ESTIMATION OF ERROR INDUCED BY A CROSSED- DIPOLE PROBE … · If the test antenna is ... The radius...

Progress In Electromagnetics Research B, Vol. 21, 27–45, 2010

ESTIMATION OF ERROR INDUCED BY A CROSSED-DIPOLE PROBE IN THE NEAR-FIELD

S. Paramesha

Department of E & CAIT, Chikmagalur, Karnataka 577102, India

A. Chakrabarty

Department of E & ECEIIT, Kharagpur, West Bengal 721302, India

Abstract—The Moment Method is used to estimate the error inducedby a compact measuring probe in the near-field. A crossed-dipole isused as a compact near-field measuring probe of a waveguide radiatorin an infinite ground plane, since it measures both co-pole and cross-pole components simultaneously. However, due to multiple reflectionsbetween radiator and probe, in addition, mutual coupling effectsbetween the poles, near-field values are changed. The relative sampledelectric field pattern (without the probe) is compared to the relativesampled co-pole voltage pattern in the scan plane and the induced erroris computed. The radiating waveguide’s reflection coefficient is alteredwith respect to the reflection coefficient when there is no probe in thenear-field. The numerical results concerning the reflection coefficientwithout the probe are compared to the measured values, and goodagreement is observed.

1. INTRODUCTION

If the test antenna is reciprocal, the receiving mode characteristics(gain, radiation pattern etc.) are identical to those transmitted bythe antenna. The ideal condition for measuring far-field radiationcharacteristics then, is the illumination of the test antenna by a planewaves: uniform amplitude and phase. Although this ideal condition isnot achievable, it can be approximated by separating the test antennafrom the illumination source by a large distance on an outdoor range.

Corresponding author: S. Paramesha (prm [email protected]).

28 Paramesha and Chakrabarty

At large radii, the curvature of the spherical phasefront produced bythe source antenna is small over the test antenna aperture. If theseparation distance is equal to the inner boundary of the far-fieldregion, 2D2/λ then the maximum phase error of the incident field froman ideal plane wave is about 22.5 degrees. In addition to phasefront,curvature due to finite separation distances, reflections from groundand nearby objects are possible sources of degradation of the testantenna illumination.

Experimental investigations suffer from a number of drawbackssuch as: 1) For pattern measurements, the distance to the far-fieldregion is too long even for outside ranges. It also becomes difficult tokeep unwanted reflections from the ground and the surrounding objectsbelow acceptable level. 2) In many cases, it may be impractical to movethe antenna from the operating environment to the measuring site. 3)For some antennas, such as phased arrays, the time required to measurethe necessary characteristics may be enormous. 4) Outside measuringsystems provide an uncontrolled environment, and they do not possesan all-weather capability. 5) Enclosed measuring systems usuallycannot accommodate large antenna systems (such as ships, aircrafts,large spacecrafts, etc.). 6) Measurement technique, in general, areexpensive. Some of the shortcomings can be overcome by using specialtechniques, such as indoor measurements, far-field pattern predictionfrom near-field measurements, etc.

The radiating structure used in the analysis is the open endof a waveguide, terminated by an infinite metallic flange. TheMethod of Moments is used to solve many waveguide and wireantenna problems [1–3]. The application of the Moment Method usingthe entire domain basis function [4] converts the integral equationsrepresenting the boundary condition at waveguide aperture intomatrix equations, from which, the coefficients of the basis functionsrepresenting the aperture field can be evaluated.

The crossed-dipole being used as a near-field measuring probeconsists of two dipoles oriented orthogonal to each other, and thecross-dipole is sensitive to electric field components oriented parallelto the axis of the co-pole and cross-pole of the probe. The scatteringproperties of the objects are polarization dependent. The ability of thereceive antenna to measure these scattered fields is determined by thepolarization match between the scattered fields and the polarizationof the receive antenna. A complex polarization mismatch using dipoleantennas results when the scattered field and the polarization of thereceive antenna are both linearly polarized and oriented at right anglesto each other. Using a crossed-dipole probe, both co-pole and cross-pole near-field components can be sampled simultaneously in the scan

Progress In Electromagnetics Research B, Vol. 21, 2010 29

plane; however, the probe itself induces error because of multiplereflections and mutual coupling effect [5].

