**CALIBRATION METHOD FOR NEAR FIELD MEASUREMENTS OF CENTIMETRE AND MILLIMETER WAVES**

GUSTAFSSON, Mats (Fersens Väg 16, Malmö, 21142, SE)

HELANDER, Jakob (Östra Varvsgatan 20A, Malmö, 21175, SE)

XU, Bo (Malmö, 21144, SE)

LUNDGREN, Johan (Malmö, 21144, SE)

GUSTAFSSON, Mats (Fersens Väg 16, Malmö, 21142, SE)

HELANDER, Jakob (Östra Varvsgatan 20A, Malmö, 21175, SE)

XU, Bo (Malmö, 21144, SE)

LUNDGREN, Johan (Malmö, 21144, SE)

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**H04B5/00***;*

**H04B17/00**

**H04B17/11**HELANDER JAKOB ET AL: "60 GHz imaging of panels for defect detection using planar scanning", 2016 IEEE INTERNATIONAL SYMPOSIUM ON ANTENNAS AND PROPAGATION (APSURSI), IEEE, 26 June 2016 (2016-06-26), pages 1025 - 1026, XP032984400, DOI: 10.1109/APS.2016.7696220

None

Claims 1. A method of calibrating a near field measurement system, the method comprising the steps of: - providing a transmitting antenna adapted to transmit electromagnetic waves in the centimeter and/or millimeter wavelength region; - providing a receiving probe adapted to measure the transmitted electromagnetic waves; - inserting a conducting sheet between the transmitting antenna and the receiving probe, said conducting sheet comprising at least one calibration aperture characterized as a radiating magnetic dipole for the transmitted electromagnetic waves; - transmitting the electromagnetic waves from the transmitting antenna through the calibration aperture; - moving the receiving probe over a surface while sampling the transmitted electromagnetic waves, thereby obtaining a field distribution; - calibrating the field distribution in relation to the transmitting antenna based on the characteristics of the calibration aperture. 2. The method according to claim 1 , further comprising the step of determining an absolute positioning of the field distribution in relation to the transmitting antenna. 3. The method according to any of the preceding claims, wherein a positioning of the transmitting antenna is determined with regard to the calibration aperture. 4. The method according to any of the preceding claims, further comprising the step of determining a scattering matrix of the receiving probe based on the characteristics of the calibration aperture. 5. The method according to any of the preceding claims, wherein the calibration aperture has a shape that is resonant at a transmission frequency employed by the transmitting antenna. 6. The method according to any of the preceding claims, wherein the aperture is shaped to have a predefined radiation characteristic for a given transmission frequency. 7. The method according to any of the preceding claims, wherein the radiation characteristics of the calibration aperture is well defined and corresponding to a magnetic dipole. 8. The method according to any of the preceding claims, wherein the calibration is a calibration of an impact of the receiving probe on the transmitted electromagnetic waves. 9. The method according to any of the preceding claims, wherein the calibration is a calibration of a relative distance between the receiving probe and the transmitting antenna. 10. The method according to any of the preceding claims, wherein the field distribution is power density map, wherein the power density indicates a number of time-averaged, incident power densities for a number of spatial points on the surface. 1 1. The method according to any of the preceding claims, wherein the sampling the transmitted electromagnetic waves is performed in a discretized grid. 12. The method according to any of the preceding claims, wherein an expected field distribution on the surface is calculated based on the characteristics of the calibration aperture, preferably using a numerical method. 13. The method according to claim 12, wherein the expected field distribution on the surface is compared to the measured field distribution. 14. A method for compliance testing an antenna, such as a millimeter wave antenna, comprising the steps of calibrating a near field measurement system according to any of claims 1 -13, wherein the antenna is the transmitting antenna; and using the near field measurement system to compliance test the antenna. 15. A calibration system, comprising: - a transmitting antenna adapted to transmit electromagnetic waves in the centimeter and/or millimeter wavelength region; - a receiving probe adapted to measure the transmitted electromagnetic waves; - a conducting sheet arranged between the transmitting antenna and the receiving probe, said conducting sheet comprising at least one calibration aperture characterized as a radiating magnetic dipole for the transmit electromagnetic waves for a predetermined transmission frequency; and - a vector network analyzer connected to the transmitting antenna and the receiving probe. 16. The calibration system according to claim 15 configured to perform the method of any of claims 1 -13. |

The present disclosure relates to a method and system of calibrating a near field measurement system.

