Design of A Multimode Monopulse Feed Horn

Transcription

1 Design of A Multimode Monopulse Feed Horn (Ren Chun)

2 Design of A Multimode Monopulse Feed Horn (Ren Chun)

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4 CONTENTS Abstract List of Firues List of Tables Abbreviations I. Introduction 1 II. Modal Analysis of The Multimode Monopulse Feed Horn Proposed Structure Ideal Distribution of Electric Field at the Horn Aperture Principle of Selecting Utilized Modes Combination of Modes Determination of Mode Ratios Calculation of the Aperture Distribution and Radiation Pattern 15 III. Design and Simulation of the Multimode Monopulse Feed Horn Design Requirements Design Procedure Design of the H-moder and E-moder Determination of the Lengths for the Phase Sections ans Horn Final Design 28

5 3.3 Simulation of the Multimode Feed Horn 30 IV. Conclusions 42 References 44 Acknowledgement 47

6 Design of A Multimode Monopulse Feed Horn * Ren Chun Department of Radio Engineering Graduate School, Chungbuk National University Cheongju, Korea Supervised by Professor Ahn, Bierng Chaerl Abstract Analysis and design of a multimode monopulse feed horn for Ka-band applications are presented in this thesis. The theory of optimum mode combination of a multimode monopulse feed horn is described. The principle of selecting higher-order modes for a single aperture multimode feed horn is presented for low side lobe and pattern symmetry. The distribution of the aperture electric field and the radiation patterns resulting from the optimum combination of modes is given. The design method of the multimode monopulse feed horn is presented, and the design procedure is described in detail. Design parameters of the multimode feed horn are optimized using the commercial electromagnetic software MWS TM by CST, from which the final design is derived. The designed multimode feed horn has a simple and compact structure that is easier to manufacture and more aseismatic. The simulation shows a good performance with low side lobes, a good agreement between the E-plane and H-plane of the sum radiation pattern, and the azimuth difference radiation pattern agrees well with the elevation difference pattern. * A thesis for the degree of Master in February 2007.

7 List of Figures Figure 1.1 Typical sum and difference patterns of a multimode feed 1 Figure 2.1 A multimode feed horn: (a) diagram; (b) structure 4 Figure 2.2 Input signals in four waveguides for (a) sum channel, (b) azimuth difference channel, and (c) elevation difference channel 5 Figure 2.3 (a) Horn aperture and its coordinate system and electric field distributions in (b) sum channel, (c) azimuth difference channel, and (d) elevation difference channel 6 Figure 2.4 Plots of E y in (a) x and (b) y directions for m = 1, 2, 3 and n = 0, 1, 2, 3 8 Figure 2.5 Mode combination for the sum channel 10 Figure 2.6 Mode combintion for the azimuth difference channel 11 Figure 2.7 Mode combination for the elevation difference channel 12 Figure 2.8 Construction of the sum channel aperture field in (a) x direction and (b) y direction 13 Figure 2.9 Construction of the elevation difference channel aperture field in (a) x direction and (b) y direction 14 Figure D distribution of electric field with (a) ideal mode ratios and (b) mode ratios shown in table Figure 2.11 Distributions of electric field in (a) sum channel and (b) difference channel 18

8 Figure 2.12 Computed radiation patterns 19 Figure 3.1 (a) Structure and (b) parameters of the multimode feed horn 22 Figure 3.2 Configuration of a common H-moder 23 Figure 3.3 H-moder of the multimode feed horn: (a) configuration; (b) simulated structure 24 Figure 3.4 Configuration of the E-moder 26 Figure 3.5 View of the multimode feed horn from (a) outside, and (b)-(c) inside 29 Figure 3.6 Ports setting of the multimode feed horn 30 Figure 3.7 S-parameters including the (a) magnitudes and (b) phases 32 Figure 3.8 2D aperture distributions in the sum and difference channels 34 Figure 3.9 Normalized aperture distributions in the sum and difference channels34 Figure D patterns of the multimode feed horn in the sum and difference channels 39 Figure 3.11 Normalized sum and difference radiation patterns 40 Figure 3.12 Phase patterns in the sum channel with different phase centers 41 Figure 3.13 Phase patterns in the sum channel 42 Figure 3.14 Phase patterns in the difference channel 42.

