I. INTRODUCTION
Despite dramatic advancements in electronics over the past few years, rising speeds and reduced volumes have posed significant challenges for electromagnetic compatibility (EMC) [1–3]. Therefore, the electromagnetic environment of components must be precisely known as early as possible in the design process to minimize both effort and cost while maximizing performance. When computational techniques fail to correctly predict the EMC of complex equipment, EMC professionals resort to measurement-based analysis tools. In this context, near-field scanning (NFS) offers several significant advantages over conventional EMC measurement approaches [4]. It is a low-cost pre-certification test method that helps evaluate the intra- and inter-system EMC behavior of devices.
Well known for its capacity to characterize radiation sources, NFS has enabled the development of high-accuracy equivalent radiation models of components [5]. However, despite the advantages of this technique [6–8], it must be noted that acquiring unperturbed near-field data with adequate resolution to measure all significant radiation phenomena is challenging. Moreover, the effective duration of the scanning process is usually long.
Several approaches for accelerating near-field measurement have been proposed in the literature [9–13]. For instance, the sequential sampling strategy described in [14, 15], which uses linear approximation and the Kriging model, achieved a considerable decrease in sample sizes. However, the authors did not present any quantifiable data to support their results.
Moreover, the main disadvantage of this approach is the processing time necessary to locate relevant regions, and the need to construct a stopping condition using the Kriging model. Another restriction is the use of random sampling. Notably, the approach proposed in the current study addresses this issue. Meanwhile, the total measurement time of the sequential spatial adaptive sampling approach proposed in [16, 17] was found to be significantly less than that of the full sampling approach. However, the inverse distance weighted interpolation technique applied in this approach has certain limitations, especially with regard to the sensitivity and effectiveness of the weighting function to dispersed or unsymmetrical inputs. Furthermore, since the highest and lowest values across an approximated region can only appear at the sampling points, slight fluctuations and peaks usually develop around the data sample locations [18]. The sequential adaptive approach developed in [19] uses, cubic spline interpolation [20, 21] to overcome the problems of sampling sparse and irregular data. However, despite employing various selection criteria, the study focused on global spatial field variations across the entire map rather than local variations. This resulted in an imbalanced distribution of measurement points and oversight of areas with low spatial gradients, which can affect both the field profile and the accuracy of equivalent models derived through inverse methods.
In this study, drawing on the methodologies developed in previous research, we introduce an algorithm for NFS that minimizes measurement time while preserving field profiles, which is essential for generating equivalent radiation models for devices. This approach involves systematically identifying optimal locations for conducting experimental measurements using both local and global search strategies. The proposed algorithm integrates windowed scanning methodology, a sequential adaptive approach, and a deterministic mesh to achieve its fundamental objective of preventing a high concentration of measurement points in any area.
The remainder of this article is structured as follows: an outline of the concept of the sequential adaptive spatial sampling process is provided in Section II, Section III describes the strategies developed to address the limitations of prior approaches, Section IV presents the measurement outcomes, and the final section provides the concluding remarks.
II. SEQUENTIAL ADAPTIVE SAMPLING ALGORITHM
A number of sample coordinate methods can be used to achieve optimal spatial coverage in the initial scan, despite the unavailability of data on the field’s spatial distribution (Ω). Notably, the exploration phase of the initial scan aims to optimally cover the scanning area, precisely evaluating electromagnetic profiles and finding key locations. Later, during the exploitation phase, more points are inserted into high-fluctuation zones to adjust the field according to zone characteristics. Notably, areas with fast variations often require a higher sampling density than areas with lower variability. Therefore, each iteration of the sequential process undergoes two phases. The first is a spatial search that identifies suitable measurement locations, while the second phase pertains to deciding whether a location is relevant for collection, with each position evaluated by accounting for the surrounding field variance. In the next section, the proposed approach is described in detail.
III. SEQUENTIAL ADAPTIVE WINDOW SCAN SAMPLING ALGORITHM
Fig. 1 presents a flowchart of the proposed algorithm, which requires determining an appropriate spatial sample to achieve swift convergence to the optimal solution. The procedure is detailed below.
