If filters may be made with only resistors, capacitors, and inductors, you might ask why anyone would want to design a variation that required the use of an op amp. This is a good question. Obviously, there must be certain shortcomings or difficulties associated with passive filter designs, or active filters would not exist. Active filters offer many advantages over passive implementations. First of all, active filters do not exhibit insertion loss. This means that the pass-band gain will equal 0 dB. Passive filters always show some signal loss in the pass band. Active filters may be made with pass-band gain, if desired. Active filters also allow for interstage isolation and control of input and output impedances. This alleviates problems with interstage loading and simplifies complex designs. It also produces modest component sizes (e.g., capacitors tend to be smaller for a given response). Another advantage of the active approach is that complex filters may be realized without using inductors. This is desirable, as practical inductors tend to be far less ideal than typical resistors and capacitors and are generally more expensive. The bottom line is that the active approach allows for the rapid design of stable, economical filters in a variety of applications.
Active filters are not perfect. First, by their very nature, active filters require a DC power supply whereas passives do not. This is usually not a problem, as the remainder of the circuit will probably require a DC supply anyway. Active filters are also limited in their frequency range. An op amp has a finite gain-bandwidth product, and the active filter produced can certainly not be expected to perform beyond it. For example, it would be impossible to design a filter that only passes frequencies above 10 MHz when using a standard \(\mu\)A741. Passive circuits do not have this limitation and can work well into the hundreds of MHz. Finally, active filters are not designed to handle large amounts of power. They are low signal-level circuits. With appropriate component ratings, passive filters may handle hundreds of watts of input power. A classic example of this is the crossover network found in most home loudspeaker systems. The crossover network splits the music signal into two or more bands and routes the results to individual transducers that are optimized to work within a given frequency range. Because the input to the loudspeaker may be as high as a few hundred watts, a passive design is in order.1 Consequently, we can say that active filters are appropriate for designs at low to moderate frequencies (generally no more than 1 MHz with typical devices) that do not have to handle large amounts of power. As you might guess, that specification covers a great deal of territory, and therefore, active filters based on op amps have become rather popular.
1In more advanced playback systems, active filters can be used. Examples include recording studio monitors and public address systems. We'll take a look at just how this is done in one of the upcoming examples.