# A Frequency-Reconfigurable Dual-Band RF Crossover Based on Coupled Lines and Open Stubs
## 1 Introduction  
A radio frequency (RF) crossover is a passive microwave device that consists of four ports: two input ports and two output ports. Its main purpose is to ensure the passage of two signals traveling across each other simultaneously with minimal interference. In this device, one signal travels from port 1 to port 3, and the second signal travels from port 2 to port 4. Also, all of the crossover ports must be matched. This microwave device is of great importance in beamforming networks (BFNs) such as butler matrices (BMs). BMs play an essential role in feeding networks of antenna arrays. Thus, it has the ability to control the steering of the main beam, can realize multi-beam response, or can provide wide coverage with high gain if properly designed [1]. BMs conventionally consist of couplers, crossovers, and phase shifters. Accordingly, the characteristics of the BM will be the same as the characteristics of its components. As a result, many investigations were conducted to enhance the performance of BMs and realize demanded features such as wideband response [2; 3], multi-band response [4], reconfigurable response [5], or reaching a compact design [6; 7]. Therefore, crossovers have been widely researched and designed using various techniques. Starting from a non-planar model using airbridges to prevent metallic connectivity between the four ports, we achieve two separate paths [8]. Another design was presented using a multi-layer structure where there exist two paths: one regular path using a transmission line (TL), and the other is physically disconnected but electrically connected by utilizing the additional PCB layer [9]. Capacitors and inductors can be employed to fulfill a compact crossover [10]. Also, a multi-section branch-line coupler(BLC) can realize crossover performance [11]. Negative-refractive-index transmission line (NRI-TL) metamaterial lines were used to design a crossover [12]. The design was accomplished by loading the TLs of three BLCs with shunt inductors and series capacitors. Moreover, filtering crossover was achieved using a ring resonator [13]. Microstrip square, circular, and hexagonal patch crossovers were investigated [14]. Also, a square patch was used to achieve a crossover design; however, in this design, the implementation of different slot shapes on the patch was researched [15]. Another approach to realizing a crossover is by utilizing CLs. Usually, crossovers based on CLs lead to a compact design [16]. Along with the rapid and continuous advancement of technology, the development of microwave devices capable of operating at different resonant frequencies [17; 18; 19; 20; 21; 22; 23; 24] or multi-tasking using the same device [25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35] became a necessity. Crossover with dual-band response was achieved by increasing the length of the vertical TLs of a branch-line crossover (BLCO) to double the length of the horizontal TLs [20]. Also, the replacement of the horizontal TLs of a BLCO by a T-network can accomplish a dual-band crossover [21]. Cascading a dual-band coupler can lead to a dual-band crossover [22]. Furthermore, CLs were utilized to realize the dual-band response [23; 24]. All of the aforementioned dual-band designs can only operate at two fixed frequencies. The following crossover designs resonate at a single frequency but with the ability to tune that operating frequency. One way of achieving frequency tuneability is by employing rectangular dielectric channels (RDCs) in a BLCO [25]. Then, by filling the RDCs with air or dielectric materials, the frequency will change as the permittivity changes. Another way of realizing tunability is by employing varactor diodes that can give different capacitances based on the applied biasing voltage. Substrate integrated waveguide (SIW) evanescent-mode cavity resonators along with four sets of varactors were used to achieve a frequency- reconfigurable crossover [26]. Two CLs, two constant capacitors, and one varactor diode have been incorporated to alter a crossover frequency [27].