The circuit shown in figure 1 is a second-order butterworth filter using an operational amplifier. The next formulas can be used to calculations involving its performance.
Formula 1
Frequency:
f = 1 / (2 x π x R x C)
Where:
f is the frequency in hertz (Hz)
R is the resistance in ohm (Ω)
C is the capacitance in farads (F)
π is 3.1416
Formula 2
Selectivity:
Q = 3 / (3 - G)
Where:
Q is the Q-factor
G is the voltage gain (see next formula)
Formula 3
Gain:
G = 1 + (R2 / R1)
Where:
G is the gain
R1 and R2 are the resistances in ohm (Ω)