9 List of Tables Table 2.1 Modes generated by H- and E-moders 9 Table 2.2 Optimum mode amplitudes realizable with waveguide junctions 15 Table 3.1 Requirements of the design 21 Table 3.2 Simulated mode ratios 25 Table 3.3 Dimensions of the multimode feed horn 29 Table 3.4 Excitation setting of the ports 30 Table 3.5 Important parameters of the sum and difference radiation patterns 41

10 I. Introduction It is of great importance for a tracking radar system that the monopulse antenna offers a good performance, which also means that a good monopulse feed is needed. Figure 1.1 shows ideal sum and difference patterns of a monopulse feed horn. The ideal shape of a sum pattern is a Gaussian beam of the specified beamwidth at -10 or -15 db level with no sidelobes. The two difference channels which are azimuth difference channel and elevation difference channel should have same radiation patterns and should have a deep null at the center. It is perferrable that the difference pattern has the same beamwidth as the sum pattern and no sidelobes. In reality the ideal monopulse feed pattern is difficult to achieve so that we try to realize a feed whose pattern is as close to the ideal one as possible. Figure 1.1 Typical sum and difference patterns of a multimode feed The monopulse feed pattern is realized using either a single common horn or

11 multiple horns (e.g. 4, or 12 horns) [1]-[2]. The multi-horn multimode feed could obtain a good compromise between the sum radiation pattern and the difference radiation patterns. However, a complicated feed network is required, the coupling between the radiation horns needs to be considered, and the radiation aperture is large for a compact antenna that it will raise up the level of the side lobes. In this paper we consider the single-horn monopulse feed which requires a less complicated comparator network. Previous work has given several design of this kind of multimode monopulse feed. The five-mode feed given in [3]has a high side lobes in elevation difference channels, the seven-mode feed given in [4]-[5] is very difficult to fabricate at W-band, and is not aseismatic. A simulation design of an eight-mode feed given in [6] has a good performance. Generally, the multimode feed utilized more high-order modes will increase the difficulty in the design, however, it seems that they will have a better performance. In this paper, we present the theory of the multimode monopulse feed horn design firstly. The method of selecting proper high-order modes in the multimode feed design is given, then, the theory of combination of modes in the design of multimode feed is described detailed with formulas and graphs. Principle of obtaining theoretic mode ratios is given. At last, the distribution of electric field in the aperture and the radiation patterns of the multimode monopulse feed are computed. Based on the above research and analysis, the method of design of a multimode mnopulse feed horn is given. Finally, an eight-mode monopulse feed horn working at 35GHz was designed. The optimize design and simulation are performed using the MWS CST 2008 software. Simulation result show that this design of multimode monopulse feed horn has a radiation pattern with low side

12 lobe levels and good radiation patterns for all the sum and difference channels which achieve the design requirements.

13 II. Modal Analysis of the Multimode Monopulse Feed Horn 2.1 Proposed Structure A multimode feed consists of four input waveguides, two H-moders, one E-moder, and a horn section terminating in a common radiating aperture as shown in Figure 2.1. The order of the H-moder and E-moder can be exchanged. It becomes possible that high-order modes could be controlled respectively. (a) (b) Figure 2.1 A multimode feed horn: (a) diagram; (b) structure. It is well-known that a multimode monopulse feed horn working on three

14 channels which are the sum channel, the azimuth difference channel and the elevation difference channel. This is realized with the aid of the monopulse comparator connected to the four input waveguides which can be seen in figure 2.2. (a) (b) (c) Figure 2.2 Input signals in four waveguides for (a) sum channel, (b) azimuth difference channel, and (c) elevation difference channel. The fundamental mode is excited in the four input feed waveguides where only the dominant TE 10 mode propagates. Higher-order modes are generated in the moders which are actually an abrupt step in waveguide across section. The horn is used for controlling the beamwidth of the feed. Negligible levels of higher-order modes are generated in the junction between the E-moder and the horn. The phase of individual modes are adjusted by properly choosing the lengths of moders and the horn. 2.2 Ideal Distribution of Electric Field at the Horn Aperture Figure 2.3 shows the horn aperture and the associated coordinate system, where we usually use a square aperture, i.e., a = b. Figs. 2.3(b), 2.3(c), and 2.3(d) show