Background of invention

The field of the invention is measurement methodology for electromagnetic waves in the centimeter and millimeter wavelength region.

Near field measurements of electromagnetic fields of a radiating antenna are performed to infer knowledge of the field distribution in a volume or on a surface. The field is sampled using a probe, which is a device transforming the electromagnetic field in its vicinity to a voltage signal in the cable attached to it. By moving the probe over a surface and taking repeated measurements, the field is sampled. The signals can be recorded at a single frequency, at multiple frequencies, or in time domain. The signals are processed by a mathematical algorithm using a computer program, to form the final field distribution. The field distribution can be defined on the measurement surface, in a volume, or on a different surface.

The probe has a finite size and has a non-local interaction with the electromagnetic field. This means it does not measure the field in a point but rather reacts to the fields in its immediate surrounding. This distorts the information that can be obtained using the near field measurement, which may lead to an error in positioning and

consequently phase, making it difficult to evaluate the power density at close ranges to the radiating antenna.

Summary of invention

The method proposed in the present disclosure aims at a method to determine the electromagnetic fields close to a radiation object. This is achieved by compensating for the probe’s interaction with the electromagnetic field and connecting the received signals with the position of the radiating object. This invention further provides a means for absolute positioning of the computed field distribution relative the radiating object. In a first embodiment, the method for calibrating a near field measurement system comprises the steps of: - providing a transmitting antenna adapted to transmit electromagnetic waves in the centimeter and/or millimeter wavelength region;

- providing a receiving probe adapted to measure the transmitted

electromagnetic waves;

- inserting a conducting sheet between the transmitting antenna and the receiving probe, said conducting sheet comprising at least one calibration aperture characterized as a radiating magnetic dipole for the transmitted electromagnetic waves;

- transmitting the electromagnetic waves from the transmitting antenna

through the calibration aperture;

- moving the receiving probe over a surface while sampling the transmitted electromagnetic waves, thereby obtaining a field distribution;

calibrating the field distribution in relation to the transmitting antenna based on the characteristics of the calibration aperture.

There are known methods for achieving similar goals. The interaction of a probe with the electromagnetic field can be characterized by numerical simulations using an accurate numerical model of the probe, or by calibration measurements against another well characterized antenna. In prior art, the absolute positioning of the computed field distribution is undetermined due to uncertainties in reference plane of the probe, and is typically the outcome of repeated, complicated computations.

The presently disclosed method and system take a different approach and describes a method based on a small aperture in an opaque device or sheet, which can be characterized as a radiating magnetic dipole. This allows an accurate determination of the probe’s scattering properties and the positioning of the antenna under test (AUT) with regard to the aperture device (AD).

The generality of such method allows the use of any antenna as measurement probe, without prior calibration.

The methodology can also be used in existing measurement systems with already calibrated probes as a means to improve positioning of the AUT.

The proposed method combines ideas from the fields of electromagnetic field theory, measurement technology, and numerical simulations. The present disclosure further relates to a calibration system, comprising:

- a transmitting antenna adapted to transmit electromagnetic waves in the centimeter and/or millimeter wavelength region;

- a receiving probe adapted to measure the transmitted electromagnetic waves;

- a conducting sheet arranged between the transmitting antenna and the receiving probe, said conducting sheet comprising at least one calibration aperture characterized as a radiating magnetic dipole for the transmit electromagnetic waves for a predetermined transmission frequency; and

- a vector network analyzer connected to the transmitting antenna and the receiving probe.

The calibration system may be used to perform any embodiment of the presently disclosed method for calibrating a near field measurement system.

The present disclosure relates to a method for calibrating an arbitrary probe for near field electromagnetic field measurements, using a small aperture in a conducting sheet. Identifying the small aperture as a magnetic dipole, the scattered electromagnetic field can be computed as a series of regular spherical vector waves incident on the probe in each measurement position. With the measured voltage wave signal at each probe position, a linear system of equations may be formulated, the solution of which produces numerical values for the elements in a probe scattering matrix. The absolute knowledge of the position of the aperture device and the probe scanning surface enables an absolute determination of the reconstructed field distribution in a volume or on a surface.

