A Method for Measuring Amplitude and Phase of Each Radiating Element of a Phased Array Antenna


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1 Electronics and Communications in Japan, Vol. 65B, No. 5, 1982 A Method for Measuring Amplitude and Phase of Each Radiating Element of a Phased Array Antenna Seiji Mano and Takashi Katagi, Regular Members Information Systems and Electronics Development Laboratory, Mitsubishi Electric Corp., Kamakura, Japan 247 SUMMARY In the phased array system, excitation amplitudes and phases based on the design are specified for each antenna element in order to synthesize desired beam scannings and radiation patterns. However, due to fluctuations of antenna and feed network characteristics, the amplitude and phase of each antenna element deviate from the desired values. To correct these deviations, the amplitude and phase of each antenna element must be accurately measured under specific operating conditions. In this paper, we employ variable phase shifters connected to the antenna elements and measure only the amplitude variation of the composite electric field of the entire array when the phase of each element is modified. The rotating element electric field vector method in which the measured amplitude variation is numerically processed for obtaining the amplitude and phase of the particular element is theoretically discussed and experimentally tested for its usefulness. The present method can be easily attained by simply adding software to the computercontrolled phased array system. 1. Introduction In a phased array system consisting of many antenna elements (henceforth referred to simply as elements), the radiating beam is controlled by means of variable phase shifters. To realize desired radiation characteristics such as beam scanning, low side amplitude and phase must be established for each element. However, in general, the amplitude and phase of each element deviate from the desired values in the array environment due to characteristic fluctuations caused by mechanical errors and ambient effects. Therefore, these deviations must be compensated for. To this end, it is necessary to know accurate values of the amplitude and phase of each element in the array operation. Although the conventional nearfield measurement of the antenna by means of a field probe [l] can be used for amplitude and phase measurement of the element, measurement errors by the probe itself can be generated and a complicated mechanism for precise scanning of the probe is needed [2]. Another method in which correct phases are established by a microcomputer with detector circuits for the interelement phase difference of elements installed in the feed network cannot be used for an array consisting of more than ten elements because analog phase shifters are used and control is done with a closed circuit [3]. Yet another scheme operates on each bit of the phase shifters in the operating condition of the array and monitors bit errors by evaluating the signal received by a test antenna placed near the array [4]. In this scheme, both the amplitude and phase of the received signal need to be measured and the detected phase must be compared with the known reference phase. In this paper, we present a new method which does not require extra equipment or reflobe pattern and pattern synthesis, appropriate erence values. We employ variable phase 58
2 2.2 Expressions for the amplitude and phase of the element In Fig. 1, the amplitude and phase of the composite field vector in the initial state are denoted by EO and $ and those of the nth element by En and Qn. When the phase of this nth element is varied by A, the composite field is ;= (Eo el'o  E,,&'n ) +En &('m+d) (1) Fig. 1. Vectors of radiated field of each element and array. shifters connected to each element of the phased array. We measure only the amplitude variation of the composite electric field of the array when the phase of one of the elements is changed under the operating condition. By numerically processing the results, we obtain the amplitude and phase of this particular element [5]. The present method can be realized by adding sogtware to the phased array system controlled by a computer. Since only the amplitude variation of the composite electric field is measured, the accuracy is better than that for the method requiring phase measurement. In the sequel we discuss the theory of the present method and investigate its usefulness by comparison of experimental results with those of the directcoupled pickup method. 