AOE 3054 Self-Taught Unit 1

3.3 Low-Pass RC Filter (contd.)

The plots show the amplitude and phase response of a low-pass RC filter. Note that at low frequencies where v_out = v_in the amplitude response is 0 dB. As v_out becomes less than v_in the response in decibels becomes negative.

A particularly important frequency in the operation of a filter is that at which the magnitude response is equal to 1 over root 2, i.e. the ratio | V_out / V_in |² = 0.5. This frequency, easily determined from the equation

| V_out / V_in | = 1 / (1 + w²R²C² )^½ is usually referred to as the "half-power" or "3dB" point since the amplitude response here is -3dB. The frequency is given by
w = 1 / RC The 3dB point is sometimes thought of as separating those frequencies that filter passes from those that it does not. This is obviously an over simplification.