# 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

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

$T={\frac {L}{R}}$ Frequency response of High pass filter

$\omega =0.v_{o}=0$ $\omega =\omega _{o}.v_{o}={\frac {v_{i}}{2}}$ $\omega =00.v_{o}=v_{i}$ Cut off frequency, $\omega _{o}$ , frequency at which $v_{o}={\frac {1}{2}}v_{i}$ $\omega _{o}={\frac {1}{T}}$ ## C-R High pass filter has a transfer function

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

$T=RC$ Frequency response of High pass filter

$\omega =0.v_{o}=0$ $\omega =\omega _{o}.v_{o}={\frac {v_{i}}{2}}$ $\omega =00.v_{o}=v_{i}$ Cut off frequency, $\omega _{o}$ , frequency at which $v_{o}={\frac {1}{2}}v_{i}$ $\omega _{o}={\frac {1}{T}}$ 