## 1 Introduction  
Recently, compact, multi-functionality, multi-band antennas have been in rising demand due to rapidly expanding wireless communication applications [1; 2; 3; 4; 5; 6; 7; 8]. This kind of antenna is more economical for today's multi-band wireless applications. Some compact printed antennas have already been designed to realize multi-band operations [1; 2; 3; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19]. Various effective approaches have been applied to obtain multi-band characteristics, such as metamaterial [6; 7], multi-radiating components [7; 14; 16], cutting slots [1; 2; 3; 9; 11; 12], employing parasitic coupling elements [11; 13; 15], modified fed line [13; 15], defected ground structure, adding slot and meander line [10; 11; 17; 18; 19]. In [20], a modified fork-shaped strip was used in a multiband antenna and covered 2.4/5.2/5.8 GHz WLAN and 3.5 GHz WiMAX bands. Additionally, dual L-shaped parasitic planes were also inserted at the bottom of the FR4 substrate to provide 3.5 GHz WiMAX band coverage. For another technique in [21], the cavity antenna with artificial magnetic conductor metamaterial was used to obtain a dual-band with a 15.2/18.8-dBi high-gain and unidirectional pattern. In [22], a bandpass filter was developed using step-impedance resonator with a first four resonance electrical lengths and a strip line. In [23], a meander line and inverted-L were incorporated into a monopole antenna to generate a dual-band operation. In [24], the also author proposed to reduce the space of the convenient to integrate the antenna with other microstrip circuits printed, in which the tri-band was generated by adjusting the u-slot shaped and two bridge elements of the antenna. For using the technique in [25], the Cassegrain circularly polarized antenna is appropriately located along the horizontal axial in order to observe the high frequency microwave, which is then downconverted and channelized by a 35-40 GHz analog front end.  
For wireless communication in some specific service areas such as on the street, highway, skywalk, corridor, tunnel, and sky train or subway stations, bidirectional radiation pattern is most desirable [18; 19; 26; 27; 28; 29; 30]. Many techniques have been proposed to achieve bidirectional propagation antenna. For an example, rings of various shapes are employed to induce more propagation in the forward and backward directions. For another example, two elements of unidirectional antennas can be combined. Other examples are modification of the ground plane of a double-sided printed circuit board, addition of coupling parasitic components, and construction of the fractal antenna with a configurable pattern.  
This study was a design and development of a tri-band bi-directional antenna, combining a rectangular patch with a wide-circular slot (WCS) and an inverted-L strip antenna, covering three frequency ranges: 2.4-2.484 GHz for 2.4 GHz WLAN, 5.15-5.825 GHz for 5 GHz WLAN and 13.4-17.7 GHz for Ku-band communication. With its compact size, the operating covered three transition bands, which is its advantage. Therefore, the proposed antenna could be applied in the urban areas where the outdoor movement was required to receive signals from WLAN towers and satellites. Nonetheless, the proposed antenna could be a part of array elements, since a very high gain antenna was required for the satellite communications. The proposed antenna theoretical design parameters were initially calculated using the design equations presented in Section 2. Then, with the CST microwave studio [31], simulation was performed using those parameters to numerically determine the output parameters. Many values of possible design parameters were then considered and simulated, and the final set of design parameters was achieved.