저작자표시 - 비영리 - 변경금지 2.0 대한민국 이용자는아래의조건을따르는경우에한하여자유롭게 이저작물을복제, 배포, 전송, 전시, 공연및방송할수있습니다. 다음과같은조건을따라야합니다 : 저작자표시. 귀하는원저작자를표시하여야합니다. 비영리. 귀하는이저작물을영리목적으로이용할

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1 저작자표시 - 비영리 - 변경금지 2.0 대한민국 이용자는아래의조건을따르는경우에한하여자유롭게 이저작물을복제, 배포, 전송, 전시, 공연및방송할수있습니다. 다음과같은조건을따라야합니다 : 저작자표시. 귀하는원저작자를표시하여야합니다. 비영리. 귀하는이저작물을영리목적으로이용할수없습니다. 변경금지. 귀하는이저작물을개작, 변형또는가공할수없습니다. 귀하는, 이저작물의재이용이나배포의경우, 이저작물에적용된이용허락조건을명확하게나타내어야합니다. 저작권자로부터별도의허가를받으면이러한조건들은적용되지않습니다. 저작권법에따른이용자의권리는위의내용에의하여영향을받지않습니다. 이것은이용허락규약 (Legal Code) 을이해하기쉽게요약한것입니다. Disclaimer

2 공학박사학위논문 Ka- 대역모노펄스반사경안테나 Ka-band Monopulse Reflector Antenna 충북대학교대학원 전기 전자 정보 컴퓨터학부전파통신공학과 Gombo Otgonbaatar 2014 년 2 월

3 공학박사학위논문 Ka- 대역모노펄스반사경안테나 Ka-band Monopulse Reflector Antenna 지도교수 안병철 전기 전자 정보 컴퓨터학부전파통신공학과 Gombo Otgonbaatar 이논문을공학박사학위논문으로제출함 년 2 월

4 본논문을검보오트건바타르의공학박사학위논문으로인정함. 심사위원장심사부위원장심사위원심사위원심사위원 안재형印김경석印안병철印노진입印방재훈印 충북대학교대학원 2014 년 2 월

5 Ka- 대역모노펄스반사경안테나 * 오트건바타르검보 충북대학교대학원전파통신공학과 지도교수안병철 요약문 본논문에서는유도탄표적탐색용 Ka-대역모노펄스반사경안테나의설계를제시하였다. 안테나는다중모드사각형혼, 도파관형모노펄스비교기및카세그레인반사경으로구성된다. 우선카세그레인반사경의광학설계를제시하였다. 주반사경크기는원하는값의합채널의이득이얻어지도록결정하였다. 부반사경의크기와초점거리를구현가능한다중모드혼의개구면크기와빔폭을고려하여반복적인방법으로구하였다. 카세그레인반사경광학구조와다중모드혼구조를동시에설계함으로써최상의결과를얻었다. 카세그레인반사경에필요한피드의빔폭이주어질경우다중대역혼피드의개구면크기가작을수록좋다. 그이유는피드의크기가작을수록피드에의한차폐와산란이적기때문이다. 다중대역혼의크기는합패턴과차패턴을방사하는사각형개구면의방사특성에의해결정된다. 다중모드혼의설계는안테나전체 * A dissertation for the degree of Doctor in February i

6 설계에있어서매우중요하다. 다음으로표적추적용으로적합한다중대역혼을설계하였다. 설계한혼은 4 개의급전포트, 모드발생용계단및단일개구면으로구성된다. 4 개의급전포트에의해도파관이여기될경우이로부터합패턴과차패턴을생성하는모드의조합을발생시키는전계면계단과자계면계단의설계가매우중요하다. 모드발생용계단의최종설계안은반복적인시뮬레이션과수동최적화를통해도출하였다. 전계면계단과자계면계단에연결된단일개구면에미라미드혼구조를추가하여다중대역혼의빔폭을줄일수있다. 피라미드혼의길이는합패턴과차패턴을생성하는모드의위상지연을결정하며이의최적값은혼의방사패턴을관측하면서결정하였다. 최종적으로다중모드혼의개구면크기는카세그레인반사경의광학설계와연계하여반복적인방법으로구하였다. 다중대역혼이정확한방사패턴을내려면 4 개의급전포트에서정확한크기와위상으로급전되어야하며이작업은모노펄스비교기에의해수행된다. 본논문에서는모노펄스비교기를이등분형태의도파관구조를이용하여구현하였다. 모노펄스비교기는 4 개의도파관형 180 링하이브리드와여러가지형태의도파관벤드와직선도파관으로구성된다. 단일 180 링하이브리드를설계한후 4 개의링하이브리드를단일평면에적절히배치하였다. 4 개링하이브리드의입력및출력포트는도파관직선부와벤드를이용하여각각다중대역혼의급전포트와안테나의합채널및차채널포트와연결된다. 도파관모노펄스비교기의구조를이등분가공기법으로가공하기에적합하도록설계하였다. 카세그레인반사경에적용하기전에다중대역혼과모노펄스비교기가연결되었을경우의특성을시뮬레이션하여접합성을검증하였다. 모노펄스비교기에의해급전되는다중모드혼피드가적용된카세그레인반사경의방사패턴을분석하여모노펄스추적안테나의성능을예측하였다. 설계된안테나를제작한후성능을측정하였다. 측정결과제작된안테나는합패턴의경우이득 34.75dB, 3-dB ii

7 빔폭 3.2, 부엽레벨 -20dB 등의양호한특성을보였다. 차패턴의경우최대이득 32.23dB, 영점깊이 -38dB 및부엽레벨 -21 db 등의양호한특성을보였다. iii

8 Ka-band Monopulse Reflector Antenna Otgonbaatar Gombo School of Electrical Engineering and Computer Science, Graduate School of Chungbuk National University, Cheongju, Korea Supervised by Professor Bierng-Chearl Ahn, Ph. D. Abstract This thesis presents the design of a Ka-band monopulse reflector antenna to be used for missile seeker applications. The antenna consists of a multimode rectangular horn, a waveguide monopulse comparator, and a Cassegrain reflector. First, the optical design of the Cassegrain reflector antenna is carried out. The main reflector size is determined for a desired sum channel gain. The subreflector size and its focal point are designed in an iterative procedure by considering the aperture size and beamwidth of the realizable multimode horn. Best results are achieved when the Cassegrain optics and the multimode horn are designed concurrently. For a given beamwidth required of the Cassegrain reflector's feed, the smaller the aperture size of the multimode horn, the better the antenna's performance, since there will be smaller blockage and scattering by the feed. * A dissertation for the degree of Doctor in February iv

9 The size of the multimode horn is dictated by the radiation properties of the rectangular aperture radiating the sum and difference patterns. Thus the crucial step in the overall antenna development is the design of the multimode horn. Next a multimode horn is designed to achieve characteristics suitable for target tracking applications. The horn has four excitation ports, mode generating steps and a single aperture. The most important part in the multimode horn design is E-plane and H- plane steps generating a required combination of modes that generate sum and difference patterns when properly excited by four input waveguides. A final design of mode generating steps is achieved by repeated numerical simulations and manual optimization. The beamwidth of the multimode horn is sharpened by adding a pyramidal horn structure to the common aperture connected to the E- and H-plane steps. The length of the pyramidal horn controls the phase delay of the modes used in forming the sum and difference patterns so that its optimum value is obtained by observing the horn's patterns. The aperture dimension is determined in an iterative procedure combined with the Cassegrain reflector's optical design. The multimode horn functions accurately only when it is excited in an exact magnitude and phase, the task of which is taken by the comparator. The monopulse comparator is realized using split-block rectangular waveguide techniques. It consists of four 180 ring hybrids and various forms of waveguide bends and runs. A single 180 ring hybrid is designed first. And then four ring hybrids are properly laid out on a single plane. Output and input ports of the four ring hybrids are routed to the multimode horn's excitation ports and the antenna's sum and difference channel ports using waveguide bends and runs. The structure of the waveguide monopulse comparator is designed in such a way that it can be easily fabricated using split-block waveguide techniques. The combined performance of the multimode horn and the comparator is simulated and verified before applying it to the Cassegrain reflector. Finally the monopulse tracking antenna performance is predicted by analyzing the patterns of the Cassegrain antenna fed by the multimode horn and the comparator. The designed antenna is fabricated and its performance is measured. Measurements v

10 show that the antenna has a sum channel gain of 34.75dB, a 3-dB beamwidth of 3.2, a sidelobe level of -20dB. The difference pattern has a maximum gain of 32.23dB, a null depth of -38dB, and side lobe level of -21 db. vi

11 Contents 요약문 i Abstract iv List of Figures viii List of Tables xii I Introduction 1 II Monopulse Tracking Antenna Monopulse Antenna Cassegrain Antenna... 7 III Design of Multimode Feed Horn Multimode Feed Horn Design Requirements Multimode Feed Horn Design Theory Multimode Feed Horn Design IV Design of Monopulse Comparator Monopulse Comparator Design Requirements Design of Monopulse Comparator V Monopulse Reflector Antena Proposed Reflector Antenna Structure and Requirements Reflector Antenna Geometry Cassegrain Antenna Simulation VI Fabrication and Measurement Multimode Horn Fabrication and Measurement Monopulse Comparator Fabrication and Measurement Reflector Antenna Fabrication and Measurement VII Conclusion 118 REFERENCES 120 ACKNOWLEDGEMENTS 126 vii

12 LIST OF FIGURES Fig. 2.1 Azimuth difference pattern beams... 5 Fig. 2.2 Signal amplitude response of each beam... 5 Fig. 2.3 Sum and difference signal response (a) sum (b) difference... 6 Fig. 2.4 Cassegrain reflector's structure and geometry... 8 Fig. 3.1 Plots of E y in (a) x and (b) y directions for m = 1, 2, 3 and n = 0, 1, 2, Fig. 3.2 Mode summation for the sum pattern Fig. 3.3 Mode summation for the azimuth difference pattern Fig. 3.4 Mode summation for the elevation difference pattern Fig. 3.5 Effect of amplitude ratio in sum pattern E-field distribution(a) x and (b) y direction Fig. 3.6 Effect of amplitude ratio in difference pattern s E-field distribution (a) x and (b) y direction Fig. 3.7 Calculated E-field distributions in (a) sum and (b) difference patterns Fig. 3.8 Computed radiation patterns of the multimode horn Fig. 3.9 Composition of the proposed multimode feed horn Fig Structure of the proposed multimode feed horn (a) A side view and (b) 3D view Fig Electric fields of the input waveguides of the multimode horn for (a) the sum pattern, (b) the azimuth difference pattern, and (c) the elevation difference pattern Fig Polarities of the input waveguide excitation for (a) the sum pattern, (b) the azimuth difference pattern, and (c) the elevation difference pattern Fig Structure of a general H-moder Fig H-moder of the feed horn: (a) configuration and (b) simulation model Fig Structure of the E-moder Fig Structure and design parameters of the multimode feed horn Fig Ports setting of multimode feed horn Fig Feed horn reflection coefficients viii