1. Sampling Process
1.1 Initial sampling
Although low spatial scatter leads to high precision, the corresponding process may require a large number of initial measurement points, which would increase the measuring time. Meanwhile, large dispersion may accelerate the initial measurement, but it often leads to severe data waste. Consequently, the performance of the adaptive algorithm will be affected. Therefore, a regular mesh, simple and cost-effective in terms of both space and time, was employed in this study [22]. The sample frequency of the initial scan step was calculated based on the scanning height (h) and field parameters [16]. Fig. 2 illustrates the position of the measurement points during the initial phase (first measurement Sequence 0).
If attenuation is set to 10 dB, the minimum sampling step can be approximated as W0 < 2h. Notably, W0 parameters for a specific attenuation of x dB remain unaffected by the measurement frequency. Moreover, if a higher attenuation is acceptable, a larger sampling step may also be performed. To achieve process convergence, the initial samples should cover all the edges of the layout region, while further samples can be selected based on a regular grid pattern.
The total number of points (N) captured in the initial scan can be calculated using the following equation:
Here, Ax and Ay refer to the lengths of the x and y-axes, respectively. Ideally, they should be multiples of W [19].
1.2 Sequential adaptive scanning
For the initial scan, N samples were placed on a regular grid. The spatial step of each sequence of samples was reduced by half, which resulted in a continuous decline of the sample resolution until it fell below or reached the minimal resolution Wf. Subsequently, a decision-making strategy was implemented to select points believed to contain relevant information.
1) Window scan position and number of candidate points Ca (exploitation phase)
To conduct an in-depth analysis of the measurement domain, the surface to be measured was partitioned into numerous square-shaped subsets, each with sides equal to the maximum step W0. For measurement at a height of 10 mm, the measuring portions were either rectangular or square, with a minimum dimension of 20 mm × 20 mm. For the calculation, we adapted the sides to obtain an integer domain number. As shown in Fig. 3, the card size was set to 80 mm × 48 mm, with its sides being adjustable at 40 mm × 22 mm.
Using the approach presented in [19], a maximum of 65% of the points in the uniform grid was examined. While this property may help accelerate the measurement process, neglecting the information provided by 35% of the points that remained untested could give rise to errors. Therefore, in the proposed method, the 35% untested points were re-introduced to the group of candidate points. Fig. 4 shows the position of the candidate points at phase A of the first sequence (first measurement Sequence n).
The Ca1 candidate point set formed by 65% of the points was defined as the points halfway between two adjacent points in the x- and y-directions [19].
Meanwhile, the Ca2 candidate point set formed by the 35% untested points (xnca2,s, ynca2,s) comprised the points at the center of the square limited with four adjacent points. Its coordinates can be defined as Pca2(xnca2,s, ynca2,s), where
Furthermore, Nnca,s signifies the new points added to the map for each sequence S, expressed as follows:
Here, Nd refers to the number of subdomains.
Fig. 5 illustrates the position of the candidate points at phase B of the first Sequence (second measurement Sequence n). Measurements were performed for locations in the Ca sets that were assessed to have important information (Fig. 6). Subsequently, an interpolator was used to identify the remaining points that were deemed to have inaccurate information.
2) Position and number of complementary points C0
A cubic interpolator [20] was employed to evaluate the fields of the candidate points rejected by the test, thereby forming a complimentary set of points, termed C0. Consequently, in the proposed approach, 100% of the points on the uniform grid in the last iteration are tested, ensuring a comprehensive examination of the measurement domain.
1.3 Final sampling resolution
The information required to characterize a device under test (DUT) can be expressed in terms of resolution. In the near-field domain, data collection is performed at a distance of less than a single wavelength. Therefore, the ideal resolution can be defined as follows [23]:
Notably, a loop probe is a highly effective crosswise magnetic field sensor. Extensive testing was conducted to select the size of the loop that would balance sensitivity and resolution. Since the highest resolution for probe diameter d should not be less than d/4 [24], the final sample resolution Wf was chosen to be less than h/2 but more than or equal to d/4.
