   
   
   
  
 (over-damped)
 
  
 (critical damped)
 
  
 (under-damped)