# Antipodal Vivaldi Antenna Arrays Fed by Substrate Integrated Waveguide Right-Angled Power Dividers
## 1 Introduction  
Substrate integrated waveguide (SIW) circuits opened a new view of microwave and mm-wave components. In comparison to conventional waveguides, SIW technology makes it feasible to design low-cost waveguide components such as filters, power dividers, couplers, phase shifters, etc. on a single-layer substrate with low radiation loss and high power handling capability. Regarding the advantages and high level of integration, SIW is considered an excellent type of feeding system for planar antennas. Thus during the last decade, many SIW feed systems have been published, e.g., [1; 2; 3; 4; 5; 6; 7]. As a tapered slot antenna, the Vivaldi antenna is well-known for its high gain, directive radiation pattern, planar structure and fairly wide bandwidth. Its small transverse spacing makes it a good candidate for antenna arrays [6]. For example, reference [8] presents a monopulse antenna using a dual V-type linearly tapered slot antenna and a multi-mode SIW feeding technology for producing sum and difference signals. A new CPW feed system for SIW Vivaldi antenna is proposed in [9] which achieves a wide bandwidth match and eliminates the need for air bridges or bond wires. A combination of coplanar waveguide and SIW is introduced for feeding a surface micro machined Vivaldi antenna with circularly shape load [10]. Reference [11] proposed an antenna system comprising two Vivaldiantennas which use a frequency-selective power divider and two SIW crossovers for providing sum and difference signals. The performance of the Vivaldi antenna array is dependent on its feeding network. Among all types of feed networks for antenna arrays, power dividers are the most popular ones. For example, in [6] an SIW T-junction and an SIW-to-microstrip transition is used for feeding an eight-element antenna array. [PERSON] and coauthors present an SIW binary splitter to decrease the insertion loss in the feed structure [1]. Based on mode matching techniques, some SIW power dividers with two, three, and four output ports are introduced in [2] for feeding arrays. A grounded coplanar waveguide (GCPW) transition is presented as a power divider input to improve the antenna array performance [4]. A dielectric loaded 1 \(\times\) 4 SIW antenna array with high gain is introduced in [7] and uses a T-junction power divider as feeding network. A planar multiway power divider network which is able to combine T-type and Y-type dividers is presented in [12]. An SIW multi-antenna system is proposed in [13] which is fed by a four-way SIW power divider consisting of a conductor-backed CPW-to-SIW transition, SIW corners and two SIW T-junctions. An SIW multi-port power divider using several cascade-connected SIW couplers and some metallic vias are designed in [14]. A two-way power divider based on ridged substrate integrated waveguide is presented in [15] for extending the bandwidth in comparison to the regular SIW. Reference [16] proposes a 1 \(\times\) 8 antipodal Vivaldi antenna array with a 1-to-8 power divider network as feed system. This design provides a maximum gain of 11.32 dB with 3.9 GHz bandwidth. Most of those individual power dividers are in-phase dividers. Out-of-phase dividers can be created by using TE\({}_{10}\)-to-TE\({}_{\text{q0}}\) mode converters and placing waveguide walls at locations of zero electric field in the output port. This has been demonstrated in all-metallic waveguide technology. For instance, an asymmetric TE\({}_{10}\)-to-TE\({}_{\text{q0}}\) mode converter with a conversion level higher than 80% is introduced in [17] and is designed based on a truncated junction of single- to over-moded waveguide. The authors of [18] introduce a novel TE\({}_{10}\)-to-TE\({}_{20}\) mode transducer with 99% mode conversion efficiency based on a compensated waveguide corner and use it for the design of a two-way out-of-phase power divider. The group extend their work in [19] to a TE\({}_{10}\)-to-TE\({}_{30}\) mode transducer. Most inline power dividers give us the ability to provide the same amplitude and phase at the output.