Circuit Theory/Introduction to Filtering

Filter is a circuit constructed from Resistor and Capacitor or Inductor in order to pass certain range of frequencies . The range of frequencies that make the circuit stable

Let examine the following circuits

RC CircuitEdit

A circuit with one resistor in series with the input and one capacitor parallel to the load

 
ω = 0   ω = Infinity
     

The RC circuit is more stable at frequencies from zero up to the response frequency :  . This circuit is ideal for Low Pass Frequency Filter .

CR CircuitEdit

A circuit with one capacitor in series with the input and one resistor parallel to the load

 
ω = 0 ω =   ω = Infinity
     

The CR circuit is more stable at frequencies from the response frequency   up to infinity. This circuit is ideal for High Pass Frequency Filter .

RL CircuitEdit

A circuit with one resistor in serires with the input and one inductor parallel to the load

 
ω = 0   ω = Infinity
     

The RL circuit is more stable at frequencies from the response frequency   up to infinity. This circuit is ideal for High Pass Frequency Filter .

LR CircuitEdit

A circuit with one inductor in serires with the input and one resistor parallel to the load

 

ω = 0   ω = Infinity
     

The LR circuit is more stable at frequencies from zero up to the response frequency   . This circuit is ideal for Low Pass Frequency Filter .

In Conclusion, Resistor and Capacitor or Inductor can be used for constructing a Filter

  • For Low Pass Filter use LR or RC
  • For High Pass Filter use RL or CR

ConclusionEdit

Filter Types High Pass Filter Low Pass Filter Low Pass Filter High Pass Filter
Circuit RL LR RC CR
ωο        
T     CR CR
Z        
         
Frequency Response
ω = 0 Vo = 0
ω = ωο Vo = Vi
ω = 0 Vo = Vi
ω = 0 Vo = Vi
ω = ωο Vo = Vi
ω = 0 Vo = 0
ω = 0 Vo = Vi
ω = ωο Vo = Vi
ω = 0 Vo = 0
ω = 0 Vo = 0
ω = ωο Vo = Vi
ω = 0 Vo = Vi
Stability Circuit is stable at Frequencies ω = ωο→Infinity Circuit is stable at Frequencies ω = 0→ωο Circuit is stable at Frequencies ω = 0→ωο Circuit is stable at Frequencies ω = ωο→Infinity