M is between H and V . For 2 cos H t and 2 sin V t , if the former is considerably larger than the latter, M H , and if the latter is considerably larger than the former, M V . Usually for half-wave wall radomes, the amplitude of T H and T V can differ greatly, and several times difference may occur. Compared with traditional half-wave wall radomes, the amplitude of T H and T V of inhomogeneous radomes which provide an excellent impedance match has two characteristics they are much larger (nearly 1) [20], and they are much closer to each other. These characteristics have a great effect on the radome IPD and will be described in Section III. It can be readily found from (3) that when t H and t V are similar, M will be determined by H , V and polarization angle H and V always have the same distribution, whereas their value interval maybe different. If H and V have nearly the same interval, M will have a similar distribution as H and V . Otherwise this will not hold. A special case is that M will have a similar distribution as polarization angle when the interval of H and V is separated greatly, that is, one is considerably larger than the other. These cases will be detailedly discussed in the following. B. The combination of two intervals Consider two intervals [a 1 , b 1 ] and [a 2 , b 2 ] which constitute anew total interval [a 0 , b 0 ], where a 0 =min(a 1 , a 2 ) and b 0 =max(b 1 , b 2 ). The interval lengths are denoted as l 1 , l 2 and l 0 , respectively. The two intervals can be classified into two categories they overlap or they separate. Fig. 3 plots the relation of the two intervals when b 2 ≥b 1 (thus, b 0 = b 2 ). ab) Fig. 3 Relation of two intervals. (a) Overlap. (b) Separation. In Fig. 3, l 3 represents the overlap length, which can be readily understood in (a, whereas in (bi li3 means the distance of the two intervals. Here we define the generalized overlap length as l 3 =min(b 2 , b 1 )-max(a 2 , a 1 ) (4) which is not confined by the assumption b 2 ≥b 1 . Define interval length ratio and overlap ratio by normalizing the interval length and generalized overlap length by l 0 , respectively, that is, 0 / , i i l l l 1, i 2,3 . (5) In this way, 3 l is in the range (-1,1] and a positive/negative value means overlap/separation exists. In (3), if the overlap ratio of the intervals of 3 l H and V is very large (close to 1), M will have the same distribution as H and V , whereas if l 3 is very small (close to -1), M will have a different distribution. When is close to -1, consider two cases 3 l (1) V > H . This is the common casein radome design. In this way, as shown in Fig. bi Vi is close to the maximum value of the total interval and H is close to the minimum value. From (3), it can be seen that when is large (close to
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