2. Measurement Theory 2.1 Measurement principle As shown in Fig. 1, the composite field vector of an array in a specific direction is given by superposition of the field vectors of the elements. When the phase of an element is changed by means of a phase shifter, the composite vector varies as the element field vector rotates. We measure the amplitude variation of the composite vector and determine the amplitude and phase of the element from the measured results. This is the principle of the present method. Note that Fig. 1 exhibits the situation in a specific observation direction. The element field vector is proportional to the product of the radiated field in such a direction and the excitation amplitude and phase of the element. Hence, in the present method, we take into account the fluctuation of radiation characteristics of the element 3s well as the excitation amplitude and phase. The aperture phase setting is disturbed appropriately from the cophasal condition in the observation direction so that the contribution of each element to the field variation is sufficiently large for measurement. We now define the relative amplitude and relative phase of the nth element as k =  En EO x = #n#o (3) We modify (1) so that the relative power expression of k is (see Appendix 1) where sinx tando = COSX  k Equation (4) indicates that the composite power Q varies cosinusoidally as the phase of one of the elements changes. From (4), it is seen that 6 is the phase making Q the maximum. From (4), the ratio of the maximum and minimum of Q is given as Hence, (Yfk r2 = (Yk)2 r=*(jq) From these r and Ao, the relative amplitude k and the relative phase X of the nth element are obtained as follows depending on the sign of r in (8) (see Appendix 2). (i) For the positive sign in (8) (the first solution) kk  1 JT+2r cos A, +r2 (ii) For the negative sign in (8) (second solution) r 59
3 where Therefore, if we measure the change in the composite power Q of the array as the phase of the nth element is changed and obtain (1) Ao: the phase making Q maximum and (2) r: the ratio of the maximum and minimum of Q, then the relative amplitude and the relative phase of the element are given by (9) and (1) or (11) and (12). Fig. 2. Relation between k and Y. 2.3 Interpretation of the two solut ions Due to different signs in (8), two sets of solutions are obtained for the relative amplitude and phase, k and X, of the element. Figure 2 shows the relation between the element field vector (amplitude k) normalized by the composite field amplitude Eg and the composite field vector (unit amplitude). Y in the figure is clearly the difference between the composite and element vectors. Since r in (7) is the ratio of the maximum and minimum levels of the power, always r > 1. Then, from the inequality relations between Y and k,rtakesoneof the signs in (8). For k < Y, r= (14) Yk In this case, the varying vector k added to the consant vector Y provides the maximumtominimum ratio of the composite vector. On the other hand, if k > Y, we obtain from (8) k +Y r=  k Y This case is in effect a superposition of the varying vector Y on the constant vector k so that the maximumtominimum ratio is expressed. For Fig. 2(b), kl is Y and k2 is k and, hence, the correct solution is k2. It is necessary to obtain both kl and k2 and to select the correct solution by the method described later. This is because, in general, inequality of k and Y is not known. We now study the relation of three vectors having amplitudes kl, k2 and Y for the case of k < Y. Let the three vectors be f, = kl ejx1 (16) f, = k, (17) Y = YeJ3 (18) Fig. 3. Relation between kl, k2 and Y (for the case of k = kl < Y). Then, from (9), (lo), (11) and (12), where * r K, =  { (cosdo+r) + j sin do 1 R2 (19) R = dl+v cos A, +f2 (21) Hence, with * as the symbol for complex conjugate quantities, we obtain i, +&*=I (22) On the other hand, as shown in Fig. 2(a), Therefore, from (22) and (23) we get *. y = K,* = k2 e ixa (24) The relation of the three vectors with amplitudes kl, k2 and Y is as shown in Fig. 3. In the case of k > Y, we get k = k2 [Eq. (ll)] and a similar vector relation is satisfied. 2.4 Discrimination of the solution The following three methods are conceivable for discriminating two sets of solutions. (a) The element vector is rotated once by changing the element phase. If the phase change of the composite field is less than 18, we choose kl. Otherwise, k2 is chosen. 6