15 the ideal distribution of the co-polarized electric field (E y ) for the sum, azimuth and elevation difference channels. The ideal distribution is in reality hard to achieve so that one tries to the distribution closely resembling the ideal one. (a) (b) (c) (d) Figure 2.3 (a) Horn aperture and its coordinate system and electric field distributions in (b) sum channel, (c) azimuth difference channel, and (d) elevation difference channel. 2.3 Principle of Selecting Utilized Modes General expressions for the propagating modes in a rectangular waveguide are given by following equations with the coordinate system defined in Figure 2.3 [7],[8]. For TE mn modes, cos cos (1)

16 cos sin (2) sin cos (3) and for TM mn modes, sin sin (4) cos sin (5) sin cos (6) Plots of E y in x and y directions are given in Figure 2.4 for a few modes. From this figure it is clear that we have to use m = 1, 3, 5, and n = 0, 2, 4, for sum patterns in x and y directions, respectively since the aperture field should have a maximum value at the center and be symmetric around the center line. Similarly, for difference patterns we use m = 2, 4, 6, and n = 1, 3, 5, etc., yielding an aperture distribution which is zero at the center and antisymmetric around the center. (a)

17 (b) Figure 2.4 Plots of E y in (a) x and (b) y directions for m = 1, 2, 3 and n = 0, 1, 2, 3. Another consideration is that we should use as few higher-order modes as possible, since it will increase the difficulties in the design of a multimode feed. For example, it is difficult to make many higher-order modes have the same phase at the horn aperture. For the sum channel, the first mode being utilized is the TE 10 mode which is the fundamental mode of the rectangular waveguide, and then, in order to make the distribution of electric field along the y axis in bell-shaped, the higher-order mode TE 12 or TM 12 is selected. We use HE mn to denote either TE mn or TM mn or a combination of both. For the mode number n greater than 0, we do not differentiate the TE mode from the TM one and vice versa, because they have the same tangential field. Finally, TE 30 mode is selected to make the distribution of electric field in feed aperture along the x axis in bell-shaped. The utilized modes in azimuth difference channel and elevation difference channel can be determined in the similar way. In the azimuth difference channel, we can use only one mode which is the TE 20 mode for a simple design. However, the distribution of the electric field along the y axis will be uniform.

18 Therefore, a better choice is to utilize the TE 20 and HE 22 modes. In the elevation difference channel, the HE 11 mode is used in a five-mode multimode feed design, the radiation pattern of this design has a high side lobe level. An improved design which is a seven-mode multimode feed utilized HE 11 and HE 31 modes, and the performance of this design is improved. However, we can still improve this design by adding the HE 13 mode which can make the distribution of electric field along the y axis goes to zero at the edge of the feed aperture. In conclusion, Table 1 shows modes generated by H- and E-moders in the sum and difference channels. Table 2.1 Modes generated by H- and E-moders. 2.4 Combination of Modes Since the modes utilized in the sum and difference channels have been determined, the combination of modes for each channel could be easily found. Assuming A 10, A 30, A 12, A 20, A 22, A 11, A 13, and A 31 are modal amplitudes for each mode utilized in the sum and difference channels. Their values will be

19 determined in the later section so that the electric field distributions in x and y directions are as similar to that shown in figure 2.3 as possible. Firstly, the aperture distribution of the sum channel shown in Figure 2.3(b) can be expressed by sin sin sin cos (7 At y = b/2, we have sin sin sin (8) and at x = a/2, we have cos (9) Figure 2.5 shows the mode combination for the sum channel. Figure 2.5 Mode combination for the sum channel Similarly for the azimuth difference channel, E y is given by, sin sin cos (10 At y = b/2, we have sin sin (11)

20 and at x = a/4, we have cos (12) The mode combination for the azimuth difference channel is shown in figure 2.6. Figure 2.6 Mode combination for the azimuth difference channel Finally, E y for the elevation difference channel is given by, sin sin cos sin cos (13 At y = b/4, we have sin sin sin (14) and at x = a/2, we have cos cos cos (15) Figure 2.7 shows the mode combination for the elevation difference channel.

