Describe the operation of an ideal four port ‘directional coupler’. Define ‘Coupling’ and ‘Directivity’ in the context of a directional coupler.
The directional coupler consists of two transmission lines or waveguides coupled together by fringing fields, or in case of a waveguide, by means of a small slot in such a manner that an incident wave on one line is partly transferred to the other with particular directional properties. It is a four port network having an input port, two mutually isolated output ports and one port isolated from the input port. Directional couplers are used as a elements in power monitors, reflector and power dividers. The standard diagram of rectangular directional coupler is given in Fig. 29.
Fig. 29 Diagram of rectangular directional coupler
In an ideal directional coupler when power incident at port 1 it will travel toward port 2 and a fixed part of it gets coupled to port 3 but no power is available at port 4. Here port 1 is called the input port or incident port, port 2 is called direct port, port 3 the coupled port and port 4 is called isolated port.
The directional coupler is characterized by the following parameters given below
Directivity(D): The directivity is the ration of power coupled to the auxiliary arm to the power following in the uncoupled auxiliary arm and is expressed in dB.According out circuit diagram
Directivity \(D=10\log{\left(\frac{P_3}{P_4}\right)}\ dB\).
Coupling Factor: The coupling factor is the ratio of power at the input (power at the incident port) to the power coupled at the output in the auxiliary arm and it is defined mathematically as
Coupling Factor \(C=10\log{\left(\frac{P_1}{P_3}\right)}\ dB\).
Insertion Loss: The insertion loss is arises due to insertion of the component over a line. It specifies the total output power from all the ports relative to the input power. The output power is less than input power for two reasons. Some of the input power is absorbed and some gets reflected due to mismatch. It is defined as
Insertion Loss \(I.L=\frac{P_2+P_3+P_4}{P_1}\ dB\).
Isolation: It is another way of specifying directivity and it is equal to the sum of directivity and coupling. It is defined as
Isolation \(I=10\log{\frac{P_1}{P_4}}\ dB\).
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Fig. 15(a)