A Compact High-Resolution Resonance-Based Capacitive Sensor for Defects Detection on PCBAs

Increased density of printed circuit board assembles (PCBAs) is diminishing physical contact test access of the in-circuit testing (ICT) solutions for defects detection. As a result, it is necessary to design contactless test solutions with high spatial resolution to overcome the current test limitations. In this paper, a compact contactless sensor is presented for monitoring the fabrication quality of PCBAs. The sensor consists of an inductor-capacitor-(LC)-based resonant circuit and it can detect defects on metallic traces of PCBAs in close proximity without a contact. The sensor is designed such that, strong electric field is confined around the sensor tip, which creates strong capacitive coupling between the sensor tip and devices under test (DUTs) within a small region for sensing, i.e. high resolution sensing. The sensitivity of the proposed sensor is verified by the simulated and experimental 2D surface mapping results with sample DUTs, and it shows that the sensor can detect the open or short defects with a size as small as 0.15 mm $\times $ 0.2 mm. Circuit models are proposed to predict the sensing behavior and for guiding the design. The proposed sensor shows great potential to be used in the real-time monitoring of defects along the manufacturing supply chain.


I. INTRODUCTION
Electronics manufacturers are continually challenged to ensure sufficient test coverage for their electronic products. In-circuit testing (ICT) [1], [2] has been a gold standard for around 40 years where defects, e.g. open and short of joints, can be detected and fixed in time. Physical contacts to the soldering points are necessary to facilitate a test. However, increasing density of the printed circuit board assembles (PCBAs) is diminishing these physical contacts [3], and ICT becomes less and less feasible and functional testing is heavily relied on. Functional testing [4] is an essential buy-off of any products and only allows an overall/global fault detection, leaving behind the information on which components on the products cause the failure. As a result, a failed PCBA is discarded rather than having the failed components fixed, which causes a large amount of electronic wastage and is environmentally unsound. To obtain a detailed and localized The associate editor coordinating the review of this manuscript and approving it for publication was Francesco Tedesco . evaluation of a PCBA so that defects can be fixed, non-contact and non-destructive sensing without powering up the PCBAs become critical. Besides, for such an evaluation on PCBAs, a 1D spatial resolution of around 0.15 mm is needed to distinguish different pins of a package for example [5]. In recent years, different potential sensing technologies have been advanced with the development of different probing techniques [6]- [13] to evaluate the fabrication quality of a PCBA, i.e. the device under test (DUT). For example, the X-ray methods have long penetration depth and high spatial resolution, but it needs high cost and possibly result with the radiation hazards [6], [7]. An alternative inspection technique for high density PCBAs is the thermography methods [8], [9]. It has the advantages such as easy operation and simple testing reconfiguration. But the DUT has to be powered up, and this method is susceptible to both non uniform heating and temporal temperature variations, which leads to unreliable sensitivity. Moreover, the acoustic method [10], [11] has excellent long-range diagnostic capability and it is suitable to detect defects on large structures such as pipelines, marine, ships, and aerospace, but for small and complex DUTs like PCBAs, it faces the challenge from heavy data processing and a large number of sensors could be needed. Among these techniques, near-field radio frequency (RF) nondestructive evaluation (NDE) offers advantages of singleside access, contactless, low cost, and high measurement speed [12], [13].
The near-field RF NDE testing methods can be categorized based on the type of fields used for sensing, the electric-field (E-field) sensing [12]- [23], and magnetic-field (H-field) sensing [24]- [29]. For E-field sensing, a popular method is open-ended coaxial probing [14]- [17]. It is widely used for in vivo measurements of permittivity of biological tissues for medical imaging and diagnostics. The permittivity of the material can be extracted from the measured reflection coefficients (S 11 ) when an open-ended coaxial transmission line is in contact with the surface of the DUT. The typical spatial resolution of this method depends on the physical size of the opening of the coaxial cables, which lies in the range from a few millimetres to a few centimetres. For a higher spatial