Planar near-field scanning in the time domain .1. Formulation

Time-domain planar near-field measurement techniques are formulated for acoustic and electromagnetic fields. Probe correction is ignored in that it is assumed that the probe measures the exact values of the field on the scan plane. Two fundamentally different approaches are used in deriving three sets of formulas that give the fields in the source-free half space z>z₀ in terms of their values on the scan plane z=z₀. In the first approach the time-domain formulas are obtained by inverse Fourier transforming the corresponding frequency-domain formulas. In the second approach the time-domain formulas are derived directly in the time domain by working with time-domain Green's functions     

Antenna coupling and near-field sampling in plane-polar coordinates

A probe-corrected vector transmission formula and a rigorous sampling-reconstruction theorem for near-field antenna measurements in plane-polar coordinates are derived from three fundamental theorems of antenna theory: the mutual coupling function between two antennas satisfies the homogeneous wave equation; a receiving antenna can be represented as a differentiator of the incident field; and the mutual coupling function is virtually bandlimited. The rigorous sampling equations are applied to compute the far fields of a circular-aperture antenna sampled in the near field at half-wavelength radial spacing     

Planar near-field scanning in the time domain .2. Sampling theoremsand computation schemes

For part 1 see ibid. vol.47, no.9, p.1280 (1994). Two computation schemes for calculating the far-field pattern in the time domain from sampled near-field data are developed and applied. The sampled near-field data consists of the values of the field on the scan plane measured at discrete times and at discrete points on the scan plane. The first computation scheme is based on a frequency-domain near-field to far-field formula and applies frequency-domain sampling theorems to the computed frequency-domain near field. The second computation scheme is based on a time-domain near-field to far-field formula and computes the time-domain far field directly from the time-domain near field. A time-domain sampling theorem is derived to determine the spacing between sample points on the scan plane. The computer time for each of the two schemes is determined and numerical examples illustrate the use and the general properties of the schemes. For large antennas the frequency-domain computation scheme takes less time to compute the full far field than the time-domain computation scheme. However, the time-domain computation scheme is simpler, more direct, and easier to program. It is also found that planar time-domain near-field antenna measurements, unlike single-frequency near-field measurements, have the capability of eliminating the error caused by the finite scan plane, and thus can be applied to broadbeam antennas     

Formulation of spherical near-field scanning for electromagneticfields in the time domain

Spherical near-field scanning techniques are formulated for electromagnetic fields in the time domain so that a single set of time-domain near-field measurements yields the far field in the time domain or over a wide range of frequencies. Probe-corrected as well as nonprobe-corrected formulations are presented. For bandlimited time-domain fields, sampling theorems and computation schemes are derived that give the field outside the scan sphere in terms of sampled near-field data     

ANALYSIS OF THE EFFECT OF THE TRUNCATED SCAN PLANE IN TIME－DOMAIN NEAR－FIELD MEASUREMENTS

The thought and formulation for near-field far-field transformation based on the direct time-domain computation scheme are given.The effect of the truncated scan plane is investigated by simulating time-domain measurement of an open-ended waveguide antenna, and a simple and effective criterion is derived for removing the truncation errors in the practical time-domain near-field measurements.     

The receiving antenna as a linear differential operator: Application to spherical near-field scanning

The general receiving antenna is represented as a linear differential operator converting the incident field and its spatial derivatives at a single point in space to an output voltage. The differential operator is specified explicitly in terms of the multipole coefficients of the antenna's complex receiving pattern. When the linear operator representation is applied to the special probes used in spherical near-field measurements, a probe-corrected spherical transmission formula is revealed that retains the form, applicability, and simplicity of the nonprobe-corrected equations. The new spherical transmission formula is shown to be consistent with the previous transmission formula derived from the rotational and translational addition theorems for spherical waves.     

Simplified approach to probe-corrected spherical near-field scanning

A multipole representation for the response of an arbitrary receiving antenna is derived that allows the formulation of probe-corrected spherical near-field scanning simply in terms of conventional vector spherical harmonics. Both the representation and formulation are free of rotational and translational addition theorems. A sampling theorem derived for Legendre functions is used to evaluate the resulting orthogonality integrals by direct summation in a computer time proportional to (ka)3.     

"时间窗"对天线时域平面近场测试结果的影响

天线时域近场测试技术是一种新兴的、测试宽带场和工作在窄脉冲激励下天线辐射场的高效的测试技术.因为它可以利用"时间窗"技术进行信号处理,使其相对频域测试具有独特的优势.本文在已建立的天线时域近场测试系统的基础上,从实验的角度,对"时间窗"参数在天线时域平面近场测试中的影响进行验证分析.举例了三个波段标准天线方向图的测试分析结果,并得出初步结论.     