2. FORMULATION OF THE PROBLEM

The crossed-dipole in the near-field of an open-ended waveguideradiator of aperture dimension 2a × 2b in an infinite ground planeis shown in Figure 1. The waveguide feeding the rectangular apertureis assumed to be excited in the dominant TE10 mode.

(a)

(b)

Figure 1. Crossed-dipole probe at the near-field of the waveguideradiator. (a) Probe in x-y plane. (b) Probe in y-z plane.


The incident magnetic field at the waveguide aperture for thedominant TE10 mode is given by:

H incx = −Y0 cos

(πx

2a

)e−jβz (1)

and the electric field at the radiating aperture is described by:−→E (x′, y′, 0) = uy

∑M

p=1Epep (2)

where the entire domain basis functions ep, (p = 1, 2, . . . , M) aredefined by:

ep =

sinpπ

2a (x + a) −a ≤ x ≤ a

−b ≤ y ≤ b0 elsewhere

(3)

The equivalent magnetic current at the waveguide aperture forcomputing the externally scattered field obtained as:

~Me = 2 ~E(x′, y′, 0)× uz

= ux

∑M

p=12Ep sin

pπ

2a(x + a)

−a ≤ x ≤ a−b ≤ y ≤ b

(4)

The radius of the co-pole and cross-pole of the crossed-dipoleprobe are assumed to be much smaller than the length L andwavelength λ. With good accuracy, the surface current density onthe thin conducting wire can be considered to have only an axialcomponent [3].

The induced current on the surface of the co-pole (parallel to y-axis) of the near-field probe is described by:

I = uy

∑M

p=1Iypiyp (5)

where the Pulse basis function iyp (p = 1, 2, 3, . . . , M) are defined by

iyp =

1 y′p−1 ≤ y′ ≤ y′p0 elsewhere

(6)

Iyp are the coefficients of the pulse basis function for the co-pole.Similarly, we can describe induced current Ix (Iz) on the surface

of the cross-pole, when it is parallel to x (z) axis.The radiated magnetic field at the plane of the waveguide aperture

is evaluated using the plane-wave spectrum approach and it is given


by:

Hextx = − ab

π2kη

M∑

p=1

Ep

∞∫

−∞

∞∫

−∞

k2 − k2x(

k2 − k2x − k2

y

)1/2sinc(kyb)

j sin (kxa) p evencos (kxa) p odd

pπ2

1−

(2akxpπ

)2 ej(kxx+kyy)dkxdky (7)

The radiated electric field at the near-field probe is also evaluatedusing the plane-wave spectrum approach and described below:

Ex = 0 (since εx = 0) (8)

Ey =12π

∞∫

−∞

∞∫

−∞εye

j(kxx+kyy−kzz)dkxdky (9)

Ez = − 12π

∞∫

−∞

∞∫

−∞

εyky

kzej(kxx+kyy−kzz)dkxdky (10)

εy is the Fourier Transform of the electric field at the radiating apertureand is given by

εy (kx, ky, k) =12π

M∑

p=1

Ep

∫∫sin

pπ

2a

(x′ + a

)e−j(kxx′+ky y′)dx′dy′

After substituting and simplifying, we obtained:

Ey =ab

π2

M∑

p=1

Ep

∞∫

−∞

∞∫

−∞sinc(kyb)

j sin(kxa) p evencos(kxa) p odd

pπ2

1−

(2akxpπ

)2

ej(kxx1+kyy1−kzz1)dkxdky (11)

Ez = −ab

π2

M∑

p=1

Ep

∞∫

−∞

∞∫

−∞

ky

kzsinc(kyb)

j sin(kxa) p evencos(kxa) p odd

pπ2

1−

(2akxpπ

)2

ej(kxx1+kyy1−kzz1)dkxdky (12)

We obtained the internally scattered magnetic field by using the


modal expansion approach; the x-component of the field is given by:

H intx =

M∑

p=1

EpYep0sin

mπ

2a(x + a)

(13)

At any observation point, the y-component of the electric fieldscattered by the induced current on the co-pole is given by:

Esy =

λ√

µ/ ∈16π3j

L/2∫

y′=−L/2

2π∫

φ′=0

Iype−jkR1

R51

[(1 + jkR1)

(2R2

1 − 3a2w

)+ k2a2

wR21

]dy′dφ′ (14)

whereR1 =

√ρ2 + a2

w − 2ρaw cosφ′ + (y − y′)2 (15)

and aw is the radius of the pole, ρ is the radial distance to theobservation point.