2. Evaluation
In [19], the gradient of the field between two adjacent points was used as a criterion:
In this study, the average of gradient D between the four vertices of a subdomain was employed as the testing approach for the Ca2 group. If this average value exceeded the selection limit G, the Pca (xnca2,s, ynca,s) points of the new mesh (Sequence S + 1) had to be included. The equation defines the mean distance D, which quantifies the average variation of the function F(P(x, y)) between neighboring measurement points in both the x- and y-directions. This provides a mathematical basis for evaluating the local continuity and spatial variation in the measurement field.
(8)
To maintain sufficient data concerning F, the allowed deviation was determined based on the G.
F represents the field to be measured, which may refer to either the electric field or the magnetic field, depending on the measurement configuration. If G is lower in Eq. (9), the chances of picking up the candidate point are high. If not, as G increases, the chances of picking the candidate point decrease.
As shown in Fig. 6, the candidate points (in blue and green) represent, respectively, the midpoints along the x- and y-directions between the points of the previous sequence, and the center points of the squares formed by four neighboring points from the previous measurement sequence. These candidate points are selected for potential measurement in the next iteration, allowing the adaptive refinement of the spatial sampling grid.
The parameter D, defined by Eq. (8), remains constant for the same field mapping, while G can either be defined by the user or determined computationally. The latter can be performed for the entire map (global search, Eq. 10) or for a specific region (local search, Eq. 11).
The candidate points are selected so that the measurement process can be performed at these locations, as they present a high probability of containing relevant information for the construction of the field map.
3. Allowable Deviation D and Selection Criteria G
Allowable deviation is the most significant feature of the proposed procedure. To establish a balance between global and local searches, two selection criteria were considered one based on the field’s fluctuations in the measurement space and the other based on local variations in the subdomain. In the following section, the two proposed bands are explained.
4. Error Evaluation
To evaluate the error and verify the performance of the proposed approach, we first had to define an indicator relevant to the algorithm’s purpose—achieving fast measurement using a small number of points while preserving the field profile through high-resolution uniform grid measurement. Eq. (12) provides the formula for the mean error indicator:
Here, Hi,s is the magnetic field collected through sequential adaptive sampling for sequence S, and Hi,u denotes the magnetic field captured using a uniform array Wunif = d/4 [24].
5. Interpolator and Estimator
Overall, the current section describes the measurement domain’s exploration phase, allowing movement from dispersed database to regular dispersion. A triangulation-based interpolator was employed to achieve fast and precise approximation [25].
IV. RESULTS AND DISCUSSION
1. Experimental Measurement
To experimentally evaluate the proposed approach, a measurement scenario was constructed. Fig. 7 depicts the near-field measurement system comprising a motion subsystem, a probe, a processing unit (Fig. 8), a magnetic probe, and a data acquisition system (Fig. 9).
The RF-R50-1 probe, featuring a circular shape with a diameter of 1 cm, was employed for the experiment owing to its low susceptibility to electric fields and exceptional sensitivity to magnetic fields.
Furthermore, to quantify the CT parameter S21 and offer phase referrals, an Agilent E5062A vector network analyzer was employed [26]. The system was operated remotely using a PC via LabVIEW software.
Fig. 10 depicts the circuit under test, bearing a configuration of 50 mm × 80 mm. The magnitude and phase of the tangential magnetic fields are were measured at different heights below the printed circuit board (PCB). Fig. 10 also illustrates the field radiation magnitude at 300 MHz, considering a 2.5 mm resolution and a 10 mm height.
2. Results
2.1 Evolution of sequence-based field mapping
Fig. 11 depicts the progression of field mapping based on sequences. The efficacy of the approach was successfully evaluated— once the last sample size was reduced, the resulting cartographies were observed to be comparable to those generated by uniform measuring, regardless of the higher quantity of the collected points.
