Practical Electronics/High Pass Filter

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Low Pass Filter[edit]

RL Network[edit]

\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[edit]

\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[edit]

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