For observation on the axis of the co-pole (ρ = 0),

R1=√

a2w + (y − y′)2 (16)

and

Esy =

λ√

µ/ ∈8π2j

L/2∫

−L/2

Iype−jkR1

R51

[(1+jkR1)

(2R2

1−3a2w

)+k2a2

wR21

]dy′

(17)Similarly, the field on the axis of the cross-pole (oriented along

x-axis) scattered by the induced current on that pole is given by:

Esx =

λ√

µ/ ∈8π2j

L/2∫

−L/2

Ixpe−jkR2

R52

[(1+jkR2)

(2R2

2−3a2w

)+k2a2

wR22

]dx′

(18)where

R2 =√

a2w + (x− x′)2 (19)

If the probe is in y-z plane and cross-pole axis is parallel to thez-axis, then electric field on the axis of the cross-pole scattered by theinduced current on that pole is given by:

Esz =

λ√

µ/∈8π2j

L/2∫

−L/2

Izpe−jkR3

R53

[(1+jkR3)

(2R2

3−3a2w

)+k2a2

wR23

]dz′

(20)


whereR3 =

√a2

w + (z − z′)2 (21)

The electric field on the axis of the co-pole due to current on thecross-pole (mutual coupling effect) is obtained as:

Emxy =

λ√

µ/ε

16π3j

L/2∫

x′=−L/2

2π∫

φ′=0

Ixpe−jkR4(x−x′)(y−y′)(3+3jkR4−k2R2

4)R5

4

dx′dφ′(22)

where R4 =√

ρ2 + a2w − 2ρaw cosφ′ + (x− x′)2 and the field on the

cross-pole due to current on the co-pole is given by:

Emyx =

λ√

µ/ε

16π3j

L/2∫

y′=−L/2

2π∫

φ′=0

Iype−jkR5(x−x′)(y−y′)(3+3jkR5−k2R2

5)R5

5

dy′dφ′(23)

The expression for R5 is same as (15).The x-component of the magnetic field at the plane of the

waveguide aperture scattered by the induced current on the co-poleof the probe is obtained as:

Hsx =

L/2∫

y′=−L/2

2π∫

φ′=0

Iype−jkR6

8π2R36

(ρ− aw cosφ′) 1 + jkR6 dy′dφ′ (24)

The expression for R6 is same as (15).

3. IMPOSITION OF BOUNDARY CONDITION

The boundary conditions are imposed at the plane of the waveguideaperture, on the axis of the co-pole and on the axis of the cross-pole.The boundary condition at the region of the waveguide aperture is thetangential component of the magnetic field both inside and outside thewaveguide is identical. The boundary condition on the axis of the poleis the total tangential component of the electric field is zero.

At the region of the aperture, we consider four sources producingthe fields — (i) The source in the waveguide exciting the TE10 mode,(ii) the magnetic current source at the aperture, (iii) the electric currentsource on the surface of the co-pole, and (iv) the electric current sourceon the surface of the cross-pole. Using the principle of superposition,


the x-component of the magnetic field at the plane of the aperture isderived. In the analysis, two cases have been considered: First case(the co-pole axis is parallel to the y-direction and the cross-pole axis isparallel to the x-direction); Second case (the co-pole axis is parallelto the y-direction and the cross-pole axis is parallel to the z-direction).

