Practical Electronics/Parallel RC

Parallel RCEdit

 

Circuit ImpedanceEdit

 
 
 

Circuit ResponseEdit

 
 
 

Parallel RLEdit

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Circuit ImpedanceEdit

 
 
 

Circuit ResponseEdit

 
 
 

Parallel LCEdit

 

Circuit ImpedanceEdit

 
 
 

Circuit responseEdit

 
 

Parallel RLCEdit

 

Circuit ImpedanceEdit

 
 
 
 

Circuit responseEdit

 
 
 
 

Natural RespondEdit

 

Forced RespondEdit

 

Second ordered equation that has two roots

ω = -α ±  

Where

 
 

The current of the network is given by

A eω1 t + B eω2 t

From above

When  , there is only one real root
ω = -α
When  , there are two real roots
ω = -α ±  
When  , there are two complex roots
ω = -α ± j 

Resonance ResponseEdit

At resonance, the impedance of the frequency dependent components cancel out . Therefore the net voltage of the circui is zero

  and  

 
 
 
 

At Resonance Frequency

  .
  . Current is at its maximum value

Further analyse the circuit

At ω = 0, Capacitor Opened circuit . Therefore, I = 0 .
At ω = 00, Inductor Opened circuit . Therefore, I = 0 .


With the values of Current at three ω = 0 ,   , 00 we have the plot of I versus ω . From the plot If current is reduced to halved of the value of peak current   , this current value is stable over a Frequency Band ω1 - ω2 where ω1 = ωo - Δω, ω2 = ωo + Δω


  • In RLC series, it is possible to have a band of frequencies where current is stable, ie. current does not change with frequency . For a wide band of frequencies respond, current must be reduced from it's peak value . The more current is reduced, the wider the bandwidth . Therefore, this network can be used as Tuned Selected Band Pass Filter . If tune either L or C to the resonance frequency   . Current is at its maximum value   . Then, adjust the value of R to have a value less than the peak current   by increasing R to have a desired frequency band .


  • If R is increased from R to 2R then the current now is   which is stable over a band of frequency
ω1 - ω2 where
ω1 = ωo - Δω
ω2 = ωo + Δω

For value of I <   . The circuit respond to Wide Band of frequencies . For value of   < I >   . The circuit respond to Narrow Band of frequencies

SummaryEdit

Circuit Symbol Series Parallel
RC
 
A parallel RC Circuit
Impedance Z    
Frequency    
 
 
 
 
 
Voltage V    
Current I    
Phase Angle Tan θ = 1/2πf RC
f = 1/2π Tan CR
t = 2π Tan CR
Tan θ = 1/2πf RC
f = 1/2π Tan CR
t = 2π Tan CR