1 INTRODUCTION

With continuous development of miniaturization and integration, the density of devices (i.e., passive devices and active devices) on the printed circuit board (PCB) or packages increases, leading to the space between devices decreasing. Besides, to satisfy the growing market requirements, more and more digital-analog hybrid modules are currently studied, while the EMI problems between digital module and analog module are highlighted. Such trends aggravate EMI problems in the PCB and package, such as electromagnetic interference between different active devices, especially in the RF systems [1, 3, 5]. During signals processing, every single device becomes a radiation source as well as a highly sensitive device. Therefore, studying the near-field radiation of electronic devices is important and meaningful for solving the EMI problems.

Near-field measurement is one of the most effective ways to study the near-field radiation of electronic devices. In the earliest time, near-field measurement is developed to study the far-field patterns of antenna, which is based on near-field to far-field transformation and plane-wave expansion method [6, 8, 9]. Such measurements are implemented in the radiating near-field region (typically 3λ ~ 5λ). Later, near-field measurement is used for the determination of the equivalent radiated emission models of the components on the PCB [7, 12]. In addition, it is implemented in the highly reactive region (typically <λ/6) [11]. In this case, equivalent radiated emission models, such as an array of magnetic dipoles and an array of electric dipoles, are obtained from the magnetic field measured from the near-field scanning. By utilizing the equivalent models, researchers can simulate the coupling effects among the components on the PCB and evaluate the electromagnetic behavior of the electronic products.

Aiming to obtain the field information at the observation surface, the probe calibration is employed to obtain the conversion factor between the realistic field information and the voltage or current signals induced by the probe. In this work, we present a calibration procedure of two kinds of magnetic probes including horizontal magnetic field probe and vertical magnetic field probe, respectively. As for other papers [2, 4, 10, 14], the calibration structure is just a microstrip line on the PCB, which is used to calibrate both the horizontal magnetic field probe and the vertical magnetic field probe. Here, we designed another calibration structure with a ring microstrip line deployed on the PCB to specially calibrate the vertical magnetic field probe. Compared with the vertical magnetic field, horizontal one is much smaller in the central zone above the ring microstrip line. It results in the negligible influence of the horizontal magnetic field on the calibration of the vertical magnetic field probe. Therefore, this calibration structure is more suitable for calibrating the vertical magnetic field probe than the microstrip line structure.

This paper is structured as follows. In section II, the probe calibration method is introduced, and then the factors that influence the accuracy of the calibration method is analyzed and discussed. In section III, the calibration system is introduced, and two kinds of magnetic probes are calibrated according to the calibration method. In section IV, near-field scanning on another radiating structure is performed to validate the calibration method, and the corresponding relative errors are calculated and discussed. Finally, section V concludes this paper.

2 Probe Calibration Method

For magnetic field measurements, a single turn, miniature magnetic loop probe is typically used. The structure of the magnetic probes is shown in Fig. 1, where the miniature magnetic loop is connected to a coaxial cable. According to the direction of the measured magnetic field components, the magnetic probes are classified into horizontal magnetic field probe and vertical magnetic field probe, as shown in Fig. 1 (a) and Fig. 1 (b) respectively. The probes can respond to horizontal magnetic field and vertical magnetic field, by which voltage or current signals are induced in the miniature magnetic loop.

Fig. 1
figure 1

The structure of the magnetic probe (a) horizontal magnetic field probe; (b) vertical magnetic field probe

Full size image

The purpose of near-field measurement is to obtain the field information at the observation surface. Therefore, the goal of probe calibration is to get the conversion factor between the realistic field information and the voltage or current signals induced by the probe. The conversion factor is called probe factor (PF). Theoretically, PF is the inherent parameter of the probe [13]. It will not change with different DUTs. Moreover, it is calculated through eqs. (1).

$$ {H}_{respond}={V}_{out}\bullet PF $$
(1)

Where V out is the output voltage of the receiver. H respond is the magnetic field intensity responded by magnetic probe. H respond cannot be received by receiver directly. Therefore, we substitute it by reference field which can be calculated accurately through analytical or numerical solutions. It is required that the calibration structure is simple enough to be calculated accurately and fast, such as monopoles, dipoles, microstrip transmission lines, or commercial calibrated radiators. Here, 50 Ω-matched microstrip transmission line on the PCB is chosen properly as the calibration structure.