First case: At the plane of the waveguide aperture (at the z = 0plane), using superposition:

H int/1x +H int/2

x +H int/3x +H int/4

x = Hext/1x +Hext/2

x +Hext/3x +Hext/4

x

or,

2H incx + H int1

x = Hext1x + Hextco1

x + Hextcr1x (25)

Along the axis of the co-pole and cross-pole, the fields are respectivelygiven by

Einc1y + Emx1

y + Escat1y = 0 (26)

Einc1x + Emy1

x + Escat1x = 0 (27)

The superscript 1 indicates First case. Hextcox is the x-component

of the magnetic field at the aperture scattered by the induced currenton the co-pole; Hextcr

x is the x-component of the magnetic field at theaperture scattered by the induced current on the cross-pole. Einc

y isthe incident electric field at the co-pole, radiated by the waveguide,Emx

y is the field in the co-pole due to induced current on the cross-pole(mutual coupling effect) and Escat

y is the y-component of the scatteredfield due to the induced current on the co-pole. Similarly, Einc

x is theincident electric field at the cross-pole, Emy

x is the field in the cross-pole due to induced current on the co-pole (mutual coupling effect) andEscat

x is the x-component of the scattered field due to induced currenton the cross-pole.

Second case: At the plane of the waveguide aperture (at thez = 0 plane), using superposition:

H int1x +H int/2

x +H int/3x +H int/4

x = Hext/1x +Hext/2

x +Hext/3+Hext/4x

x

or,

2H incx + H int2

x = Hext2x + Hextco2

x + Hextcr2x (28)

Along the axis of the co-pole and cross-pole, the fields arerespectively given by

Einc2y + Emz2

y + Escat2y = 0 (29)

Einc2z + Emy2

z + Escat2z = 0 (30)

The superscript 2 indicates Second case.


4. SOLVING FOR THE APERTURE ELECTRIC FIELDAND PROBE CURRENTS

To determine the electric field and current distributions at thewaveguide aperture and on the probe respectively, it is necessary todetermine the basis function coefficients.

Since the field at the aperture is described by M basis functions,M unknowns are to be determined from the boundary condition.The weighting functions and the moment of the field are defined asbelow [6]:

w1q =

sin qπ

2a (x + a) −a ≤ x ≤ a

−b ≤ y ≤ b

0 elsewhere(31)

⟨H,w1

q

⟩=

∫∫

Aperture

H · w1qdxdy (32)

In addition, since the current on the pole of the probe is describedby M basis functions, M unknowns are to be determined from theboundary condition. The weighting functions and the moment of thefield are defined as:

w2q = [δ (h− hq)] = [δ (h− h1) , δ (h− h2) , . . .] (33)

where h specifies a position with respect to some reference (origin),and hq represents a point at which the boundary condition is enforced.

⟨E,w2

q

⟩=

∫∫

surface

E · w2qds (34)

w1q and w2

q are the entire domain and point matching weighting(testing) functions at the waveguide aperture and pole axisrespectively.

For the First case, using the boundary conditions given by (25),(26) and (27), and the definition in (32) and (34), and converting intomatrix form:

2[Linc

]+

[Lint1

][E1

p

]=

[Lext1

][E1

p

]+

[Lextco1

][I1yp

]+

[Lextcr1

][I1xp

](35)[

Lcoinc1] [

E1p

]+

[Lymx1

] [I1xp

]+

[Lcoscat1

] [I1yp

]= 0 (36)[

Lcrinc1] [

E1p

]+

[Lxmy1

] [I1yp

]+

[Lcrscat1

] [I1xp

]= 0 (37)

For the Second case, using the boundary conditions givenby (28), (29) and (30), and the definition in (32) and (34), and


converting into matrix form:2[Linc

]+

[Lint2

][E2

p

]=

[Lext2

][E2

p

]+

[Lextco2

][I2yp

]+

[Lextcr2

][I2zp

](38)[

Lcoinc2] [

E2p

]+

[Lymz2

] [I2zp

]+

[Lcoscat2

] [I2yp

]= 0 (39)[

Lcrinc2] [

E2p

]+

[Lzmy2

] [I2yp

]+

[Lcrscat2

] [I2zp

]= 0 (40)

