Active High-Pass Filter (HPF)
An active high-pass filter (HPF) is a filter that makes use of both op-amp and passive components. It passes high frequencies, but attenuates frequencies lower than the cut-off frequency. The actual amount of attenuation for each frequency varies from filter to filter and depends on the size of the passive components as well as the circuit configurations. The figure below shows an example of an active HPF. Notice the location of the R and C are swapped compared to the LPF.
w frequencies, where f « fc, the capacitor acts as a short circuit, hence the gain of the amplifier goes to zero.
At high frequencies, where f » fc , the capacitor acts as an open circuit and the gain of the circuit is –R1/R2, where fc =1(/2 pi R2 C), f is in Hertz, R is in Ohms, and C is in Farads.
The bode plot of the active HPF is shown below. The closed-loop gain of the HPF = Vout/Vin, fC = 1/(2 pi R1 C)