Multilevel Plane Wave Based Near-Field Far-Field Transformation for Electrically Large Antennas in Free-Space or Above Material Halfspace

A recently presented fully probe-corrected near-field far-field transformation employing plane wave expansion and diagonal translation operators enables near-field far-field transformation for arbitrary measurement contours and arbitrary antennas. A multilevel extension, inspired by the multilevel fast multipole method, is presented that is suitable for the efficient transformation of electrically large antennas with a size of tens or even hundreds of wavelengths. The measurement points are grouped in a multilevel fashion and translations are carried out to the box centers on the highest level only. The plane waves are processed through the different levels to the measurement points using a disaggregation and anterpolation procedure resulting in a reduced overall complexity. In the second part of this paper, the influence of perfectly conducting ground planes and dielectric halfspaces, as an approximation for ground effects in a real measurement setup, is investigated. As such ground reflected waves are assumed, which propagate from the investigated antenna to the field probe and add to the direct wave contributions. The far-field conditions required for these assumptions are achieved by a source box grouping scheme. By this extension ground effects are directly considered within the near-field far-field transformation. Transformation results using simulated and measured near-field data are shown.      

Reduction of Truncation Errors in Planar Near-Field Aperture Antenna Measurements Using the Gerchberg-Papoulis Algorithm

A simple and effective procedure for the reduction of truncation errors in planar near-field measurements of aperture antennas is presented. The procedure relies on the consideration that, due to the scan plane truncation, the calculated plane wave spectrum of the field radiated by the antenna is reliable only within a certain portion of the visible region. Accordingly, the truncation error is reduced by extrapolating the remaining portion of the visible region by the Gerchberg-Papoulis iterative algorithm, exploiting a condition of spatial concentration of the fields on the antenna aperture plane. The proposed procedure is simple and computationally efficient; it does not require any modification of the measurement procedure and it allows for the usual probe correction. Far-field patterns reconstructed from both simulated and measured truncated near-field data demonstrate its effectiveness and stability against measurement inaccuracies.      

时域近场测量的间接频域算法和直接时域算法研究

时域近远场变换是时域近场天线测量的关键技术。本文对时域近远场变换的间接频域算法和直接时域算法进行了数值模拟和分析。针对开口矩形波导天线的时域近场测量 ,选取时空采样参数和内插公式 ,用两种算法计算时域远场方向图 ,分析周期性、时域混叠问题和扫描面截断效应 ,在相互比较和验证的基础上 ,指出两者的优、缺点及适用的情况。     

A direct derivation of a single-antenna reciprocity relation for the time domain

In this paper, a single-antenna reciprocity relation is derived for the time domain. First, the antenna is considered on transmission; next, the same antenna is considered when it is receiving an incident plane wave. The two states, transmission and reception, are related by the application of a modified form of the reciprocity theorem for electromagnetic fields with general time dependence due to Cheo. The derivation of the reciprocity relation for the antenna makes use of simple geometric arguments to evaluate the spatial/temporal integrals that occur in the theorem. A few extensions of the reciprocity relation are also described.     

Time-domain spherical near-field formulas in the case where theradial components of the electromagnetic field are measured

Spherical near-field formulas in the time-domain are derived so that the electromagnetic field outside a given scan sphere can be found from measurements of the radial electric and magnetic field components on that scan sphere     

平面波谱恢复算法在平面近场测量中的应用

介绍用于天线平面近场测量的一种近远场变换新算法。该法利用被测天线的平面波谱和口径场幅相分布之间的关系,以及天线口面的约束条件,用G-P迭代算法从平面波谱的置信谱域部分恢复出置信谱域外的平面波谱。这种方法减小了较小截断角下有限扫描面对测量精度的影响,并提高了天线近场测量的效率。     

Time-domain electromagnetic computations using a modified EFIE kernel and field-source equilibrium relations

A form for the electric-field dyadic Green's function for free space is derived that allows explicit time evolution of the modified electric-field integral equation (EFIE) applied to surface scattering. The modified EFIE kernel, here called a "source function," has an integrable singularity in the source region, and is shown to be equivalent, in the frequency domain, to the standard dyadic Green's function. With definitions of "local" and "non-local" fields at a conductor surface, both electric and magnetic versions of the relations between non-local fields and equilibrium surface sources (currents and charges) are derived. These field-source equilibrium (FSE) relations are exact if all the non-local fields are included: the interaction fields, as well as the usual incident fields from distant sources. When the interaction fields are neglected, the magnetic-field version of the FSE relations becomes the usual physical optics approximation. Source functions and the FSE relations were used in two three-dimensional, time-domain numerical simulations to compute radiation patterns from a conical helical antenna driven at a fixed frequency, and scattering of a CW plane wave by a perfectly conducting sphere. This surface-scattering simulation was explicit but remained stable. Excellent agreement between the computed and known results validated the approach.     

