on the matrix antidiagonal are a consequence of perfect isolation between the input and isolated port. For a passive lossless directional coupler, we must in addition have, since the power entering the input port must all leave by one of the other two ports. Insertion loss is related to by; Coupling factor is related to by; Non-zero main diagonal entries are related to return loss, and non-zero antidiagonal entries are related to isolation by similar expressions. Some authors define the port numbers with ports 3 and 4 interchanged. This results in a scattering matrix that is no longer all-zeroes on the antidiagonal. Amplitude balance This terminology defines the power difference in dB between the two output ports of a hybrid. In an ideal hybrid circuit, the difference should be . However, in a practical device the amplitude balance is frequency dependent and departs from the ideal difference. Phase balance The phase difference between the two output ports of a hybrid coupler should be 0°, 90°, or 180° depending on the type used. However, like amplitude balance, the phase difference is sensitive to the input frequency and typically will vary a few degrees. Transmission line types Directional couplers Coupled transmission lines The most common form of directional coupler is a pair of coupled transmission lines. They can be realised in a number of technologies including coaxial and the planar technologies (stripline and microstrip). An implementation in stripline is shown in figure 4 of a quarter-wavelength (λ/4) directional coupler. The power on the coupled line flows in the opposite direction to the power on the main line, hence the port arrangement is not the same as shown in figure 1, but the numbering remains the same. For this reason it is sometimes called a backward coupler. The main line is the section between ports 1 and 2 and the coupled line is the section between ports 3 and 4. Since the directional coupler is a linear device, the notations on figure 1 are arbitrary. Any port can be the input, (an example is seen in figure 20) which will result in the directly connected port being the transmitted port, the adjacent port being the coupled port, and the diagonal port being the isolated port. On some directional couplers, the main line is designed for high power operation (large connectors), while the coupled port may use a small connector, such as an SMA