The moments of the incident and scattered fields are given by:[Linc

]= Linc

q =⟨H inc

x , w1q

⟩

= −Y0

a∫

−a

b∫

−b

cos(πx

2a

)sin

qπ

2a(x+a)

dxdy

= −2abY 0 q = 1

0 otherwise (41)[Lint1

]= Lint1

q,p =⟨H int1

x (ep) , w1q

⟩

= Y ep0

a∫

−a

b∫

−b

sinqπ

2a(x + a)

sin

mπ

2a(x + a)

dxdy

=

2abY ep0 p = q = m, n = 0

0 otherwise (42)[Lext1

]= Lext1

q,p =⟨Hext1

x (ep) , w1q

⟩

=− ab

π2kη

∞∫

−∞

∞∫

−∞

k2 − k2x(

k2−k2x−k2

y

)1/2sinc(kyb)

j sin (kxa) p evencos (kxa) p odd

pπ2

1−

(2akxpπ

)2

a∫

−a

b∫

−b

sinqπ

2a(x + a)

ej(kxx+kyy)dxdydkxdky

= −4a2b2

π2kη

∞∫

−∞

∞∫

−∞

(k2 − k2

x

)(k2 − k2

x − k2y

)1/2sinc2 (kyb)

sin2 (kxa) p, q both evencos2 (kxa) p, q both odd0 otherwise

pπ2

1−

(2akxpπ

)2

qπ2

1−

(2akxqπ

)2dkxdky (43)

To carry out the integral in the spectral domain, we make the


following substitutions to obtain the real and imaginary parts of theintegral:

kx = k sin θ cosφ

ky = k sin θ sinφ

dkxdky = k2 sin θ cos θdθdφ

(44)

in the visible region, i.e., k2x + k2

y ≤ k2, and

kx = k cosh θ cosφky = k cosh θ sinφdkxdky = k2 sinh θ cosh θdθdφ

(45)

in the invisible region, where k2x + k2

y Â k2. The final expressions forthe elements of the moment matrices are obtained as:

Lext1q,p visible region

=−16a2b2

λ2η

π2∫

θ=0

2π∫

φ=0

(1−sin2θ cos2ϕ

)sinc2 (bk sin θ sinφ)

sin2 (ak sin θ cosφ) p, q both evencos2 (ak sin θ cosφ) p, q both odd0 otherwise

pπ2

1−

(2ak sin θ cos φ

pπ

)2

qπ2

1−

(2ak sin θ cos φ

qπ

)2 sin θdθdφ (46)

Lext1q,p invisible region

=−j16a2b2

λ2η

∞∫

θ=0

2π∫

φ=0

(1−cosh2 θ cos2 φ

)sinc2 (bk cosh θ sinφ)

sin2 (ak cosh θ cosφ) p, q both evencos2 (ak cosh θ cosφ) p, q both odd0 otherwise

pπ2

1−

(2ak cosh θ cos φ

pπ

)2

qπ2

1−

(2ak cosh θ cos φ

qπ

)2 cosh θdθdφ(47)

[Lextco1

]= Lextco1

q,p =⟨Hextco1

x (iyp) , w1q

⟩

=

L/2∫

y′=−L/2

2π∫

φ′=0

e−jkR

8π2R36

(ρ−aw cosφ′

)(1+jkR6)

0 q even8abqπ q odd

dy′dφ′(48)

[Lextcr1

]= Lextcr1

q,p =⟨Hextcr1

x (ixp) , w1q

⟩= 0 (49)


[Lcoinc1

]= Lcoinc1

q,p =⟨Einc1

y (ep) , w2q

⟩

=ab

π2

∞∫

−∞

∞∫

−∞sinc(kyb)

j sin (kxa) p evencos(kxa) p odd

p2

1−

(2akxpπ

)2 e−j(kxx1+kyy+kzz)dkxdky(50)

[Lymx1

]=

⟨Emx1

y (ixp) , w2q

⟩=

λ√

µ/ε

16π3jL/2∫

x′=−L/2

2π∫

φ′=0

e−jkR4(x− x′)(y − y′)(3 + 3jkR4 − k2R2

4)R5

4

dx′dφ′ (51)

