Villa Galileo Firenze, 12 ottobre 2017 Antenna Pattern Measurement: Theory and Techniques

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1 Villa Galileo Firenze, 12 ottobre 2017 Antenna Pattern Measurement: Theory and Techniques F. D Agostino, M. Migliozzi University of Salerno, Italy

2 ANTENNAE REGIONS The REACTIVE NEAR-FIELD REGION is the zone immediately surrounding the antenna wherein the reactive field predominates. It extends up to a distance of about /2 from the antenna surface, being the wavelength. However, experience with NF measurements indicates that is a more reasonable limiting distance for such a region. Outside this zone the reactive field decays rapidly and it can be neglected at a distance of a few wavelengths from the antenna surface. The RADIATING NEAR-FIELD REGION is the intermediate zone between the reactive near-field and the farfield regions. In such a region the radiation fields predominate, but the angular distribution of the field is dependent on the distance from the antenna and the field does not exhibit the dependence e - jr /r typical of the antenna far field, being the wavenumber.

3 ANTENNAE REGIONS ( ) The FAR-FIELD REGION is the zone of the free space where the relative angular field distribution is independent of the distance from the antenna and the electric and magnetic fields vary according to the e -jr /r dependence. Commonly, for electrically large antennas, the inner boundaries of the Fraunhofer and Fresnel regions are set at 2D 2 / and D, respectively, where D is the maximum dimension of the antenna. These boundaries are determined by assuming acceptable a maximum phase error of 8, when a linear or quadratic phase approximation is used in the expression of the vector potential integral.

4 ANTENNAE REGIONS ( ) When measuring antennas having low ( 30 to 40 db) and ultralow (below 40 db) sidelobe levels, a distance far larger than 2D 2 / is needed. AsshowninFigs.1 and 2, particularly for antennas having low sidelobes, a significant increase in the sidelobe level and a more considerable raising of the null between it and the main lobe occur. Fig. 1 Fig. 2

5 Pros: No need of phase measurement Easy to build Cons: Erratic measurement with changes in surrounding environment. External signals may interfere with the direct signal and cause measurement errors. Error related to the finiteness of the antenna range length. OPEN SITE TEST RANGE Why do not measure the antenna pattern directly?

6 ANECHOIC CHAMBER NF measurements can be performed in a controlled environment, as an indoor shielded anechoic chamber, which allows to overcome those drawbacks that cannot be eliminated in far-field measurements. Antenna Radiating NF FFT transformation measurement surface NF FF transformation FF The measured NF data are usually transformed into FF patterns by using an expansion of the antenna field in terms of modes, namely, a complete set of solutions of the vector wave equation in the region outside the source.

ANECHOIC CHAMBER ( ) An anechoic chamber is a room designed to completely absorb

The quality of an anechoic chamber is described by the reflectivity level, which is

Traditionally, a chamber is evaluated by the Free-space VSWR method, a probe being

Radiation Absorber Material (RAM) is designed and shaped to absorb incident RF

7 ANECHOIC CHAMBER ( ) An anechoic chamber is a room designed to completely absorb reflections of electromagnetic waves. The quality of an anechoic chamber is described by the reflectivity level, which is the ratio of the reflected signal to the direct signal in the quiet zone. Traditionally, a chamber is evaluated by the Free-space VSWR method, a probe being scanned linearly in the region where the antenna under test (AUT) is to be located. Radiation Absorber Material (RAM) is designed and shaped to absorb incident RF radiation as effectively as possible, from as many incident directions as possible. The more effective the RAM, the lower the resulting level of reflected RF radiation.

COMPACT ANTENNA TEST RANGE (CATR) The CATR uses a source antenna which radiates a spherical wavefront and one or more secondary reflectors to collimate the radiated spherical

$The Feed doesn t illuminate directly the AUT The size of the reflector is related to the AUT dimensions The edge of reflector is shaped to minimize diffraction contributions Pros:$

8 COMPACT ANTENNA TEST RANGE (CATR) The CATR uses a source antenna which radiates a spherical wavefront and one or more secondary reflectors to collimate the radiated spherical wavefront into a planar wavefront within the desired test zone. One typical embodiment uses a horn feed antenna and a parabolic reflector to accomplish this. The Feed doesn t illuminate directly the AUT The size of the reflector is related to the AUT dimensions The edge of reflector is shaped to minimize diffraction contributions Pros: Cons: The absorbers avoid the multiple reflections on the anechoic chamber s wall DRAWBACKS: CATR is more expensive (3X-4X NF facility). Requires a heavy 3 axes positioner Requires larger space than NF facility