resolution, cavity resonance technique was proposed in [18], [19] for measuring surface dielectric properties, typically in the micrometer to sub-micrometer range. For this method, the measurement is based on the perturbation of the resonance of a coaxial cavity through a probe tip mounted to the center conductor of an coaxial cable attached to the aperture in the end wall of the resonator. The probe's metal tip is sharpened to obtain a high spatial resolution. However, the sharpen tip is sensitive to vibration and thus a sophisticated anti-vibration system is needed for the measurement, which dramatically increases both the complexity and the cost of the measurement. Recently, split-ring resonators (SRRs) have been applied for near-field sensing [13], [20], [21]. The sensing is conducted through the strong electrical field at the slit of the ring where the size of the slit decides the spatial resolution of sensing. A DUT placed near the slit changes the resonant frequency due to its electrical properties, thus the electrical properties can be deduced from the measured shifted of resonant frequencies [13], [20], [21]. For a high spatial resolution, the size of the SRR has to be reduced, which increases the resonant frequency and subsequently the cost of the driving circuit. Another existing near-field sensing solution is open-ended waveguide slit based on the shift of resonant frequency [22], [23]. Although the waveguide slit can provide a resolution of better than 0.1 mm, it has to operate at a high frequency for a high resolution, which increases the cost of the testing instrumentation. Sensing using the E-field of a capacitor is another approach where a parallel-plate capacitor is used to form a resonator with a lumped inductor [12]. The spatial resolution of such a sensor is determined by the physical size of the capacitor. For example in [12], the resolution is limited at 3 mm.
For H-field sensing [24]- [29], it mainly relies on the eddy current testing (ECT) method, which has been utilized in NDE for a long time and widely applied to inspect conductive material structure in order to verify their structural integrity. For the principle of the ECT, it can be summarized as follows. The exciting signal produces the principal magnetic flux through the excitation coils. Then the principal magnetic flux induces the eddy current (EC) in the conductive sample, which produces a secondary magnetic flux in an opposing direction and alternates the input impedance of the excitation coil and receiving probe. Therefore, defects in the sample can be detected since they perturbs the EC and results in variation of the impedance. There are mainly two types of excitation mechanisms for ECT, which are AC eddy current signal [24]- [28] and pulse eddy current (PEC) signal [29]. There are three major types of probing techniques, coil probe [24], [25], giant magneto-resistance (GMR) probe [26]- [28], and the hall sensor [29]. In general, the ECT does not have enough spatial resolution to distinguish errors on different pins of an IC package for example and is not suitable for complex structures such as PCBAs.
In this paper, a compact high-resolution resonance-based capacitive sensor is proposed to detect the defects on the PCBAs, i.e. the shorts and opens. The structure of the sensor can be modeled as a simple LC resonant tank, with a resonant frequency dependent on the sensor trace design and inductance connected to the sensor structure. The simplistic design of the sensor eliminates the need of complex matching circuits design, which makes it easy to fabricate with low cost. Sensor parameters are designed to make the sensor compact and able to detect defects with sufficient sensitivity and spatial resolution. Moreover, simulation and practical results demonstrate the feasibility of the sensor to detect small open and short defects on DUTs. Finally, detail analysis on the sensing principle for the sensor is illustrated using the equivalent circuits which describes the capacitive coupling between the sensor tip and the DUT. Fig. 1 (a) and (b) show 3D view and front view of the proposed resonance-based capacitive sensor, respectively. It consists of a capacitive sensing tip (at the bottom, with a zoomed-in view in the insert on the right of Fig. 1 (a)), lumped inductors (at the top), and a connection region that links them (with a zoomed-in view in the insert on the left of Fig. 1 (a)). On top of the inductors, there are input points where signals are fed to the sensor through, e.g. an SMA connector. For the proposed sensor, sensing is obtained by measuring the shift of the resonant frequency which is caused by an interaction between the DUT and the E-field of the capacitive sensing tip, that alters the capacitance of the tip, as shown by the side-view in Fig. 1 (c).

