**3. The configuration for multiprobe array systems as OTA system**

The hardware of the EMC near-field measurement solution is based on multiprobe systems in combination with the acquisition through a low-cost receiver. The system is based on an arch where the different wideband dualpolarized probes are located. For this specific work, two systems are used: StarLab [20] and MiniLab [21]. These two systems are compact and allow a faster design process and shorter time to market times while keeping a reasonable cost. The use of the low-cost receiver reduces the complexity drastically and cost in comparison with traditional spectrum or vector network analyzers. Moreover, the systems are scalable; thus, the size or low-frequency limitation can be overcome by increasing the measurement solution using other multiprobe configurations.

**Figure 4** shows both systems: MiniLab is the smallest system and works from 650 MHz up to 6 GHz. The radius of the arch is 30 cm with 12 dual linear polarized probes separated by fixed angular steps of 15 degrees. The maximum size of the device under test is 40 cm. StarLab can work from 650 MHz up to 18 GHz for a maximum size of DUT of 45 cm, with up to 15 probes (depending on the model and frequency band). In this case, the system allows a rotation of the arch to increase the number of samples in elevation. In both cases, the use of special receivers allows the working in an over-the-air mode, useful for EMC, 5G, IoT, MIMO, and other special measurement systems. A system calibration process is necessary to assure a reasonable calculation of amplitude, polarization, and phase in the multiprobe system.

In all these systems, the receiver is switching among the different probes, and the amplitude and phase of both polarizations are acquired. One antenna is used as a reference to extract the relative phase among the different probes. As it was already stated before, there are two ways to extract the phase: either by using the on-axis probe of the multiprobe system or by displacing another reference antenna. In the second case, the coupling with the system can be more significant, but still, acceptable results can be achieved [9, 10].

**Figure 4.** *Microwave vision group minilab (left) and StarLab (right).*

#### **4. Amplitude and phase extraction using SDR receivers**

The low-cost reference-less receiver is implemented using the Zynq Evaluation and Development Board (Zed- Board) with the transceiver AD-FMCOMMS3- EBZ. This RF transceiver includes a configurable digital interface to an FPGA to communicate the ZedBoard and the RF module. The 2x2 transceiver module consists of a 12-bit ADC with a receiver band from 70 MHz to 6 GHz and a tunable channel bandwidth up to 56 MHz. This receiver is homodyne, and the signal is directly down-converted to baseband for digitization purposes. The I-Q samples are generated by the transceiver module. The receiver chain can be externally controlled, and it consists of two programmable low-pass filters, decimating filters and gains control for each channel.

The receiver is based on time-domain measurements. Then, the amplitude extraction is done by means of frequency-domain techniques. The power calculation is based on Parseval's theorem on the discrete-time form, see Eq. (1). In the equation, X(k) refers to the Fourier basis functions, while x(n) represents the sampled time-domain signal received by the probe. The number of samples N plays an important role if noise averaging is implemented. Post-processing steps like windowing and filtering are applied in order to get accurate results, see [12].

$$\frac{1}{N} \sum\_{n=0}^{N-1} \left| \mathbf{x}(n) \right|^2 = \frac{1}{N^2} \sum\_{k=0}^{N-1} \left| X(k) \right|^2 \tag{1}$$

Phase reconstruction is not that straightforward, and the method depends on the system architecture: reference antenna independent from measurement arch or onaxis reference antenna. For this application, the transmitters are not necessary.

### **4.1 Phase extraction for reference antenna independent from measurement arch**

If the reference antenna is displaced around the AUT in a fixed relative position, the reference channel emulates the conventional sample taken from a vector network analyzer. In that case, the relative phase between measurement points of the DUT can be extracted as described by Eq. (2). The value of *k*<sup>1</sup> determines the intermediate frequency of the computation.

$$\phi\_i = \arg \left\{ \frac{\sum\_{n=0}^{N-1} E\_{multiprobe}(n) e^{-j\frac{2x}{N}k\_1}}{\sum\_{n=0}^{N-1} E\_{reference}(n) e^{-j\frac{2x}{N}k\_1}} \right\} \tag{2}$$

This method considers possible drifts in the transmitted signal of the DUT since the reference sample is taken by radiation. In contrast with other existing solutions for phase retrieval that could be used for EMC measurements, this one exploits the intrinsic advantages of multiprobe solutions that allow for better isolation of the reference antenna while providing an anechoic and shielded measurement environment. Besides, the reference is accurate as long as the interference from the reference antenna is kept small. This method has already been applied for planar as well as for spherical multiprobe measurements by the authors [12].

