fourth order node is the last in a chain of four PRR’s connecting the PCC’s at that fourth order node to the reference element of the ARA. The error in the value of the phase reference produced by this last PRR is the sum of the errors arising in all the PRR’s in the chain. If these errors arise from independent and identical random processes in each PRR, then the probable error of the output of the last PRR is [] (PE) where PE is the probable error of each PRR. Thus the error buildup due to repeated regeneration of the phase reference is moderate even for large arrays. B. Phase Conjugation Circuits The simplest phase conjugation circuit (PCC) is shown in Figure 4. Unfortunately, this circuit is impractical because of isolation problems. Unwanted coupling occurs in three ways: 1) through the imperfect circulator, 2) leakage from the input to the output of the mixer, and 3) by mutual coupling between neighboring elements of the array. Shifting the output frequency may solve the isolation problem, but we may, depending on how the shifting is done, find that the transmitted beam is no longer retrodirected. For example, the output frequency of this PCC can be shifted simply by offsetting the frequency of the phase reference by Aco. The result is a sort of approximate phase conjugation which, in a planar ARA, causes a pointing error called ’’squint” given by for small Aco, where 0 is the scan angle (angle between direction of arrival of the pilot signal and the normal to the array). Aco has a practical lower bound due to the imperfect isolation of real diplexer filters. Therefore, A0 may be too large for applications requiring both very precise pointing and a wide scan range. (4)
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