Description of drawings

The drawings are exemplary and are intended to illustrate some of the features of the presently disclosed calibration method for near field measurements of centimetre and millimeter waves, and are not to be construed as limiting to the presently disclosed invention. FIG. 1 is a principal sketch of the experimental setup. The indicated parts are: 1 is the scanning probe, which can be moved on an arbitrary 3D-surface or volume using a combination of linear positioners and rotary stages, programmable by a computer script; 2 is the transmitting antenna, illuminating the calibration screen; 3 is the AD, consisting of a conducting sheet with a small aperture (5) in it; 4 is a vector network analyzer, measuring the transmission between its ports; 5 is a calibration aperture.

FIG. 2 is a frontal view of the AD. The indicated parts are: 3 is a planar conducting sheet; 5 is a small aperture in the conducting sheet, designed to be resonant at one of the scanning frequencies.

FIG. 3 shows a further example of the presently disclosed calibration system. In FIG. 3A a receiving probe (2) is situated in the center (7) of a planar measurement surface, a distance d away from a small aperture (5) in a finite metallic plane (3). A transmitting antenna (1 ) is positioned on the other side of the metallic plane (3). A high gain broadside antenna (1 ) ensures sufficient power flow through the aperture, although in theory nothing prohibits the usage of the DUT itself (1 of FIG. 3C). In FIG. 3B the transmitting antenna (1 ) excites the aperture (5) which then radiates as an electrically very small dipole. The reference measurement is conducted by sampling the fields in a discretized grid across the measurement surface using the receiving probe (2). In FIG. 3C the (reference) transmitting antenna (1 ) is removed, and the DUT (1 ) is aligned with respect to the previous position of the aperture (5). In FIG. 3D a second measurement is conducted on the DUT (1 ), and the field is sampled in the same grid as before.

FIG. 4 shows a test setup using a mobile phone mockup operating at 28 GHz with four independently fed antennas. Two reconstruction planes (Plane 1 , Plane 2) are defined for the DUT.

FIGS. 5-6 depict a comparison between measured and simulated results for Plane 1 and 2 of the mobile phone test setup of FIG. 4, respectively.

FIG. 5. shows normalized power density for Plane 1 at 28 GHz in the reconstruction planes distanced 5 mm, 10 mm, and 20 mm for the mobile phone test setup of FIG. 4. The rows depict: full-wave simulations of the DUT in FEKO (top), and the results of the measurement data as input to the reconstruction technique (bottom). The white lines depict the outline of the DUT, and the black crosshair marks the mutual origin. The dynamic range of all plots is 40 dB.

FIG. 6. shows normalized power density for Plane 2 at 28 GHz in the reconstruction planes distanced 5 mm, 10 mm, and 20 mm for the mobile phone test setup of FIG. 4. The rows depict: full-wave simulations of the DUT in FEKO (top), and the results of the measurement data as input to the reconstruction technique (bottom). The white lines depict the outline of the DUT, and the black crosshair marks the mutual origin. The dynamic range of all plots is 40 dB.

Detailed description of the invention

The disclosed invention provides a calibration method for determining the

electromagnetic field around the AUT. The method is based on separating the AUT with an AD that has a well-defined radiation pattern and can be used to position the AUT relative to the AD.

The roles of the transmitting and the receiving antenna can be interchanged without changing the calibration procedure.

To increase the signal-to-noise-ratio, additional amplifiers can be introduced on either side of the transmitting or receiving antennas.

Having determined the probe scattering matrix using the AD, a measured sequence of signals for an arbitrary AUT can be processed to remove the influence of the probe, which allows the accurate determination of the electromagnetic field.

Calibration algorithms based on a plane wave spectrum can also be used. A simplified calibration is performed by dividing the measured signals of the AUT with the signals from the AD. This is an approximate calibration which provides a simple phase and amplitude relation of the AUT with the AD.

The AD can be a surface with a single or multiple apertures enclosing the AUT or a large sheet separating them. To ensure that no edge effects occur, and that the radiated field is accurately described by the field originating from the aperture, the size of the conducting sheet - in which the calibration aperture is introduced - is determined by:

1 ) the geometrical distance to the illuminating antenna, and

2) the directivity of the illuminating antenna. The sizes typically range from 1 dm ^{2 } to 1 m ^{2 }.

A general antenna, including the special case of a measurement probe, can be described by its scattering matrix, which relates the incoming waves to the outgoing waves. The waves consist of incoming and outgoing spherical vector waves, as well as incoming and outgoing waves on the transmission line connected to the antenna port. The scattering matrix has infinite dimension, but the finite size of the antenna means it can be effectively truncated to a number of terms proportional to ka = 2ua/A, where a is the radius of a sphere enclosing the antenna, and l is the wavelength. A two-stage calibration procedure is then defined as follows.

