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

A(s)=1RCs+1RC=11+sRC

image
where the complex frequency variable, s =  + 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, ωC, and has these relationships:

s=sωC=jωωC=jffC=jΩ

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

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