4 (b) Obtain two sets of soiutions in the two states with different initial phase distributions. Choose as the solution the set for which values of kejx remain identical. (c) By adjusting the phase of each element, set the initial composite vector EO such that k < Y always holds. Choose the set for kl. Fig. 4. Case that only El is too large. Of these three, (a) is relatively simple for discrimination. However, it requires both the amplitude and the phase of the composite field. Although there is a possibility of erroneous discrimination in method (b) due to measurement errors, correct discrimination can be attained if the number of initial settings is increased. Method (c) cannot be applied to the cases in which the amplitude of one particular element En is extremely large, as in Fig. 4, and k < Y cannot be attained even when all the remaining elements are adjusted in phase. However, this method is applicable to the cases in which none of the elements has an extremely large amplitude. 2.5 Leastsquare approximation of measured values Theoretically, the composite field amplitude (power) versus the element phase changes in a cosinusoidal manner. In practice, however, the measured values fluctuate due to measurement errors in the maximumtominimum ratio r and the phase A giving the maximum, which are needed for computing the amplitude and phase of the element. Therefore, more accurate values may result if a cosinusoidal curve (4) that fits the measured values best is derived and r and A are obtained from such a curve. This procedure also makes numerical processing easier via computer. Such curves may be derived by means of the leastsquare approximations (LSA). 3. Experimental Discussion 3.1 Comparison with pickup method We use a 32element linear array operated in the X band (~OGHZ range). Experimental results are shown for the case where the phase is adjusted so that cophasal excitation occurs in the broadside direction. Also given are the results by the conventional pickup probe method for detecting the amplitude and phase of the element. The designed amplitude distribution is 32dB linear taper and is fixed. Analoglphase shifters are connected to each element. In the pickup method, an antenna identical to the element (circular horn) is used as the probe and the amplitude is detected by contacting the probe with the aperture of the element in order to obtain mechanical accuracy. This mechanism is for avoidance of positional irregularity in the nearfield measurement. In the new method, the observation point is in the broadside direction of the array and the aperture initial phase was appropriately disturbed from the cophasal condition. Hybrid circuits and circulators have been used in the feed network of the array to eliminate the effect of the circuit. Figure 5(a) shows the measured radiation pattern in the plane containing the array axis when the phases are set by the pickup method. Figure 5(b) is the corresponding result based on the new method. In both parts of this figure the dashed lines indicate the computed values when ideal amplitude and phase distributions are given. In the pickup method shown in Fig. 5(a), the sidelobe level is 22 db, which is substantially higher than the computed db. On the other hand, in Fig. 5(b) based on the new method, the sidelobe level is improved to db. The difference in the phase shift set by the two methods is shown in Fig. 6. The phase shift set has a maximum of 22' difference. Although the sidelobe level in Fig. 5(b) is still higher than the computed value, this difference is considered to be caused by poor reproducibility of the phase shift set in the analog phase shifters used for six elements each at both ends of the 32element linear array. It is clear, however, in parts (a) and (b) of Fig. 5 that the phase set accuracy is better in the new method than in the pickup method. 3.2 Experiments with a lowsidelobe antenna Here we report the results of experiments conducted with an antenna system in which the linear array described in the previous section is used as the feed array (primary radiator) of a 1.8 m x 1.8 m reflector. The antenna is oriented into the boresight and the aperture initial phase distribution is disturbed from the cophasal condition. A uniform phase distribution is realized by the new 61
