## 16.2. Fundamentals of Low-Pass Filters

The most simple low-pass filter is the passive RC low-pass network shown in Fig. 16.2.

Its transfer function is

$\text{A}\left(\text{s}\right)=\frac{\frac{1}{\text{RC}}}{\text{s}+\frac{1}{\text{RC}}}=\frac{1}{1+\text{sRC}}$

where the complex frequency variable, s = jω + σ, allows for any time variable signals. For pure sine waves, the damping constant, σ, becomes zero and s = jω.

For a normalized presentation of the transfer function, s is referred to the filter's corner frequency, or −3 dB frequency, ω

_{C}, and has these relationships:$\text{s}=\frac{\text{s}}{{\omega}_{\text{C}}}=\frac{\text{j}\omega}{{\omega}_{\text{C}}}=\text{j}\frac{\text{f}}{{\text{f}}_{\text{C}}}=\text{j}\Omega $

With the corner frequency of the low-pass in Fig. 16.2 ...

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