This paper is focused on the application of complementary split-ring resonators (CSRRs) to the suppression of the common (even) mode in microstrip differential transmission lines. By periodically and symmetrically etching CSRRs in the ground plane of microstrip differential lines, the common mode can be efficiently suppressed over a wide band whereas the differential signals are not affected. Throughout the paper, we present and discuss the principle for the selective common-mode suppression, the circuit model of the structure (including the models under even-and odd-mode excitation), the strategies for bandwidth enhancement of the rejected common mode, and a methodology for common-mode filter design. On the basis of the dispersion relation for the common mode, it is shown that the maximum achievable rejection bandwidth can be estimated. Finally, theory is validated by designing and measuring a differential line and a balanced bandpass filter with common-mode suppression, where double-slit CSRRs (DS-CSRRs) are used in order to enhance the common-mode rejection bandwidth. Due to the presence of DS-CSRRs, the balanced filter exhibits more than 40 dB of common-mode rejection within a 34% bandwidth around the filter pass band.

In this paper, an analytical method to estimate the complex dielectric constant of liquids is presented. The method is based on the measurement of the transmission coefficient in an embedded microstrip line loaded with a complementary split ring resonator (CSRR), which is etched in the ground plane. From this response, the dielectric constant and loss tangent of the liquid under test (LUT) can be extracted, provided that the CSRR is surrounded by such LUT, and the liquid level extends beyond the region where the electromagnetic fields generated by the CSRR are present. For that purpose, a liquid container acting as a pool is added to the structure. The main advantage of this method, which is validated from the measurement of the complex dielectric constant of olive and castor oil, is that reference samples for calibration are not required.

A unifying principle explaining the numerical bounds of quantum correlations remains elusive, despite the efforts devoted to identifying it. Here, we show that these bounds are indeed not exclusive to quantum theory: for any abstract correlation scenario with compatible measurements, models based on classical waves produce probability distributions indistinguishable from those of quantum theory and, therefore, share the same bounds. We demonstrate this finding by implementing classical microwaves that propagate along meter-size transmission-line circuits and reproduce the probabilities of three emblematic quantum experiments. Our results show that the "quantum" bounds would also occur in a classical universe without quanta. The implications of this observation are discussed.

Differential (balanced) microstrip bandpass filters (BPFs) implemented by combining open split ring resonators (OSRRs) and open complementary split ring resonators (OC-SRRs) are proposed. The OSRRs are series connected in both strips of the differential line, whereas the OCSRRs are paired face-to-face and connected between both line strips in a symmetric configuration. For the differential mode, the OCSRRs are virtually connected to ground and the structure can be modeled, to a first-order approximation, by a cascade of series resonators (OSRRs) alternating with shunt resonators (OCSRRs), i.e., the canonical circuit model of a BPF. These filters have the ability to suppress the common mode by properly adjusting the metallic area surrounding the OCSRRs. An order-3 balanced Chebyshev BPF is designed and fabricated to illustrate the possibilities of the approach. The filter does not require vias (contrary to previous single-ended microstrip BPFs based on OSRRs and OCSRRs), filter dimensions are small, and the common mode is efficiently suppressed with more than 20 dB rejection within the differential filter pass band.

A simple strategy is proposed to design differential-mode bandpass filters with good common-mode (CM) rejection using simple resonators. Specifically, the CM rejection is enhanced by using conventional open-loop resonators as well as folded stepped-impedance resonators without the addition of printed or lumped elements along the symmetry plane of the filter or the use of defected ground solutions. The novelty of the present proposal is that a good CM rejection is achieved by the use of magnetic coupling instead of the more commonly employed electrical coupling. Magnetic coupling inherently yields poorer CM transmission as requested by good differential filters. The resonators, due to their geometrical simplicity, can easily be cascaded to implement high-order filters. The use of simple geometries also simplifies the design methodology and makes final tuning based on electromagnetic simulation simpler or unnecessary.