13 Fig Simulated 2D aperture distributions of (a) sum, (b) azimuth and (c) elevation difference patterns Fig Normalized aperture distributions of the sum and difference patterns Fig D radiation patterns of the multimode feed horn. (a) Sum channel absolute gain, (b) sum channel theta gain, (c) sum channel phi gain, (d) azimuth difference channel absolute gain, (e) azimuth difference channel theta gain, (f) azimuth difference channel phi gain, (f) elevation difference channel absolute gain, (h) elevation difference channel theta gain, and (i) elevation difference channel phi gain Fig Sum and difference radiation patterns Fig Phase pattern in the sum channel Fig Phase pattern in the difference channels (a) azimuth and (b) elevation Fig. 4.1 Monopulse comparator design structure Fig. 4.2 Hybrid ring coupler structure Fig. 4.3 Hybrid ring coupler simulation model Fig. 4.4 E-field propagation in hybrid ring coupler (a) sum port (b) difference port Fig. 4.5 Reflection coefficients of coupler ports Fig. 4.6 Transmission coefficients Fig. 4.7 Phase difference at two output ports Fig. 4.8 Four hybrid ring couplers combination Fig. 4.9 Round waveguide bend geometry Fig Final monopulse comparator design (a) front view and (b) back view Fig Waveguide bend geometry (a) round and (b) stepped Fig Connecting bend combinations Fig Reflection coefficients of monopulse comparator. (a) At output ports and (b) input ports Fig Sum pattern channel's (a) transmission coefficients and (b) phase differences. 60 Fig Azimuth differnce pattern channel's (a) transmission coefficients and (b) phase differences ix

14 Fig Elevation differnce pattern channel's (a) transmission coefficients and (b) phase differences Fig Transition between horn and comparator (a) 3D simulation model (b) insertion and return losses Fig Combined horn and comparator Fig Combined monopulse feed horn (a) reflection and (b) isolation coefficients Fig Far-field plots (a) sum E-plane and elevation difference (b) sum H-plane and azimuth difference Fig. 5.1 Structure of the monopulse antenna Fig. 5.2 Cassegrain antenna geometry and design parameter Fig. 5.3 Relation between blockage efficiency and Ds / Dm Fig. 5.4 Relation between the subtended angle and Fm / Dm Fig. 5.5 Cassegrain antenna simulation model with feed horn far-field source (a) sum (b) azimuth (c) elevation pattern (d) reflector itself Fig. 5.6 Simulated far-field pattern of Cassegrain antenna (a) azimuth and sum H-plane (b) elevation and sum E-plane (c) sum 3D pattern Fig. 6.1 Fabricated multimode horn (a) disassembled and (b) assembled Fig. 6.2 Round waveguide corners for fabrication Fig. 6.3 Measured reflection coefficients of the multimode horn... Fig. 6.4 Measured far-field patterns of the multimode horn. (a) E-plane pattern of the sum channel, (b) the H-plane pattern of the sum channel, (c) elevation difference pattern, and (d) azimuth difference pattern Fig. 6.5 Splitting diagram for the fabrication of the monopulse comparator Fig. 6.6 Fabricated monopulse comparator. (a) block 1, (b) block 2, (c) block 3, and (d) assembled comparator Fig. 6.7 Measurement setup for the monopulse comparator Fig. 6.8 Waveguide matched load used for in the monopulse comparator measurements (a) Rectangular waveguide and (b) tapered ferrite absorber x

15 Fig. 6.9 Reflection coefficients at the output of the fabricated monopulse comparator. (a) At port 1, (b) at port 2, (c) at port 3, and (d) at port Fig Reflection coefficients at the input of the fabricated monopulse comparator. (a) At port 5, (b) at port 6, and (c) at port Fig Measured transmission coefficient of the sum port. (a) S51 (b) S52 (c) S53 (d) S Fig Azimuth difference port transmission coefficient measurements (a) S61 (b) S62 (c) S63 (d) S Fig Elevation difference port transmission coefficient measurements (a) S71 (b) S72 (c) S73 (d) S Fig Sum channel phase difference (a) at port 1, (b) at port 2,and (c) port Fig Azimuth difference channel phase difference (a) at port 1, (b) at port 2, and (c) at port Fig Elevation difference channel phase difference (a) at port 1, (b) at port 2, and (c) at port Fig Comparator input port isolations (a) S56, (b) S75, (c) S Fig Fabricated main and sub reflectors. (a) Main reflector back side and (b) front side of the main and sub reflectors Fig Sub reflector on the radome Fig Radome (a) geometry and (b) design parameter Fig Overall reflector antenna Fig Reflection coefficient versus feed horn displacement (a) sum port, (b) azimuth difference port, and (c) elevation difference port Fig E-field distribution (a) abs value and (b) phase in sum pattern (c) abs value (d) phase in azimuth difference pattern (e) abs value (f) phase in elevation difference pattern Fig Far-field pattern of the fabricated monopulse reflector antenna (a) E-plane pattern of the sum and azimuth difference channel and (b) H-plane pattern of the sum and elevation difference channel xi

16 LIST OF TABLES Table 3.1 Design requirements of the multimode horn Table 3.2 Mode summary Table 3.3 Optimum realizable mode amplitudes Table 3.4 Step size ratio versus amplitude and phase Table 3.5 Optimized dimensions of the multimode feed horn (mm) Table 3.6 Ports excitation settings Table 3.7 Important parameters of the sum and difference radiation patterns Table 4.1 Design requirements of the monopulse comparator Table 4.2 Simulation results summery Table 5.1 Reflector antenna specifications Table 5.2 Determined parameters Table 5.3 Determined parameters Table 5.4 Summarized simulation results of proposed Cassegrain antenna Table 6.1 Comparator measurement summery xii

17 Chapter I Introduction The monopulse antennas are used in the tracking systems, which usually track the aircrafts, missiles or satellites. The tracking system measures its target coordinates, which may be used to calculate the target trajectory and the future position. The target coordinate information may include the elevation angle, the azimuth angle, the distance, and the Doppler frequency shift. The tracking systems can be divided into two types, the continuous tracking system and the track-while-scan system. The continuous tracking system provides continuous tracking data (coordinate data) on a particular target, whereas the track-while-scan system provides sampled data on one or more targets [1]. There are several techniques used in the continuous tracking system such as the sequential lobing, the conical scan, and the monopulse. The monopulse tracking technique uses the monopulse antenna [2]. The monopulse tracking technique uses a resulting single pulse and derives angular error information on the basis of a single pulse. In the monopulse technique, more than one beam are formed simultaneously and then the echo signals are received from respective beams. The received echo signal's amplitude and phase are used to extract the angular error. The monopulse tracking technique can be divided into two forms, the amplitude-comparison monopulse and the phase-comparison monopulse [3]. The monopulse antennas are usually in reflector [4]-[7], lens [8]-[10] or array [11]- [18] forms. The monopulse reflector antennas are usually implemented in prime-focus [4] and Cassegrain forms [5]-[7]. The monopulse array antennas are usually implemented in printed [11]-[16] and slotted [17]-[18] forms. Also there are several different feed networks for the monopulse array antenna [12], [19]-[20]. In the monopulse reflector antenna, the reflector antenna is fed by a feed, which radiates sum and difference patterns. 1

18 The monopulse reflector antenna feed can be in different forms such as a multimode horn [21]-[29], a dielectric rod [30], a twelve-horn feed [31]-[32], and an array [33]. Multimode horns are usually powered by the four-waveguide feed and its monopulse comparator. Monopulse comparators are usually implemented in waveguide [34]-[36] and microstrip [37]-[41] forms and it is composed of 180 hybrid couplers [42]. Researchers Qian Song-song, Li Xing-guo, Wang Ben-qing designed a Ka-band monopulse antenna [5]. They implemented their design with a Cassegrain reflector, the four dielectric tapered rod antennas as the feed, and a monopulse comparator. In this design the dielectric tapered rod antennas form the sum and the difference patterns just like other types of feed horns. In order to form the sum and difference patterns the rod antennas have to be excited with various phase settings. Thus they designed waveguide monopulse comparator which is composed of four magic-t couplers and a few waveguide bends. Using the dielectric rod antennas as the feed, the blockage caused by the feed is reduced, and the wideband performance is achieved. Also the dielectric rod antennas can be fabricated precisely compared to the horn antennas. The sub reflector is supported by a tripod. Using a tripod has advantages such as low cost, simple fabrication, and less effort in the antenna performance calculation compared to other feed supporting techniques. In this thesis, a Ka-band monopulse Cassegrain antenna is developed for missile seeker applications. The development of the proposed antenna involves designing a multimode feed horn, a monopulse comparator and a Cassegrain reflector. In the multimode feed horn design, the E-field distribution transforming method is implemented. The implementation is done by using H- and E- plane moders (steps) with particular phasing sections. Also the desired radiation pattern beamwidth and gain are achieved by properly adjusting the aperture size in a pyramidal horn structure. In the monopulse comparator design, 180 degree hybrid ring couplers are employed. The proposed monopulse comparator is composed of four 180 hybrid ring couplers and various types of the waveguide bends. The Cassegrain antenna's initial dimensions are calculated from 2

19 the overall antenna gain and the multimode feed horn specifications such as aperture diameter and the edge taper angle. The Cassegrain antenna design is optimized using the multimode feed horn radiation pattern data. The Microwave Studio 2012 by CST is used during the all components simulation and optimization. This dissertation is organized as follows. Chapter II introduces the structure of the monopulse antenna and its operating principle, and a general Cassegrain antenna structure. Chapter III discusses the multimode feed horn design theory, and its design and design procedure. Chapter IV discusses the monopulse comparator's operating principle and its design including the 180 hybrid ring coupler. Chapter V discusses the design of the Cassegrain reflector antenna or its geometry calculation and the reflector antenna simulation. Chapter VI gives the fabrication and measurement information of each component. Finally Chapter VII provides the conclusion and discussion. 3

20 Chapter II Monopulse Tracking Antenna 2.1 Monopulse Antenna There are several radio signal tracking methods such as the sequential lobing technique, the conical scan and the monopulse tracking. In the sequential lobing technique, the antenna beam is switched between two beams in the horizontal or vertical direction. The received signal amplitudes from each beam are the key information for determining the received signal direction. The conical scan method is an extension of the sequential lobing technique. Instead of switching the beams, the antenna itself rotates around its boresight axis. The monopulse technique is similar to the conical scanning method in concept, but the monopulse antenna splits its radiating beam into more than one beam in slightly different directions instead of rotating and then sends a resulting pulse signals out of the antenna. The signals from the monopulse antenna are reflected if there is any target in their traveling paths. The monopulse system picks the reflected signals up in each of the split beams and amplifies separately and then compares their amplitude or phase to each other so that the target direction can be determined. Since the direction where the target moving is determined, tracking the target would be possible. The monopulse tracking method which compares the received signal's amplitude is called "amplitude-comparison monopulse", whereas the monopulse tracking method which compares the phases is called "phase-comparison monopulse". The amplitude comparison monopulse method uses two overlapping radiation patterns in azimuth and elevation direction to obtain the azimuth or elevation angular error, and those patterns are called the sum, azimuth and elevation difference patterns. For instance, one-directional monopulse measurement process is explained as follows. The direction 4

