3.3 Low-Pass RC Filter (contd.)
We may express this mathematically using the notion of impedance.
Consider the capacitor and use its equation:
Vout = Iin /
jwC
where V and I are the amplitudes of the voltage, v,
and current, i, fluctuations. Thus,
Vout - Vin = Vout
jwCR
rearranging gives
Vout / Vin = ( 1 -
jwRC ) /
(1 +w2R2C2 )
The amplitude and phase response of the circuits may be obtained by
taking the magnitude and phase of the complex number in the above equation.
Remembering that
Magnitude2 = Real2 + Imag2
and Phase = arctan( Real / Imag )
we obtain
| Vout / Vin | = 1 /
(1 + w2R2C2 )½
and ∠Vout - ∠Vin
= -arctan(wRC)