High-pass filter

The simple first-order electronic high-pass filter shown in Figure 1 is implemented by placing an input voltage across the series combination of a capacitor and a resistor and using the voltage across the resistor as an output. The product of the resistance and capacitance (R×C) is the time constant (τ); it is inversely proportional to the cutoff frequency f_c, at which the output power is half the input power. That is,

where f_c is in hertz, τ is in seconds, R is in ohms, and C is in farads.

Figure 2 shows an active electronic implementation of a first-order high-pass filter using anoperational amplifier. In this case, the filter has a passband gain of -R₂/R₁ and has a corner frequency of

Because this filter is active, it may have non-unity passband gain. That is, high-frequency signals are inverted and amplified by R₂/R