21 could be either the azimuth or elevation. As mentioned above, the monopulse tracking antenna has more than one radiating beam. To measure angular errors in the azimuth direction, the azimuth difference pattern is used, which includes two beams as shown in Fig Reflected or received signal's response of each beam can be defined as functions f 1 (θ) and f 2 (θ) given by f ( q ) = f ( q ) = f ( q - q ) (2.1) k f ( q ) = f ( q ) = f ( q + q ) (2.2) k Fig. 2.2 shows the signal amplitude response of each beam (amplitude versus angle). Fig. 2.1 Azimuth difference pattern beams Fig. 2.2 Signal amplitude response of each beam Received signals from each beam are subtracted to form a difference response or error signal as shown in Fig. 2.3(a). This error signal or difference response is given by: D ( q ) = f ( q ) - f ( q ) (2.3) 1 2 5

22 This difference response is used as a feedback signal in the closed-loop system of monopulse tracking. A null is formed in the middle of the two beams. The monopulse tracking system keeps its target within the null of the difference pattern. When the target is within the null, the error signal becomes very small due to the subtraction of signal responses. This type of the system is called a "null tracker". The error signal becomes very small when the target enters the null region or gets out from the radar range or enters the null region that is not in the tracking direction. These conditions could lead to a wrong tracking direction. In order to overcome this situation, one more signal response is used which is the sum response. The sum response is a summation of signal responses of each beam. The sum response is given by S ( q ) = f ( q ) + f ( q ) (2.4) 1 2 The sum response function is shown in Fig. 2.3 (b). (a) (b) Fig. 2.3 Sum and difference signal response (a) difference and (b) sum The sum response is actually used for target detection and to avoid unambiguous tracking conditions. If the offset q k is very small, the difference pattern expression can also be written as follows. ( ) D ( z)» 2 q f ' q = 2q d f / dq (2.5) k 0 k 6

23 The difference response normalized by the sum response is given by: 1( ) 2( ) d / d / f q - f q qk f q D å =» f ( q ) + f ( q ) f ( q ) (2.6) In the difference response shown in Fig. 2.3(a), the slope crossing the zero point on the measurement axis is called the difference slope of the monopulse measurement. The rate of change in the slope of the curve at this point expresses the relative measurement sensitivity of the system. A sharply rising slope indicates a high sensitivity, and a slow rising slope indicates a low sensitivity. The normalized difference slope as a differential function is given by: k m d( D / S) = - (2.7) d( q / q ) 3 q = q 0 where q3 is the 3-dB beamwidth. The equation (2.8) expresses the fundamental relationship of the RMS position error of the monopulse estimate in a thermal noise environment. q3 q3 q3 s q = =» (2.8) k 2 E / N k 2( S / N) 2 ( S / N) m 0 m n n 2.2 Cassegrain Antenna The Cassegrain antennas are widely used in telecommunication and radar systems. A Cassegrain antenna is a reflector antenna that a feed antenna is mounted at or near the surface of a concave main reflector and is aimed at a convex sub-reflector. Energy from 7

24 the feed antenna illuminates the sub-reflector, which reflects it back to the main reflector, which then forms the desired forward beam. The Cassegrain antenna has many advantages. The feed antenna is easily supported at the back side of the main reflector and it makes the antenna geometry compact. A receiver unit or circuit is attached directly to the feed antenna thus loss is low. The sub-reflector illuminates the main reflector more uniformly thus the gain is maximized. The focal length is longer than the prime focus antenna and it improves the cross polarization discrimination. Another advantage is that the feed antenna is directed forward so the spill-over sidelobes are directed to the sky which prevents the ground noise. The Cassegrain reflector antenna generally consists of a main reflector, a sub-reflector and a feed. Fig. 2.4 shows the Cassegrain antenna structure and geometry. From the Fig. 2.4 it can be seen that reflected wave from the main reflector travels to +z direction. The point where the two reflectors focal points exist is called the virtual focal point. x Actual Focal Point D m D b f r D s f n Virtual Focal Point z Feed Horn L r L v F S F C F m Fig. 2.4 Cassegrain reflector's structure and geometry 8

25 In Cassegrain antenna design the main reflector surface geometry can be calculated in the same way as in the prime-focus reflector case and it is expressed as follows. 2 m m m m x = 4 F ( z + F ) (2.9) The main reflector diameter, the actual focal point, the sub-reflector diameter, and the virtual focal point satisfy the following relations. -1 Dm fv = 2tan ( ) (2.10) 4F m 1 1 Fc 2 tanf + tanf = D (2.11) v r s 1 sin ( fv -fr ) 1 2 L - = 2 1 sin ( fv + fr ) F 2 v c (2.12) The sub-reflector illuminated from the actual focal point acts like that it is illuminating the main reflector from the virtual focal point. The sub-reflector's surface geometry is given by x s æ zs + a + Lr ö = b ç -1 a è ø 2 (2.13) where a and b are the eccentricities of the hyperbolic function and can be obtained from following equations. é1 ù sin ê ( fv -fr ) 2 ú e = ë û é 1 ù sin ê ( fv + fr ) ë 2 ú û (2.14) 9

26 F c a = (2.15) e 2 b = a e - 1 (2.16) In a typical Cassegrain antenna design, the antenna gain, the half power beamwidth and the side lobe level are important characteristics. The electrical performances of the main reflector and the sub-reflector design are calculated from the feed horn edge taper level and the reflector's aperture diameter. 10

27 Chapter III Design of Multimode Feed Horn 3.1 Multimode Feed Horn Design Requirements There are several essential requirements in designing a multimode monopulse feed horn such as the reflection coefficient, the radiation pattern symmetry, the edge taper level, the horn aperture size, and the side lobe level. The horn aperture should be as small as possible so that the center blockage caused by the feed horn is small. The center blockage of the reflector radiation pattern directly depends on the feed horn aperture size. But the small horn aperture gives a broad beamwidth and the big horn aperture gives a narrow beamwidth. The horn aperture size is an important consideration in meeting the design requirements. Table 3.1 shows the multimode feed horn antenna requirements. The edge taper is specified at an angle where the feed sees the sub-reflector edge. Table 3.1 Design requirements of the multimode horn Items Edge taper Sidelobe at 32.8 level Σ 8-20 db -20 db AZ-Δ 3-12 db -15 db EL-Δ 3-12 db -15 db Polarization Vertical and linear Maximum aperture size 3.5λ 0 x 3.5λ 0 Operating frequency GHz 3.2 Multimode Feed Horn Design Theory Designing a multimode feed horn involves forming the E-field distribution at the horn aperture to get the desired radiation pattern. In order to obtain a suitable E-field 11

28 distribution, we use more than one higher-order propagating modes. The desired E-field distributions are obtained in the following steps. First we choose high-order modes and next make a summation of chosen higher-order modes and finally determine the amplitude of each higher-order mode. After doing all these steps, the design implementation begins. This section describes the E-field distribution forming steps. A. Choosing High-order Modes In order to obtain a desired E-field distribution, we use a sum or combination of more than one higher-order propagating mode. Higher-order modes are chosen as follows. General equations for the E-field of the TE mn and TM mn propagating modes in a rectangular waveguide are given by following equations [43], [44] for TE mn modes mp x np y - jb cos cos mnz H z = Amn e (3.1) a b jwmnp mp x np y - jb cos sin mnz Ex = Amn e (3.2) k b a b 2 c - jwmmp mp x np y - jb E sin cos mn y = Amn e k a a b 2 c z (3.3) and for TM mn modes with mp x np y - jb sin cos mnz Ez = Bmn e (3.4) a b - jb mp mp x np y - jb cos sin mnz Ex = Bmn e (3.5) k a a b mn 2 c - jb np mp x np y - jb sin cos mnz Ey = Bmn e (3.6) k b a b mn 2 c 12

29 mn k kc, k, kc ( m / a) ( n / b) b = - = w me = p + p (3.7) where a and b are the width (in x direction) and the height (in y direction) of the waveguide cross section, A mn and B mn are modal amplitudes, k c is the cutoff wave number and β mn is the propagation constant. Since the feed is required to radiate a vertically polarized wave, we consider the y component of the electric field (E y ) of various modes. Different propagating modes of the E y component plots in x and y directions are shown in Fig It is obvious that we should use m = 1, 3, 5, and n = 0, 2, 4, modes for the sum pattern, since these E- field distributions should have an even symmetry in both x and y directions. Similarly, for the azimuth difference pattern, we use m = 2, 4, 6, and n = 0, 2, 4,..., while for the elevation difference pattern we use m = 1, 3, 5,...and n = 1, 3, 5, (a) (b) Fig. 3.1 Plots of E y in (a) x and (b) y directions for m = 1, 2, 3 and n = 0, 1, 2, 3. 13

30 Another consideration is the number of higher-order modes to be used in the multimode horn antenna design. Using many higher-order modes increases difficulties in implementing a multimode horn antenna. For the sum pattern, we use the TE 10, TE 30, TE 12, and TM 12 modes to obtain a bell-shaped distribution in both x and y directions. When n is not zero, both TE mn and TM mn modes have a non-zero E x, which is the cross polarized component. From (3.1)-(3.6), it follows that the E x of the TE mn mode is cancelled by that of the TM mn mode when the following condition is met. wmn A b mn bmnm = B mn (3.8) a With n 0, we use both TE mn and TM mn modes to have the E x cancelled. We denote a proper combination of the TE mn and TM mn modes as the HE mn mode. The modes for the azimuth and elevation difference patterns can be chosen in the similar way. In the azimuth difference pattern, we may use only one mode which is the TE 20 mode to simplify the design. In this case the E-field distribution along the vertical axis will be uniform. Therefore, a better choice is to utilize the TE 20 and HE 22 modes together. In the elevation difference pattern, HE 11, HE 13 and HE 31 modes were chosen. Finally, Table 3.2 shows the modes used the sum and difference patterns. Table 3.2 Mode summary. Channel H-moder E-moder TE Sum TE 10 TE 10, TE 10 TE 10, HE TE 30 TE 30 Az. diff. TE 10 TE 20 TE 20 TE 20, HE 22 TE El. diff. TE 10 TE 10, TE 10 HE 11, HE TE 30 HE 31 14

