# Fundamental Physics/Electronics/Electronics Filter/Low pass filter

## Low pass filter

Low pass filter is an electronics device that has a constant voltage over low frequency . Low pass filter can be constructed from LR and RC as shown .

## R-C

Low pass filter has a transfer function

${\displaystyle H(j\omega )={\frac {v_{o}}{v_{i}}}={\frac {1/j\omega c}{R+1/j\omega c}}={\frac {1}{1+j\omega T}}}$

Time constant

${\displaystyle T=RC}$

Frequency response of Low pass filter

${\displaystyle \omega =0.v_{o}=v_{i}}$
${\displaystyle \omega =\omega _{o}.v_{o}={\frac {v_{i}}{2}}}$
${\displaystyle \omega =00.v_{o}=0}$

Cut off frequency, ${\displaystyle \omega _{o}}$ , frequency at which ${\displaystyle v_{o}={\frac {1}{2}}v_{i}}$

${\displaystyle \omega _{o}={\frac {1}{T}}}$

## L-R

Low pass filter has a transfer function

${\displaystyle H(j\omega )={\frac {v_{o}}{v_{i}}}={\frac {R}{R+j\omega L}}={\frac {1}{1+j\omega T}}}$

Time constant

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

Frequency response of Low pass filter

${\displaystyle \omega =0.v_{o}=v_{i}}$
${\displaystyle \omega =\omega _{o}.v_{o}={\frac {v_{i}}{2}}}$
${\displaystyle \omega =00.v_{o}=0}$

Cut off frequency, ${\displaystyle \omega _{o}}$ , frequency at which ${\displaystyle v_{o}={\frac {1}{2}}v_{i}}$

${\displaystyle \omega _{o}={\frac {1}{T}}}$