The calibration method is presented as follows. The probe is fixed at the observation point above the calibration structure. By the probes, fields can be converted into voltage or current signals, which are displayed in receiver. However, the magnetic field cannot be measured directly, so the reference field from a standard calibration structure is introduced. The reference field is obtained from 3D full wave simulator. Thus the probe factor can be calculated from the measured voltage signals and the simulated reference field.

The whole near-field measurement system consists of probes, motor system, signal generator, receiver, and some cables. In calibration process, the receiver is a vector network analyzer (VNA), which integrates the internal source. The acquired probe factor is actually system PF, which includes all the effects of the probe, cables, and amplifiers and other electrical probe parameters. However, in near-field scanning process, the receiver is a spectrum analyzer (SA), which needs an external signal generator.

Based on the near-field measurement system, the accuracy of the calibration method is influenced by some factors. Firstly, the electrical characteristics of the calibration system, such as the background noise of the system, the loss in the cables, reduce the sensitivity of the system. Secondly, the location deviation, which results from the locating of the observation point, the mechanical error of the equipment, the warpage of the DUTs, brings in the measurement error. Thirdly, the characteristics of the probe affect the accuracy of the calibration method directly. The first and the second factors will be discussed in section III. And the effects of the probe will be analyzed from three aspects in this section.

2.1 The Non-ideality of the Real Probe

In simulation, the obtained magnetic field is that at the observation point. However, the measured magnetic field is the average of the magnetic flux in the area of the loop. The difference results in the error of the simulated magnetic field and the measured magnetic field. Compared with the larger loop area, the magnetic field is relatively uniform in the smaller loop area. To reduce the non-ideality of the real probe, we can choose the probe with smaller magnetic loop.

2.2 H/E Rejection

Practical magnetic probe may respond to more than one magnetic field components as well as electric field components, because the loop structure can also behave like an electric monopole. In order to shield the electric field, the loop is designed as a semi-rigid coaxial cable with a gap cut at the low point of the loop. The model of the loop is shown in Fig. 2.

Fig. 2
figure 2

Simulation model (a) microstrip line on the PCB with the probe; (b) side view of the loop; (c) bottom view of the loop without the outer conductor

Full size image

2.3 Probe Disturbance to Field

The existence of the probe leads to the interference with field. To evaluate the interference, numerical full wave simulations are performed in the 3D simulator ANSYS HFSS, which is based on finite element method (FEM). The simulation model is shown in Fig. 2. The radiator is a microstrip line with the width of 1 mm and the characteristic resistance of 50 Ω. Because the size of the complete commercial probe is hard to get, we construct a simple probe model. The tip of the probe is a single turn, miniature magnetic loop with the diameter of 150 um, as shown in Fig. 2 (b) and (c). The loop is a semi-rigid coaxial cable with a gap cut at the low point of the loop, which is the same as the real commercial probe. A coaxial cable is connected with the loop, and the characteristic resistance of the coaxial cable is 50 Ω. For keeping consistent with practical calibration, the normal direction to the loop is vertical to the microstrip line shown in Fig. 2 (a) where h is the vertical stand-off distance between the center of the loop and the surface of the microstrip line. In addition, three groups of simulations for the probe disturbance are performed, with different h (1, 3 and 5 mm) selected, respectively.

Considering the probe and h influences, simulation results of the horizontal magnetic field (H y ) distribution along the cutline in the model are shown in Fig. 3(a). The cutline is vertical to the microstrip line and across the center of the loop, as shown in Fig. 2. In practical process of the near-field scanning, the probe moves along the observation surface or the observation line. In such condition, the measured field is the perturbed field at the center of the loop. Therefore, the simulations focus on the perturbed field at the center of the loop. Obviously seen from Fig. 3, the horizontal magnetic field (H y ) is perturbed at the center of the loop, and the perturbed horizontal magnetic field is larger than the original horizontal magnetic field. To further study the influence of the probe location on the perturbation, relative errors (\( {\varepsilon}_y^r \)) between the perturbed field and the original field are extracted from the results in Fig. 3(a). \( {\varepsilon}_y^r \) is calculated according to eq. (2).

$$ {\varepsilon}_y^r=\frac{\left|{H}_y^p-{H}_y^o\right|}{H_y^o} $$
(2)
Fig. 3
figure 3

(a) H y distribution along the cutline in the model with and without the probe and with different h of 1 mm, 3 mm and 5 mm; (b) relative errors (\( {\varepsilon}_y^r \)) between the perturbed field and the original field along the cutline with different h of 1 mm, 3 mm and 5 mm.

