# Practical Electronics/High Pass Filter

## Low Pass Filter

### RL Network

$\frac{V_o}{V_i} = \frac{Z_L}{Z_R + Z_L} = \frac{j\omega L}{R + j\omega L} = \frac{1}{1 + j\omega T}$
$T = \frac{L}{R}$

$\omega = 0 V_o = 0$
$\omega_o = \sqrt{\frac{1}{RC}} V_o = \frac{V_i}{2}$
$\omega = 00 V_o = 00$
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

$\frac{V_o}{V_i} = \frac{Z_R}{Z_R + Z_C} = \frac{R}{R + \frac{1}{j\omega C}} = \frac{j \omega T}{1 + j\omega T}$
$T = RC$

$\omega = 0 V_o = 0$
$\omega_o = \sqrt{\frac{1}{LC}} V_o = \frac{V_i}{2}$
$\omega = 00 V_o = 00$
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