Practical Electronics/Low Pass Filter

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Low Pass Filter[edit]

LR Network[edit]

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


\omega = 0 V_o = V_i
\omega_o = \sqrt{\frac{1}{LC}} V_o = \frac{V_i}{2}
\omega = 00 V_o = 0
Plot three points above we have a graph Vo - \omega . From graph, we see voltage does not change with frequency on Low Frequency therefore LR network can be used as Low Pass Filter


RC Network[edit]

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


\omega = 0 V_o = V_i
\omega_o = \sqrt{\frac{1}{LC}} V_o = \frac{V_i}{2}
\omega = 00 V_o = 0
Plot three points above we have a graph Vo - \omega . From graph, we see voltage does not change with frequency on Low Frequency therefore LR network can be used as Low Pass Filter

Summary[edit]

In general

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