5 mea cal. Observ. angle (deg) Observ. angle (deg) (a) Pickup method (b) This paper's method Fig. 5. Radiation patterns due to two phase setting methods, pickup method and this paper's method. 3 *O = 1 r 5  % 1 r a 2 j\. /,\,./\,  to'/ 25. $ CI Element number meas.  LSA Fig. 6. Difference of phase shift set by this paper's method and pickup method. I I I I A (deg) Fig. 7. Amplitude variation of array field by varying phase shift of one element. method. Such operating conditions as the fre cussed in 2.5. The standard deviation of the quency and array amplitude distribution error between the approximate curve and the (lowsidelobe distribution) are kept identical measured values at all points is.6 db in to those in 3.1. the case of Fig. 7. For all 32 elements, the maximum is.25 db and the average is (1) Element phase change and composite.6 db. Within the range of experiment, amplitude change the variation of the composite amplitude due to the element phase agrees well with the Figure 7 is an example of the measured theoretical curve given by [6]. variation of the composite amplitude when the phase of one of the elements is changed. The (2) Element amplitude solid line is a cosinusoidal curve approximated in the leastsquare sense (LSA) dis The composite amplitude variations described above were measured for all 32 62
6 1  m v al U 7.z 1 s a. al. w c) a a 2c (3) Radiation pattern Let us fix the amplitude distribution and set the phase based on the related phase Xi corresponding to kl in Fig. 8. The radiation pattern measured in the plane containing the array axis is shown in Fig. 9 for this case. The dashed lines in the figure show the computed values. In the angular range on the left of the main beam, the pattern is not shown because the effect of the ground reflection prevented measurement. Figure 9 shows that the sidelobe level of db agrees well with the designed value and the phase shift set on the aperture is accurately realized although the sidelobe structures are somehwat different. Fig. 8. I I I I Element number Distribution of amplitude kl and k2 of element. 1bII 2oc I it1 i 9 4. Conclusion A theoretical discussion was conducted and experimental verification was given for the usefulness of a new element method called the element fieldvector rotation method. In this method, the composite field amplitude of a phased array due to variation of the element phase shift was measured and the result was used for identifying the amplitude and phase of the element. The present method can be adapted by the addition of software to the phased array system with computercontrolled phase shifters. It can also be used for diagnosis of defects of elements and phase shifters as well as for checking wiring errors in the feed network. Acknowledgement. The authors thank Mr. T. Tsutsumi of the Communication Equipment Division of Mitsubishi Electric Company for his experimental assistance. REFERENCES Fig. 9. Low sidelobe pattern by uniform phasesetting due to this paper's method. 2. elements under the array condition. The distributions of the two solutions kl and k2 of the relative amplitude obtained numerically in the leastsquare approximation are shown in Fig. 8. The o symbols in this figure are the products of the measured amplitude of the element radiation field in the boresight direction and the designed excitation amplitude of that element. These o symbols and kl are well correlated, and hence kl is the correct solution in this case J.D. Dyson. Measurement of near field of antennas and scatters, I.E.E.E., Trans. Antennas and Propag., E, pp (July 1973). W.A. Harmening. Implementing a nearfield antenna test facility, Microwave J., 22, 9. pp (Sept. 1979). A.R. Skatvold, Jr. Beam steering antenna control technique, 1981 I.E.E.E. MTTS Internat. Microwave Symp. Digest, pp (June 1981). J.F. White. Phased array technology workshop, Microwave J., 3, 2, pp (Feb. 1981). Mano and Katagi. A method for measuring amplitude and phase of phase array antenna elements in the operating condition, Natl. Conv. Record of I.E.C.E., Japan, 69 (1981).
7 APPENDIX Hence, 1. Derivation of (4) From (1) clr (3), i = {E,eJX+E, (el  1) 1 el '(x+&) (Al) I h I = (Eo cosx+e, cos A  E,, ) +(E,sinXE,,sind)' NOW, we obtain where = (E,COSXE,)~ +Eo2 sin2x+e,2 +2E,{(~ocosXE,)cos~EosinXsind~ (A21 substituting Y2 = (cosx k +sin2x (5) sinx sind ) =Y2+kz+2kY cos (A+do) (4) we get (A4 1 From (5), (6) and (A4) we eliminate Y and obtain the following simultaneous equations for k and X: r+l sinx= (7) k sindo r (z) cosx= k (1+ cos do} (A6) Solution of the above results in (9) and (1). since we get (ii) When the sign in (8) is negative,?= (yk) Y= ( 2 ) k Eliminating Y from (5), (6) and (A8), we get the following simultaneous equations for k and X: sid= ( s+l e ) k sindo 2. Derivation of (9) Q (12) since (i) When the sign in (8) is positive, 7 G Yk Solution of the above results in (11) and (12). 64
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