combination of coupling loss, dielectric loss, conductor loss, and VSWR loss. Depending on the frequency range, coupling loss becomes less significant above coupling where the other losses constitute the majority of the total loss. The theoretical insertion loss (dB) vs coupling (dB) for a dissipationless coupler is shown in the graph of figure 3 and the table below. Isolation Isolation of a directional coupler can be defined as the difference in signal levels in dB between the input port and the isolated port when the two other ports are terminated by matched loads, or: Isolation: Isolation can also be defined between the two output ports. In this case, one of the output ports is used as the input; the other is considered the output port while the other two ports (input and isolated) are terminated by matched loads. Consequently: The isolation between the input and the isolated ports may be different from the isolation between the two output ports. For example, the isolation between ports 1 and 4 can be while the isolation between ports 2 and 3 can be a different value such as . Isolation can be estimated from the coupling plus return loss. The isolation should be as high as possible. In actual couplers the isolated port is never completely isolated. Some RF power will always be present. Waveguide directional couplers will have the best isolation. Directivity Directivity is directly related to isolation. It is defined as: Directivity: where: P3 is the output power from the coupled port and P4 is the power output from the isolated port. The directivity should be as high as possible. The directivity is very high at the design frequency and is a more sensitive function of frequency because it depends on the cancellation of two wave components. Waveguide directional couplers will have the best directivity. Directivity is not directly measurable, and is calculated from the addition of the isolation and (negative) coupling measurements as: Note that if the positive definition of coupling is used, the formula results in: S-parameters The S-matrix for an ideal (infinite isolation and perfectly matched) symmetrical directional coupler is given by, is the transmission coefficient and, is the coupling coefficient In general, and are complex, frequency dependent, numbers. The zeroes on the matrix main diagonal are a consequence of perfect matching – power input to any port is not reflected back to that same port. The zeroes