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

C Rizzo MI Technologies (Europe), United Kingdom

• F. D’Agostino

University of Salerno, Italy “PROBE COMPENSATED NEAR-FIELD TO FAR-FIELD TRANSFORMATIONS WITH HELICOIDAL AND SPIRAL SCANNING GEOMETRIES” “PROBE COMPENSATED NEAR-FIELD TO FAR-FIELD TRANSFORMATIONS WITH HELICOIDAL AND SPIRAL SCANNING GEOMETRIES”

COST Action IC0603

3rd Management Committee Meeting & Workshop

• n

"Antenna Systems & Sensors for Information Society Technologies" Limassol, Cyprus April 9 - 11, 2008

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
• f 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

The reduction of the time needed for data acquisition SPIRAL SCANS are obtained by means of continuous movements of the positioning systems

• f the probe and of the antenna under test (AUT)

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

• Both
• and M have the same

rotational simmetry M = observation surface

If the AUT is enclosed in ball with radius a and the scanning helix is described by an analytical parameterization r = r (

• )

“REDUCED PROBE VOLTAGE”

• j

V V e

• THE REDUCED FIELD

can be approximated by a spatially bandlimited function, [Bucci, Franceschetti, 1987]

• V
• ptimal phase function to be determined

parameterization to be determined

r r

The voltage measured by a non directive probe has the same effective spatial bandwidth of the field.

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.

• i

i

x dcos y dsin z dcot

• THE SPIRAL (…)

d = cylinder radius; = angular parameter describing the spiral; = k The coordinates of P are The coordinates of P are

O

The elevation step of the helix is fixed equal to the sample spacing needed to interpolate along a cylinder generatrix. Accordingly

2 2N" 1

• N"

Int 1 N'

where

• N'

Int 1 ' a

• > 1 is an oversampling factor;

> 1 is an enlargement factor. Being = 2k, it follows that:

1 k 2N" 1

• THE SPIRAL (…)

• is proportional to the curvilinear abscissa along the spiral

wrapping the sphere modelling the source.

• 2

2 1

s r a a cos a r

THE OPTIMAL PHASE FUNCTION AND PARAMETERIZATION

• 2

2

a k sin k ' d ' W

A nonredundant representation can be obtained by choosing:

THE OPTIMAL PHASE FUNCTION AND PARAMETERIZATION (…)

The bandwidth W is chosen such that covers a 2 range when the whole curve

• n

the sphere modelling the source is described.

• 2N" 1

2 2

a k sin k ' d '

• 2

2

a k sin k ' d ' W

• n

q N N" n n n n q 1 n

D , V V

• n

Int

n n i

k n n

• N

N" N'

THE INTERPOLATION SCHEME

• !

" # $

• !

" # $

N"

sin 2N" 1 2 D sin 2N" 1 2

• !

"

• #

$

• 2

N N N 2

cos 2 T 2 1 cos q 2 2 1 T cos q 2

THE INTERPOLATION SCHEME (…)

• m

p M M" m m m m p 1 m

n

D V V

i

m Int

• m

i i

2 m m 2M" 1

• M"

Int 1 M' 'W M' Int 1 M M"M'

HELICOIDAL SCAN FOR ELONGATED ANTENNAS

• 1

2 1 2

r r r r u v 2f 2a

• %
• &
• !

" % ! " %

• %

# $

• 2

2 1 2 2 2 2 2

v 1 1 a v E cos v v

By adopting W 2

'

• ( being the length of the intersection curve

C'

between the meridian plane through P and the ellipsoid), we get:

• %
• '
• %
• 2

1 2

E sin u 1 2 E 2

( (

E = the elliptic integral of second kind % f a = the eccentricity of C’

HELICOIDAL SCAN FOR ELONGATED ANTENNAS (…)

The parametric equations of the helix become:

• '
• i

i

x dcos y dsin z dcot where ' = k

• %
• &
• !

