2022-12-19 14:34 Status: # Directional coupler aka Backward coupler ## Operation  In odd mode, a small 's' means a lower odd-mode (differential mode) impedance. In even mode, there is low even mode impedance when 't' is small.  The mutual coupling allows for the signal to be sampled. This can be used to take a small sample of the signal.  ## Design  Work out the impedances of the system based on how much of each signal you want to come out of each port. The amount of coupling is a factor of the odd and even mode impedance. We want to design for an impedance controlled differential pair. Coupling in a PCB depends on substrate thickness (t), single ended impedance (width) and the gap between traces (s). The coupling coefficient is between 0 and 1. You can't have an exact 3dB split because that would require perfect coupling (i.e. connection). ### Equations $Z_0=Z_{0e}\cdot Z_{0o}$ $Z_{0e} = \sqrt{\frac{1+CF}{1-CF}}$ $Z_{0e} = \sqrt{\frac{1-CF}{1+CF}}$ [^1] $C_{dB}=-20log_{10}\frac{Z_{even}-Z_{odd}}{Z_{even}+Z_{odd}}$ [^2] ## Simulation I use this image more as an example of how isolation might look.  [^3] --- # References [^1]: [RF and Microwave PCB Design - Part 5: Couplers - YouTube](https://www.youtube.com/watch?v=Yg0diblMQBI) [^2]: [10.1109/ACCESS.2022.3201865](https://doi.org/10.1109/ACCESS.2022.3201865) [^3]: [Microwaves101 | Short-Slot Waveguide Hybrid](https://www.microwaves101.com/encyclopedias/short-slot-waveguide-hybrid)