## 1 Introduction  
Transmission lines loaded with electrically small resonant elements, such as stepped impedance resonators (SIRs) [1], split ring resonators (SRRs) [2; 3; 4; 5], spiral resonators [6], and other resonators related to the previous ones, including the complementary (or slotted) counterparts [7; 8; 9; 10; 11], have been applied to the implementation of planar microwave filters [1; 8; 12; 13], spurious suppression [14], metamaterial-inspired devices [15; 16], microwave sensors [17; 18; 19; 20; 21], radiofrequency barcodes [22; 23], _etc._ In most of these applications, the resonator is electrically and/or magnetically coupled to the line, providing a notch at the fundamental resonance frequency of the resonant element. However, the fact that the resonant elements are etched close to the line does not guarantee that (effective or net) line-to-resonator coupling arises. Indeed, the relative orientation between the line and the resonant element is a key factor to determine whether coupling is present or not, and the nature (electric, magnetic or mixed) of such coupling. For instance, it was demonstrated in [24] that in coplanar waveguide (CPW) transmission lines loaded with pairs of SRRs symmetrically etched in the slot regions, mixed coupling (electric and magnetic) arises unless the SRRs are etched with their symmetry planes orthogonally oriented to the line axis (in that case, the coupling between the line and the SRRs is only magnetic). Similarly, in microstrip lines loaded with complementary split ring resonators (CSRRs), the line-to-resonator coupling is electric for orthogonal orientation, and mixed coupling appears for any other particle orientation (see Figure 1). Both SRRs and CSRRs are bianisotropic particles [25] that can be excited by either a time-varying electric or magnetic field (conveniently oriented), and for that reason particle orientation with regard to the line is fundamental to control the nature of coupling.  
However, resonator orientation and position are not only important to control the coupling mechanism, but also to control the presence and level of coupling in certain lines loaded with single symmetric resonant particles [19], or to control the number of notches in the transmission coefficient in transmission lines loaded with pairs of resonant elements [26]. In this work, it will be shown that particle  
Figure 1: (**a**) CPW (Coplanar waveguide) transmission line loaded with a pair of SRRs (split ring resonators) with the symmetry plane orthogonally oriented to the line axis; (**b**) Microstrip transmission line loaded with a CSRR (complementary split ring resonator) with the symmetry plane orthogonally oriented to the line axis. If the particles are rotated (\(\phi\
eq 0\)), mixed coupling arises.  
orientation and symmetry are fundamental to control the transmission properties of resonator loaded lines. Moreover, an exhaustive analysis, on the basis of lumped element equivalent circuit models of the considered structures, is carried out. Moreover, some applications derived from the symmetry related electromagnetic properties of these lines mainly based on selective mode suppression [27; 28; 29] or symmetry disruption [19; 30] will be pointed out, including common-mode suppressed balanced lines, microwave sensors for spatial (angular) measurement, and microwave differential permittivity sensors (actually comparators).  
The work is organized as follows. In Section 2, the symmetry-related electromagnetic properties that lead us to the control of the transmission characteristics in transmission lines loaded with symmetric configurations of resonant elements are explained in detail. In Section 3, the circuit models of certain representative structures are presented. The considered structures are differential microstrip lines loaded with CSRRs, CPW transmission lines loaded with electric LC (ELC) resonators, and CPWs loaded with pairs of SRRs. Section 4 is devoted to the applications. Finally, the main concluding remarks are summarized in Section 5.