31 B. Mode Summation Since the modes utilized in the sum and difference patterns have been chosen, the mode summation for each pattern can be expressed easily. Assuming that A 10, A 30, A 12, A 20, A 22, A 11, A 13, and A 31 are mode amplitudes for each mode utilized in the sum and difference patterns, their values will be determined in a later section so that the E-field distributions in the horizontal and vertical directions are as close as possible to the desired shape. First, the aperture distribution of the sum pattern shown in Fig. 3.2 can be expressed by following equations p x 3p x p x 2p y E A A A a a a b y å = 10 sin + 30 sin + 12 sin cos (3.9) At y = b/2 (maximum amplitude), we have p x 3p x p x E A A A a a a y å = 10 sin + 30 sin - 12 sin (3.10) and at x = a/2 (maximum amplitude), we have E A A A 2p y b y å = cos (3.11) Similarly for the azimuth difference pattern, E y is given by, 2p x 2p x 2p y E A A a a b yd = 20 sin + 22 sin cos (3.12) az At y = b/2, we have 2 p x 2 p x E A A a a yd = 20 sin - 22 sin (3.13) az 15

32 and at x = a/4, we have E A A 2p y b yd = cos (3.14) az The mode summation for the azimuth difference pattern is shown in Fig A 10 sin( p x / a) A 30 sin(3 p x / a) A 12 sin( p x / a) A10 30 A A 12 cos(2 p x / b) Fig. 3.2 Mode summation for the sum pattern 16

33 TE 20 HE 22 x A 20 sin(2 p x / a) A 22 sin(2 p x / a) A 20 A 22 cos(2 p y / b) y Fig. 3.3 Mode summation for the azimuth difference pattern Finally, E y for the elevation difference pattern is given by, p x p y 3p x p y p x 3p y E A A A a b a b a b yd = 11 sin cos + 31 sin cos - 13 sin cos (3.15) el At y = b/4, we have 1 æ p x 3p x p x ö EyD = A11 sin A31 sin A13 sin el ç è a a a ø (3.16) and at x = a/2, we have p y p y 3p y E A A A b b b yd = 11 cos - 31 cos + 13 cos (3.17) el Fig. 3.4 shows the mode summation for the elevation difference pattern. 17

34 HE 11 HE 31 HE 13 x A 11 sin( p x / a) A 31 sin(3 p x / a) A 13 sin( p x / a) y A 11 cos( p y / b) A 31 cos( p y / b) A 13 cos(3 p y / b) Fig. 3.4 Mode summation for the elevation difference pattern C. Determining Mode Amplitudes By properly adjusting the mode ratios (amplitude ratios), the E-field distribution can be obtained to satisfy the beamwidth and sidelobe requirements in Table 3.1. First for the sum pattern, from equations (3.9)-(3.11) and Fig. 3.2, we should have A 10 = 1 (reference amplitude) (3.18) A + A = A (3.19) to let E y = 0 at y = 0 and y = b. Here we have only one equation and two unknowns A 30 and A 12. Defining r = A 30 /A 12, we adjust r until E y in the vertical and horizontal distributions get symmetric (in x and y directions). Fig. 3.5 shows the plots of E y in x and y directions depending on r. For each case we calculate the sum pattern and check how closely the design requirements of Table 3.1 are met. The result is r = 0.3. Since r is known A 12 and A 30 can be determined. A = , A = (3.20)

35 (a) (b) Fig. 3.5 Effect of the amplitude ratio in the sum pattern E-field distribution. (a) x and (b) y direction For the azimuth difference pattern, we use equations (3.12)-(3.14) and Fig. 3.6 to 19

36 obtain the following condition. A = A (3.19) so that E y vanishes at y = 0 and y = b. As shown in Fig. 3.3, the E-field distribution in the horizontal and vertical directions for the azimuth difference pattern is neatly realized using only two modes TE 20 and HE 22. Finally for the elevation difference pattern, we should have A 11 = 1 (reference amplitude) (3.20) A + A = A (3.21) to let E y = 0 at y = 0 and y = b. Here again we have only one equation and two unknowns A 31 and A 13. Defining s = A 31 / A 13, we adjust s until the E y 's horizontal distribution becomes same as the sum pattern distribution and the vertical distribution becomes same as the azimuth difference pattern's horizontal distribution. Fig. 3.6 shows the plots of E y in the x and y directions versus the mode amplitude ratio s. From these graphs we can see the optimum value of s = 0.3. Since s is known, A 13 and A 31 can be determined as follows. A = , A = (3.22) In the above analysis, amplitudes of higher-order modes A 12 and A 13 are greater than the fundamental TE 10 mode, which is impossible to realize in reality using the step junction in a rectangular waveguide. In practice there is a maximum realizable amplitude level of the higher-order modes using the E- or H-plane steps and therefore we have to determine mode amplitudes with this constraint [44]. Table 3.3 shows a realizable set of mode ratios. For the optimum mode amplitudes derived above, we let them as close as possible to realizable values, which inevitably leads to sub-optimum aperture distributions. 20

37 (a) (b) Fig. 3.6 Effect of the amplitude ratio in the difference pattern's E-field distribution. (a) x and (b) y direction 21

38 Table 3.3 Optimum realizable mode amplitudes Σ AZ-Δ EL-Δ A 10 A 30 A 12 A 20 A 22 A 11 A 31 A D. Determination of Lengths for Phase Sections and Horn In obtaining a good E-field distribution at the horn aperture, it is very important to make the modes used to form a desired aperture distribution be all in the same phase. The phase of each mode at the aperture is determined by the lengths of the phase sections A, B, and C, the length of the radiator horn D, and the average phase velocity (phase constant) b mn E H of the higher-order modes. b mn and b mn are phase velocites of TE mn and TM mn. E H a mn and a mn are initial phase velocities at the E-moder and H-moder. Let's denote A and B, C, D with l, l 1, l 2 respectively. In the sum pattern case, to keep the modes in the same phase, it is required that l, l 1, and l 2 satisfy the following equations: E E E ( b - b ) l + ( b - b ) l - a = 2 pp (3.23) H H E E H ( b - b ) l + ( b - b ) l + ( b - b ) l - a = 2qp (3.24) Similarly in the azimuth and elevation difference patterns cases, it is required that l, l 1, and l 2 satisfy the following equations: E E E ( b - b ) l + ( b - b ) l - a = 2rp (3.25) E E E ( b - b ) l + ( b - b ) l - a = 2tp (3.26) 22

39 H H E E H E E ( b - b ) l + ( b - b ) l + ( b - b ) l -a -a - a = 2kp (3.27) b Here, p, q, r, t, k are all integers. mn is the propagation constant of TE mn or TM mn in the moders which is given by: b mn æ mp ö æ np ö = k - ç - ç è a ø è b ø (3.28) b mn is the average value of propagation constant TE mn and TM mn mode, which is given by: b mn l æ mp l ö æ np l ö k ç ç dz (3.29) ò 0 a1l + ( a - a1) z b1 l + ( b - b1 ) z = - - è ø è ø The E-field distributions of the sum and the difference patterns obtained from the realizable mode ratio are shown in Fig Using software simulation instead of mathematically calculating the lengths of the horn and the phasing sections is a simpler way to find the optimum lengths. In this study the higher-order modes phases were determined by using CAD software. In Fig. 3.7(a), the aperture distributions for the sum pattern in the x and y directions closely match each other for x/a or y/b from 0.13 to The aperture distribution in the y direction for the azimuth difference pattern nicely resembles a bell shape with a taper higher than that for the sum pattern. The aperture distribution in the x direction for the elevation pattern is bell-shaped with a highest taper. In Fig. 3.7(b), the anti-symmetric aperture distributions for the azimuth and elevation difference patterns closely match each other. The aperture distribution for the elevation pattern does not go to zero at edges due to the limitations in the realizable amplitudes of higher-order modes. 23

40 The sum and the difference radiation patterns can be computed from their calculated E-field distributions by integrating the aperture field. The computed radiation patterns are shown in Fig Fig. 3.7 Calculated E-field distributions in (a) sum and (b) difference patterns. (a) 24

41 (b) Fig. 3.8 Continued Radiation patterns in Fig. 3.8 show good performances for the sum and difference patterns. The symmetries in E- and H-plane sum and difference patterns are excellent. The sum pattern shows an edge taper of 17 db at 32.8, a sidelobe level of -25 db. The azimuth difference pattern shows a null depth greater than 45 db relative to the sum pattern maximum, an edge taper of 11 db at 32.8, and a sidelobe level of db. The elevation difference pattern shows a null depth greater than 45 db relative to the sum pattern maximum, an edge taper of 11 db at 32.8, and a sidelobe level of -25 db. 25

42 Fig. 3.9 Computed radiation patterns of the multimode horn 3.3 Multimode Feed Horn Design The composition and structure of the proposed multimode feed horn are shown in Fig. 3.9 and Fig respectively. The proposed feed horn antenna consists of four input feed waveguides, H-moders with phasing sections A and B, an E-moder with phasing section C. The pyramidal horn has a length of D. The input feed waveguides are used to transmit the waves from the monopulse comparator to the horn moders. The moders convert part of the propagating mode TE 10 's energy into those of higher-order modes. The phasing sections guide the fundamental and higher-order propagating modes to the horn. The phasing sections are simple rectangular waveguides with a certain length that gives a desired phase delay. 26

43 Fig Composition of the proposed multimode feed horn A C D Feed waveguides B H-moders E-moder (a) Horn (b) Fig Structure of the proposed multimode feed horn. (a) A side view and (b) 3D view A. Operating Principles It is well-known that the multimode monopulse feed horn has three different types of radiation patterns the sum pattern, the azimuth difference pattern and the elevation 27

44 difference pattern. In the proposed multimode horn design, those three different radiation patterns can be obtained by exciting TE 10 modes in four input waveguides with correct phase combinations. Fig shows the electric fields of the input waveguides for the sum pattern, the azimuth difference pattern, and the elevation difference pattern. Polarities of the input waveguide excitation are shown in Fig (a) (b) (c) Fig Electric fields of the input waveguides of the multimode horn for (a) the sum pattern, (b) the azimuth difference pattern, and (c) the elevation difference pattern (a) (b) (c) Fig Polarities of the input waveguide excitation for (a) the sum pattern, (b) the azimuth difference pattern, and (c) the elevation difference pattern Four input waveguides are excited in the fundamental TE 10 mode by the monopulse comparator. Higher-order modes, which characterize the multimode horn antenna radiation pattern together with the fundamental TE 10 mode, are generated in the H- and E- moders due to abrupt steps in H- and E-planes. The pyramidal horn is used for controlling 28

45 the beamwidth of the radiation pattern. Individual higher-order mode's phases are adjusted by changing the lengths of the H-moders, E-moder and the horn (A, B, C and D parameters in Fig. 3.10). B. Design of the H- and E-moders Fig shows the structure of of a general H-moder. As shown in Fig. 3.13, the H- moder consists of a step discontinuity in the x direction at z = 0. Guided waves travel toward the +z direction. Starting from z = 0, TE 10 and TE 30 modes propagate together through the phasing sections following the H-moder. Fig Structure of a general H-moder The H-moders used in proposed multimode feed horn are not same as a general H- moder shown in Fig In proposed multimode horn design, we use a two H-moder combination as shown in Fig In the sum and elevation difference pattern case, the two H-moders are excited with the TE 10 mode and the TE 30 mode is generated by the discontinuity at z = 0. In the following phasing section, both TE 10 and TE 30 modes propagate. In the azimuth difference pattern case, the two H-moders are excited with the TE 10 mode with 180-degree phase difference and the TE 20 mode is generated at the discontinuity. In this case, there is only one mode which is the TE 20 mode propagating in the phasing section. 29

