# Compact High-Diectivity Contra-Directional Coupler
## 1 Introduction  
Microstrip parallel coupled-line directional couplers are widely used in microwave and millimeter-wave circuits. The power detection and VSWR (voltage standing wave ratio) detection circuits in high-power systems are important areas. The microstrip structure is the most popular choice for this application because it is compact and flexible for integration into other circuits. Power and VSWR detection in high-power systems should have weak coupling to feed sufficiently low power to the detector component. The directivity should be high so that the load impedance of the high-power systems will have a minimal effect on the power detection, and the forward and reverse power can be detected as independently as possible. Lastly, the circuit should be small and compact to ensure minimum loss in the power systems and easy integration. However, the microstrip parallel coupled-line directional coupler with weak coupling shows poor directivity, due to the inherent difference between the phase velocities of its even- and odd-mode in the microstrip transmission line. Many studies have been carried out to overcome poor directivity. One group of approaches is to compensate for the difference in even- and odd-mode phase velocities. Wiggly lines [1; 2; 3] were proposed, and they increased the odd-mode electrical length to compensate for the difference. Another compensation method is overlaying a dielectric on a microstrip line [4; 5; 6] to make an inhomogeneous microstrip transmission line, much like a homogeneous line. Those methods are intuitively clear and reasonable; however, there is a lack of a straightforward design equation which requires more rigorous analysis and trial and error. Moreover, adding an external dielectric material on the PCB is an additional burden for practical implementation. In [7; 8; 9; 10], an interdigital capacitor or thin periodic stubs are inserted between two coupled lines, and in [11; 12; 13], short stub distributed inductors are placed in the middle of a coupled line, while [14] uses both inductive and capacitive stubs. Some approaches use a feedback path [15; 16]. However, all of these used thin and sharp structures that are vulnerable to high power, and as such,they are not suitable for high-power systems. Ref. [17] proposed multiple coupled-lines approaches, and [18; 19; 20; 21] added capacitive and inductive stubs for compensation. Other multiple coupled-lines approaches involve inserting a non-coupling line between the couplers [22; 23; 24; 25]. The multiple coupled-lines approaches show broadband characteristics; however, they are cumbersome for integration into power systems due to their larger size and greater corresponding loss. There are also lumped-element compensation methods, where [26; 27] use capacitors at the end of couplers, and [28] uses periodic capacitors inside couplers. However, the lumped-component approaches are unsuitable for microwave and millimeter-wave applications. Refs. [29; 30] used distributed version of capacitors at the end of couplers. [31; 32] modulated the port impedance with an inductor at the coupler ports, but there are more suitable approaches for power systems. Most microwave and millimeter-wave power systems operate in a specific frequency band. In light of this, the present study emphasizes high-directivity, compact size and a correspondingly low insertion loss characteristic, rather than wideband operation. To this end, this paper proposes a high-directivity compact microwave directional coupler suitable for integration into high-power systems. This paper derived the design equation for compact, weak coupling and high-directivity couplers for high-power systems, where the coupled line length can be selected arbitrarily. The proposed design is demonstrated in a specific frequency band for Ku-band satellite up-link applications. For the coupled line, 60\({}^{\circ}\) electrical length is selected for compact size.