Electronics Handbook/Circuits/Two Port Network

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RC

{\frac {V_{o}}{V_{i}}}={\frac {\frac {1}{j\omega C}}{R+{\frac {1}{j\omega C}}}}={\frac {1}{1+j\omega T}}

T=RC

\omega _{o}={\frac {1}{T}}={\frac {1}{RC}}

This circuit has Stable voltage at low frequency therefore suitable for filtering low frequency therefore the name Low Pass Filter

CR

{\frac {V_{o}}{V_{i}}}={\frac {R}{R+{\frac {1}{j\omega C}}}}={\frac {j\omega T}{1+j\omega T}}

T=RC

\omega _{o}={\frac {1}{T}}={\frac {1}{RC}}

This circuit has Stable voltage at high frequency therefore suitable for filtering high frequency therefore the name High Pass Filter

LR

{\frac {V_{o}}{V_{i}}}={\frac {R}{R+j\omega L}}={\frac {1}{1+j\omega T}}

T=RC

\omega _{o}={\frac {j\omega L}{R+j\omega L}}={\frac {1}{1+j\omega T}}

This circuit has Stable voltage at low frequency therefore suitable for filtering low frequency therefore the name Low Pass Filter

RL

{\frac {V_{o}}{V_{i}}}={\frac {R}{R+{\frac {1}{j\omega C}}}}={\frac {j\omega T}{1+j\omega T}}

T={\frac {L}{R}}

\omega _{o}={\frac {1}{T}}={\frac {1}{RC}}

This circuit has Stable voltage at high frequency therefore suitable for filtering high frequency therefore the name High Pass Filter

LC - R

{\frac {V_{o}}{V_{i}}}={\frac {R}{R+j\omega L+{\frac {1}{j\omega C}}}}

Tuned Resonance Selected Band Pass Filter

R - LC

{\frac {V_{o}}{V_{i}}}={\frac {j\omega L+{\frac {1}{j\omega C}}}{R+j\omega L+{\frac {1}{j\omega C}}}}

T=RC

\omega _{o}={\frac {1}{T}}={\frac {1}{RC}}

Tuned Resonance Selected Band Reject Filter

LC// - R

{\frac {V_{o}}{V_{i}}}={\frac {R}{R+j\omega C+{\frac {1}{j\omega L}}}}

Tuned Resonance Selected Band Pass Filter

R - LC//

{\frac {V_{o}}{V_{i}}}={\frac {j\omega C+{\frac {1}{j\omega L}}}{R+j\omega C+{\frac {1}{j\omega L}}}}

Tuned Resonance Selected Band Pass Filter

Tuned Resonance Selected Band Pass Filter

LR + CR

Transfer Function

{\frac {V_{o}}{V_{i}}}=({\frac {1}{1+j\omega {\frac {L}{R}}}})({\frac {j\omega RC}{1+j\omega RC}})

Band Pass or band of frequencies that has a stable voltage

{\frac {R}{L}}-{\frac {1}{RC}}

provided that

{\frac {1}{RC}}>{\frac {R}{L}}

Band Pass Filter

RC - RL

Transfer Function

{\frac {V_{o}}{V_{i}}}=()()

Band Pass or band of frequencies that has a stable voltage

{\frac {1}{RC}}-{\frac {R}{L}}

provided that

{\frac {R}{L}}>{\frac {1}{RC}}

Band Pass Filter

Summary

Low Pass Filter

{\frac {V_{o}}{V_{i}}}={\frac {\frac {1}{j\omega C}}{R+{\frac {1}{j\omega C}}}}={\frac {1}{1+j\omega T}}

T=RC

\omega _{o}={\frac {1}{T}}={\frac {1}{RC}}

High Pass Filter

{\frac {V_{o}}{V_{i}}}={\frac {R}{R+{\frac {1}{j\omega C}}}}={\frac {j\omega T}{1+j\omega T}}

T=RC

\omega _{o}={\frac {1}{T}}={\frac {1}{RC}}

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