21 Figure 2.7 Mode combination for the elevation difference channel. 2.5 Determination of Mode Ratios By proper adjusting the mode ratios, one can make the distribution of the electric field in feed aperture give a good performance. First for the sum pattern, from Eqs. (7)-(9) and Figure 2.5, we should have (reference amplitude) Here we have only one equation and two unknowns A 30 and A 12. Defining r = A 30/A 12, we adjust r so that E y has as similar shape as possible in x and y directions. Figure 2.8 shows the graphs of E y in x and y directions for various values of r, from which we find the optimum value of r is 0.3 leading to the following design formula.

22 (a) Figure 2.8 Construction of the sum channel aperture field in (a) x direction and (b) (b) y direction For the azimuth difference channel, we use Eqs. (10)-(12) and Figure 2.6 to obtain

23 As we can see later, horizontal and vertical patterns of the azimuth difference channel are neatly realized using only two modes, viz. TE 20 and HE 22. Finally for the elevation difference channel, we should have (reference amplitude) Here again we have only one equation and two unknowns A 31 and A 13. Defining s = A 31 / A 13, we adjust s so that E y has as a sum shape close to that of the sum channel in x direction, and a difference shape very similar to that of the azimuth channel. Figure 2.9 shows the graphs of E y in x and y directions for various values of s, from which we find the optimum value of s is 0.3 leading to the following design formula. (a)

24 Figure 2.9 Construction of the elevation difference channel aperture field in (a) x (b) direction and (b) y direction In the above analysis, amplitudes of higher-order modes A 12 and A 13 are greater than that of the fundamental TE 10 mode, which in reality is difficult to realize using the step junction in the waveguide. In fact there is a maximum level of the amplitude of a higher-order mode realizable using E- or H-plane steps so that we have to determine mode amplitudes with this constraint in mind [9]. Table 2 shows a proper set of mode ratios. Table 2.2 Optimum mode amplitudes realizable with waveguide junctions. Σ Δ Δ A 10 A 30 A 12 A 20 A 22 A 11 A 31 A

25 2.6 Calculation of the Aperture Distribution and Radiation Pattern From the mode amplitudes shown in table 2.2, using the Eqs. (7)-(15), the distribution of electric field in the aperture for the sum and difference channels can be computed. The calculation was performed using the MATHCAD 14 program. Figure 2.10 shows the 2D distribution of the electric field with both the ideal mode ratio and the mode ratio shown in table 2.2. The distribution of the electric field in both sum and difference channels for the mode ratio shown in table 2.2 is shown in Figure (a) Σ (b) Σ (a) AZ- Δ (b) AZ-Δ

26 (a) EL- Δ (b) EL-Δ Figure D distribution of electric field with (a) ideal mode ratios and (b) mode ratios shown in table 2.2. It can be seen from Figure 2.11 that aperture distributions in sum channel and azimuth difference channel agree well with the expected distributions. However, the distributions of electric field in elevation difference channel are little different from the expected ones with this assign of mode ratios. If we make the distribution in elevation channel at the edge to be zero, the aperture distribution of elevation difference channel will be quite different from the aperture distribution of azimuth difference channel, then the radiation patterns in the two difference channels will not have a good agreement.

27 (a) Figure 2.11 Distributions of electric field in (a) sum channel and (b) difference (b) channel. The radiation pattern of the multimode feed can be obtained using the integration method [10] from the aperture distribution shown in Figure The computed radiation patterns of the multimode feed are shown in Figure 2.12.

28 Figure 2.12 Computed radiation patterns Radiation pattern in Figure 2.12 shows a good performance of a multimode monopulse feed. The E-plane pattern and H-plane pattern in sum channel agree very well, and the radiation pattern in the azimuth difference channel has a good agreement with that in the elevation difference channel as well. All of the radiation patterns have a low side lobe level.

