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This paper describes the theory behind the "coil-enhancement" principle: The impedance of an inductor is made controllable as a function of the frequency by means of a transconductance function g m (s) that is located in the feedback loop. In order to show the potential of the coil-enhancement circuit, the effect of several basic transconductance functions onto the synthesized impedance is presented. The specific case of g m (s) ˜ s -1 produces the coil-enhancement situation and is discussed in detail. One drawback of the coil-enhancement circuit is found in the series resistance of a second inductor, also positioned in the feedback loop. The influence of this series resistance onto the synthesized impedance is addressed and a work-around is presented. A newly developed active "plain old telephone service" (POTS) splitter, based upon the coil-enhancement principle, is derived from a fully passive POTS splitter in which two large inductors are merged together into one active inductor. The active POTS splitter is fully tested and is found compliant with the standard "TS 101 952-1-1 V1.2.1 (option A)" of the European Telecommunications Standards Institute. The area reduction that comes together with the passive-to-active conversion is 40%.