[Lcos cat1

]= Lcoscat1

q,p =⟨Escat1

y (iyp) , w2q

⟩

=λ√

µ/ε

8π2j

L/2∫

−L/2

e−jkR1

R51

[(1 + jkR1)

(2R2

1 − 3a2w

)+ k2a2

wR21

]dy′ (52)

[Lcrinc1

]= Lcrinc1

q,p =⟨Einc1

x (ep) , w2q

⟩= 0 (53)[

Lxmy1]

= Lxmy1q,p =

⟨Emy1

x (iyp) , w2q

⟩

=λ√

µ/ε

16π3j

L/2∫

−L/2

2π∫

φ′=0

e−jkR5(x−x′)(y−y′)(3+3jkR5−k2R2

5)R5

5

dy′dφ′(54)

[Lcrscat1

]= Lcrscat1

q,p =⟨Escat1

x (ixp) , w2q

⟩

=λ√

µ/ε

8π2j

L/2∫

−L/2

e−jkR2

R52

[(1 + jkR2)

(2R2

2 − 3a2w

)+ k2a2

wR22

]dx′ (55)

From Equations (35), (36) and (37), solving coefficients E1p , I1

yp andI1xp we obtain:

[E1

p

][I1yp

][I1xp

]

=

[Lext1

]− [Lint1

] [Lextco1

] [Lextcr1

][Lcoinc1

] [Lcoscat1

] [Lymx1

][Lcrinc1

] [Lxmy1

] [Lcrscat1

]

−1

2[Linc

]

[0][0]

(56)If M basis functions are used to describe the electric field atthe radiating aperture then there are M unknowns, namely,Ep (p = 1, 2, . . . , M) and to solve for these, M weighting functionsw1

q (q = 1, 2, . . . , M) are required. Similarly, if M basis functions


are used to describe the current on the surface of the pole of theprobe, namely, Ip (p = 1, 2, . . . ,M) and to solve for these, M weightingfunctions w2

q (q = 1, 2, . . . ,M) are required.Reflection coefficient Γ1 (in the First case) is given by:

Γ1 = −1 + E11 (57)

The pole voltage of the probe is then obtained across 50 ohmsterminating impedance [7].

Similarly, from Equations (38), (39) and (40), the coefficients E2p ,

I2yp and I2

zp can be obtained for the Second case:

[E2

p

][I2yp

][I2xp

]

=

[Lext2

]− [Lint2

] [Lextco2

] [Lextcr2

][Lcoinc2

] [Lcoscat2

] [Lymx2

][Lcrinc2

] [Lxmy2

] [Lcrscat2

]

−1

2[Linc

]

[0][0]

(58)

5. RESULTS AND DISCUSSION

The aperture in an infinite ground plane fed by a standard X-bandWR-90 rectangular waveguide is used as a radiator, and two dipoles,each of length 0.47λ and radius 0.005λ, in crossed configuration areused as a near-field probe. The lumped load of 50 Ω is connected atthe centre of each pole and the junction of the cross is at a distanceof one segment (one pulse basis function) away from the center of

-2 -1 0 1 2

-50

-40

-30

-20

-10

0

10

Re

lative

Fie

ld a

nd

Pro

be

vo

lta

ge

(d

B)

Position along y (wavelengths) in z=0.15 lambda

Relative probe voltage Relative electric field (without probe)

Figure 2. Relative sampled electric field (without probe) and relativesampled co-pole voltage in x-y plane at x = 0, z = 0.15λ, and at10GHz.


the poles as shown in Figure 1. The junction (cross) point of theprobe is taken as the reference point in the computation. For thedetermination of the coefficients of the basis functions, the programwritten in MATLAB 7 was run on a 3 GHz Pentium 4, computer.Convergence is obtained with M = 11 entire domain basis functions(aperture field is represented) and with M = 21 pulse basis functions(each pole current of the probe is represented).

