Substrate-integrated waveguide phase shifter with rod ... - IEEE Xplore

Substrate-integrated waveguide phase shifter with rod-loaded artificial dielectric slab T. Djerafi✉, K. Wu and S.O. Tatu A substrate-integrated waveguide (SIW) broadband phase shifter is presented and studied. The phase shift mechanism is based on the synthesis of an artificial dielectric slab using an array of metallic rods in the middle of a SIW. This technique enables a large phase shift within a compact size and enhances the density of integration. As an example, 45° and 90° phase shifters are designed and showcased on a single-layer substrate at a centre frequency of 26 GHz. The amplitude imbalance between the two paths is also avoided while the phase error is less than 5° over a frequency band of 20–32 GHz or around 46% relative bandwidth. The measured return loss is found to be better than 12 dB over the whole frequency band.

The cross-section of the rod-loaded waveguide and its equivalent dielectric substrate slab in a rectangular waveguide are shown in Fig. 1b. The rod region is replaced by a dielectric with permittivity ε2 higher than the substrate permittivity of the main waveguide ε1. The rod-loaded SIW can be treated as a periodic structure loaded by capacitance. In [8], a periodic structure was analysed as one row of posts confined by perfect magnetic planes. The equivalent permittivity is defined as
2
 Cp d 12 = 1+ (1) p C0 d where C0 is the capacitance per unit length without the post and Cp is the capacitance of the post. d

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e2

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Fig. 1 Proposed phase shifter with cylindrical metallic rods (artificial dielectric) and equivalent dielectric slab a Perspective view b Cross-section of loaded waveguide

The Ka-band SIW is loaded by a cylindrical rod. Rogers 5880 substrate with a relative permittivity ε1 of 2.2 and a thickness of 0.787 mm is used. Parameters are as follows: the SIW width a is 6 mm, the diameter of the metallic rod d is 0.4 mm, the space between adjacent rods p is 0.8 mm, the depth h = 0.25 mm and the calculated relative effective permittivity ε2 is equal to 4. Fig. 2 shows the propagation constant of the fundamental mode in the rod-loaded SIW structure. The propagation constant of a partially loaded SIW that numerically yields the same cutoff frequency as the rod-loaded SIW is designed to exhibit. As shown in the Figure, the propagation constants of the two waveguides are in good agreement. This waveguide is filled with ε2 = 3.7 which is very close to the calculated value. A deviation is observed at higher frequency; in fact the inductive effect increases with frequency. 1200 1000 800 600 400 200 0 10

Design considerations: The phase shifter based on a partially loaded waveguide is well known [6, 7]. The insertion of a dielectric into the waveguide as shown in Fig. 1a increases the effective dielectric constant, which decreases the wavelength. With a defined permittivity, the width and length of the slab are determined according to [7]. From the characteristic impedance of the resulting partially loaded waveguide, a multi-section impedance transformer is designed according to the given input return-loss specifications. To substitute the usually considered dielectric slab, a 2-D array of a metallic post structure is proposed as illustrated in Fig. 1a. Fringe planes parallel to each other are used to achieve the needed permittivity artificially. The effective permittivity is mainly a function of the grating height. They can also be modified by changing the radius of the air hole and the distance between adjacent holes. Nevertheless, these parameters are defined by perforation and metallisation processing constraints.

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Introduction: Phase shifters in fixed and variable categories are extremely desired components [1, 2]. They are used in a wide variety of applications including wireless communication, radar, measurement and instrumentation systems, as well as antenna array feed and beamforming networks. The use of substrate-integrated waveguide (SIW) technology allows the development of a compact circuit with low radiation loss at millimetre-wave frequencies. Several SIW phase shifters have been proposed and demonstrated [3–5]. In [3], the phase shifting was realised by means of unequal length, unequal width transmission lines. A differential phase shift of 45 ± 0.4° was achieved together with a reflection coefficient of less than −20 dB over 31–40 GHz (25%) and an insertion loss of