Compact and Spherical Range Design, Application and Evaluation Walter D. Burnside and Inder J. Gupta The Ohio State University ElectroScience Laboratory 1320 Kinnear Road Columbus, Ohio (614) and (614) Presented on September 21-22, 2005 for Raytheon (Tucson, AZ).

Course Outline  Basic Range Design Guidelines (Burnside)  Compact Range Reflector Design (Gupta)  Absorber Design and Layout (Burnside)  Critical Range Evaluation (Gupta) Second Half Day First Full Day  R-Card Fences for Outdoor Ranges (Gupta)  Summary of Range Design Issues (Burnside)

Compact Range Reflector Design Inder (Jiti) Gupta ElectroScience Laboratory Electrical & Computer Engineering Dept. The Ohio State University 1320 Kinnear Raod Columbus, OH Phone: Fax:

Outline  Design parameters – Feed location – Reflector size – Focal length – Edge treatment  Performance comparison – Serrated edge – Rolled edge reflector  Low frequency reflector design

Feed Location  Floor  Side wall  Near a walkway (corner fed system  Subreflector fed system

Feed Location  Aperture blockage, feed accessibility and focal length are the main factors.  Subreflector fed is the most desired but is also the most expensive  Corner fed system also provides good feed accessibility and low aperture blockage. Focal length can be a little large.

Reflector Size Minimum reflector size is 20 min x 20 min, where min is the wavelength at the lowest frequency of operation.

Focal Length  To keep the length of the range small, the focal length should be the shortest possible.  A small focal length will lead to large taper and high cross-polarization in the quiet zone fields.  Conventionally, for a single reflector system (no subreflector), the focal length is selected such that the angle from the feed to the center of the reflector is 25° - 30°.  Assuming a 20 x 20 reflector and a 28° feed tilt angle, the focal lengths for various reflectors are – Floor-fed ≈ 20 – Side wall-fed ≈ 20 – Corner – fed ≈ 27.5

Edge Treatment  Edge treatment is applied to the compact range reflector to reduce the reflector edge diffracted fields in the quiet zone.  The two most popular edge treatments are – Edge serrations. – Rolled edges.

Serrated Edge Reflectors  The whole reflector is a section of a paraboloid.  For optimum performance, the serrations should be designed such that the edge diffracted rays do not reach the target zone.  One can use ray tracing to design serrations.

Serrated Edge Reflectors  The edge diffracted rays lie on a conical surface. The angle between the conical surface and the edge is equal to the angle between the incident ray and the edge.  Since the feed location and the edge is known, the conical surface is well defined.  In the design of serrations, one makes sure that the conical surface does not intersect the quiet zone.  For design purposes, the quiet zone is defined by a rectangle or an ellipse on a vertical plane which passes through the center of the quiet zone and is perpendicular to the desired planar wavefront.  We have developed an iterative computer code for the design of serrations.

Design of Serrations

Serrated Edge Reflector  The computer code is used to design serrations for a 20 x 20 floor-fed reflector.  Note that the basic reflector size is 10 x 10.  The focal length of the reflector is 20.  The performance of the reflector is evaluated using physical optics (PO) plus a PTD edge correction.  An AEL horn is used to illuminate the reflector.

Reflector With No Serrations

Reflector with Well Designed Serrations

Serrated Edge Reflector  As expected, the performance improves with an increase in the size of serrations.  Considering the cost issue, 5 serrations are a good choice.  One should add a serration every 1.5 to 2.

Rolled Edge Reflector  The elliptical section is added to the rolled edge such that the slope of the surface is continuous  The semi-major axis and the semi-minor axis of the ellipse are selected such that – the total size of the reflector does not exceed the desired limit – the minimum radius of curvature of the rolled edge is 0 /4 where 0 is the wavelength at the lowest frequency of operation.

Rolled Edge Reflector Surface where and  is a parametric angle such that 0 ≤  ≤  m

 Note that  m defines how much of the ellipse is used as the rolled edge.  Choice of  m does not affect a e or b e.  For cost reasons,  m is kept small.  Normally 105° ≤  m ≤ 150° Rolled Edge Reflector Surface

Blended Rolled Edge Reflector where b (  ) is the blending function which varies between [0,1] such that b (0) = 0 and b (  m ) = 1.

Blended Rolled Edge Reflector  The extended parabola is defined as where x m defines the section of the parabola used in blending.  Note that for a given junction height one can select a e, b e, x m and  m to satisfy various design constraints.  One also has to select the blending function.