46 (a) (b) Fig H-moder of the feed horn. (a) Configuration and (b) simulation model In the design shown in Fig. 3.14, the parameter a 0 is chosen to be as small as possible for the TE 10 mode and the parameter a s is chosen to excite the TE 30 mode. This means that the TE 10 mode cut-off frequency of the input waveguide with a width of a 0 is slightly below the operating frequency. The TE 30 mode cut-off frequency of the H-moder having a width of 2a s is also slightly below the operating frequency. The mode amplitude ratios mentioned in the previous section (A 11, A 20, A 30...) are obtained from simulation using the Microwave Studio TM 2012 by CST. The mode ratios including amplitudes and phases are extracted from the simulated S parameters of the H- moder. The simulation model is shown in Fig. 3.14(b). Table 3.4 shows the step size ratio of the simulation model versus the corresponding amplitude and phase. 30

47 Step-size ratio a 1 /a 0 Table 3.4 Step size ratio versus amplitude and phase. TE 10 mode TE 20 mode TE 30 mode Amplitude Phase Amplitude Phase Amplitude Phase Judging from Table 3.4, the amplitudes and phases of the TE 10 and TE 20 modes do not change much as the step ratio changes compared to those of the TE 30 mode. It means that the TE 30 mode is more sensitive than the other two modes. Designing the E-moder can be done in the exactly same way as in the H-moder case. Fig shows the E-moder configuration. The E-moder is excited by the two H- moder phasing sections A and B. In the sum pattern case, the E-moder is excited with the TE 10 and TE 30 modes from the two H-moder phasing sections, then the higher-order mode HE 12 is generated at the discontinuity (z=0) and then the TE 10, TE 30 and HE 12 mode waves propagate through the E-moder phasing section. In the azimuth difference pattern case, the E-moder is excited with the TE 20 mode and then the HE 22 mode is generated at the discontinuity. In the elevation difference pattern case, the E-moder is excited by the TE 10 and TE 30 modes in 180-degree phase and then the HE 11, HE 13 and HE 31 modes are generated at the discontinuity. The E-moder has been optimized in the same way as the H-moders. 31

48 Fig Structure of the E-moder In this design step, the critical design parameters are a 1, a 2, b 1, and b 2. The next step is to determine the waveguide dimensions a 1 and b 1 at the horn throat. From the waveguide transmission theory [44], we know that, if the conditions l / a1» 0.54 and l / b1» 0.62 are satisfied, only selected modes could be propagated though the waveguide. 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. C. Optimized Feed Horn Design The design parameters of the proposed multimode horn have been obtained using the methods described above and a CAD simulation tool. The structure of the multimode feed horn is shown in Fig The optimized parameters of the multimode feed horn are shown in Table

49 Fig Structure and design parameters of the multimode feed horn Table 3.5 Optimized 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 D. Simulation and Results The simulation of the proposed horn antenna with dimension given in Table 3.5 has been done in the following way. Waveguide ports are defined at the four input waveguides with appropriate phase relations for the sum, azimuth and elevation difference patterns as shown in Table 3.6. Fig shows the simulation model and its port attachment. Table 3.6 Port excitation settings Port Sum Azimuth difference Elevation difference number Amp. Phase Amp. Phase Amp. Phase

50 Fig Ports setting of multimode feed horn The simulation was performed in the frequency range of 33 GHz to 37 GHz. Fig shows the reflection coefficients of different port excitations. The reflection coefficients for the sum and difference pattern configurations are less than -10 db over GHz. The sum pattern configuration shows the widest bandwidth ( GHz) although the impedance matching is slightly inferior to other cases. Due to the non-symmetry in the structure, azimuth and elevation difference configurations show slightly different reflection coefficients. The elevation difference case shows the best impedance matching. Reflection Coefficient (db) Sum AZ EL Frequency (GHz) Fig Feed horn reflection coefficients 34

51 The simulated 2D E-field distribution at the horn aperture is shown in Fig The magnitude of the aperture electric field for the sum pattern is of a circular symmetric shape although not perfect. Due to limitations in the realizable amplitudes of higher-order modes, the distribution in the y direction is not exactly same as that in the x direction. It is, however, far superior than the uniform distribution of the TE 10 mode alone. The same remarks apply to the aperture distributions in the y direction for the azimuth and elevation difference patterns. The anti-symmetric aperture distributions for the azimuth and elevation patterns do not match each other closely. A detailed quantitative analysis can be done using the 1D aperture field distributions shown in Fig First, one can notice that the realized aperture distributions are significantly different from the sub-optimal distributions shown in Fig In the sum pattern case, the aperture distribution in the y direction does not closely match that in the x direction. The field at the top and bottom aperture edges is as large as 0.4 compared to 0 at the left and right edges. The anti-symmetric aperture distribution for the elevation difference pattern is significantly different from that for the azimuth difference pattern. All of the above mismatches in the aperture distributions are due to the limitations inherent in the multimode horn itself. (a) Fig Simulated 2D aperture distributions of (a) sum, (b) azimuth and (c) elevation difference patterns 35

52 (b) (c) Fig Continued 36

53 Normalized E-field distributions Fig Normalized aperture distributions of the sum and difference patterns The 3D far-field patterns of sum and difference patterns at 35GHz are shown in Fig

54 (a) (b) Fig D radiation patterns of the multimode feed horn. (a) Sum channel absolute gain, (b) sum channel theta gain, (c) sum channel phi gain, (d) azimuth difference channel absolute gain, (e) azimuth difference channel theta gain, (f) azimuth difference channel phi gain, (f) elevation difference channel absolute gain, (h) elevation difference channel theta gain, and (i) elevation difference channel phi gain 38

55 (c) (d) Fig Continued 39

56 (e) (f) Fig Continued 40

57 (g) (h) Fig Continued 41

58 (i) Fig Continued The sum and difference radiation pattern plots at 35GHz are shown in Fig The important parameters of the radiation patterns are summarized in Table 3.7. It can be seen from Fig that in the sum channel, the H-plane and E-plane patterns are nearly symmetric within ±33, and the azimuth difference and the elevation difference radiation patterns are symmetric within ±50. Table 3.8 shows that the gain in the azimuth and elevation difference patterns is smaller than that of the sum pattern by 1.4 db and 1.9 db, respectively. Side lobe levels in both the sum and the azimuth difference patterns are lower than -20 db, while the elevation difference pattern sidelobe is db. The gain at the null of the difference pattern is less than -40 db. 42

59 Gain (db) Angle (deg) Fig Sum and difference radiation patterns. AZ EL CoPol H-plane E-plane Table 3.7 Important parameters of the sum and difference radiation patterns H-Σ E-Σ AZ-Δ EL-Δ Gain (db) SLL (db) Edge taper (db) at The phase center is calculated for a range of ±32.8 which is approximately the -15 db beamwidth of the sum radiation pattern. The location of the aperture center is (0, 0, 0), and the phase center has been determined at z = -4.5 point. The E- and H-plane phase patterns of the sum radiation pattern are shown in Fig The phase patterns of the azimuth and elevation difference channels are shown in Fig. 3.24, from which we find that the phase center for the sum channel is also the phase centers for the difference 43

60 channels. The maximum phase variations within ±32.8 of the pattern angle are 50, 16, and 11 in the sum, azimuth difference and elevation difference channels. Phase (degree) E-plane H-plane Angle (deg) Phase (deg) Fig Phase pattern in the sum channel Angle (deg) (a) Fig Phase pattern in the difference channels (a) Azimuth and (b) elevation 44

61 Phase (degree) Angle(deg) (b) Fig Continued 45

62 Chapter IV Design of Monopulse Comparator 4.1 Monopulse Comparator Design Requirements There are several important requirements for the monopulse comparators such as the reflection coefficients of each input port and the isolation between them, the transmission coefficients, the attenuation coefficient, the phase delay, and the waveguide port size. Table 4.1 shows the monopulse comparator design requirements. Table 4.1 Design requirements of a monopulse comparator Key specifications Reflection coefficient at each port Port-to-port isolation Insertion loss Input port size Values < -15 db > 25 db < 1 db WR-28 ( mm) 4.2 Design of Monopulse Comparator The monopulse comparator is widely used in monopulse tracking systems and it works as a feed network. The monopulse multi-mode horn antenna requires that the electromagnetic waves in its input ports have different phases and the same amplitudes so that it has different shapes of the radiation pattern. In order to feed the monopulse horn, the monopulse comparator is used to provide the electromagnetic waves with different phases and the same amplitudes as described in the previous section. 46

63 The monopulse comparator is actually a combination of four 180 hybrid couplers. In practice there are many monopulse comparator designs composed of different types of 180 couplers such as the magic tee coupler, the V tee, the hybrid ring coupler and the folded tee etc. In this thesis a design of monopulse comparator has been implemented with hybrid ring couplers for ease of fabrication and simplicity. A. Structure of the Proposed Monopulse Comparator The proposed monopulse comparator consists of four 180 hybrid couplers and a few connecting waveguide bends just like a typical waveguide monopulse comparator design. Fig. 4.1 shows a block diagram of the proposed monopulse comparator. The proposed monopulse comparator has four input ports for the sum and difference patterns, one of them connected to a waveguide matched load. The hybrid coupler has two input ports and two outputs. The electromagnetic wave in the sum port is divided into two waves with 0 phase difference and then guided to two output ports. For the difference input case, the electromagnetic wave in difference port is divided into two waves with 180 phase difference and then guided to two output ports. For the whole monopulse comparator case, the electromagnetic wave in the hybrid coupler 3's sum port (Σ) divided into two waves with 0 phase difference and then guided to hybrid coupler 1's and hybrid coupler 2's sum ports, so all four output port have waves with 0 phase difference from each other. This is the way sum pattern channel works. Difference pattern channels can be explained in the same way. The electromagnetic wave in the hybrid coupler 3's difference port (Δ AZ ) is divided into two waves with 180 phase difference and guided to hybrid coupler 1's and hybrid coupler 2's sum port, then output four ports have two sets of waves with 180 phase difference for the azimuth difference patterns. 47

64 S D S D S D AZ S D S D D EL Fig. 4.1 Monopulse comparator design structure B. Hybrid Coupler Design In the proposed monopulse comparator design, a waveguide E-plane hybrid ring coupler was chosen for its simplicity and ease of fabrication. Fig. 4.2 shows a schematic representation of the ring hybrid coupler with its design parameters r 0 and c. The parameter r 0 controls the length of ring waveguide which is common for all four waveguide ports, so that the distances between each port ( l g / 4 and 3 l g / 4 ) can be obtained properly. The parameter c is actually ring waveguide's height, which controls characteristic impedance ( 2Z 0 ) of the ring waveguide. All four waveguide ports are in the standard WR-28 waveguide size (7.11 x 3.56 mm). 48

