© Springer Science+Business Media, LLC 2017

Abstract This paper proposes a third-order miniaturized H -plane dual-band bandstop waveguide Þlter. Split ring resonators (SRRs), in the form of printed-circuit inserts, are used for the Þlter design. A simple and straightforward novel design algorithm for the waveguide SRR is introduced, which provides essential foundation for the development of the H -plane Þlter with multiple individually tunable stopbands. The third-order H -plane dual-band bandstop Þlter is implemented using SRRs for each stopband separated by quarter-wavelength waveguide sections to realize the immittance inverters for the corresponding center frequencies. Miniaturization of the Þlter is accomplished by the use of a properly designed insert within the waveguide section acting as the inverter. To demonstrate the usefulness of the proposed novel design algorithm and miniaturization concept, a compact H -plane dual-band bandstop waveguide Þlter is designed featuring independent control of the speciÞed stopbands. The stopbands are located at center frequencies f01 = 8.90 GHz and f02 = 10.90 GHz and exhibit equal bandwidths of 340 MHz. The undesirable coupling between the SRRs for different stopbands on the insert is eliminated, along with their respective couplings to the additional insert for the inverter miniaturization. Thus, each of the stopbands is ßexibly tuned by the adjustment of dimensions of the particular SRR. The proposed design using a shorter inverter preserves the characteristics of the conventional Þlter, while

B Milka M. Potrebi«c

milka_potrebic@etf.rs

Marija V. Mrvi«c marija.mrvic@gmail.com

Dejan V. Toši«c tosic@etf.rs

1School of Electrical Engineering, University of Belgrade, Bulevar kralja Aleksandra 73, Belgrade 11120, Serbia

the improvement of the overall device in terms of compactness is 32%. The designed compact H -plane dual-band bandstop waveguide Þlter is experimentally validated, and the three-dimensional electromagnetic simulation and measurement results are in good agreement.

Keywords Dual-band bandstop Þlter · H -plane waveguide Þlter · Inverter · Split ring resonator · Miniaturization

1 Introduction

Bandstop Þlters are key components in front ends of any microwave and millimeter-wave communication systems, used to eliminate the undesirable frequency band or particularly strong signal at one frequency inside the useful passband [1]. Advantages in the development of the communication systems have endorsed the design of high-performance compact Þlters used for suppression of multiple unwanted and spurious harmonic frequencies of signals. Thus, Þlters operating in distinct frequency bands are highly desirable devices. The choice of Þlter fabrication technology ultimately depends on predeÞned requirements, contained in the Þlter speciÞcation [2].

Rectangular waveguide technology is frequently encountered for implementing microwave and millimeter-wave Þlters, beside the planar technology [3,4] and substrate integrated waveguide (SIW) technology [5]. Waveguide Þlters are widely exploited because of their ability to handle high power and have low losses. Additional advantages over other technologies are attributed to the simplicity of the geometry and the possibility to design high-quality Þlters [6]. To fulÞll the demand for compact Þlters, the physical size of the waveguide is considered as an important practical

design parameter. Many efforts have been devoted to achieve a desired outcome, which is the size reduction improvement.

Classical waveguide miniaturization can be achieved by Þlling the waveguides with a dielectric material [7]. Another possible approach to miniaturization of the waveguide Þlters is based on the loadings of arrays of split ring resonators (SRRs) in the longitudinal direction of the rectangular waveguide. Multiple narrow stopbands are designed using inserts attached to the lateral sidewalls of the waveguide [8,9]. The prior design used two inserts each comprising two arrays of SRRs, arranged in such a way that every second SRR on insert belongs to a particular array. The latter used arrays of SRRs of identical size printed on the same insert, so designed stopbands are independent of each other. Proper combination of arrays of deformed omega resonators (DORs), with the ability to reject undesirable bands, is applied for the low-pass waveguide Þlter design [10]. For the purpose of size reduction, loading of the waveguides with electric-Þeld-coupled (ELC) resonators and SRRs is applied in [11]. Transversely inserted frequency selective surfaces (FSS) empower waveguide size reduction. Proposed waveguide Þlters based on arbitrarily shaped FSS are very compact, lightweight and easy to be fabricated [12,13].

