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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
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why we are going to realization of digital filter after finding the H(z).
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For the circuit of Figure, obtain the complete solution for the current i L (t) through the 5-H inductor and the voltage v x (t) across the 6- resistor.
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