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Home Mediumfrequency Broadcast Antennas Input Impedance in a Directive Array Phase Diagrams  
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Phase DiagramsAuthor: Edmund A. Laport
In the phase diagram for this problem (Fig. 2.25), I_{2} is taken as reference phase, I_{1} will lag by 45 degrees, and I_{3} will lead by 45 degrees. The phase shift across A was found to be 77.5 degrees, the current I_{2} leading the main line current I_{0} by this amount. This brings I_{0} at 77.5 degrees in the diagram. Next the phase lag in the secondary lines is shown with reference to I_{0}, so that the 135degree line and A together total 212.5 degrees. An auxiliary vector is drawn for this.
It is seen that the smallest angle between this auxiliary vector and I_{1} is counterclockwise, the direction of advance of phase. The angle is 167.5 degrees. Network B has been computed to have an advance of 55 degrees, leaving a phase advance of 112.5 degrees to be obtained in network D. For the last branch of the circuit, it is noted that the angle between the auxiliary vector at 212.5 degrees and I_{3} is 102.5 degrees (clockwise). If C is an L network, its phase lag is 66 degrees, and the values are as shown in Fig. 2.28. This leaves a lag of 36.5 degrees for network E.
After completing the synthesis of network E we have the circuits and values shown in Fig. 2.30. Now we note that networks A, B, and C all have a parallel reactance directly across the main line. Thus, their combined parallel value can be obtained by using one reactance instead of three. There are values of j87, j536, and j425 in parallel, which is equivalent to j83.5 ohms. Combining all the circuits for the system, we have the diagram of Fig. 2.31. See Chap. 5 for a simple method of network synthesis for problems of this type.


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