### **4.2 Phase extraction for on-axis reference antenna from multiprobe measurement arch**

When the reference antenna belongs to the measurement arch, the solution is simplified. In comparison with the external reference antenna solution, there are some substantial changes:

*EMC Measurement Setup Based on Near-Field Multiprobe System DOI: http://dx.doi.org/10.5772/intechopen.99604*


The change in the phase reference is translated into phase unknowns for every azimuthal cut, as described by Eq. (3). These unknowns are solved by appealing to Ludwig's III definition of polarization that allows retrieving the phase unknowns of the measured signals in a direct way, as explained in [15].

$$\begin{aligned} \stackrel{\rightarrow}{E}\_{meas}(\phi\_1) &= \stackrel{\rightarrow}{E}\_{ref} \\ \stackrel{\rightarrow}{E}\_{meas}(\phi\_2) &= \stackrel{\rightarrow}{E}(\phi\_2)e^{j\phi\_2} \\ &\vdots \\ \stackrel{\rightarrow}{E}\_{meas}(\phi\_N) &= \stackrel{\rightarrow}{E}(\phi\_N)e^{j\phi\_N} \end{aligned} \tag{3}$$

#### **5. Near to far-field spherical transformation algorithm for EMC**

Every receiving probe measures the field radiated by the DUT. The well-known transmission formula [16] gives the relation between the signal measured by the probe and the spherical modes coefficients:

$$w(r, \chi, \theta, \rho) = \sum\_{smn\mu} Q\_{smn} \mathfrak{e}^{jm\rho} d\_{\mu m}^{\mathfrak{n}}(\theta) \mathfrak{e}^{j\mu\chi} P\_{s\mu n}(r) \tag{4}$$

being ð Þ *r*, *θ*, *φ* spherical coordinates,*χ* the probe orientation, *Qsmn* the AUT spherical wave coefficients,*dn <sup>μ</sup>m*ð Þ*θ* a rotation operator and *Ps<sup>μ</sup>n*ð Þ*r* the probe response constants. The summation in Eq. (4) spans for *s*∈½ � 1, 2 ,*n*∈ ½ � 1, *N* , *m* ∈½ � �*n*, *n* and *μ*∈½ � �*V*,*V* .*N* and *V* are the expansion truncation numbers for the AUT and antenna probe, respectively. In principle, this number is infinite. However, depending on the antenna, the number of SWC with significant power is finite for both AUT and probe, and there exists the following practical rule for maintaining good accuracy:

$$N = \lceil kr\_0 \rceil + \mathbf{10} \tag{5}$$

where *k* is the wavenumber, *r*<sup>0</sup> the radius of the smallest sphere circumscribing the AUT (or probe in the case of *V*), and the brackets indicate the largest integer smaller than or equal to the number inside them. However, this rule of Eq. (5) can be replaced by more complicated expressions depending on the signal to noise [22]. For a mode power of 40 dB below the maximum, a more accurate expression is shown in Eq. (6).

$$\mathbf{N} = \lceil kr\_0 \rceil + \mathbf{1.6} \sqrt[3]{kr\_0} \tag{6}$$

Once the spherical modes are calculated, the field generated by the probe can be calculated for each specific point at a finite or infinite distance.

A representative example of the spherical wave expansion of an EMC device can be simulated by taking as DUT a 15 cm dipole excited with 1 μA current. The field

**Figure 5.** *Comparison of analytical electromagnetic field and field after the spherical transformation process to 3 m.*

generated at 3 meters is analytically calculated and compared with the one obtained by following the near-field acquisition by an EMC multiprobe system. In this case, the probes are modeled with antenna factors of 0.1 (to represent a poor performance), the receiver includes a Gaussian noise equal to 120 dBm (the one of the SDR platform), and 12 dual linear polarized probes separated 15 degrees at a radial distance of 30 cm are considered, to emulate the MiniLab multiprobe system.

**Figure 5** shows the results for the peak values, comparing them with the UNE-EN 55032:2016 Std. [18]. The standard level is included to show that the process has the required low power to ensure that the noise effect is negligible. For low frequencies, a spherical mode truncation is applied to run the transformation algorithm without numerical problems. In higher frequencies, the differences are due to undersampling effects: this is due to the limited number of samples, 15 degrees separation between probes, compared with the dimension of the device under test and higher frequencies. However, up to 6 GHz, the system works very well. For frequencies up to 18 GHz, the solution is to implement the arch rotation and use a non-convex optimization for phase retrieval [15].