65 Port2 input Port3 Σ input Z 0 l g 4 Z 0 Port1 Δ input Z 0 l g 4 r 0 C 2Z 0 l g 4 b Z 0 Port4 output 3 l g 4 Fig. 4.2 Hybrid ring coupler structure The ring hybrid coupler can be implemented in waveguide, micro-strip and strip line form. In this monopulse comparator design, a waveguide hybrid ring coupler has been designed. The 180 hybrid ring coupler is a lossless, matched and reciprocal 4-port device with a scattering matrix S given by ìs11 S12 S13 S14 ü ì0 a b 0 ü ï ï ï ï S21 S22 S23 S24 ï ï ï a b ï S = í ý = í ý ïs31 S32 S33 S34 ï ïb 0 0 a ï ï ï ï ï ïî S41 S42 S43 S44 ïþ ïî 0 - b a 0 ïþ (4.1) Just like the quadrature coupler, we find that 1 a = b = (4.2) 2 49

66 So the scattering matrix will be: ì ü 2 2 ï ï ï ï ï 2 2 ï S = í ý ï ï 2 2 ï ï ï ï ï - î 2 2 ïþ (4.3) Hence, this coupler is likewise 3 db coupler, the power into a given port is equally divided between two of the two output ports. Of course the phase difference between the output ports, is dependent on which port is the input. Fig. 4.3 shows a 3D simulation model. Fig. 4.3 Hybrid ring coupler simulation model In the Fig. 4.4, sum and difference input ports' E-field distributions are shown. The input ports are excited with the fundamental TE 10 mode. As shown in Fig. 4.4(a), the sum input port E-field is propagating into port 1 and port 3, also it is well shown the E-field directions in port 1 and port 3 are opposite, in other words they have 180 degree phase difference. Exactly, the same thing happens in Fig. 4.4(b). The difference input port E- field is propagating into port 1 and port 3 with no phase difference. 50

67 (a) (b) Fig. 4.4 E-field propagation in hybrid ring coupler (a) sum port (b) difference port The proposed hybrid ring coupler has been optimized by using the commercial simulation software Microwave Studio 2012 by CST. Fig. 4.5 shows the reflection coefficients of the optimized ring hybrid coupler. All reflection coefficients are less than -25 db at the operating frequency 35 GHz. Fig. 4.6 shows the transmission coefficients of sum and difference input ports. The amplitudes are balanced within ±0.5 db over GHz. Fig. 4.7 shows the phases of the transmission coefficients. The phase balance of the sum mode is within ±10 over GHz, while it is within ±10 over GHz in the difference mode. 51

68 Reflection coefficient (db) S1,1 S2,2 S3,3 S4, Frequence/GHz Fig. 4.5 Reflection coefficients of coupler ports Transmission coefficient (db) S1,1 S2,2 S3,3 S4, Frequence/GHz Fig. 4.6 Transmission coefficients 52

69 Phase (deg) S4,1 S4, Frequence/GHz (a) Phase (deg) S2,1 S2, Frequence/GHz (b) Fig. 4.7 Phase difference at two output ports 53

70 C. Combining Four Ring Hybrid ring Couplers The proposed monopulse comparator is composed of four ring hybrid ring couplers. The four ring hybrid couplers are laid out in the same plane for split-block fabrication. Fig. 4.7(a) shows the layout of the four hybrid ring couplers. Fig. 4.7(b) shows its dimensions, where d 1 = mm, d 2 = mm, and d 3 = mm. The E-field directions or phase differences are illustrated in Fig Output ports Δ AZ Σ Δ EL (a) Fig. 4.8 Four hybrid ring couplers combination 54

71 (b) Fig. 4.8 Continued Round E-plane waveguide bends are used to connect four ring hybrid couplers. Fig. 4.9 shows a round bend and its design parameters. Optimized dimensions are r 0 = 2.25 mm, r 1 = 5.81 mm and b = 3.56 mm. Its reflection coefficient is less than -30 db and its transmission coefficient is higher than db over the frequency range of GHz. Fig. 4.9 Round waveguide bend geometry A final monopulse comparator design is shown in Fig The output ports are 55

72 extended in order to be connected the multimode horn. There is a realizable space between the four hybrid ring couplers and the output waveguide ports, which is intended to make the fabrication process realizable. (a) (b) Fig Final monopulse comparator design. (a) Front view and (b) back view 56

73 In the final design, round and stepped H-plane waveguide bends are used to connect four ring hybrid couplers to the multimode horn. Fig shows round and stepped bend geometry. Optimized dimensions are a = 7.11 mm, Δ R = 1.5 mm, and R = 8.61 mm for the round bend and α = 0.92 mm, β = 2.0 mm, γ = 2.14 mm, and δ = 2.0 mm for the stepped bend. Reflection coefficients of the stepped and round bends are less than -26 db and -34 db respectively over the frequency range of GHz. Also the transmission coefficients of stepped and round bends are higher than db and db respectively over the frequency range of GHz. (a) (b) Fig. 4.1 Waveguide bend geometry. (a) Round and (b) stepped Fig shows the waveguide bends connecting the monopulse comparator to the multimode horn. There are four independent bend combinations, each of them changes the waveguide direction by 90 in both horizontal and vertical directions. The operating principles are a little tricky. For instance, consider the sum channel case. From fourcoupler combination, four guided waves are generated which are out of phase as illustrated in Fig In the illustration, each of the arrows indicates the instantaneous phase or E-field direction in the waveguide. But at the horn input, all the waves are in phase, even though they were out of phase at the comparator output because of the bend combination's action. 57

74 Fig. 4.2 Connecting bend combinations Fig shows the reflection coefficients of the designed monopulse comparator. Output ports' (ports 1-4) simulated reflection coefficients shown in Fig. 4.13(a) are all less than -20 db and input ports' reflection coefficients shown in Fig. 4.13(b) are all less than -15 db over the frequency range of GHz. It is natural that after connecting the multimode horn to the monopulse comparator the input ports' reflection coefficients will be increased due to multiple reflections. 58

75 0 Reflection Coefficient (db) S1,1-50 S2,2 S3,3 S4, Frequency (GHz) (a) Reflection Coefficient (db) S5,5 S6,6 S7, Frequency (GHz) (b) Fig. 4.3 Reflection coefficients of monopulse comparator. (a) At output ports and (b) at input ports 59

76 The sum channel input port transmission coefficients and phase differences at the output ports are shown in Fig From Fig. 4.14, the transmission coefficients are within -6±0.5 db and phase differences are within 0±2.5 over GHz. Transmission Coefficient (db) Frequency (GHz) (a) S5,1 S5,2 S5,3 S5,4 Phase difference (degree) arg(s5,1/s5,4) arg(s5,2/s5,4) arg(s5,3/s5,4) Frequency (GHz) (b) Fig. 4.4 Sum pattern channel's (a) transmission coefficients and (b) phase differences 60

77 The azimuth difference channel input port transmission coefficients and phase differences at the output ports are shown in Fig From Fig. 4.15, the transmission coefficients are within -6±0.5 db and the phase differences are within 0±2.5 over GHz. Transmission Coefficient (db) Frequency (GHz) (a) S6,1 S6,2 S6,3 S6,4 Phase difference (degree) arg(S6,1/S6,4) 180-arg(S6,2/S6,4) arg(s6,3/s6,4) Frequency (GHz) (b) Fig Azimuth difference pattern channel's (a) transmission coefficients and (b) phase differences 61

78 The elevation difference channel input port transmission coefficients and phase differences at the output ports are shown in Fig From Fig. 4.16, the transmission coefficients are within -6±0.5 db and normalized phase differences are within 0±5 over GHz. Transmission Coefficient (db) Frequency (GHz) (a) S7,1 S7,2 S7,3 S7,4 Fig Elevation difference pattern channel's (a) transmission coefficients and (b) phase differences 62

79 20 15 Phase difference (degree) arg(S7,1/S7,4) arg(s7,2/s7,4) 180-arg(S7,3/S7,4) Frequency (GHz) (b) Fig Continued D. Multimode Feed Horn This section deals with a combination of the monopulse comparator and the multimode horn discussed in previous chapter. The multimode horn feed has nonstandard size input ports. It means that the multimode horn antenna input ports do not match the monopulse comparator output ports. In order to match these ports, a rectangular waveguide transition is necessary. The transition transforms the waveguide size from small to large or vice versa. The designed transition is shown in Fig with its performance. A four-step transition is employed instead of a continuous one for smaller length. The reflection coefficient of the designed transition is less than -20 db at frequencies greater than 34.5 GHz. 63

80 (a) (b) Fig Transition between horn and comparator (a) 3D simulation model (b) insertion and return losses Since the transition has been designed, the multimode horn and the monopulse comparator can be connected to each other. Fig shows a combined structure of the multimode horn and the monopulse comparator. After combining them, the input reflection and isolation coefficients, far-field patterns are investigated. 64

81 Fig Combined horn and comparator The combined monopulse antenna sum and difference port reflection and isolation coefficients are shown in Fig The reflection coefficient of each port is all less than -15 db. The three input ports are isolated from each other very well. The isolation coefficients are less than -30 db. (a) Fig Combined monopulse feed horn (a) reflection and (b) isolation coefficients 65

82 (b) Fig Continued For the far-field patterns, simulation results show that in the case of the multimode horn itself and in the case of the horn with the monopulse comparator, far-field radiation patterns are close enough, but there are some differences. In case of the multimode horn alone, the horn excited with waveguide ports and there is no phase and amplitude error at the horn input ports, and the far-field pattern is the one with perfect excitation. In case of the horn with the monopulse comparator, the phase differences in the excitation are not exactly 0 or 180, and the amplitudes of the excitation are not exactly be -6 db. Fig shows the far-field radiation pattern plots of the multimode horn with the monopulse comparator. 66

83 Radiation Pattern (db) Sum_E Del_EL Theta (degree) (a) Radiation Pattern (db) Sum_H Del_AZ Theta (degree) (b) Fig Far-field plots (a) sum E-plane and elevation difference (b) sum H-plane and azimuth difference The multimode horn with monopulse comparator and without comparator simulation results summarized comparisons are shown in Table

84 Table 4.2 Simulation results summery Radiation pattern H-plane in sum E-plane in sum Azimuth difference Elevation difference Specification Feed horn itself Feed horn with comparator Gain (db) Main beam direction (deg.) Gain (db) Main beam direction (deg.) Gain (L / R) (db) / / Main beam direction (L / R) (deg.) Null depth (db) relative to the difference pattern max / / Null direction (deg.) Gain (L / R) (db) / / Main beam direction (L / R) (deg) Null depth (db) relative to the difference pattern max / / Null direction (deg.) From the comparison in Table 4.2, we can see that the sum pattern beam is tilted by 1.16 degree in the H-plane pattern and 0.61 degree in the E-plane pattern. The beam tilt is caused by the monopulse comparator's physical behavior. The most significant point in the multimode horn degradation due the imperfections in the monopulse comparator is a large increase in the null depths of the difference patterns. The null depth increase is caused by a combination of the amplitude and phase imbalances in the feed network. The null depth can be estimated by the following 68