Pattern calibration.

Introduce a very small aperture in a conducting sheet to form the AD, which is illuminated from the back by an arbitrary antenna. The aperture can have arbitrary shape, as long as it is resonant at one of the considered frequencies: circular, rectangular, hexagonal, split ring resonator, Jerusalem cross, arbitrarily shaped narrow slot, or any shape typically considered in frequency selective surfaces and extra ordinary transmission applications.

The field radiated from the aperture is accurately described by a magnetic dipole. The incident field on the probe at its different positions can be expanded in terms of spherical vector waves, centered on an arbitrary, but well defined, point of the probe, and obtained from the magnetic dipole and standard translation matrices representing the change of origin. The received signal in the probe at different physical positions provide enough equations to determine the coefficients of the probe’s scattering matrix. There will be a remaining undetermined scaling factor due to the unknown amplitude of the dipole.

Absolute power calibration.

Remove the conducting sheet and center the probe in front of a standard gain horn.

The radiated power from the horn is known from the output power of the vector network analyzer (VNA), the cable losses, and the tabulated gain of the horn. This determines the remaining scaling factor of the scattering matrix of the probe.

The position of the AD determines the origin of the measurement coordinate system. Given an accurate position of the probe measurement plane, this permits the absolute positioning of the computed field distribution.

One embodiment of the present disclosure relates to:

1. Method of calibration of near field measurement system, using a small scattering aperture in a conducting sheet, a scanning probe, and a vector network analyzer.

2. Method of absolute positioning of computed field distribution, using knowledge of position of calibration object.

Examples, tests, further embodiments

The invention will in the following be described in greater detail with reference to further aspects, embodiments, non-limiting examples and tests.

The present disclosure relates to a measurement and calibration technique - based on amplitude and phase retrieval - for obtaining for obtaining the power density at a given surface situated some arbitrary distance away from a DUT, using a reference measurement of a small aperture. The term power density indicates the time-averaged, incident power density in a single spatial point at a single frequency. The technique is adapted here on antennas operating at the millimeter wave (mm-wave) frequencies 28 GHz and 60 GHz or at the centimeter wave (3-30 GHz), and is preferably based on two sets of measurements; one of the DUT, and one of a small aperture. The calibration measurement needs only to be conducted once and may be utilized for multiple DUTs, presuming the setup is not subject to substantial drifting over the complete

measurement time frame.

FIG. 3 shows an example of the measurement procedure and setup; the calibration aperture is shown in FIG. 3A, and an example DUT is shown in FIG. 3C and 3D. With the measurement data retrieved and the calibration performed, numerical integral equation solvers are used to reconstruct equivalent currents on a predefined surface representing the DUT, and subsequently to compute the power density at any plane of interest.

The calibration approach using the small aperture measurement has the substantial benefit of not only correcting for the receiving probe’s impact on the measured signal, but also of handling the spatial alignment of the DUT relative to the scan plane. This second feature may be important when conducting RF EMF exposure tests at said frequencies, since the power density must be reconstructed in planes residing in the near-field region of the DUT. In accordance with the field’s radial dependence in this region, a distance offset of e.g., 1 mm (corresponding to l/5 at 60 GHz) would result in a substantial change in both the amplitude and phase of the reconstructed radiated electromagnetic fields. The small aperture calibration measurement suppresses this margin of error.

The DUT in FIG. 4 is a mobile phone mockup operating at 28 GHz with four independently fed antennas. The cross polarization is low and the radiating elements are covered by a plastic chassis. Two reconstruction planes were defined for this DUT, labeled plane 1 and 2, respectively, as shown in FIG. 4. The mockup shown in FIG. 4 was measured by scanning a probe in a plane, parallel to the closest surface of the DUT, distanced d = 60mm away, see FIG. 3. The power

density was then reconstructed in planar surfaces distanced 5 mm, 10 mm and 20 mm away from the DUT.

Preferably, a calibration method relying on a reference measurement of a small aperture is employed in order to obtain accurate reconstruction of the radiated power density from a measured DUT. In essence, this is achieved by reconstructing he equivalent currents on a surface representing the radiating part of the DUT and thereafter calculating the corresponding radiated fields in the evaluation planes of interest using computational codes based on the method of moments (MoM), i.e.

numerical integral equation solvers. In one embodiment, the technique is explained by the following steps:

1 ) Processing of raw measurement data.

