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