29 III. Design and Simulation of the Multimode Monopulse Feed Horn 3.1 Design Requirements The multimod monopulse feed horn is used in the tracking radar system as a feed of a reflector antenna such as the cassegrain antenna. The center frequency is defined at 35GHz. There are several important requirements for the design of the multimode monopulse feed horn. Firstly, it is the aperture size of the multimode monopulse feed horn. In order to decrease the side lobe level of the radiation pattern from the reflector antenna, the blockage by the feed horn needs to be as small as possible which means the aperture size of the multimode monopulse feed horn should be as small as possible. In another hand, a broad radiation pattern will be obtained due to the small aperture size. Then, a large reflector antenna is also required. Therefore, we must design the aperture of the multimode monopulse feed with that two considerations. A single-aperture multimode monopulse feed horn is the best choice to satisfy this requirement. Secondly, it is the radiation pattern of the multimode monopulse feed horn. A multimode feed horn has three types of radiation patterns due to the three channels applications. The radiation pattern of E-plane and H-plane in the sum channel as well as the radiation pattern of azimuth and elevation difference channels requires to be as same as possible. The -10dB beamwidth for both the sum and difference channels should be as small as possible to realize a compact

30 tracking radar system. It is better to make the beamwidth of the radiation pattern in sum and difference channel as close as possible, however, that is difficult for a single-aperture multimode monopulse feed horn. Finally, the sidelobe level in both sum and difference channel is required to be as low as possible. In summarize, the design goal of the multimode monopulse feed horn is shown in table 3.1. Table 3.1 Requirements of the design -10dB beamwidth Side-lobe level Σ 40-20dB AZ-Δ -20dB 60 EL-Δ -20dB Aperture size f0 3.5 λ*3.5λ 35GHz 3.2 Design Procedure Structure and dimension parameters of the designed multimode monopulse feed horn are shown in figure 3.1(a) and figure 3.1(b) respectively. From figure 3.1 we can see that the main design task is to design the feed waveguides, phase sections A and B following the H-moders, Phase section C following the E-moder, and the radiation horn D. In this section the design procedure will be described in detail, and the determination of the dimension parameters shown in figure 3(b) will be presented.

31 (a) (b) Figure 3.1 (a) Structure and (b) parameters of the multimode feed horn Design of the H-moder and E-moder A moder is actually an abrupt step in cross-section at the beginning of the phase section generating high-order modes. Figure 3.2 shows the configuration of a common H-mode from wich we can see that, When z < 0, the fundamental

32 mode TE 10 propagate through the rectangular waveguide towards z direction. At z = 0, an abrupt step which is the H-moder exist along the x direction, high-order mode TE 30 is generated. Then, from z > 0, TE 10 mode and TE 30 mode propagate together toward z direction in the phase section following the H-moder. Figure 3.2 Configuration of a common H-moder In this design of multimode monopulse feed horn, the H-moders are not the same as the typical one which can be seen in figure 3.3(a), it seems to be a combination of two H-moders which are shown in figure 3.2. However, since there is no separation in the middle of the phase section following the H-moder, we can not treat it as a simple combination of two typical H-moders. Working principle of the H-moder could be explained as following. In the sum and elevation difference channels, the H-moder is excited by TE 10 mode in phase from the two feed waveguides, TE 30 mode is generated at the discontinuity part where z = 0. In the following phase section, there are TE 10 and TE 30 modes. In the azimuth difference channel, the H-moder is excied by TE 10 mode in phase opposition, TE 20 mode is generated at the discontinuity. In this condition, there is only one mode which is TE 20 mode propagated in the following phase section.

33 (a) (b) Figure 3.3 H-moder of the feed horn: (a) configuration (b) simulated structure We using simulation to obtain mode ratios for TE 10 mode, TE 20 mode, and TE 30 mode. The simulation was performed using the commercial software MWS CST2008. The mode ratios including the amplitudes and phases are extracted from the simulated S parameters of the H-moder. The simulated structure can be seen in figure 3.3(b). From table 3 we can see that both the amplitude and phase of the mode ratio of TE 10 mode do not change much as the step-size ratios increasing, this could be also found in the mode ratio of TE 20 mode. However, the mode ratio of TE 30 mode has a remarkable variation versus the changing of the step-size ratios. Same method could be used in the design of the E-moder. Figure 3.4 shows the configuration of the E-moder, it can be seen that the E-moder is excited by the two H-moders A and B. In the sum channel, E-moder is excited by TE 10 and TE 30 mode in phase from the two H-moders, high-order mode HE 12 is generated. In the azimuth difference channel, E-moder is excited by TE 20 mode in phase, HE 22 mode is generated at the discontinuity. In the elevation difference channel, E-moder is excited by TE 10 and TE 30 modes in phase opposition, HE 11, HE 13, and

