Circuit Theory/Introduction to Filtering

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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 Circuit[edit]

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 Circuit[edit]

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 Circuit[edit]

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 Circuit[edit]

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

Conclusion[edit]

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