II. THE PROPOSED SENSOR
For the proposed structure, the resonant frequency, f r , is expressed as follows, where C s = C cr + C tip (2) and L s is the total inductance of the sensor, C s is the total capacitance of the sensor which is the sum of C cr and C tip , the capacitance contributed by the connection region and that by the sensing tip, respectively. The capacitance from the tip, C tip , has the contribution from the two face-to-face arms, C arm tip , and that from the capacitor in a slit, C slit tip as illustrated in Fig. 1 (a).
For sensing, the shift of the resonance frequency (denoted as f r ) is used. When the DUT is underneath the sensing tip, it causes a change in the capacitance of the tip, C tip . Based on Eq. (1)-(3), f r can be expressed using C tip as follows, When the sensor is placed above a metal surface, the electric field is disturbed and there is additional capacitive coupling, resulting in an increase in the capacitance of the sensor, i.e. C tip > 0, and thus a downward shifting of the resonant frequency, i.e. f r < 0, based on Eq. (4).
Upon Eq. (4), the sensitivity for the proposed sensor, denoted as K , is defined as follows, As shown in Eq. (5), a small intrinsic capacitance of the sensor, C s , leads to a high sensitivity of the sensor. Therefore, to achieve a high sensitivity, it is preferable to keep the intrinsic C s low where C s = C cr + C arm tip + C slit tip according to Eq. (2) and (3). To have a low C cr , in the connection region, the arms are moved apart in the x-direction by introducing a 90 o arch with a radius of r, as shown in Fig. 1 To obtain a small C cr , r is set to be 1.6 mm in this design. After the arch, each arm has a straight section with a length of L before it is connected to the lumped inductors. The length of L + r is decided to be long enough to mitigate the interference of the DUT to the inductors. Thus L is set to 8.4 mm. Besides, the sensor arms have a width of m and a thickness of t. m and t are set to 0.1 mm and 0.01 mm to reduce the C cr and C arm tip with the considerations of the manufacturing capability and cost for the flexible PCB used to produce the sensor.
For the sensing tip, it is designed to have a small physical size in order to have a high spatial sensing resolution to match that of a PCBA, i.e. about 0.15 mm. As shown in Figs. 1 (a) and (b), it has a length of h, an arm-to-arm distance of d, and width of w, and a slit size of s. They are set to 1.8 mm, 0.6 mm, 0.25 mm, and 0.1 mm, respectively. It should be noted that the width of the tip w should be large the guarantee the sensitivity. Meanwhile, it should be small enough to maintain a spatial resolution and to minimize interference from the surrounding of the object under sense. For the slit size s, it need to be kept small to confine the E-field between the sensor slit and guide the E-field pointing to the DUT. In addition, h is chosen to be 1.8 mm to avoid the coupling from the connection region to the DUT since the E-field generated from the connection region spreads broadly in a large area and is not concentrated. To have a compact size, d is preferred to be small. But a small d leads to a high C cr and C arm tip , which leads to a reduction in sensitivity. Therefore, d is decided to be 0.6 mm based the considerations on the physical size and sensitivity. The dimensions of the proposed sensor are tabulated in Table 1.

III. EVALUATION OF THE SENSITIVITY
A. THE DUT Fig. 2 shows the DUT designed for the evaluation of the proposed sensor. This design is to mimic the metallic traces on PCBAs such as the parallel soldering joints of a chip package, surface mount capacitors or resistors. It is composed  with an open defect, and the latter is a reference for the case with a short defect. As can be seen in both figures, f r is relatively low when the sensing tip is above the metal trace whereas it is high when the sensing tip is above the air gap, which is agreeable with the analysis based on Eq. (4) in the previous section. In Fig. 3, only the cases when the DUT is terminated with open ends (shown in Fig. 2 (c)) are shown for the reference conditions because the effect of termination is minor and the cases when the DUT is shorted (shown in Fig. 2 (d)) show similar f r distribution as those shown in Fig. 3