Blended Rolled Edge Reflector  The blending function is chosen such that its first ( n -1) derivatives are zero at the junction. Let us call such a function an n th order blending function.  For an n th order blending function, the radius of curvature of the surface and its first n -1 derivatives are continuous across the junction.  The higher order blending functions, however, are effective for large rolled edges.  A cosine blending function is recommended.

Blended Rolled Edge Reflector  Cosine blending is a second order blending function. Thus, the surface curvature and its first derivative are continuous across the junction.  The discontinuity in the second derivative of the radius of curvature is given by where  One can select a e, b e, x m and  m such that  = 0. However, one has to meet the other two design constraints; – the total height – the minimum radius of curvature

Blended Rolled Edge Reflector  The two constraints can be defined as and where h max is the maximum desired height of the reflector surface, h is the total height of the reflector, and R sh is the radius of curvature of the reflector at the incident shadow boundary.  One can select a e, b e, x m and  m to minimize 2 under these two constraints.  A Lagrange multipliers method can be used for optimization. The function is then defined by where L 1 and L 2 are the Lagrange multipliers.

Blended Rolled Edge Reflector  The function G is not well behaved.  One can fix  m and vary a e, b e and x m to minimize G.  For (105° ≤  m ≤ 150°), the minimum value of G is approximately the same.  For large value of a e, the error term ( 2 ) increases very rapidly.  For small values of a e the increase in the error term is rather slow.  One should select a e such that it is smaller than its threshold value and then should find b e and x m to satisfy the two constraints for a given  m.

Blended Rolled Edge Reflector  The blended rolled edge should be added such that the total surface is smooth and continuous  The choice of the rolled edge plane for various points on the reflector rim is important.

Blended Rolled Edge Reflector  Let ( x av, y av, z av ) be the center of the reflector.  Define a new coordinate system, such that x = x ′ + x av y = y ′ + y av z = z ′ + z av  Next, define a cylindrical coordinate system (  ′,  ′, z ′) such that x′ =  ′ cos  ′ y′ =  ′ sin  ′ z ′ = z  For a given  ′, the rolled edge is added in the (  ′, z ′) plane.

Blended Rolled Edge Reflector  In the cylindrical coordinate system, the reflector surface is defined as where 0 ≤  ′ ≤ 2p, and 0 ≤  ′ ≤  j ′(  ′).  For a given  ′, the above equation represents a parabola of focal length F. The vertex of the parabola is at  The junction height in the rolled edge plane is  One can use the 2-D procedure to add the rolled edge and obtain the rolled edge parameters.  Since the height of the junction,  j ′′, varies with   ′, the rolled edge parameters will vary with  ′. The variation, however, is slow.

Blended Rolled Edge Reflector  Illustrative Example – 10 x 10 floor-fed reflector – 20 focal length – 5 rolled edge – Total reflector is 20 x 20

Blended Rolled Edge Reflector  PO edge correction is used for analysis.  The same results hold true for higher frequencies.

Performance Comparison  Focal length = 20 l.  A broadband double ridge AEL horn is used as the feed.  The test zone is located at 35 from the vertex of the reflector.

Performance Comparison Contour plot of the quiet zone field magnitude. Frequency of operation is 2 f l. Serrated edge reflectorRolled edge reflector

Performance Comparison  Antenna Measurement – Two phase scanned arrays of isotropic elements. – One of the antennas is 6 l x6 l, whereas the second antenna is 8 l x 8 l. – The amplitude taper of the antenna array is defined by a Kaiser-Bessel function, such that the first sidelobe is more than 40 dB below the main-lobe level. – The phase of the array elements is adjusted to scan the beams in the azimuthal plane. – Frequency of operation is 2 f l.

Performance Comparison Measured and actual pattern of the 6 l x 6 l antenna. Serrated edge reflectorRolled edge reflector

Performance Comparison Measured and actual pattern of the 8 l x 8 l antenna. Serrated edge reflectorRolled edge reflector

Performance Comparison  Scattering Measurement – Two diagonal flat plates of sizes 4 l x 4 l and 6 l x 6 l, respectively – For each rotation angle, the incident fields on the plate are calculated. – Next, the equivalent surface currents on the plate are calculated and integrated to obtain the far-zone scattered fields. – Frequency of operation is 2 f l.