The computation has been carried out to sample the electricfield (without probe) and co-pole voltage in the transverse (x-y) scan

-2 -1 0 1 2

-40

-35

-30

-25

-20

-15

-10

-5

0

5

10

Rela

tive fie

ld a

nd c

o-p

ole

voltage (

dB

)

Relative co-pole voltage Relative electric field (without probe)

Position position along y (wavelengths) in z=0.25 lambda plane

Figure 3. Relative sampled electric field (without probe) and relativesampled co-pole voltage in x-y plane at x = 0, z = 0.25λ, and at10GHz.

-2 -1 0 1 2-30

-25

-20

-15

-10

-5

0

5

Rela

tive fie

ld a

nd c

o-p

ole

voltage (

dB

)

Relative co-pole voltage Relative electric field (without probe)

Position position along y (wavelengths) in z=0.5 lambda plane

Figure 4. Relative sampled electric field (without probe) and relativesampled co-pole voltage in x-y plane at x = 0, z = 0.5λ, and at 10 GHz.


plane (First case) at 10 GHz to compare the normalized (relative)sampled electric field pattern (without probe) with the normalized(relative) sampled co-pole voltage pattern. Since the normalized valuesare taken, zero error is enforced at the center of the scan plane.These plots are shown in Figures 2, 3 and 4 in the scan plane atx = 0, and z = 0.15λ, 0.25λ and 0.5λ respectively. The error in thenormalized voltage pattern with respect to the normalized electric field(without probe) pattern is estimated. The radiator absolute reflectioncoefficients in the presence of the near-field measuring probe witheach pole length L = 1.41 cm and radius aw = 0.015 cm (designed

8 9 10 11 12-22

-20

-18

-16

-14

-12

-10

-8

-6

-4

Frequency (GHz)

Without probe With probe at 0.75cm With probe at 1.5cm With probe at 3.0cm Measured (without probe)A

bso

lute

Re

fle

ctio

n c

oe

ffic

ien

t (d

B)

(b)

(a)

Figure 5. (a) Experimental setup used to measure reflectioncoefficient. (b) Waveguide radiator reflection coefficient (abs.) in thepresence of the crossed-dipole in x-y plane with the length of each poleL = 1.41 cm and radius aw = 0.015 cm, over 8 to 12 GHz at x = 0,y = 0 and z = 0.75 cm/1.5 cm/3.0 cm, and in absence of the probe.


8 9 10 11 12

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

Frequency (GHz)

Without probe With probe at 0.75cm With probe at 1.5cm With probe at 3.0cm

Reflection c

oeffic

ient phase (

Degre

es)

Figure 6. Waveguide radiator reflection coefficient phases in thepresence of the crossed-dipole in x-y plane with the length of eachpole L = 1.41 cm and radius aw = 0.015 cm, over 8 to 12GHz at x = 0,y = 0 and z = 0.75 cm/1.5 cm/3.0 cm, and in absence of the probe.

-2 -1 0 1 2

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Fie

ld s

tre

ng

th (

vo

lts/m

ete

r)

Position along y (wavelengths) in y-z plane

Field at z=0.3 lambda in co-pole direction

Field at z=0.3 lambda in cross-pole directionField at z=0.5 lambda in co-pole directionField at z=0.5 lambda in cross-pole direction

Figure 7. Sampled fields (without probe) in y-z the plane at 10GHzand at x = 0, z = 0.3λ/0.5λ.

at 10 GHz) at x = 0, y = 0 and z = 0.75 cm/1.5 cm/3.0 cm, and inthe absence of the probe, over 8 to 12 GHz, are plotted. These resultsare compared to the measured results and are shown in Figure 5(b).The corresponding reflection coefficient phases are shown in Figure 6.Experiment has been carried out to measure the reflection coefficientsof an open-ended waveguide radiator using the scalar network analyzerHP-8757C as shown in the Figure 5(a).


-2 -1 0 1 2

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7 Co-pole voltage at z=0.3 lambda Cross-pole votage at z=0.3 lambda

Probe position along y (wavelengths) in y-z plane

Vo

lta

ge

(m

v)

Co-pole voltage at z=0.5 lambdaCross-pole votage at z=0.5 lambda

Figure 8. Sampled pole voltages in the y-z plane at 10GHz and atx = 0, z = 0.3λ/0.5λ.