Full size image

Where \( {\mathrm{H}}_{\mathrm{y}}^{\mathrm{p}} \) is the perturbed magnetic field in y direction, and \( {\mathrm{H}}_{\mathrm{y}}^{\mathrm{o}} \) is the original magnetic field in y direction. The \( {\varepsilon}_y^r \) with different h are shown in Fig. 3(b). Comparing the different \( {\varepsilon}_y^r \) at the center of the loop (y = 0 mm) with different h, \( {\varepsilon}_y^r \) with h = 1 mm is the smallest. It indicates that the relative perturbation of the field is smaller with the loop location getting lower during probe calibration. In addition, in the region far away from the location of the probe, the smaller magnetic field leads to the larger relative error. It results from the little denominator in eq. (2).

3 Process of Calibration

Considering the process of probe calibration as a process of near-field measurement, the calibration system is just the near-field measurement system. Besides, the desired PF is a frequency-response curve, which requires the calibration system has the function of automatic frequency sweep. In the process of calibration, a vector network analyzer (VNA) is used as the receiver. Because the VNA includes internal source, an extra signal generator is not necessary in the system. The schematic and the physical setup of the calibration system are shown in Fig. 4. In order to increase the sensitivity of the calibration system, we choose the well-calibrated VNA and the low-loss cables. The probe can move automatically in the horizontal plane following two orthogonal directions by means of stepper motors. It can move along the vertical direction. The motors are controlled by a personal computer. The minimum step size is 20um, and the accuracy is +/− 20um. The initial point of the near-field scanning is set manually by means of the camera fixed in the equipment. In order to reduce the location error, an alignment mark is made on the calibration structure.

Fig. 4
figure 4

(a) Schematic of the calibration system; (b) physical setup of the calibration system

Full size image

To verify this calibration method, calibrations of two commercial magnetic probes are implemented. One is horizontal magnetic field probe, and the other is vertical magnetic field probe, as shown in Fig. 5. There is a miniature loop at the tip of the probe with the diameter as 150um. In addition, the loop of the horizontal (vertical) magnetic field probe locates at the vertical (horizontal) plane and responds to the magnetic field component in horizontal (vertical) direction. Based on probe size and manufacturing technique, the applicable frequency range is 1 MHz-6GHz. Besides, in order to increase the sensitivity of the probes, a pre-amplifier is integrated in the probes.

Fig. 5
figure 5

Magnetic probes calibrated in this paper (a) horizontal magnetic field probe; (b) vertical magnetic field probe

Full size image

Calibrations of the two probes are implemented with two calibration structures. The horizontal magnetic field probe is calibrated with a microstrip line structure, while the vertical magnetic field probe is calibrated with a ring-line structure, as shown in Fig. 6. The horizontal magnetic field component H y right above the microstrip line is much larger than other field components H x and H z . The vertical magnetic field component H z right above the center of the ring-line is much larger than other field components H x and H y . Adopting these calibration structures will reduce the influence of other field components on the calibration.

Fig. 6
figure 6

(a) Calibration structure of horizontal magnetic field probe; (b) Calibration structure of vertical magnetic field probe

Full size image

3.1 Calibration of Horizontal Magnetic Field Probe

To measure the responding field, a standard calibration device is designed and fabricated. According to the standard of IEC, it is a 50 Ω-matched microstrip transmission line on the PCB, as shown in Fig. 6 (a). The design parameters are shown as follows: the size of the PCB is 100 mm×100 mm; the width of the line is 1 mm; the thickness of the dielectric is 0.6 mm. When implementing the measurement, one terminal of the microstrip line is connected to the output port of the VNA through a cable, and the other terminal is terminated with a 50 Ω load. The probe is connected to the input port of the VNA through another cable. According to the standard of IEC, the input power of the microstrip line is set to 0 dBm. The frequency sweep range is 1 MHz-6GHz. Theoretically, in the observation surface of a definite height, the horizontal magnetic field intensity right above the center of the microstrip line is the largest. Therefore, the probe is fixed right above the center of the microstrip line. The vertical distance between the microstrip line and the center of the loop is set to 1 mm. In account of the small size of the probe, the center of the loop is considered as the observation point. When the S21 parameters of the two ports are obtained, the voltage signals of the probe’s response are achieved from the S21 data.

