Define crossover frequency in active filters.

In active filters, the crossover frequency is particularly relevant in filter designs like low-pass, high-pass, band-pass, and band-stop filters. For instance:

Low-Pass Filter: The crossover frequency in a low-pass filter is the frequency at which the filter's magnitude response starts attenuating, allowing lower frequencies to pass through relatively unaffected, while higher frequencies are attenuated.

High-Pass Filter: In a high-pass filter, the crossover frequency marks the point where the magnitude response begins to drop, allowing higher frequencies to pass with little attenuation, while lower frequencies are attenuated.

Band-Pass Filter: For a band-pass filter, there are two crossover frequencies: the lower crossover frequency (frequencies below which are attenuated) and the upper crossover frequency (frequencies above which are attenuated). These frequencies define the bandwidth of frequencies that the filter allows to pass through relatively unattenuated.

Band-Stop (Notch) Filter: In a band-stop filter, there are also two crossover frequencies, but they define the range of frequencies that are attenuated, creating a "notch" in the filter's response.

The -3 dB point is commonly used to define the crossover frequency because it represents the point at which the filter's magnitude response has dropped to about 70.7% of its maximum value (which corresponds to a power reduction of half). This point is often considered the boundary between the passband and the transition band (or stopband), depending on the type of filter.

Designing filters to achieve desired crossover frequencies is a critical aspect of active filter design, as it determines the filter's frequency response characteristics and its suitability for specific applications.