" % ! " %

• %

# $

• 2

2 1 2 2 2 2 2

v 1 1 a v E cos 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 (…)

) *

• ' '

' ' '

• '
• n

q N N" n n n n q 1 n

D , V V

• The NF data required to carry out the NF-FF

transformation can be recovered by means of the expansion:

HELICOIDAL SCAN FOR ELONGATED ANTENNAS (…)

• '
• 'W

N' Int 1

now where

• '
• m

p M M" m m m m p 1 m

n

D V V

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 + WR-90 at 10 GHz

NUMERICAL TEST

NF RECONSTRUCTION

• 70
• 60
• 50
• 40
• 30
• 20
• 10

10 20 30 40 50 60 70 p = q = 6 χ = 1.20 χ' = 1.20

z (wavelengths) Relative output voltage amplitude (dB)

Amplitude of the probe output voltage V on the generatrix at = 90° . Solid line: exact. Crosses: interpolated.

RECONSTRUCTION ERRORS

Maximum reconstruction error of the probe output voltage V.

• 85
• 75
• 65
• 55
• 45
• 35
• 25
• 15

2 3 4 5 6 7 8 9 10 11 χ' = 1.20 χ = 1.10 χ = 1.15 χ = 1.20 χ = 1.25

p=q Normalized maximum error (dB)

RECONSTRUCTION ERRORS

Mean-square reconstruction error of the probe output voltage V.

• 100
• 90
• 80
• 70
• 60
• 50
• 40

2 3 4 5 6 7 8 9 10 11 χ' = 1.20 χ = 1.10 χ = 1.15 χ = 1.20 χ = 1.25

p=q Normalized mean-square error (dB)

STABILITY

Amplitude of the probe output voltage V on the generatrix at = 90° . Solid line: exact. Crosses: interpolated from error affected data.

• 70
• 60
• 50
• 40
• 30
• 20
• 10

10 20 30 40 50 60 70 ∆α = 5 ∆a = - 50 dB r ∆a = 0.5 dB p = q = 6 χ = 1.20 χ' = 1.20

z (wavelengths) Relative output voltage amplitude (dB)

FF pattern in the E-plane. Solid line: exact field. Crosses: reconstructed from NF measurements.

FF RECONSTRUCTION

• 80
• 70
• 60
• 50
• 40
• 30
• 20
• 10

20 30 40 50 60 70 80 90 p = q = 6 χ = 1.20 χ' = 1.20

(degrees) Relative field amplitude (dB)

FF pattern in the H-plane. Solid line: exact field. Crosses: reconstructed from NF measurements.

FF RECONSTRUCTION

• 80
• 70
• 60
• 50
• 40
• 30
• 20
• 10

90 120 150 180 210 240 270 p = q = 6 χ = 1.20 χ' = 1.20

(degrees) Relative field amplitude (dB)

EXPERIMENTAL VALIDATION

Dimensions of the chamber are 8mx5mx4m. The vertical scanner has a height of 270 cm The AUT is an MI-12-8.2 standard gain horn with aperture 19.4 cm x 14.4 cm Measurements performed at using the 10GHz MI3000 MI Technologies Acquisition & Analysis Software

Amp NF Data at Generatrix phi=0

Solid: measured Cross: interpolated

Near-field Data

Phase NF Data at Generatrix phi=0

Solid: measured Cross: interpolated

Near-field Data

FF pattern in the E-plane Solid line: reference. Crosses: reconstructed from NF data acquired via helicoidal scanning.

Measured Patterns

FF pattern in the H-plane Solid line: reference. Crosses: reconstructed from NF data acquired via helicoidal scanning.

Measured Patterns

• Good Agreement in both Planes
• Reduced number of points 1921 needed by the proposed

NF–FF transformation helicoidal scan compared with 11160 in the classical approach

• The helicoidal scanning allows one to remarkably reduce the

number of measurements, without losing the accuracy of the classical approach

• MI Technologies and University of Salerno are ready to start

work on the spherical spiral. www.mi-technologies.com (ex Scientic-Atlanta)

Conclusions