To get the reference field, a model is constructed in the 3D full wave simulator HFSS. The size of the model is the same as the actual microstrip line structure. Other parameters, such as port excitation, sweep frequency range, location of observation point, are also the same as the actual structure. In addition, the probe is included in the model. The simulation results donated to the field data extraction, which is the reference horizontal magnetic field of the observation point in the definite frequency range (1 MHz-6GHz). By implement of the same measurement structure for the observation point, the reference horizontal magnetic field can be compared with the voltage signals. Moreover, PF is obtained through eq. (3).

$$ \mathrm{PF}\left(\mathrm{dB}\ A/ Vm\right)={H}_{simu}\left( dB\ uA/m\right)-{V}_{out}\left( dB\ uV\right) $$
(3)

Equation (3) is derived from eq. (2). Here, some details should be considered in equation (2) as follows: the unit of amplitude V out is V; the unit of H respond is A/m. In addition, in equation (3), the unit of the output voltage V out displayed in VNA is dB uV, so it doesn’t need to be converted; the unit of the simulation data H simu is A/m, so it should be converted to dB uA/m. The conversion relation is described as equation (4).

$$ {H}_{simu}\left( dB\ uA/m\right)=20\times {\mathit{\log}}_{10}\left({H}_{simu}\left(A/m\right)\times {10}^6\right) $$
(4)

Finally, the unit of PF is dB A/Vm, and the calculated PF depending on frequency is plotted in Fig. 7.

Fig. 7
figure 7

Measured responding voltage, simulated reference field and the calculated PF of horizontal magnetic field probe

Full size image

3.2 Calibration of Vertical Magnetic Field Probe

The calibration process of the vertical magnetic field probe is similar with the horizontal magnetic field probe. However, the difference is that the calibration device here is a ring-line on the PCB. This calibration structure is shown in Fig. 6 (b), with the same laminated construction of the PCB as the microstrip line calibration structure. The size of the PCB is 50 mm×50 mm and the ring-line is at the center. Moreover, the diameter of the outer edge of the ring is 4 mm, and the width of the ring is 1 mm.

The other difference is the choosing of the observation point. The point is determined to be right above the center of the ring. The vertical magnetic field intensity of this point is the largest on the 1 mm-high surface. After frequency sweep measurement and corresponding simulation, PF of the vertical magnetic field probe is calculated, as shown in Fig. 8.

Fig. 8
figure 8

Measured responding voltage, simulated reference field and the calculated PF of vertical magnetic field probe

Full size image

4 Validation of the Obtained PFs

To validate the applicability of the obtained PF, another sample is designed and fabricated, as shown in Fig. 9. It is a cross-line on the PCB and gets the same laminated construction of the PCB with the microstrip line used for calibration. The width of the line is 2 mm and the length of each arm is 40 mm. In fact, it is an open-circuit structure. Signal is fed into the intersection of the cross through SMA connector and via. Besides, the SMA connector is at the bottom of the PCB. Finally, the similar model is constructed in simulator HFSS.

Fig. 9
figure 9

The structure of the validation device

Full size image

The validation process is a near-field scanning process. In the near-field scanning system, the receiver is a spectrum analyzer. Thus an external signal generator is necessary. In this experiment, near field scanning is implemented on the observation surface with horizontal and vertical magnetic field probes, respectively. The parameter configure is shown as follows: the distance between the observation surface and the sample is 1 mm; the frequency is set to 1GHz; the scanning area is 42 mm×42 mm, which covers the whole cross. It could be confirmed that the received data contains enough information to represent the radiation source. Furthermore, the horizontal magnetic fields \( {H}_x^m \) and \( {H}_y^m \) are measured with the same horizontal magnetic field probe in two near-field scanning processes, respectively. Besides, the probe is rotated 90 degrees around the z-axis between the two processes. With the vertical magnetic field probe, the vertical magnetic field \( {H}_z^m \) is measured in one near-field scanning process. In fact, the original measured data acquired from the near-field scanning system is voltage signal V out (dB uV) that the probe responds. After processing with the corresponding PFs according to equations (5), (6) and (7), \( {H}_x^m \), \( {H}_y^m \) and \( {H}_z^m\left(A/m\right) \) are achieved as follows.