Time-domain version of the physical theory of diffraction

A time-domain version of the equivalent edge current (EEC) formulation of the physical theory of diffraction is derived. The time-domain EECs (TD-EECs) apply to the far-field analysis of diffraction by edges of perfectly conducting three dimensional (3-D) structures with planar faces illuminated by a time-domain plane wave. By adding the field predicted by the TD-EECs to the time-domain physical optics (TD-PO) field, a significant improvement is obtained compared to what can be achieved by using TD-PO alone. The TD-EECs are expressed as the integral of the time-domain fringe wave current (the exact current minus the TD-PO current) on the canonical wedge along truncated incremental strips. Closed-form expressions for the TD-EECs are obtained in the half-plane case by analytically carrying out the integration along the truncated incremental strip directly in the time domain. In the general wedge case, closed-form expressions for the TD-EECs are obtained by transforming the corresponding frequency-domain EECs to the time-domain. The TD-EECs are tested numerically on the triangular cylinder and the results are compared with those obtained using the method of moments in combination with the inverse fast Fourier transform     

Time-domain fields exterior to a two-dimensional FDTD space

A transformation algorithm for the near-zone and far-zone fields exterior to a two-dimensional (2-D) finite-difference time-domain (FDTD) field lattice has been developed entirely in the time domain. The fields are found from a surface integration of the convolution of the time derivative of equivalent currents and charges along a contour that encloses the scatterer or radiator of interest. The kernel of the convolution integral has a square-root singularity for which an efficient numerical integration rule is presented. Using this technique, a very accurate solution is obtained; however, convolution integrals are computationally expensive with or without singularities. As an alternative, a rapidly convergent approximate series expansion for the convolution integral is presented, which can be used both in the near and far zone. Results using the new 2-D transform are compared with analytical expressions for the fields generated by a modulated Gaussian pulse for TE and TM line sources. In addition, the 2-D transform solution for the near-zone fields scattered from an open-ended cavity for a TE incident modulated Gaussian pulse plane wave is compared against a full-grid FDTD solution for accuracy and efficiency. The 2-D transform far-zone fields are compared against an alternative technique, which uses a double Fourier transform to perform the convolution in the frequency domain     

Spherical near-field scanning at the Technical University ofDenmark

The early work (1969-79) on spherical near-field antenna measurements at the Technical University of Denmark (TUD) is outlined. A spherical near-field transmission formula is described and the first probe-corrected spherical near-field measurements are discussed. The TUD-ESA (European Space Agency) joint effort on spherical near-field testing is also described     

Time-Domain Analysis of Millimeter Wave Circulation Around a Magnetised Ferrite Sphere

An efficient numerical method has been devised for the study of wave circulated by a magnetised ferrite sphere. It is a finite-difference time-domain formulation that incorporates Mur's absorbing boundary conditions and a perfectly matched layer. The electromagnetic fields inside the ferrite body are calculated using special updating equations derived from the equation of motion of the magnetization vector and Maxwell's curl equations in consistency. The electromagnetic fields inside ferrite and the power-density distribution on the ferrite's surface normal to the bias external magnetic field are obtained in a wide frequency band with a single time domain run. It is observed that an incident plane wave would circulate around the magnetised ferrite body in an open space as if the ferrite were placed inside a waveguide / microstrip junction circulators.     

A path integral time-domain method for electromagnetic scattering

A new full wave time-domain formulation for the electromagnetic field is obtained by means of a path integral. The path integral propagator is derived via a state variable approach starting with Maxwell's differential equations in tensor form. A numerical method for evaluating the path integral is presented and numerical dispersion and stability conditions are derived and numerical error is discussed. An absorbing boundary condition is demonstrated for the one-dimensional (1-D) case. It is shown that this time domain method is characterized by the unconditional stability of the path integral equations and by its ability to propagate an electromagnetic wave at the Nyquist limit, two numerical points per wavelength. As a consequence the calculated fields are not subject to numerical dispersion. Other advantages in comparison to presently popular time-domain techniques are that it avoids time interval interleaving and it does not require the methods of linear algebra such as basis function selection or matrix methods