9 NEAR FIELD TO FAR FIELD TRANSFORMATIONS The magnitude and phase of the tangential E field are measured at regular intervals over a canonical surface (plane, cylinder, or sphere) located close to the AUT. The sampled E field is used to calculate the angular spectrum of the plane, the cylindrical or the spherical wave. This spectrum matches closely the radiated field angular distribution. This is called modal expansion of the radiated field.

10 PLANAR NF-FF TRANSFORMATION Any arbitrary monochromatic wave can be represented as a superposition of plane waves with different amplitudes and propagating in different directions. jk r Er Eke ˆ ( ) ( ) dk dk x y 1 jkz d jkx x ky y Eˆ x kx, ky e E 2 xx, y, de dxdy 4 1 jkz d jkx x ky y Eˆ y kx, ky e E 2 yx, y, de dxdy 4 Eˆ Eˆ k Eˆ k k z x x y y z

11 PLANAR NF-FF TRANSFORMATION TRUNCATION ERROR Since the measurement region is truncated in the plane-rectangular scanning, the reconstructed far field is affected by an inevitable truncation error, whose amount depends on the level of the neglected NF data external to the scanning area. When considering a scanning plane at distance d from the AUT, a convenient rule-ofthumb to predict the angular region of validity of the recovered FF pattern is given by: c tan L 1 x c c a d A ripple caused by the discontinuity of the near field at the edges of the scanning plane can appear even in the region of validity Such a validity angular region criterion was developed empirically from extensive NF measurements involving a large number of antenna and probe combinations and derived using a theoretical analysis.

12 In the cylindrical coordinate system (,, z), the tangential components of the electric field radiated by the AUT can be represented on the scanning cylinder as a superposition of elementary cylindrical waves: where a and b are the modal expansion coefficients: ( ) 1 j jz b H d E,z e e ddz CYLINDRICAL NF-FF TRANSFORMATION 2 2 j jz d d E,z b H d a H e e d 2 2 j jz E z,z b H d e e d z ( ) ( ) 1 j jz b H d a H E,z e e ddz H 2 2 ( 2) n d 2 d 4 Hankel function of second kind of order n ( )

13 CYLINDRICAL NF-FF TRANSFORMATION ( ) Once the modal coefficients are determined, the FF components of the electric field in the spherical coordinate system (R,,) can be evaluated by: jr e ER,, j2 sin j bcose R jr e ER,, 2 sin j acose R j j

14 SPHERICAL NF-FF TRANSFORMATION In the spherical coordinate system (r,, ), the transverse electric field radiated by an AUT can be expressed on a sphere of radius r = d containing it as a superposition of elementary spherical waves: Nmax n E d,, a g ( d)f, a g ( d)f, t 1nm 1n 1nm 2nm 2n 2nm n mn Where a 1nm, a 2nm are the spherical wave expansion coefficients, and: jm F, f e nm 1 1 nm jm F, f e nm 2 2 nm The expansion coefficients in can be evaluated from the knowledge of the tangential electric field on the measurement sphere ( 2) g 1 ( d) h ( d) n n 1 d ( 2) g 2n( d) rh n ( r) rd( r) r d

15 SPHERICAL NF-FF TRANSFORMATION ( ) Harmonic vectorial functions m m 1 jm m d m f 1nm P ˆ n (cos ) P n (cos ) ˆ m 2n(n 1) sin d m m 1 d m jm m f 2nm P ˆ n (cos ) P n (cos ) ˆ m 2n(n 1) d sin Where: ( 2 h ) (x) being the spherical Hankel function of second kind and order n n m n P (x) normalized associated Legendre functions [Belusov, 1962] In the classical approach, the choice of the highest spherical wave is usually determined according to the following rule-of-thumb [Hald, Hansen, Jensen, Larsen, 1988]: N max Int a 10