$$ {H}_{x,y}^m\left( dB\ uA/m\right)={\mathrm{PF}}_H\left(\mathrm{dB}\ A/ Vm\right)+{V}_{out\ x,y}\left( dB\ uV\right) $$
(5)
$$ {H}_z^m\left( dB\ uA/m\right)={\mathrm{PF}}_V\left(\mathrm{dB}\ A/ Vm\right)+{V}_{out\ z}\left( dB\ uV\right) $$
(6)
$$ {H}_{x,y,z}^m\left(A/m\right)={10}^{\frac{H_{x,y,z}^m\left( dB\ uA/m\right)}{20}-6} $$
(7)

Where PF H is the probe factor of the horizontal magnetic probe, and PF V is the probe factor of the vertical magnetic probe. By conducting the corresponding simulations the magnitude and distribution of the reference horizontal magnetic fields \( {H}_x^s \), \( {H}_y^s\left(A/m\right) \) and vertical magnetic field \( {H}_z^s\left(A/m\right) \) are presented on the observation surface. The magnitude and distribution of the simulation results and the measurement results are shown in Fig. 10.

Fig. 10
figure 10

Magnitude and distribution of magnetic field and the corresponding relative error on 1 mm-height observation surface (a) simulation result \( {H}_x^s \); (b) simulation result \( {H}_y^s \); (c) simulation result \( {H}_z^s \); (d) measurement result \( {H}_x^m \); (e) measurement result \( {H}_y^m \); (f) measurement result \( {H}_z^m \); (g) relative error \( {E}_x^r \); (h) relative error \( {E}_y^r \); (i) relative error \( {E}_z^r \)

Full size image

In Fig. 10 (a), (b), (c), (d), (e) and (f), the unit of the magnitude is A/m. From these pictures, we found that the measurement results agree well with the simulation results on the 1 mm observation surface. Compared with measurement results, the distribution of simulation results is more regular and symmetrical. In the process of near-field scanning, there exists deviation on the locating of the probe. However, the location of each point is accurate in simulation. Besides, other factors, such as the fixation of DUT, the PCB warpage caused by low-level manufacturing technology, also introduce locating deviation. In order to evaluate the accuracy of the measured results, the relative error of each magnetic field component is calculated according to equations (8), (9) and (10).

$$ {E}_x^r=\frac{\left|{H}_x^s-{H}_x^m\right|}{H_x^s} $$
(8)
$$ {E}_y^r=\frac{\left|{H}_y^s-{H}_y^m\right|}{H_y^s} $$
(9)
$$ {E}_z^r=\frac{\left|{H}_z^s-{H}_z^m\right|}{H_z^s} $$
(10)

Where \( {H}_x^s \),\( {H}_y^s \) and \( {H}_z^s \) are the simulated magnetic field components in x-, y- and z-direction, respectively. \( {H}_x^m \), \( {H}_y^m \) and \( {H}_z^m \) are the measured magnetic field components. The unit of both the simulated and the measured magnetic field components is A/m.

The distributions of the relative errors are plotted in Fig. 10 (g), (h) and (i), where the error value was clamped up to 100%. In the region where the field strength level is relatively small, a small measurement error could also cause huge relative error according to (8), (9) and (10). However, this type of large relative error does not have much influence on the near-field to far-field transformation or source reconstruction, due to the small field strength [14]. From Fig. 10(g), (h) and (i), we can notice that the “large error region” is always associated with the “small signal region”; while in the “large signal region”, the relative error between measurements and simulation is usually lower than 20%.

5 Conclusion

Near-field scanning is an effective method to study the EMI problems in PCB and packages. Particularly, probe calibration is a very important process in near-field scanning and has a great influence on the accuracy of the measurement results. In this paper, we studied a magnetic probe calibration method used for near-field measurement. The novelty is that adopting appropriate calibration structures to calibrate corresponding magnetic probes including horizontal magnetic field probe and vertical magnetic field probe. Furthermore, some factors, such as the electrical characteristics of the calibration system, the location deviation and the characteristics of the probe, influence the accuracy of the calibration method. A series of simulations are performed to analyze the influence of the probes on the near-field measurement. The existence of the probes results in field perturbation at the location of the probes. Besides, the relative perturbation decreases with the dropping of the probe location. To achieve the PFs of the two probes, two calibration structures are designed and fabricated. One is the microstrip line on the PCB, and the other one is the ring-line on the PCB. To validate the PFs of the two probes, another sample is designed and fabricated, which is a cross-line on the PCB. After applying the PFs achieved in the calibration process, the measurement results show a good agreement with the simulation results of the validation sample. The relative errors of the measurement results are calculated less than 20% in the “large signal regions”. It is proved that the achieved PFs are accurate and the calibration method is effective.