COST Action IC0603 3rd Management Committee Meeting & Workshop - PowerPoint PPT Presentation

COST Action IC0603 3rd Management Committee Meeting & Workshop on "Antenna Systems & Sensors for Information Society Technologies" Limassol, Cyprus April 9 - 11, 2008 “PROBE COMPENSATED NEAR-FIELD TO FAR-FIELD “PROBE COMPENSATED NEAR-FIELD TO FAR-FIELD TRANSFORMATIONS WITH HELICOIDAL AND SPIRAL SCANNING TRANSFORMATIONS WITH HELICOIDAL AND SPIRAL SCANNING GEOMETRIES” GEOMETRIES” C Rizzo MI Technologies (Europe), United Kingdom F. D’Agostino University of Salerno, Italy

The Near-field Technique • Evolved from the beginning of the 70’s • Today processing power and receiver/VNA speed are readily available. • Bottleneck is acquisition time due to multiple axis scans. • A spherical measurement at 18GHz on a full sized aircraft or satellite can take days!

How do we speed up the measurement process? • Using a combined mechanical/electronic array of horn probes (SATIMO) Limited in frequency and accuracy!. • Using a combined mechanical/fibre optic probe array (University of Naples) • Substantial reduction of acquired samples by means of helicoidal and spiral scanning

Advantages of helicoidal scanning: No need for increment steps during scans. The data can be acquired by one continuous scan resulting in a 30 to 40% reduction of samples which means faster scans. Existing positioning systems can be used provided the controller has simultaneous axis movement capability. Acquired data interpolated to classical grids and then transformed to the far-field using the well known NIST-TICRA routines. The technique is well suited for production facilities where testing throughput is of paramount importance.

INTEREST AND MOTIVATIONS SPIRAL SCANS are obtained by means of continuous movements of the positioning systems of the probe and of the antenna under test (AUT) The reduction of the time needed for data acquisition

3 AVAILABLE SPIRAL SCANS

THEORETICAL BACKGROUND [O.M.BUCCI, C.GENNARELLI, C.SAVARESE, 1998] S = source enclosed in a convex domain D bounded by a surface � � � � M = observation surface Both � � � � and M have the same rotational simmetry

THE REDUCED FIELD If the AUT is enclosed in ball with radius a and the scanning helix is described by an analytical parameterization r = r ( � � � � ) � � � � � � � � � j � � � V V e “REDUCED PROBE VOLTAGE” � � � � optimal phase function to be determined � � r � r � parameterization to be determined � � � � V can be approximated by a spatially bandlimited function, [Bucci, Franceschetti, 1987] The voltage measured by a non directive probe has the same effective spatial bandwidth of the field.

THE SPIRAL

THE SPIRAL (…) It is obtained as intersection of the scanning surface with the line from O to the point which moves on a spiral wrapping a sphere of unit radius. The coordinates of P are The coordinates of P are � � � � � � � x dcos i � O � � � � � � � y dsin i � � � � � � z dcot d = cylinder radius; � = angular parameter describing the spiral; � = k �

THE SPIRAL (…) The elevation step �� of the helix is fixed equal to the sample spacing needed to interpolate along a cylinder generatrix. Accordingly � 2 �� � � 2N" 1 where � � � � � � � � � � � N" Int 1 N' N' Int ' a 1 � > 1 is an oversampling factor; �� > 1 is an enlargement factor. Being �� = 2 � k, it follows that: 1 � k � 2N" 1

THE OPTIMAL PHASE FUNCTION AND PARAMETERIZATION A nonredundant representation can be obtained by choosing: � � � � � � �� 2 � 2 � � 1 s r a a cos a r � � � a � � 2 � 2 � � k sin k ' d ' W � 0 � � is proportional to the curvilinear abscissa along the spiral � � wrapping the sphere modelling the source.

THE OPTIMAL PHASE FUNCTION AND PARAMETERIZATION (…) � � � a � � 2 � 2 � � k sin k ' d ' W � 0 The bandwidth W � is chosen such that � covers a 2 � range when the whole curve on the sphere modelling the source is described. � � � � 2N" 1 � � � a � � 2 � 2 � � k sin k ' d ' 0

THE INTERPOLATION SCHEME � n q � 0 � � � � � � � � � � � � � � � � � � � � � V , V D n N n N" n � � � n n q 1 0 � � � � � � � � � � � � � �� � � � �� � k n n n n i 0 � � � � � � � � N N" N' n Int 0 � � 0 � �� � � � 2 � � � � cos 2 � � � � � � � T ! " 2 1 � sin ! " N � � 2N" 1 2 � �� � cos q 2 # $ # $ � � � � � � � � � � � D N" � � N � � 2 � � � � ! " 2N" 1 sin 1 � � T � � # $ N 2 �� 2 cos q 2 � �

THE INTERPOLATION SCHEME (…) � m p � 0 � � � � � � � � � � � � � � � � � � � � � � � V V D � � n m M m M" m � � � m m p 1 0 � 2 m � � � � � � � � � �� � � � � m m i i � 2M" 1 � � Int � � � � � � � i m � � 0 �� � � � � � � � � M" Int 1 M' � � M � M" � M' � � � � � � � 'W M' Int 1 �

HELICOIDAL SCAN FOR ELONGATED ANTENNAS

HELICOIDAL SCAN FOR ELONGATED ANTENNAS (…) ' � � � � ( � being the length of the intersection curve C ' By adopting W 2 between the meridian plane through P and the ellipsoid), we get: � � � 2 � � % 2 v 1 1 � � & � � � � ! " 1 a v E cos % 2 ! " � 2 � % 2 � 2 � % 2 v # $ � � v � � � � � % 2 1 � � E sin u ' � � � 1 � � � � 2 % 2 � � � E 2 � � E = the elliptic integral of ( ( second kind � � r r r r ���������������� � � 1 2 1 2 u v 2f 2a % � f a = the eccentricity of C ’

HELICOIDAL SCAN FOR ELONGATED ANTENNAS (…) � � � � � � � The parametric equations of x dcos i � � � the helix become: � � � � � y dsin i � � � � � � � ' z dcot � � � where ' = k � � � � 2 � � % 2 v 1 1 � � & � � � � � � ! " a v 1 E cos % 2 ! " � 2 � % 2 � 2 � % 2 v # $ � � v The parameter � � � � is � � � � /W � times the curvilinear abscissa of the projecting point that lies on the spiral wrapping the ellipsoid and W � must be equal to � � � � / � times the length of such a spiral from pole to pole.

HELICOIDAL SCAN FOR ELONGATED ANTENNAS (…) The NF data required to carry out the NF-FF transformation can be recovered by means of the expansion: � n q � 0 ) * � � � � � � � � � � ' � � ' � ' � ' ' � ' � V , V D n N n N" n � � � n n q 1 0 where � m p � 0 � � � � � � � � � � � � � ' � � � � � � � � � V V D � � n m M m M" m � � � m m p 1 0 now � � � � � 'W N' Int 1 '

NUMERICAL TEST WR-90 at 10 GHz SOURCE: Elliptical uniform planar array lying on the plane y = 0 Elements:elementary Huygens sources polarized along the z axis Spacing: 0.5 + Cylinder radius: d = 12 +

NF RECONSTRUCTION Relative output voltage amplitude (dB) 0 p = q = 6 -10 χ = 1.20 -20 χ ' = 1.20 -30 -40 -50 -60 -70 0 10 20 30 40 50 60 70 z (wavelengths) Amplitude of the probe output voltage V on the generatrix at � = 90° . Solid line: exact. Crosses: interpolated.

RECONSTRUCTION ERRORS -15 Normalized maximum error (dB) χ ' = 1.20 -25 -35 -45 -55 χ = 1.10 χ = 1.15 -65 χ = 1.20 -75 χ = 1.25 -85 2 3 4 5 6 7 8 9 10 11 p=q Maximum reconstruction error of the probe output voltage V.

RECONSTRUCTION ERRORS Normalized mean-square error (dB) -40 χ ' = 1.20 -50 -60 -70 χ = 1.10 -80 χ = 1.15 χ = 1.20 -90 χ = 1.25 -100 2 3 4 5 6 7 8 9 10 11 p=q Mean-square reconstruction error of the probe output voltage V.

STABILITY Relative output voltage amplitude (dB) 0 p = q = 6 -10 χ = 1.20 -20 χ ' = 1.20 -30 -40 ∆ a = - 50 dB -50 ∆ a = 0.5 dB r ∆α = 5 -60 -70 0 10 20 30 40 50 60 70 z (wavelengths) Amplitude of the probe output voltage V on the generatrix at � = 90° . Solid line: exact. Crosses: interpolated from error affected data.

FF RECONSTRUCTION 0 p = q = 6 Relative field amplitude (dB) χ = 1.20 -10 χ ' = 1.20 -20 -30 -40 -50 -60 -70 -80 20 30 40 50 60 70 80 90 � (degrees) FF pattern in the E-plane. Solid line: exact field. Crosses: reconstructed from NF measurements.