34 HE 31 modes are generated. Again, mode ratios including the amplitudes and phases of the modes HE 11, HE 12, HE 22, HE 13, HE 31 could be obtained using the method described in the design of the H-moder. The simulated mode ratios are shown in table 3.2. Figure 3.4 Configuration of the E-moder Table 3.2. Simulated mode ratios Sum AZ EL Modes Magnitude Phase (degree) TE TE TM TE TE TE TM TE TM TE TM

35 TE TM By proper adjusting the dimensions of a 1, a 2, b 1, and b 2, a proper set of mode ratios could be obtained which will realize a good performance of the multimode monopulse feed horn. A proper step-size ratios are gotten at the same time. The next step is to determine the waveguide dimensions a 1 and b 1 at the horn throat. From the waveguide transmission theory [9] we know that, if conditions and are satisfied, only selected modes could propagated though the multimode feed horn. Thus, the dimensions a 1 and b 1 are determined, and then, a 2 and b 2 could be determined automatically from the step-size ratios Determination of the Lengths for the Phase Sections and Horn For the feed horn to work efficiently, it is an important task to make all the utilized modes at the aperture in phase in the sum and difference channels. The phase at the aperture for each mode is determined by the lengths of the phase sections A, B, and C, and the length of the radiation horn. Therefore, by proper adjusting the lengths of l, l 1, and l 2, all the propagated modes at the aperture could be in phase. In sum channel to keep the modes in phase, it is required that l, l 1, and l 2 satisfy the following equations: (11) (12) In the same way, in order to make TE 20 and HE 22 of azimuth difference

36 channel, HE 11, and HE 31, HE 11 and HE 13 of elevation difference channel in phase, it is required that l, l 1, and l 2 satisfy the following equations: (13) (14) (15) Here, p, q, r, t, k are integers. is the propagation constant of mode TE mn or TM mn in the moders. It is given by: (16) is the average propagation constant of mode TE mn and TM mn in the horn which is given by: (17) There are five equations and, however, only three unknown parameters, so the equations could not be solved strictly, which means that the modes in each equation can not be made in phase strictly, yet we can make them to be closest to the ideal condition. Another method is using the simulation software to get the optimum solution of these parameters. This could be a better and simple way to find the optimum lengths for each part of the multimode feed horn Final Design The dimensions which have not been determined are the aperture size a and b of the horn, the separation a th and b th between the four feed waveguides, and the length l 3 of the feed waveguide. The dimensions a and b are adjusted to obtain the designed 10dB beamwidth of the radiation pattern. Parameters a th and b th

37 could be optimized by simulation, and the length of the feed waveguide can be arbitrary. Following the design procedure which has been described, after adjusting all the parameters carefully and properly by the simulation, a multimode feed horn with a good performance is obtained at last. The structure of the multimode feed horn is shown in figure 3.5(a)-(c), the optimized parameters of the multimode feed horn are shown in table 3.3. (a) (b)

38 (c) Figure 3.5 View of the multimode feed horn from (a) outside, and (b)-(c) inside Table 3.3 Dimensions of the multimode feed horn (mm) a a 1 a 2 a th b b 1 b 2 b th l l 1 l From figure 3.5(a)-(c) and table 3.3 we can see that the designed multimode feed horn has a aperture size of about. It is of a simple structure which is easily to be manufactured. 3.3 Simulation of the Multimode Feed Horn As we have described, the multimode monopulse feed horn has three working channels which are the sum, azimuth difference, and elevation difference channels. There are four feed waveguides in the multimode feed horn which can be seen in

39 figure 3.5. In the CST program we set four ports at the beginning of the feed waveguide which can be seen in figure 3.6. The input signals for the sum and difference channels are realized by setting the magnitudes and phase for each port which can be seen in figure 3.7. Figure 3.6 Ports setting of the multimode feed horn Table 3.4 Excitation setting of the ports Simulation was performed in the frequency range of 33GHz to 37GHz. The S-parameters including both the amplitude and phase are shown in figure 3.7(a)-(b). Since the symmetry of the arrangement of the four ports, it can be easily found that. Therefore, only the S i1 parameters are shown in the

40 figure. It can be senn that the reflection coefficient is smaller than -25dB and the isolation is smaller than -20dB for almost the full frequency range. (a)

