GIC filter
Generalized Impedance Converter (GIC). is a 2-port device capable of making the input impedance of one of its two ports the product of the impedance terminating its remaining port and some internal impedances.
Frequency-Dependent Negative Resistor (FDNR). An FDNR is a 1-port device with an impedance lf(s2D), where D is a positive constant and has the unit Farad squared, or F2. Under sinusoidal steady-state operations, the impedance Z(s) of an FDNR becomes
Z(jw)= 1/w2D
which is equivalent to a resistor whose negative resistance depends on the operating frequency. This is the reason for its lengthy name.
realization of an FDNR can be obtained by terminating port 1 of the GIC with a capacitor. The driving-point impedance of the resulting 1-port is given by
Z11=R5/S2R2R4C1C5
It is known that inductors are extremely difficult to fabricate in integrated
circuits. At this time, grounded inductors can be designed by gyrator-capacitor
pairs without too much problem, but floating inductors realized actively (i.e.,
via gyrators, op. amps., and NICs) are extremely unstable, sensitive, and not
very practical. One way to avoid inductors in circuits is by a variable
impedance scaling mechanism, with the scaling factor being 1/s.
By completing this process, we arrived at a new circuit without inductors. Moreover,
both the original circuit and the variable-frequency-scaled circuit have the
same voltage or current ratio transfer function.