Decreasing the electric length of an antenna results in increasing its input reactance that becomes greater than its input resistance, resulting in a significant rise in its quality factor and in a drastic reduction of its potential operating bandwidth. For such small antennas, namely ESA for Electrically Small Antenna, passive matching is restricted by the gain-bandwidth theory, providing narrow bandwidths and/or poor gain. This limitation can be overtaken by using antenna matching networks based on non-Foster components. In previous studies, non-Foster components are used to cancel the reactance part of the ESA, and then passive matching may be introduced to transform the net input impedance toward 50Ω, which leads to an increase in the bandwidth. In this paper, a design methodology is put forward on three different topologies all based on combined passive and active matching networks. A described step-by-step design to decrease the antenna quality factor is discussed. A comparison is made between these topologies along with a discussion on their limitations and ability to increase the bandwidth and radiation efficiency of ESA. The third topology presented in this paper is a novel one that proposes a three-stage matching network and exhibits both the widest matched bandwidth and an increase in the efficiency of the whole system compared to previous approaches. In order to make this comparison, a new indicator to estimate the whole system radiated power efficiency is introduced and validated by comparison with a full EM simulation. Moreover, actual implementation of the two most interesting techniques are detailed and associated measured results are carefully compared to simulations.