-2 -1 0 1 2

-200

-150

-100

-50

0

50

100

150

200

250

300

Ph

ase

(D

eg

ree

s)

Position along y (wavelenghts) in y-z plane at z=0.3 lambda

Co-pole voltage phaseField (co-pole direction) phaseCross-pole voltage phaseField (cross-pole direction) phase

Figure 9. Sampled electric field (without probe) and pole voltagephases in the y-z plane at x = 0, z = 0.3λ, and at 10 GHz.

In the second case, the probe is in the longitudinal (y-z) planeand the cross-pole is parallel to the z-axis. In this case, we cannotcompare the electric field pattern (without probe) with the inducedcross-pole voltage pattern in the z-direction, since the field in the z-direction is zero at the center of the scan plane and it is non-zeroat other positions. Computation has been carried out to determinethe sampled fields (without the probe) and sampled pole voltages atx = 0 and z = 0.3λ/0.5λ, and at 10 GHz, and these plots are shownin Figures 7 and 8. Also, the sampled electric field (without probe)and pole voltage phases at x = 0, and z = 0.3λ/0.5λ, are shown inFigures 9 and 10.


-2 -1 0 1 2

Position along y (wavelenghts) in y-z plane at z=0.5 lambda

-200

-150

-100

-50

0

50

100

150

200

250

300

Ph

ase

(D

eg

ree

s)

Co-pole voltage phaseField (co-pole direction) phaseCross-pole voltage phaseField (cross-pole direction) phase

Figure 10. Sampled electric field (without probe) and pole voltagephases in the y-z plane at x = 0, z = 0.5λ, and at 10 GHz.

6. CONCLUSION

The crossed-dipole, which is used as a near-field measuring probeinduces error in the near-field, because of multiple reflections betweenthe radiator and probe, and effects of mutual coupling between polesof the probe. In the presence of the near-field measuring probe,the radiator reflection coefficient is changed. When the separationbetween radiator and the probe is small, the deviation of the reflectioncoefficient is large with respect to the corresponding values when thereis no near-field probe. As the separation increases, the deviationis smaller, and for larger separation, the reflection coefficient valuesapproach the values obtained, when there is no probe in the near-field. The variations of the fields at the near-field are same asthe theoretically predicted; this shows the validation of the presentformulation. Since the junction of the cross of the probe is taken asthe reference and it is not at the center of poles, the maximum co-polevoltage is slightly deviated from the center of the scan plane. Similarlythe minimum cross-pole voltage is slightly deviated from the center ofthe scan plane

REFERENCES

1. Harrington, R. F., Time-harmonic Electromagnetic Fields,McGraw-Hill, New York, 1961.

2. Harrington, R. F., Field Computation by Moment Method, RogerE. Krieger Publishing Company, USA, 1968.


3. Richmond, J. H., “Digital computer solutions of the rigorousequations for scattering problems,” Proceedings of the IEEE,Vol. 53, 796–804, 1965.

4. Paramesha, S. and A. Chakrabarty, “Moment method analysisof rectangular waveguide as near-field measuring probe,” MOTL,Vol. 48, No. 9, 2006.

5. Paramesha, S. and A. Chakrabarty, “Waveguide as a near-fieldmeasuring probe of the two-element array radiator,” Progress InElectromagnetics Research B, Vol. 7, 245–255, 2008.

6. Gupta, S., A. Bhattacharya, and A. Chakrabarty, “Analysis of anopen-ended waveguide radiator with dielectric plug,” IEE Proc.Microwave, Antenna and Propagation, Vol. 144, No. 2, 126–130,1997.

7. Pisano III, F. A. and C. M. Butler, “Methods for modeling wireantenna loaded with shielded network,” IEEE Trans. on Antennasand Propagation, Vol. 52, No. 4, 2004.

ESTIMATION OF ERROR INDUCED BY A CROSSED- DIPOLE PROBE … · If the test antenna is ... The radius...

Documents

Transcript of ESTIMATION OF ERROR INDUCED BY A CROSSED- DIPOLE PROBE … · If the test antenna is ... The radius...