Fundamental Physics/Electronics/Electronics Filter/High pass filter

R-L

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

High pass filter has a transfer function

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

Time constant

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

Frequency response of High pass filter

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

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

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

C-R

High pass filter has a transfer function

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

Time constant

${\displaystyle T=RC}$

Frequency response of High pass filter

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

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

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