Attenuator R1R1 R1R1 R2R2 Let R 1 and R 2 be the normalized resistances

Directional Couplers Multihole Waveguide Couplers Port 1 Port 3 Port 2 Port 4 a1a1 0 b4b4 b2b2 b3b3 K f a 1 -L-L K r a 1 -2  L K f a 1 -L-L K r a 1 0 a1a1 -L-L L and reverse aperture coupling coeffiecients K f and K r are the forward

Parallel-Coupled Lines Directional Coupler Input Coupled Port 3 Direct Port 4 Isolated Port 2 Port 1 L Input Coupled Port 3 Direct Port 4 Isolated Port 2 Port 1 L H wall a 1 /2 Even Mode excitation

Input Coupled Port 3 Direct Port 4 Isolated Port 2 Port 1 L E wall a 1 /2 -a 1 /2 Odd-mode excitation Lossless Transmission Line Z 0k,  l The ABCD of a Use the even and odd impedance, from the ABCD we can Obtain the reflection and transmission coefficients for even and odd cases.

For a perfect input match b 1 =0, which requires that:

Branch-Line Coupler Z 02 Z 01 l l Z0Z0 Z0Z0 Z0Z0 Z0Z0 Port 1 Port 4 Port 3Port 2 Even-mode pair Odd-mode pair a 1 /2 -a 1 /2 b1b1 b2b2 b3b3 b4b4

Open circuits Short circuits Even-mode excitationOdd-mode excitation