16 SPHERICAL NF-FF TRANSFORMATION ( ) The expansion coefficients a 1nm and a 2nm can be evaluated from the knowledge of the tangential electric field on the scanning sphere by taking into account that the spherical vector wave functions are orthonormal. As a matter of fact: t nm 12, 12, and therefore: 0 0 t * 12, 12, E,F E d,, F, sindd a g ( d) nm 1 * jm a12, E d,, f e sindd 12, nm t nm g 12, n( d) 0 0 Once the spherical wave expansion coefficients have been determined, in the FF region we get: nm n E t r,, ejr r N max n n j n1 a 1nm f 1nm mn j n a 2nm f 2nm ejm

17 PROBE COMPENSATION ( ) The modal coefficients c n and d m associated to the probe can be determined from the measured amplitude and phase of the field radiated by it in the FF region: jr e n R n n 2 E R,, j sin j d cos e jr e n R n n 2 E R,, sin j c cos e jn jn

18 NON REDUNDANT NF-FF TRANSFORMATIONS In this context, the application of the theoretical results concerning the nonredundant sampling representations of the EM field has allowed a remarkable reduction of the number of needed NF measurements.

NON REDUNDANT NF-FF TRANSFORMATIONS ( ) F S = source enclosed in a convex domain D bounded by a surface Σ M = observation surface C = meridian curve or azimuthal circumference Both Σ and M have the

19 NON REDUNDANT NF-FF TRANSFORMATIONS ( ) F S = source enclosed in a convex domain D bounded by a surface Σ M = observation surface C = meridian curve or azimuthal circumference Both Σ and M have the same rotational simmetry REDUCTED FIELD r r F E e j optimal phase function to be determined parameterization to be determined can be approximated by a spatially bandlimited function [Bucci, Franceschetti, 1987]

20 NON REDUNDANT NF-FF TRANSFORMATIONS ( ) When considering elongated or quasi-planar antennas, the spherical AUT modelling induces a volumetrical redundancy which implies an unnecessary increase in the number of required data. S N area of 2 2 area of area of S

21 INNOVATIVE

22 Flexible NF facility

23 Thanks for attention!

24 ADDENDUM: PROBE COMPENSATION In an actual scanning the ideal probe assumption must be removed. In the planar or cylindrical facility, the AUT center is not seen under a constant direction when the probe moves on the scanning surface fpe t vp

25 PROBE COMPENSATION ( ) The AUT is in the FF region of the probe, while this latter is in the AUT NF region the AUT elements are seen under different directions from the probe

26 PROBE COMPENSATION ( ) When using a non directive probe, the probe output voltage has the same effective bandwidth of the AUT The previous results can be used for interpolating the samples of the reduced probe voltage

27 PROBE COMPENSATION ( ) As well known, the far field is given by: E R,, j2 e jr n R sin jn b n cos e jn E R,, 2 e jr n R sin jn a n cos e jn

28 PROBE COMPENSATION ( ) The cylindrical wave expansion coefficients a n and b n are related to [Leach e Paris, 1973]: the two-dimensional Fourier transform I n and I n of the output voltage of the probe for two independent sets of measurements (the probe is rotated 90 in the second set); the modal coefficients of the cylindrical wave expansion of the field radiated by the probe and rotated probe, when used as transmitting antennas.

29 PROBE COMPENSATION ( ) 2 2 an I 2 n dm Hnm d n m 2 In dmhn md m 2 2 bn I 2 n cm Hnm d n m 2 In cm Hnmd m

30 PROBE COMPENSATION ( ) where: I n () v(d, 0,z 0 ) e jn 0 e jz 0 d 0 dz 0 I n ' () v'(d, 0,z 0 ) e jn 0 e jz 0 d 0 dz 0

31 PROBE COMPENSATION ( ) 2 n cmhnmd m 2 dm Hnmd m 2 cm Hnmd m 2 dmhnmd m ( 2 H ) (x) being the n spherical Hankel function of second kind and order n and 2 2 ( )

FAR-FIELD RECONSTRUCTION FROM A MINIMUM NUMBER OF SPHERICAL SPIRAL DATA USING EF- FECTIVE ANTENNA MODELINGS

Progress In Electromagnetics Research B, Vol. 37, 43 58, 2012 FAR-FIELD RECONSTRUCTION FROM A MINIMUM NUMBER OF SPHERICAL SPIRAL DATA USING EF- FECTIVE ANTENNA MODELINGS F. D Agostino, F. Ferrara, C. Gennarelli