Performance Comparison Measured and actual scattered fields of the 4 l x 4 l plate. Serrated edge reflectorRolled edge reflector

Performance Comparison Serrated edge reflectorRolled edge reflector Measured and actual scattered fields of the 6 l x 6 l plate.

Performance Comparison  The blended rolled edge reflector performs better for antennas as well as for scattering measurements.  The blended rolled edge reflector is, however, costly.  The blended rolled edge reflector illuminates the walls, ceiling and floor of the chamber more strongly than the serrated edge reflector, but the impact of this on the measurement accuracy can be made negligible by lining the inside of the chamber with good absorbing material.

Low Frequency Reflector Design  In the previous design, the compact range reflector was designed for a target size of 10 min or larger, where min is the wavelength at the lowest frequency of operation.  An important parameter in the selection of a measurement range is the chamber size.  For a shperical range, the range size is given by ND 2 /, where D is the largest target dimension. N is normally selected between one and four.  For a compact range system the range size is approximately 4 D.

Low Frequency Reflector Design Range size versus the target size

Low Frequency Reflector Design  A 20 x 20 reflector is used to control the edge diffraction in the quiet zone.  By properly selecting the rolled edge parameters in a compact range reflector, one can reduce the diffracted fields to very low values.  In a blended rolled edge reflector the edge diffracted fields are controlled by extending the parabolic reflector such that the resulting reflected fields are smooth and continuous  The concept could be extended to much lower frequencies.

Low Frequency Reflector Design  The edge diffracted fields, as expected, decrease with an increase in the rolled edge size.  A reflector with total height of 90’ to 100’ should be able to measure a 30’ target at 100 MHz and higher frequencies.  The reflector is inefficient in the sense that the potential target zone is less than half of the total size of the reflector.  In the case of blended rolled edge reflectors, one can trade the parabolic section with the rolled edge section (up to a certain limit) without any significant degradation in the quiet zone fields.  A part of the blended rolled edge can also be used to generate a planar wavefront.

Low Frequency Reflector Size Reflector parameters for various sizes of test zones Minimum frequency = 100 MHz Test zone size Total height of reflector Focal length Parabola section Rolled edge section Backend of target zone Ratio of reflector to test zone

Low Frequency Reflector Design  3-D Reflector – 30’ target at 100 MHz – Total reflector size 90′ x 90′ – Potential target zone 45′ x 45′ – Floor-fed system with focal length 84′ – Concave rim – Cosine blended rolled edge

Low Frequency Reflector Design Front view of the 3-D reflector to measure 30-ft target at 100 MHz and above frequencies

Low Frequency Reflector Design Quiet zone fields of the 3-D reflector at the back end of the target zone. Frequency = 100 MHz.

Low Frequency Reflector Design  The compact range reflectors can be designed to measure targets as small as 3.  In other words, the compact range reflectors can be used to measure targets at frequencies as low as 3 c / D, where c is the velocity of light and D is the largest dimension of the target.  For lower frequencies, one should consider a spherical range.

Compact Range Reflector Design (Summary)  Conventional reflector design – Serrated edge reflector – Rolled edge reflector  Compared the performance of a rolled edge reflector to a serrated edge reflector  Low frequency reflector design.

References  W.D. Burnside, M.C. Gilreath and B.M. Kent, “Rolled edge modification of compact range reflector,” AMTA’84, San Diego, CA.  W.D. Burnside, A.K. Dominek and R. Barger, “Blended surface concept for a compact range reflector,” AMTA’85, Melbourne, FL.  C.W.I. Pistorius and W.D. Burnside, “An improved main reflector design for compact range application,” IEEE Trans. Ant. Prop., vol.35, pp , March  I.J. Gupta, K.P. Ericksen and W.D. Burnside, “A method to design blended rolled edges for compact range reflectors,” IEEE Trans. Ant. Prop. Vol.38, pp , June  I.J. Gupta and W.D. Burnside, “Compact range measurement system for electrically small test zones,” IEEE Trans. Ant. Prop., vol. 39, pp , May  T.-H. Lee and W.D. Burnside, “Performance trade-off between serrated edge and blended rolled edge compact range reflectors,” IEEE Trans. Ant. Prop., vol. 44, pp , January  T.-H. Lee and W.D. Burnside, “Compact range reflector edge treatment impact on antenna and scattering measurements,” IEEE Trans. Ant. Prop., vol. 45, pp , January 1997.