How do you design a lange coupler of impedance 50ohms?

To design a Lange coupler with a characteristic impedance of 50 ohms, you start by determining the required dimensions of the coupling lines, which are typically made of microstrip or stripline. The coupler consists of multiple parallel transmission lines that are spaced appropriately to achieve the desired coupling level, often using a specific ratio of line widths and lengths based on the design frequency. Utilize simulation tools to optimize the layout, ensuring that the input and output ports maintain a 50-ohm impedance match. Finally, validate the design through electromagnetic simulation or prototyping to check for performance metrics such as insertion loss and isolation.