Additional approach to miniaturization is to exploit fractal curves, since they proved as useful for the design of the miniaturized components, such as wideband highly efÞcient antennas [14,15] and Þlters [16]. Bandpass waveguide Þlters are designed using Koch [17] and Sierpinski fractal-shaped irises [18] as main resonating elements, outlining that advantages using fractal-shaped irises over rectangular ones are increasing the bandwidth and reducing the overall size of the Þlter.

Due to the small dimensions and its resonant behavior, the use of the individual SRR and complementary split ring resonator (CSRR) for the compact Þlter design is investigated in [19Ð21]. These resonators are of prime interest for the waveguide Þlter solutions, because of their implementation in the form of printed-circuit inserts placed in the H -plane or E-plane of the rectangular waveguide. For compact E- plane bandstop waveguide Þlters, SRRs [22], folded SRRs (FSRRs) [23], twist SRRs [24] and quarter-wave resonators (QWRs) [25,26] were inserted. H -plane bandpass waveguide Þlters using CSRRs are designed in [27,28], while in [29] authors suggest the use of the second-order resonance of the CSRR instead of the Þrst resonance for the design of a very compact bandpass Þlter with large bandwidth. SigniÞcant improvement of size reduction in a bandpass waveguide Þlter is achieved using the miniaturized admittance inverter proposed in [30].

Waveguide Þlter using H -plane inserts with different size SRRs to design two stopbands is presented in [31], while a triple-band bandstop Þlter using H -plane inserts with

QWRs is reported in [32]. As for the third-order singleband bandstop Þlter with SRRs, a very compact design using the perturbed quarter-wave transformer is reported in [33]. The third-order dual-band bandstop Þlter using SRRs is designed in [34], where SRRs for the speciÞed stopband are separated by the quarter-wave waveguide sections acting as immittance inverters. The length of the dual-band bandstop Þlter is attributed to the quarter-wave inverter for the lower stopband. Effect of the fabrication parameters on the response of the H -plane Þlter is investigated in [35].

The main purpose of this paper is to propose a compact third-order H -plane dual-band bandstop waveguide Þlter. Novel design algorithm of the waveguide SRR is introduced to simplify the development of the H -plane Þlter with multiple stopbands that are independently tuned. Useful design equations are given to facilitate the computation of the desired resonant frequency of the waveguide SRR.

SRR, implemented as a printed-circuit insert, is a key element used for the design of the presented Þlters. Therefore, the inßuence of the important practical parameters on the response of the waveguide SRR is examined. The comparative analysis is carried out using a square SRR placed in air in the absence of dielectric and implemented on three different dielectric substrates, as well. Considered substrates are the most commonly used for the design of planar structures intended to operate at RF/microwave frequencies.

Conventional design of the third-order dual-band bandstop waveguide Þlter using SRRs is demonstrated, and the strategy for the miniaturization is proposed. The idea behind is based on replacement of the conventional quarter-wave inverter for the lower stopband by the shorter one. The miniaturization is achieved by the use of an additional insert, which provides the necessary impedance required to reduce the length of the waveguide section acting as an inverter.

The performance of the proposed design algorithm and miniaturization is exempliÞed by a compact dual-band bandstop Þlter featuring independent control of the designed stopbands. The stopbands are separately tuned due to the elimination of the undesirable coupling. The unwanted coupling among the SRRs on the insert is removed by increasing the interspace between SRRs. The undesirable coupling between each of the SRRs and additional insert for the inverter miniaturization is avoided by Þnding the optimum position of the additional insert.

Equivalent electrical circuits are presented for all of the considered Þlters, contributing to Þlter design reducing the computation time and resources. These circuits exactly correspond to the decomposed three-dimensional electromagnetic (3D EM) structures, and they are developed in WIPL-D Microwave Pro [36]. Filter designs have been validated by full-wave 3D EM simulations using WIPL-D Pro [37].