Educational Procedure for Designing and Teaching Reflector Antennas in Electrical Engineering Programs. Abstract. Introduction

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1 Educational Procedure or Designing and Teaching Relector Antennas in Electrical Engineering Programs Marco A.B. Terada Klipsch School o Electrical and Computer Engineering New Mexico State University Las Cruces, New Mexico mterada@nmsu.edu Session II A 5 Abstract This paper summarizes a simple procedure to design axisymmetric and oset single parabolic relector antennas with circular apertures. The proposed procedure yields reasonably good results in practice and is specially suitable or introducing students to the geometry and basic electrical characteristics o relector antennas. Computer simulations and measured data are also presented in support and validation o the analytical procedure. Together with the proposed procedure, the computer simulations and measurements were identiied as the three major oundations necessary or properly teaching relector antennas in Electrical Engineering programs. Introduction Relector antennas can be considered as one o the most successul electrical devices o all time, in view o their importance in extensive and diverse modern engineering applications, ranging rom communication systems and electronic warare to radio astronomy and deep-space exploration 1. Although there are several procedures available in the literature or designing relector antennas, the ew applicable to the oset geometry are not very practical and didactic 1. In addition, an attempt is made to deine and use design parameters within limits that are consistent with the current production o relector antennas in the industry, in which the oset relector represents more than 90% o the market 1. The procedure herein introduced is derived rom 1 and was developed with the sole intent o making the design o relector antennas more accessible to undergraduate students. One o the main challenges o integrating design problems in the electrical engineering curriculum is to constrain an open-ended complex problem into a closed-orm simple procedure valid within useul limits. Furthermore, in order or the students ully understand the electrical behavior o the device being designed, rather than just ollow a step-by-step recipe, it is imperative to correlate perormance results almost immediately ater a given coniguration is obtained. An attractive way to accomplish that is through computer simulations. Finally, real measured data is also needed to validate the whole process, while also providing the students with valuable manuacturing experience when possible. Proceedings o the 2002 ASEE Gul-Southwest Annual Conerence, The University o Louisiana at Laayette, March 20 22, Copyright 2002, American Society or Engineering Education

2 Geometrical Parameters The general geometry o the parabolic relector antenna is shown in Fig. 1 and the parameters are deined in Table 1. θ Figure 1. Geometry or the parabolic relector antenna. See Table 1 or deinition o symbols. Table 1. Deinitions o symbols or the parabolic relector antenna o Fig. 1. Symbols: Deinitions: D Diameter o the projected aperture o the parabolic main relector (D = D p or an axisymmetric paraboloid). D p Diameter o the projected aperture o the parent paraboloid; D p = D + 2H. H Oset o relector center (H = 0 or an axisymmetric paraboloid). F Paraboloid ocal length. Point F Focal point. Point A Apex o the parent paraboloid. Point B Point on relector which bisects subtended angle viewed rom Point F. Point C Point on relector which projects to the center o the projected aperture. Point P Point on relector corresponding to the ray rom the peak o eed pattern. ψ Angle o eed antenna pattern peak relative to relector axis o symmetry (S); ψ = 0 0 or an axisymmetric paraboloid. ψ B Value o ψ which bisects the relector subtended angle (ψ U - ψ L ). ψ C Value o ψ when the eed is aimed at the relector point C. Proceedings o the 2002 ASEE Gul-Southwest Annual Conerence, The University o Louisiana at Laayette, March 20 22, Copyright 2002, American Society or Engineering Education