2) Calibration, using measurement data of the small aperture, to remove the effects that the receiving probe has on the retrieved data, and to obtain a well-defined spatial position. 3) Reconstruction of equivalent currents on the surface of the DUT.

4) Computation of the electric and magnetic fields at a surface of interest from the reconstructed equivalent currents.

5) Calculation of the incident power density from the field in the previous step.

1 ) Measurement Data Processing

There is no inherent restriction on the shape of the measurement and reconstruction surfaces. However, only planar surfaces parallel to that of the radiating DUT are considered, since this constitute an appropriate setting for the purpose of EMF exposure assessment. The first measured plane is that of the aperture as disclosed in FIGS. 3A and B. The aperture is then removed, and the DUT - aligned with respect to the previous position of the aperture - is measured in the same plane as the aperture was measured, see FIGS. 1 C and D. Samples of the transmitted signal are taken in discrete sampling points over the entire scan plane. The sampled data are extracted in order to retrieve the necessary field information in the following steps. The response is measured for several discrete frequency points in a given range f _{0 }±Af _{0 }. The frequency bandwidth, 2 Af _{0 }, enables the use of time gating procedures to suppress interactions with far away objects, and is specified as to realize a certain resolution of the signal in time domain. Af _{0 } may be set to 2 GHz or 1 GHz.

2) Probe Correction Using an Electrically Small Aperture

Any given physical probe has a finite size and a non-local interaction with the electromagnetic field in its immediate surrounding. The probe is connected to a vector network analyzer (VNA) and the registered value in the receiving device is a complex valued voltage signal accounting for the full probe interaction, rather than the complex valued field in that particular discrete point of the finite aperture. This effect can be atoned for using probe correction techniques, of which there are several presented in classic literature. These techniques calibrate for the interaction of the probe with the drawback of not having precise information on the position In each discrete point, a correction term is obtained by normalizing the MoM simulation of the co-polarized component of the field from the aperture with the measurement of the aperture. These correction terms are then applied to the data of the measured DUT, and a probe corrected field with absolute positioning calibrated to the mathematical model used in the reconstruction algorithm is obtained. In this work only single polarized

measurements were conducted; however, both polarizations can be incorporated by conducting a second set of measurements with a different orientation, e.g. a 90 ^{Q } rotation, of the probe.

3) Reconstruction of Equivalent Currents

The reconstruction of the sources may be performed by expressing the solutions to Maxwell’s equations using an electric field integral representation:

where h _{0 } is the intrinsic impedance of free space, k is the free space wave number, G is the free space Green function, J and M are the electric and magnetic equivalent currents respectively that are positioned at r’, S is the reconstruction surface and r is the position vector belonging to the measurement surface. J is needed if the problem is a half-space and J and M are needed for arbitrary geometries on the surface of the DUT. The computation of J given E is a type of problem arising in many scientific fields namely an inverse source problem, and it is mathematically ill-posed.

Numerically, the problem may be addressed by defining an area representing the radiating aperture of the DUT. This area is discretized and the above equation is reshaped into a matrix equation, using a suitable discretization method as,

E = N ^{e } J + N ^{m }M, where E contains the measured component of the electric field in all spatial sampling points, J contains the spatially discretized currents on the reconstruction surface and the matrix operators N ^{e } and N ^{m } describe the mapping from J and M to E for two surfaces, thus it will differ depending

on the chosen plane.

4) Fields from Equivalent Currents

With the equivalent currents reconstructed, the equation is executed to retrieve the electric field originating from these currents in any arbitrary evaluation surface after defining the appropriate matrix operator N ^{e } that describes the electric field integral representation for the new observation points. Similarly, the magnetic field is retrieved using the corresponding matrix form of the magnetic field integral representation.

5) Power Density Computation

The power density in a spatial reconstruction point r is given by where the real part is denoted Re{}, E and H ^{* } denote the electric field and the complex- conjugate of the magnetic field, respectively, c denotes the cross product, and n denotes the unit vector normal to the evaluation surface. The power density is obtained once the full near-field measurement technique - including the previously mentioned processing steps - has been applied, and the measurement setup has been calibrated with respect to the total radiated power P _{r } (presuming all system gains and losses have been accounted for). A spatial average can subsequently be acquired through a convolution between the power density profile in the full reconstruction plane and the predefined averaging area.

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