# Practical Electronics/Circuits Analysis/Two Port Network

## 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

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