## 1 Introduction  
Resonators are key elements in radiofrequency (RF) and microwave engineering. Many passive and active circuits (such as filters, diplexers, oscillators, amplifiers, _etc._) and antennas contain resonant elements in their designs [1, 2]. There are many types of resonators of interest for RF and microwave applications, such as cavity resonators, dielectric resonators, acoustic wave resonators, lumped element resonators, quartz crystal resonators, transmission line resonators, and semilumped resonators, among others. In this paper, the focus is on semilumped resonators, namely, planar resonators with dimensions much smaller than the signal wavelength, \(\lambda\), at their fundamental resonance frequency [3].  
Transmission line resonators are also planar resonators, but their dimensions scale with the resonance frequency. It is well known, for instance, that a short-circuited \(\lambda\)/2 transmission line behaves as a series resonator, whereas it can be modeled by a parallel resonator if it is open ended [1]. Conversely, for \(\lambda\)/4 lines, a short-circuit load provides a parallel resonance, whereas for an open ended line the input impedance is that of a series resonator. Such transmission line resonators have been used in many microwave applications, such as filters (parallel coupled line bandpass filters, gap coupled \(\lambda\)/2-resonator filters, bandpass and bandstop filters based on shunt stubs, _etc._) and antennas (printed dipole and monopole antennas, for instance) [1]. However, the fact that their dimensions scale with frequency is a limiting aspect in terms of device miniaturization.  
To reduce device size, a possible strategy is to replace transmission line resonators with semilumped resonators. The advantage of this approach is the full compatibility with planar technology. As mentioned above, semilumped resonators are electrically small resonant elements. In such resonators, the resonance, rather than being related to a distributed Fabry-Perot type phenomenon, can be interpreted in terms of an LC equivalent circuit, with a clearly identifiable inductance, \(L\), and capacitance, \(C\), in the resonator topology. As long as semilumped resonators are small (as compared to transmission line resonators) and fully planar, they are of special interest in applications where size reduction and cost are important. However, as the resonator's size is reduced, the quality factor, \(Q\), is also degraded, and for certain applications (such as reference oscillators, very narrow band pass filters, _etc._), other high-\(Q\) resonators (such as cavity resonators, or crystal resonators, among others) are a necessity. Nevertheless, semilumped resonators may find application in a wide variety of scenarios, such as microwave front ends (in image rejection filters, in intermediate frequency -IF- filters, _etc._), or as constitutive building blocks of a new class of artificial structures known as metamaterials [4; 5; 6; 7; 8; 9; 10]. Let us now briefly consider in the next section the potentiality of electrically small resonators for the design of microwave circuits and metamaterials based on two illustrative examples. In Section 3, the different semilumped resonators considered in this paper will be presented and analyzed. Some illustrative applications will be presented in Section 4. Finally, the main conclusions will be highlighted in Section 5.