85 equation. jq A jq B j( q B -q A) 10 Ae Be 10 A Be Null depth (db) = 20log - = 20log - For example, an amplitude imbalance of ±0.5 db without phase error will lead to a null depths of up to db rather than an ideal value of negative infinite db. A phase imbalance of ±5 without amplitude error will increase the null depth up to db. 69

86 Chapter V Monopulse Reflector Antenna In this chapter, the monopulse reflector antenna design is discussed. The chapter stars with explaining proposed reflector antenna structure and requirements. Next the Cassegrain antenna geometry calculation and simulation methods are explained. 5.1 Proposed Reflector Antenna Structure and Requirements A. Proposed Antenna Structure The proposed reflector antenna consists of a multimode feed horn fed by a monopulse comparator and a Cassegrain dual reflector as shown in Fig The multimode horn and the monopulse comparator discussed in Chapters 3 and 4 are used in the proposed reflector design. Operating principles of this structure have been explained in Chapter 2. å AZ EL Fig. 5.1 Structure of the monopulse antenna 70

87 B. Design Requirements Antenna specifications or requirements are key information in the antenna design process. All of the design parameters are based on these requirements. In other words, antenna geometry and dimensions are calculated referring to the design requirements. In a monopulse reflector antenna design, basic requirements are the far-field gain, the side lobe level, the beamwidth, the radiation efficiency, and the monopulse slope. The design specifications of the proposed monopulse reflector antenna are shown in Table 5.1. Table 5.1 Reflector antenna specifications Center frequency Specifications 35 GHz Bandwidth > 3% Polarization Cross-polarization level Gain Monopulse slope Beamwidth Vertical < -20 dbc > 36 dbi TBD Azimuth: 1.5 ± 0.15 Elevation: 1.5 ± Reflector Antenna Geometry Reflector geometry or dimensions are calculated from the specifications for the proposed structure. The proposed reflector's geometry and design parameters are shown in Fig The key specifications are the sum pattern gain and the feed horn edge taper angle. The main reflector and sub-reflector diameter D m and D s are determined from the sum pattern gain. 71

88 f r f v Fig. 5.2 Cassegrain antenna geometry and design parameters Since the sum pattern gain is known, the main reflector and sub-reflector diameters are calculated from equation 5.1. In this case, we use a ratio of D s / D m. Fig. 5.3 shows a plot for the blockage efficiency versus D s / D m ratio. The diameters of main and sub reflector can be determined [46] Dm - Ds 2 l0 p ( ) G = h (5.1) where G is the specified gain, η is the illumination efficiency. In practice, the illumination efficiency η is typically between 55 and 75 %. Next the main reflector focal length F m can be determined. The focal length value is inversely proportional to the reflector dish depth, thus an appropriate value for the focal length F m should be chosen by the designer to prevent the reflector dish from becoming neither too deep nor too shallow. In practice, the ratio F m / D m of between 0.25 and 0.8 is 72

89 used. The reflector dish diameter and its focal length define the subtended angle. The subtended angle of a reflector dish versus F m / D m is shown in Fig Blockage efficiency Ds/Dm ratio Fig. 5.3 Relation between blockage efficiency and D s / D m Subtended angle (deg) F/D ratio Fig. 5.4 Relation between the subtended angle and F m / D m. 73

90 The main reflector subtended angle φ v is expressed as follows, and it also can be determined from the Fig f n -1 æ Dm ö = 2tan ç è 4Fm ø (5.2) Since the main reflector diameter, its focal length, and the sub-reflector diameter are known, other parameters are determined in the following way. The sub-reflector focal length is determined using the following minimum-blockage condition [45]. Fm 2F s Ds = (5.3) D f Where, D f is the multimode feed horn's aperture diameter discussed in Chapter 3. Now we can determine L r and L v, since the main reflector and sub-reflector diameters and focal lengths are known. L r can be found as follows. L r Ds = - Hs (5.4) 2tan( f ) r where φ r is the sub-reflector subtended angle seen from the feed horn. H s 2 s D = (5.5) 16F s L v is determined in the same way as L r. L v Ds = + H s (5.6) 2tan( f ) v Now all initial parameters can be determined using the above equations and ratios. 74

91 Table 5.2 shows the determined parameters, where F m / D m = 0.3, D s / D m = 0.2. There are a few design tips [46], and two of them are shown below. The ratios F m / D m and D s / D m are chosen referring to those tips. For D s / D m = 0.2, the blockage efficiency is 96 % as shown in Fig The feed horn aperture diameter D f is chosen to be 25 mm referring to the designed feed horn antenna in Chapter 3. - The ratio F m / D m should be between 0.25 and D s should be greater than > 5λ 0, to avoid excessive diffraction losses. Table 5.2 Determined parameters Parameters Determined value Description D m 240 mm Calculated from (5.1), where η = 55% F m 72 mm Obtained from the ratio F m / D m = 0.3 D s 48 mm To satisfy D s > 5λ 0 and 36 db gain mm Sub-reflector focal length from (5.3) F s r 32.8 D f = 25 mm Sub-reflector subtended angle seen from the feed horn v 79.6 Calculated from (5.2) L r mm Calculated from (5.4) L v mm Calculated from (5.6) 5.3 Cassegrain Antenna Simulation Simulating the whole Cassegrain antenna including the feed horn and the monopulse comparator is a difficult task. Limitations in the simulation software and hardware make the simulation time very long, and make the results inaccurate. In this case the simulation time could be a few days. It is not a good way to design any reflector antenna. There are many ways to overcome this situation. One of them is to simulate each component separately and using the individual results in other component simulation. In 75

92 any reflector antenna case, we use the feed horn antenna radiation pattern data in the reflector simulation. Since the radiation patterns of the feed horn discussed in Chapter 3 are the same as the case with the monopulse comparator, we can use only the feed horn simulation results or the simulated radiation patterns. The proposed Cassegrain antenna simulation has been done by Microwave Studio TM 2012 by CST. Fig. 5.5 shows the simulation model of the proposed Cassegrain antenna with the feed horn radiation pattern source. In this simulation case only the reflector antenna far-field is calculated. The Cassegrain antenna design parameters calculated in the previous section are used in the simulation as initial parameters and these initial parameters have been optimized. The optimized design parameters are shown in Table 5.3. (a) (b) (c) Fig. 5.5 Cassegrain antenna simulation model with a feed horn far-field source. (a) Sum (b) azimuth (c) elevation pattern (d) reflector itself. 76

93 Main reflector Sub reflector Actual focal point (d) Fig. 5.6 Continued Table 5.3 Determined parameters Parameters Optimized value Predicted value D m 240 mm 240 mm F m 67.2 mm 72 mm D s 45.6 mm 48 mm F s mm mm φ r 32.8 deg 32.8 φ v 83.5 deg 79.6 L r mm mm L v 9.42 mm mm Simulated far-field patterns of the proposed Cassegrain antenna with optimized dimensions are shown in Fig

94 Gain (db) AZ H-plane Angle (deg) Gain (db) Angle (deg) (a) AZ H-plane Fig. 5.7 Simulated far-field patterns of Cassegrain antenna. (a) Azimuth and sum H-plane, (b) elevation and sum E-plane, and (c) sum 3D pattern 78

95 Gain (db) EL E-plane Angle (deg) Gain (db) Angle (deg) (b) Fig. 5.8 Continued EL E-plane 79

96 (c) Fig. 5.9 Continued The proposed Cassegrain antenna simulation results are summerized in Table 5.4. Table 5.4 Summarized simulation results of the proposed Cassegrain antenna Sum Azimuth difference Elevation difference Gain 37 db Side lobe level db 3 db beamwidth 2.3 Gain 33.2 db Side lobe level db Null depth -38 db Gain 33.4 db Side lobe level 13.3 db Null depth -40 db 80

97 Chapter VI Fabrication and Measurement 6.1 Multimode Horn Fabrication and Measurement A. Fabrication of Multimode horn The multimode horn antenna has been produced in three pieces as shown in Fig. 6.1 considering fabrication possibilities. As shown in Fig. 6.1 the transitions used to connect the comparator to the horn, the H- and E- moders and the radiator horn were fabricated in separate solid pieces separately. It can be seen that each of the components look different from their simulation models, the outside of them have been extended to have holes for bolts so that they can be interconnected. Two fabrication methods have been utilized to produce the multimode horn, which are milling and electrical discharge methods. (a) Fig. 6.1 Fabricated multimode horn. (a) disassembled and (b) assembled 81

98 (b) Fig. 6.2 Continued We made the waveguide corner round with radius of 0.3 mm as shown in Fig. 6.2 due to fabrication limitations arising from the fact that the minimum diameter of the end mill drill is 0.3 mm. Fig. 6.3 Round waveguide corners for fabrication The corner structure has a negligible effect on the waveguide characteristic impedance. B. Measurement of the Multimode Horn Measurements were taken in the frequency range of GHz, and multimode horn's port reflection coefficients were measured. Fig. 6.3 shows the port 1's and 3's measured 82

99 reflection coefficients. The multimode horn has a symmetric structure and the measurements of ports 2 and 4 are not illustrated. There are some differences between the predicted and measured reflection coefficients, which are believed to be due to the fabrication errors. Measured reflection coefficients are less than -10 db over GHz, whereas the simulated ones are less than -10 db over GHz. (a) (b) Fig. 6.4 Measured reflection coefficients of the multimode horn 83

100 The far-field sum and difference patterns were taken in an anechoic chamber facility. Fig. 6.4 shows measured far-field patterns of the multimode horn. The agreements between the simulation and measurements are excellent except at angles beyond ±90. In the elevation difference pattern, the null depth is only db compared to the simulated value of -31 db relative to the difference pattern maximum. 0 Sum GHz Normalized Gain (db) Measurement Simulation Theta (degree) (a) Fig. 6.5 Measured far-field patterns of the multimode horn. (a) E-plane pattern of the sum channel, (b) the H-plane pattern of the sum channel, (c) elevation differnce pattern, and (d) azimuth difference pattern 84

101 0 Sum GHz Normalized Gain (db) Measurement Simulation Theta (degree) 0 (b) Normalized Gain (db) Measurement Simulation Theta (degree) (c) Fig. 6.6 Continued 85

102 0 Normalized Gain (db) Measurement Simulation Theta (degree) (d) Fig. 6.7 Continued 86

103 6.2 Monopulse Comparator Fabrication and Measurement A. Fabrication of Monopulse Comparator The monopulse comparator fabrication has been implemented by split-block method and it consists of three blocks. Each of the blocks was fabricated using a numerically controlled milling machine. Fig. 6.4 shows the splitting diagram. From Fig. 6.5 each of the blocks should be drilled from their two sides bottom and top. Fig. 6.8 Splitting diagram for the fabrication of the monopulse comparator Fig. 6.6 shows the fabricated blocks with front and back side view. As shown in Fig. 6.6(g) the blocks are screwed tightly with bolts so that the separate blocks are able to stick to each other tightly. 87