2.2 Evolution of sequence-based field mapping
Fig. 12 shows the locations of the sample points selected by the adaptive approach for mapping the magnetic field component HX (W0 = 8 mm, Wf = 2 mm), illustrating how the adaptive sampling technique strategically places points to capture key features of the field distribution. Notably, the placement of the sample points was influenced by the spatial characteristics of the field, including gradient variations and local changes in field strength. This implies that the effectiveness of the sampling strategy is greatly dependent on the selected criteria, which should prioritize areas with more significant field variations, ensuring higher accuracy in these regions while avoiding unnecessary measurements in areas exhibiting lower variation. Consequently, the number and distribution of the sample points were not uniform, but were optimized based on the field’s complexity. This adaptive approach, by focusing resources on areas providing the most valuable data for accurate mapping of the HX component, led to improvements in measurement efficiency. Fig. 12 highlights both the precision and computational efficiency gained through the use of the adaptive approach.
3. Discussion
3.2 Gm and Gl criterion precision
Figs. 13–17 clearly indicates that local search is more effective than global search. Moreover, the intersection of the two criteria produces better results, regardless of the number of points selected, implying that the local–global union provides higher precision. Notably, this result was validated by considering a large number of chosen points, which increased the time of the measurement.
3.3 Efficiency based on the number of points measured
Figs. 18–21 depict the variation in accuracy as a function of the number of points in response to a change in the selection criterion. It is observed that increasing the number of points enhanced the measuring precision while decreasing the speed. In addition, the number of selected points was directly affected by changes in the G limit. The VNA acquiring time Tmes may also vary depending on the frequency band and averaging function.
3.4 Accuracy vs. measurement time
The measurement time was directly affected by changes in the G limit.
3.5 Comparison of measurement times
The time needed to complete a near-field scan depends on a number of parameters, such as the computer storing time Tstr and file size Tstr = 1 s/point, among others. The VNA acquiring time Tmes may also vary depending on the frequency band and averaging function parameters. In this context, the acquisition time can be defined as Tmes = 1.5 s/point. Finally, the motor’s movement profile (acceleration, deceleration, and speed) may influence the probe’s displacement time Tdisp.
Notably, according to practical observation, Tdisp can be estimated using the following equation:
When sequential measurement is employed, more time is necessary to account for the delay (d) in performing path optimization, gradient evaluation, and point position computation using the selection method. Luckily, the duration of the algorithm’s execution in this study was only a couple of milliseconds, and the application frequency was exceedingly low, rendering them insignificant. Table 1 compares the time required by the conventional method, the method presented in [19], and the new approach proposed in this article to perform measurements. Notably, the results obtained using the G2 criterion are based on the method described in [19]. It must also be noted that although the measurement time was reduced by 30% to 60% using adaptive scanning, a reduction in the scanning period always results in decreased precision.
V. CONCLUSION
The present study describes an improved automated sequential adaptive approach based on local and global searches that uses window scanning to minimize the time required for near-field scan measurements. The approach involves running a series of near-field captures and examining the predetermined parameters to select the optimum positions for performing additional scans.
To achieve this, new selection criteria were developed to reduce inaccuracies in all near-field sectors. Selection criteria Gl focused on searching for locations with high field dynamics, thereby allowing for a substantial decrease in the number of measurement points and, in turn, operating time. Nevertheless, it must be noted that this criterion ignored local fluctuations, potentially leading to increased inaccuracy. The Gg criterion enhanced the measurement space exploration by analyzing the average sub-zone gradients. Considered together, the Gl, Gg union served to enhance measurement precision but led to an increase in the number of points selected, whereas the intersection of the two criteria resulted in a decrease in the number of points while increasing error. This study also confirms that browsing by window ensures high precision, regardless of the initial resolution. The proposed technique successfully reduced the measurement time to 30% of the conventional sampling time while adding no significant measurement errors, with the mean error being in the order of 0.1 dB.
Future research should examine the effectiveness of the proposed approach for multi-frequency measurements. It is also crucial to investigate the impact of including the amplitude and phase of the field on the gradient when constructing selection criteria. Finally, employing methodologies for evaluating induced phenomena can be valuable for investigating EMC issues.
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