Q. Explain Inductorless Filters

Inductorless (Active) Filters

Filters (used to pass or eliminate certain frequency components of a signal) that are suitable for IC fabrication, but which do not contain inductors, are known as active filters. They have the op amp as a common component. Figure 5.4.13 shows the basic op-amp circuit with frequency-dependent impedances. The voltage gain or voltage transfer function of this circuit is given by

with Zi = Ri and Zf = Rf (1/j ωCf ) (i.e., Rf and Cf in parallel). We have a low-pass filter with

is sketched in Figure 5.4.14, from which one can see that at the half-power or 3-dB point of fl, the dc value Rf /Ri goes down by a factor of 1/ √ 2 or 0.707. With Zf = Rf and Zi = Ri + 1/j ωCi (i.e., Ri and Ci in series), we have a high-pass filter for which we obtain