104 (a) Front side Back side (b) (c) Fig. 6.9 Fabricated monopulse comparator. (a) Block 1, (b) block 2, (c) block 3, and (d) assembled comparator 88

105 (d) Fig Continued B. Measurement of Monopulse Comparator The measurements were taken in frequency range of GHz, and all input ports reflection coefficients, transmission coefficients and phase differences were measured. Fig. 6.7 shows the measurements setup. Measurements have been done using Agilent E8364B vector network analyzer. Five pieces of the waveguide matched load were used during the measurements. The matched load is shown in Fig

106 Agilent E8364B Vector Network Analyzer Port 1 Port 2 Waveguide matched load Monopulse Comparator WR-28 waveguide adaptor Fig Measurement setup for the monopulse comparator (a) (b) Fig Waveguide matched load used for in the monopulse comparator measurements. (a) Rectangular waveguide and (b) tapered ferrite absorber Fig. 6.9 shows the reflection coefficients at the output of the fabricated monopulse comparator. In Fig. 6.9, all measured reflection coefficients are less than -15 db over the frequency range of GHz. Simulated and measured results are in good agreements. 90

107 0-5 Simulation Measurement Reflection Coefficient (db) Frequency (GHz) (a) 0-5 Simulation Measurement Reflection Coefficient (db) Frequency (GHz) (b) Fig Reflection coefficients at the output of the fabricated monopulse comparator. (a) At port 1, (b) at port 2, (c) at port 3, and (d) at port 4 91

108 Reflection Coefficient (db) Simulation Measurement Frequency (GHz) (c) 0-5 Simulation Measurement Reflection Coefficient (db) Frequency (GHz) (d) Fig Continued The reflection coefficients at the input of the fabricated monopulse comparator are shown in Fig The measured results show that all of the reflection coefficients are less than -17 db in the GHz frequency range. 92

109 0-5 Simulation Measurement Reflection Coefficient (db) Frequency (GHz) (a) 0-5 Simulation Measurement Reflection Coefficient (db) Frequency (GHz) (b) Fig Reflection coefficients at the input of the fabricated monopulse comparator. (a) At port 5, (b) at port 6, and (c) at port 7 93

110 0-5 Simulation Measurement Reflection Coefficient (db) Frequency (GHz) (c) Fig Continued Sum pattern port's transmission coefficients are shown in Fig The measured results show that transmission coefficients are between -5.9 db and -6.5 db over GHz. Measured transmission coefficients are smaller than the simulated ones by about 0.2 db, which is believed to be due to accumulated losses at joining contacts at split blocks and waveguide-to-coax adapters. 94

111 Transmission Coefficient (db) Simulation Measurement Frequency (GHz) (a) Transmission Coefficient (db) Simulation Measurement Frequency (GHz) (b) Fig Measured transmission coefficients of the sum port. (a) S 51 (b) S 52 (c) S 53 (d) S 54 95

112 Transmission Coefficient (db) Simulation Measurement Frequency (GHz) (c) Transmission Coefficient (db) Simulation Measurement Frequency (GHz) (d) Fig Continued Transmission coefficients of the azimuth difference port are shown in Fig The measured results show that transmission coefficients are between -5.8 db and -6.6 db over GHz. Similar amount of differences between measured and simulated 96

113 transmission coefficients are observed as in the case of the sum port. Transmission Coefficient (db) Simulation Measurement Frequency (GHz) (a) Transmission Coefficient (db) Simulation Measurement Frequency (GHz) (b) Fig Azimuth difference port transmission coefficient measurements (a) S 61 (b) S 62 (c) S 63 (d) S 64 97

114 Transmission Coefficient (db) Simulation Measurement Frequency (GHz) (c) Transmission Coefficient (db) Simulation Measurement Frequency (GHz) (d) Fig Continued Transmission coefficients of the elevation difference port are shown in Fig The measured results show that transmission coefficients are between -5.9 db and -6.6 db 98

115 over GHz. Measured transmission coefficients are less than the simulated ones by about 0.2 db. Transmission Coefficient (db) Simulation Measurement Frequency (GHz) (a) Transmission Coefficient (db) Simulation Measurement Frequency (GHz) (b) Fig Elevation difference port transmission coefficient measurements (a) S 71 (b) S 72 (c) S 73 (d) S 74 99

116 Transmission Coefficient (db) Simulation Measurement Frequency (GHz) (c) Transmission Coefficient (db) Simulation Measurement Frequency (GHz) (d) Fig Continued Fig shows the sum channel's normalized phase difference. Simulated and measured results agree well and the difference between them is less than

117 Phase difference (degree) arg(s5,1/s5,4)_simul arg(s5,1/s5,4)_measure Frequency (GHz) (a) Phase difference (degree) arg(s5,2/s5,4)_simul arg(s5,2/s5,4)_measure Frequency (GHz) (b) Fig Sum channel phase difference (a) at port 1, (b) at port 2, and (c) at port 3 101

118 Phase difference (degree) arg(s5,3/s5,4)_simul arg(s5,3/s5,4)_measure Frequency (GHz) (c) Fig Continued Fig shows the azimuth difference channel's normalized phase difference. Simulated and measured results agree well and the difference between them is less than

119 Phase difference (degree) arg(S6,1/S6,4)_simul 180-arg(S6,1/S6,4)_measure Frequency (GHz) (a) Phase difference (degree) arg(S6,2/S6,4)_simul 180-arg(S6,2/S6,4)_measure Frequency (GHz) (b) Fig Azimuth difference channel phase difference (a) at port 1, (b) at port 2, and (c) at port 3 103

120 Phase difference (degree) arg(s6,3/s6,4)_simul arg(s6,3/s6,4)_measure Frequency (GHz) (c) Fig Continued Fig shows the elevation difference channel's normalized phase difference. Simulated and measured results agree well and the difference between them is less than Phase difference (degree) arg(S7,1/S7,4)_simul arg(S7,1/S7,4)_measure Frequency (GHz) (a) Fig Elevation difference channel phase difference (a) port 1, (b) port 2, (c) port 3 104

121 Phase difference (degree) arg(s7,2/s7,4)_simul arg(s7,2/s7,4)_measure Frequency (GHz) (b) Phase difference (degree) arg(S7,3/S7,4)_simul 180-arg(S7,3/S7,4)_measure Frequency (GHz) (c) Fig Continued Measured isolations between comparator input ports are shown in Fig The measured isolations are all greater than than 27 db over GHz. 105

122 0-5 Simulation Measurement Isolation (db) Frequency (GHz) (a) 0-5 Simulation Measurement Isolation (db) Frequency (GHz) (b) Fig Comparator input port isolation. (a) S 56, (b) S 75, (c) S

123 Isolation (db) Frequency (GHz) (c) Fig Continued Simulation Measurement Performances of the fabricated monopulse comparator are summarized in Table

124 Table 6.1 Comparator measurement summery Sum pattern channel Transmission coefficient (db) Phase difference (degree) Mean RMS Mean RMS S S S S Azimuth pattern channel S S S S Elevation pattern channel S S S S Reflector Antenna Fabrication and Measurement A. Cassegrain Reflector Fabrication Designed Cassegrain reflector antenna has been fabricated using a numerically controlled milling machine. The main reflector is made from one piece solid aluminum block. It is composed of an attachment fixture, a flange for radome assembly and a feed horn supporting structure. The sub-reflector is also made from a solid aluminum block. The fabricated main reflector and sub-reflector are shown in Fig

125 (a) Main reflector Sub reflector (b) Fig Fabricated main and sub reflectors. (a) Main reflector back side and (b) front side of the main and sub reflectors The sub-reflector is supported by a dielectric radome (ε r = 2.7, polycarbonate) that is screwed to the main reflector's flange with bolts. The sub-reflector is placed to the center of the radome and screwed with a bolt so that the sub reflector does not move from the radome surface. Fig shows the sub-reflector on the radome. 109

126 Fig Sub-reflector on the radome The dielectric radome can influence the reflector antenna radiation pattern and the reflection coefficient, and it also produces a loss when the wave is travelling through it. Since the radome thickness is small compared to the free space wavelength, the effects on the radiation pattern and the loss can be negligible. Fig shows the dielectric radome geometry and design parameter. The radome geometry is chosen to be of a simple cone shape considering the design and fabrication simplicity. In using the cone shaped radome, the incidence angle on the radome surface is constant. To minimize the reflection on the radome surface, the radome thickness should satisfy following condition. d = n l 2 l = r l 0 2 e - sin q i (6.1) (6.2) where n = 1,2,3..., ε r = 2.7, and θ i is the incidence angle of the wave traveling in the direction of the reflector's axis of rotation. Fig shows the overall reflector antenna. 110

127 (a) (b) Fig Radome (a) geometry and (b) design parameter Radome Multimode Feed Horn Main Reflector Monopulse Comparator Fig Overall reflector antenna. B. Measurement of Reflector Antenna The overall reflector antenna measurements including the far-field pattern and the input reflection coefficients were carried out. The reflection coefficient measurements were taken at different positions of feed horn in order to determine the phase center displacement. It means the multimode feed horn antenna phase center position is changed 111

128 while the reflection coefficient is being measured. Fig shows the reflection coefficient versus the feed horn phase center displacement. 0 Sum channel Return loss (db) Phase center -0.5mm -1.0mm Frequency / GHz 0 Sum channel Return loss (db) mm +0.5mm Phase center Frequency / GHz (a) Fig Reflection coefficient versus feed horn displacement (a) sum port, (b) azimuth difference port, and (c) elevation difference port 112

129 0 DEL_AZ channel Return loss (db) Phase center -0.5mm -1.0mm Frequency / GHz 0 DEL_AZ channel Return loss (db) mm +0.5mm Phase center Frequency / GHz (b) Fig Continued 113

130 0 DEL_EL channel Return loss (db) mm +0.5mm Phase center Frequency / GHz 0 DEL_EL channel Return loss (db) Phase center -0.5mm -1.0mm Frequency / GHz (c) Fig Continued Measurements show that the sum channel reflection coefficient is barely less than -10 db over GHz and it seems to be very sensitive to the feed displacement. For the 114

131 azimuth difference channel, the reflection coefficient is less than -10 db over GHz and it is not that sensitive to the feed displacement compared to sum channel case. In the elevation difference channel measurements, the reflection coefficient is less than -10 db over GHz. The overall reflector antenna far-field patterns were measured in the near-field measurement facility. Fig shows the reflector antenna E-field distributions. The farfield measurements are shown in Fig The far-field measurement shows that side lobe levels in the sum and difference patterns are less than -20 db, and the sum pattern gain is db, and the difference patterns gains are around db. Null depths of the azimuth and elevation difference channels are, respectively, -16 db and -35 db relative to the difference channel maximum gain. (a) (b) Fig E-field distribution (a) abs value and (b) phase in sum pattern (c) abs value (d) phase in azimuth difference pattern (e) abs value (f) phase in elevation difference pattern 115

132 (c) (d) (e) (f) Fig Continued 116