# Practical Electronics/High Pass Filter

## Low Pass Filter

### RL Network

${\frac {V_{o}}{V_{i}}}={\frac {Z_{L}}{Z_{R}+Z_{L}}}={\frac {j\omega L}{R+j\omega L}}={\frac {1}{1+j\omega T}}$ $T={\frac {L}{R}}$ $\omega _{o}={\frac {1}{T}}={\frac {R}{L}}$ $\omega =0V_{o}=0$ $\omega _{o}={\sqrt {\frac {1}{RC}}}V_{o}={\frac {V_{i}}{2}}$ $\omega =00V_{o}=00$ Plot three points above we have a graph $Vo-\omega$ . From graph, we see voltage does not change with frequency on High Frequency therefore RL network can be used as High Pass Filter

### CR Network

${\frac {V_{o}}{V_{i}}}={\frac {Z_{R}}{Z_{R}+Z_{C}}}={\frac {R}{R+{\frac {1}{j\omega C}}}}={\frac {j\omega T}{1+j\omega T}}$ $T=RC$ $\omega _{o}={\frac {1}{T}}={\frac {1}{RC}}$ $\omega =0V_{o}=0$ $\omega _{o}={\sqrt {\frac {1}{LC}}}V_{o}={\frac {V_{i}}{2}}$ $\omega =00V_{o}=00$ Plot three points above we have a graph $Vo-\omega$ . From graph, we see voltage does not change with frequency on High Frequency therefore LR network can be used as High Pass Filter

## Summary

In general

1. High Pass Filter can be constructed from the two networks RL or CR network .
2. High Pass Filter has stable voltage does not change with frequency on Low Frequency .
3. High pass filter can be expressed in a mathematical form of
${\frac {V_{o}}{V_{i}}}={\frac {j\omega T}{1+j\omega T}}$ T = RC for RC network
$T={\frac {L}{R}}$ for RL network