3 Procedure or Designing Parabolic Relector Antennas The ollowing steps summarize a simple procedure and corresponding rationale to design axisymmetric (H = 0) and oset relector antennas. A. Determination o Relector Diameter: The ollowing equation is very useul to estimate a value o D to achieve a required gain 2 G 2 4πAp πd g [ Not in db] = ε ap = ε 2 ap (1) λ λ where A p is the physical area o the antenna aperture and ε ap is the aperture eiciency, typically 0.6 to 0.7 (60% to 70%) or many parabolic relector systems used in practice. Note that G =10log g [db]. B. Determination o Oset Distance: The oset distance H controls the amount o blockage caused by the eed and supporting structure on the relector projected aperture. Many relectors nowadays are just ully oset paraboloids (H = D/2); i.e., the bottom o the relector just touches its axis o symmetry. This coniguration avoids the blockage rom the eed supporting structure and waveguide, although part o the eed aperture is still directly in ront o the relector. Nevertheless, the total blockage area is still signiicantly smaller than the one presented by axisymmetric conigurations (H = 0). Values o H larger than D/2 can overcome blockage but also increase the total volume occupied by the relector, which in some cases is not recommended. In addition, the manuacturing process and associated adjustments become more diicult as H increases. C. Selection o Relector Curvature: Values usually encountered in practice or the relector curvature, F/D p, are between 0.25 and 1.0, where D p = D + 2H. Higher values ease the manuacturing process (i.e., the relector is latter), but require a narrower eed pattern to illuminate the relector which results in larger eed antennas. A typical value nowadays is (F/D p ) = 0.3 which yields a compact design. D. Determination o Feed Pattern: An important parameter or determining the necessary eed pattern is the relector illumination RI, which in db is given by 2 θ + ψ q RI = 20 log cos + 20 log (cos θ ) (2) 2 where the irst term in the right side o (2) is normally reerred to as spherical spreading loss, and accounts or the power spreading due to spherical propagation o the wave between the ocal point and the parabolic relector surace. The second term in the right side o (2) is the normalized eed pattern in db o Proceedings o the 2002 ASEE Gul-Southwest Annual Conerence, The University o Louisiana at Laayette, March 20 22, Copyright 2002, American Society or Engineering Education

4 q ( θ ) cos θ C = (3) which is a pattern model widely used in practice. The main advantage o (3) is that the directivity o the eed, or its gain g i ohmic losses are not taken into account, can be ound analytically in closed orm with g (4) [ ] = 4q 2 Not in db + The parameter q can be obtained rom (2) or a required relector illumination RI in db at a direction θ as RI 2 θ + ψ log cos 20 2 q = (5) log cosθ ( ) An usual value or RI at the relector edges, oten reerred to as edge illumination EI, is -11 db and assures optimal gain perormance or axisymmetric paraboloids 2 (ψ = 0 o and θ = ψ L = ψ U ). In oset relectors, ψ L ψ U as shown in Fig. 1, but a speciied value o EI at both edges can still be obtained, by solving or ψ the equation ormed by imposing that q(θ + ψ = ψ L ) = q(θ + ψ = ψ U ), which yields q(θ = ψ L - ψ ) = q(θ = ψ U - ψ ). Once ψ is determined, the parameter q can be calculated directly rom (5) or the speciied value o RI (i.e., EI), at either θ + ψ = ψ L or θ + ψ = ψ U, since they now should yield the same result. Under this condition, the edge illumination is called balanced, and yields near-minimum sidelobe levels over practical ranges o eed pointing, with only small penalties in gain and cross polarization 1. A graphical technique to determine ψ or the same condition is particularly recommended when only measured eed patterns are available 1. In practice, however, it is common to ind oset systems employing ψ = ψ B or ψ = ψ C ; See Fig. 1. For either case the edge illumination EI is in general unbalanced. As a consequence, dierent values o q are obtained with (5), depending whether θ + ψ = ψ L or θ + ψ = ψ U. A simple arithmetic mean can then be taken to speciy the required eed pattern. Although approximate, this simple procedure yields reasonably good results in practice and is well suited or our purposes. Once the parameter q is determined, (4) and (1) can be used to estimate the aperture diameter, or area, o the required eed antenna. A typical value o ε ap = 0.55 (55%) can be used or eed horns. A more exact approach is available when the eed antenna is an open-ended rectangular waveguide o wide and narrow dimensions a and b, or an open-ended circular waveguide o radius a. For those cases, the waveguide dimensions can be determined rom (4) respectively with g = 32ab / πλ (εap 0.81) or g = 10.5π a / λ (εap 0.84). I the result indicates a eed antenna with an aperture considered too large, a higher value o RI (i.e., EI at the relector edges) should be employed to avoid unnecessary blockage. For an oset relector, a larger value o H can also be tried and the whole procedure needs to be repeated. Proceedings o the 2002 ASEE Gul-Southwest Annual Conerence, The University o Louisiana at Laayette, March 20 22, Copyright 2002, American Society or Engineering Education