41 (b) Figure 3.7 S-parameters including the (a) magnitude and (b) phase of the multimode feed horn. The simulated 2D distribution of the electric field at the horn aperture is shown in figure 3.8, and the normalized 1D cut of the aperture distribution in the sum and difference channels is shown in figure 3.9. It can be seen that the aperture distributions in the sum and difference channels are not same as the ideal distributions, especially for the E-plane of the sum channel and the elevation difference channel. The apertuer distributions of E-plane in sum channel and the elevation difference channel do not go to zero at the edge of the aperture, thus the side lobes a little higher than the ideal case. The sum distribution in x direction does not agree very well with that in y direction, we make the aperture size a larger than b so that to obtain a good agreement of the radiation patterns. (a)

42 (b) AZ- (c) EL- Figure 3.8 2D aperture distributions in the sum and difference channels

43 Figure 3.9 Normalized aperture distributions in the sum and difference channels The 3D radiation patterns at 35GHz in the sum and difference channels are shown in figure 3.10(a)-(i) from which we can see that and are the co-polarization in the E- and H-plane of the sum channel respectively, in the azimuth difference channel is the co-polarization, and is the co-polarization in the elevation difference channel. The gain of the sum radiation pattern is 19.21dB, which is 2.58dB greater than that of the azimuth difference radiation pattern and 2.85dB greater than that of the elevation difference radiation pattern.

44 (a) G in (b) in

45 (c) in (d) in AZ-

46 (e) in AZ- (f) in AZ-

47 (g) in EL- (h) in EL-

48 (i) in EL- Figure D patterns of the multimode feed horn in the sum and difference channels. The normalized sum and difference radiation patterns at the center frequency which is 35GHz are shown in figure 3.11 and the important parameters of the radiation pattern are summarized in table 3.5. It can be seen from figure 3.11 that in the sum channel, H-plane radiation pattern agrees well with the E-plane radiation pattern, and the azimuth difference radiation pattern agrees well with the elevation difference radiation pattern. The side lobe is lower than -29.1dB and -24.4dB in H- and E-plane for the sum radiation pattern respectively. The side lobe is about -30.6dB for the azimuth difference radiation pattern, and -24.5dB for the elevation difference radiation pattern. A zero depth in both the azimuth and the elevation difference channels is obtained.

49 Figure 3.11 Normalized sum and difference radiation patterns. Table 3.5 Important parameters of the sum and difference radiation patterns H-Σ E-Σ AZ-Δ EL-Δ Gain (db) Side lobe (db) Beamwidth (-10dB) 17.8 ± ±0.2 The phase center is calculated for a range of ±18 which is approximately the -10dB beamwidth of the sum radiation pattern. The location of the aperture center is (0, 0, 0), the phase center of the E-plane of the sum radiation pattern is located at (0, 0, -9.83), however, the phase center of the H-plane of the sum radiation pattern is (0, 0, 5.09). The E-plane phase pattern and H-plane phase pattern with different phase centers are shown in figure 3.12.

50 Figure 3.12 Phase patterns in the sum channel with different phase centers It can be seen from figure 3.12 that there is only a slight changing in both the the E- and H-plane phase patterns of the sum channel, however, the phase centers for the two patterns are different. We have to find a phase center for both the E- and H- plane phase patterns in the sum channel. After carefully adjusting and comparison the phase center for the sum radiation pattern is determined to be (0, 0, -3.7). The E- and H-plane phase patterns of the sum radiation pattern is shown in figure The phase patterns of the azimuth and elevation difference channels are shown in figure 3.14, from which we find that the phase center for the sum channel is also the phase centers for the difference channels.

51 Figure 3.13 Phase Pattern in the sum channel Figure 3.14 Phase pattern in the difference channel. The phase variation in -10dB beamwidth could be neglectable in both the

52 azimuth and elevation difference channels. It has a variation of about 22 which is acceptable in the E- and H-plane phase patterns of the sum channel.