5 Design Results and Computer Simulations The design procedure described in the previous section was successully employed to design a 1.6-m just ully oset paraboloid, built and tested or satellite TV reception at the University o Brasilia Brazil, where the author was previously teaching; See Fig. 2. The geometrical parameters are listed in Table 2 in conjunction with the simulation results obtained at 3.95 GHz with the computer code PRAC (Parabolic Relector Analysis Code), developed by the author 1. PRAC is a user-riendly code developed to analyze axisymmetric and oset parabolic relector antennas, evaluating the radiation integral (physical optics surace current integration) with the Jacobi-Bessel method 1. PRAC is currently being distributed with a textbook 2 and used by many universities and antenna manuacturers worldwide. Note rom Table 2 that the computed aperture eiciency is higher than the values usually encountered in practice (overestimation o about 10% to 15% is typical), due mostly to losses and system imbalances not modeled by the computer simulations. Figure 2. Oset parabolic relector built and tested or satellite TV reception at C-band. Conclusions A simple educational procedure to design relector antennas was described in detail. The procedure was specially developed to introduce the designing o relector antennas to undergraduate students. The procedure yields results that present good correlation to computer and measured data, and was employed to design and manuacture a 1.6-m oset relector antenna or satellite TV reception at the C-band. Three major blocks were ound essential or the eective teaching o relector antennas in Electrical Engineering: 1) Closed-orm, step-by-step analytical design procedures, 2) Analysis sotware, and 3) Manuacturing o prototypes and measurements. Finally, it is worth mentioning that the computer programming o the design procedure itsel must be avoided initially, as the use o simple analytical expressions aid the students to comprehend the basic geometry and electrical characteristics o the device being designed. Although the main conclusions herein addressed appear to be extendable to other engineering areas and devices, more evidence is currently needed to provide a more generic assessment o adroit design methodologies and their impact in engineering education. Proceedings o the 2002 ASEE Gul-Southwest Annual Conerence, The University o Louisiana at Laayette, March 20 22, Copyright 2002, American Society or Engineering Education

6 Table 2. Geometrical parameters and perormance values computed with the code PRAC at 3.95 GHz or the oset parabolic relector o Fig. 2. Parameters: Values and relation to design procedure: D 160 cm; design goal o at least 34.5 dbi in gain with ε ap = 0.65 or 65% (see step A or urther details). A gain o at least 34.5 dbi is recommended or satisactory reception o satellite TV signals, as determined by a simple downlink analysis perormed on-site. H 80 cm; H = D/2 or a just ully oset paraboloid (see step B). D p 320 cm; D p = D + 2H. (F/D p ) 0.3 (see step C). F 96 cm Angles ψ L & ψ U ψ L = 0 0 and ψ U = ψ , yielding a balanced illumination with RI = EI = db at both relector edges or a eed with q = 5.83 (see step D or urther details). Note that q = 5.83 (measured eed taper o 13.5 db at 40 0 ) represents a eed gain o about 14 dbi with an aperture diameter o 16.4 cm and ε ap = 55% at 3.95 GHz. Perormance values computed with PRAC at 3.95 GHz: Gain dbi Crosspolar level db ε ap % Reerences 1. Marco A.B. Terada, "Relector Antennas", Encyclopedia o Electrical and Electronics Engineering (invited), edited by John Webster, Vol. 18, pp , John Wiley & Sons, Warren L. Stutzman and Gary A. Thiele, Antenna Theory and Design, 2nd edition, John Wiley & Sons, MARCO A.B. TERADA Dr. Terada currently serves as an Assistant Proessor o Electrical Engineering at New Mexico State University. His interests in research and development include applied electromagnetics and numerical methods, with emphasis on the design, manuacturing and testing o antennas and microwave devices applied to wireless networks (satellites, cellular, WLANs, etc.). Previous unded research included the application o neural networks, uzzy logic and genetic algorithms to the synthesis o antennas and to the reduction o intererences in digital satellite communication systems. In addition, Dr. Terada has also interest in the development and implementation o technologies applied to distance learning, such as VSAT and wireless networks, cable, video, Internet and CDs. Dr. Terada has extensive academic, industrial and consulting experiences, having published several journal articles and symposium papers, including an invited chapter on relector antennas or the Wiley Encyclopedia o Electrical and Electronics Engineering (John Wiley and Sons, 1999). Dr. Terada was a co-ounder and has served as Editor-in- Chie o the Journal o Microwaves and Optoelectronics (ISSN ), and has been recently involved with the design, manuacturing and testing o the INTELSAT IX satellite leet (seven spacecrat operating in C and Ku bands). Proceedings o the 2002 ASEE Gul-Southwest Annual Conerence, The University o Louisiana at Laayette, March 20 22, Copyright 2002, American Society or Engineering Education