53 IV. Conclusions In this thesis, the analysis and design of a mulitmode monopulse feed horn for a tracking radar system applications are presented. From the ideal distribution of the electric field at the aperture of a single-aperture multimode monopulse feed horn, the modes which are utilized in the feed horn for the sum and difference channels are selected. There are totally eight modes which are the TE 10, TE 30, and HE 12 in the sum channel, TE 20 and HE 22 modes in the azimuth difference channel, and HE 11, HE 13, and HE 31 modes in the elevation difference channel utilized in this design. The mode combination for the sum, azimuth difference, and the elevation difference channels are presented. The mode raios for each mode are determined by theoretical analysis and program optimization. The distribution of the electric field at the aperture is computed for each channel. The sum radiation pattern and the difference radiation patterns are computed. The computed radiation patterns show a good performance with low side lobes, good agreement between the H-plane and E-plane of the sum radiation pattern, and the azimuth difference pattern agrees well to the elevation difference pattern. Based on the modal analysis of the multimode feed horn, the design procedure has been given. The mode raitos extracitng from simulation which is performed by the commercial software MWS CST2008 has been introduced, and the E-moder and H-moder are designed from the simulated mode raios. The method of making the modes in phase at the horn aperture has been presented. The final design of the multimode monopulse feed horn shows a simple and compact structure which can be easily manufactured. The 3D and 2D radiation

54 patterns in the sum channels and the two difference channels are presented and good performance with low side lobes and good symmetry has been obtained. The phase patterns in each channel have been presented. The S-parameters of the feed waveguide has also been presented which shows a low reflection coefficient of the multimode feed horn.

55 References [1] P. W. Hannan and P. A. Loth, "A monopulse antenna having independent optimization of the sum and difference modes," IRE Conv. Rec., No. 9, Pt. 1, pp , Mar [2] L. J. Ricardi and L. Niro, "Design of a twelve horn monopulse feed," IRE Conv. Rec., No. 9, Pt. 1, pp , Mar [3] Y. P. Wang, "Design of millimeter tracking radar system," Shipboard Electronic Countermeasure, Vol. 1, pp , Jan [4] U. Lidvall and M. Persson, G. Larsson, "Broadband multimode feed for monopulse tracking antenna," Dig. 18th European Microwave Conf., pp , Oct [5] X. L. Ding, "Design of the feed system of millimeter monopulse feed system," Remote Monitoring and Control, Vol. 25, Season 1, pp , Sept [6] R. J. Liu and W. B. Dou., "Design and analysis of 3mm multimode monopulse feed," Dig. Int. Conf. on Microwave and Millimeter Wave Tech. (ICMMT 07), pp. 1-4, Apr [7] R. Q. Yan and Y. H. Li, Basis of Microwave Technology, Beijing Institute of Technology Press, p. 90, 2004 [8] D. M. Pozar, Microwave Engineering, New York: John Wiley & Sons, p. 113, 2005 [9] C. A. Balanis, Antenna Theory, New York: John Wiley & Sons, pp , 2005.

56 Acknowledgements During near the two years studying as well as living in korea, I received great help from the lab, university and so many korean friends. First and foremost, a very special place in my thanks is reserved for professor Biering-Cherl Ahn, my advisor, whose encouragement, support, and advice are unforgettable. For his suggestion and direct guidance. I appreciated the discussions on the theoretical knowledge, and gained more insight into the design of antennas and RF engineering. Then, I wish to thank professor Ik-Guen Choi, the chairman of my thesis work review committee, and professor Wang-Zu Kim., a member of my thesis work review committee, they gave me so much valuable advice and help on my thesis work. I would also like to take this opportunity to express my deep appreciation to my teacher Bang Jai-hong who have so graciously shared his knowledge and wisdom with me during my graduate studies. I appreciated your help as well as our various discussions about research and design of the antenna. I would like to express my special thanks to Li Junwen, a brother as well as my best chinese friend in lab. He provided great help for me on the application for admitance to Chungbuk National University, he also gave great help on my study of the major subjects. I thank my best Korean friend Chun-Won Kim, who living with me for two years, his great help on the life in Korea as well as study in lab is unforgettable. I also thank BAYANMUNKH ENKHBAYAR, a friend of Mongolia, he gave great help on the design and simulation of the feed horn. I am grateful to the BK21 Research-Oriented Consortium of Chungbuk National University. They supported my tuition and living expense during my graduate

57 studies. Finally, there is my family: Mother, Liu Guihua, Father, Zhai Shenhou, Sister, Zhai Xiaoyan and Girl Friend, Pang Xue. Words can never express my love in lab Ren Chun