(a) and (d).
When there is an open or short defect, the 2D f r distributions are distorted dramatically with distinguishable patterns. As shown in Fig. 3 (b) and (c), when there is an open defect at the center of ROI, compared with the reference in Fig. 3 (a), it is found that f r increases around the defect which is due to a decrease in the capacitance near the sensor tip based on Eq. (4). It forms a distinguishable bright pattern for detection.
When the traces are shorted, as shown in Fig. 3 (c), a distinguishable pattern is still seen with a relatively small increase in f r .
Meanwhile, a short defect also shows a distinguishable pattern in the f r distributions, as shown in Fig. 3 (e) and (f) for the cases when the traces are open and short, respectively. With a metallic block introduced between the two traces to mimic a short defect, the region around the defect has a decrease in f r forming a dark pattern for detection. The   decreased f r is due to an increase in the capacitance near the sensor tip based on Eq. (4). For both types of defects, a detailed circuit analysis on the interaction of the sensor tip and the DUT traces will be presented in Section IV.

C. EXPERIMENTAL VALIDATIONS
Both the proposed sensor and the DUTs were fabricated for experimental validations. Fig. 4 shows a photo of the DUT with open and short defects. Flexible PCB was used for the fabrication of the proposed sensor, the metallic traces of the sensor was etched from flexible copper clad laminate (FCCL) (the FCCL is from Hubei Hengchi Electronic Technology Co., Ltd). And the polyethylene terephthalate (PET) layer and copper layer of the FCCL have a thickness of around 0.02 mm and 0.01 mm, respectively. Then the fabricated flexible PCB was folded and pasted on a FR-4 board (with a thickness of 0.6 mm), as shown in Fig. 5 (a). Fig. 5 (b) shows the photos of the front and back view of the built sensor with a SMA connector soldered to facilitate a connection to a vector network analyzer (VNA) for a measurement. The sensor was characterized by measuring the S 11 using a VNA (N5249B, Keysight Technologies) over a frequency range from 530 MHz to 550 MHz with 1001 sampling points in between. Fig. 6 shows the S 11 versus the frequency. As shown in Fig. 6, the sensor resonates at around 540.24 MHz with good matching (i.e. a |S 11 | of around −38 dB).
The experimental validations for the detection of defects were conducted by sweeping the DUT within the same ROI as the simulations using the sensor when it was placed vertically 0.05 mm above the DUT. Fig. 7 shows the experimental setup of the measurement which consists of the positioning platform (VT-80 linear stage, Physik Instrumente) that can precisely controls the movement of the sensor (a minimum step size of 1 um) in the x-, y-, and z-direction and a VNA (N5249B, Keysight Technologies). The sensor was moved with respect to the DUT to cover the ROI and the S 11 's 203762 VOLUME 8, 2020  over the frequency range from 530 MHz to 550 MHz (with 1001 sampling points in between) were recorded. Fig. 8 shows the normalized measured f r distributions of the fabricated samples when there was an open or a short defect. Comparing the measured results in Fig. 8 to the simulated ones in Fig. 3, they agree well with each other in each case. It is noted that the frequencies that f r is normalized to have slightly difference between simulation and practical results, and it is mainly due to the discrepancy of L s and C s value in practical fabrication. The agreements strongly imply detection of either open or short are practically possible by using the proposed sensor design.

IV. DISCUSSION
The detection of open or short in a group of parallel metallic traces is accomplished through a distinguishable pattern in the f r distribution in a 2D scan using the proposed sensor tip. In both Fig. 3 and Fig. 8, it is observed that the pattern is slightly larger than the defect, and different terminations of the traces may result in difference in f r . In this section, circuit models of the sensor tip with the DUT are proposed to explain the observations, and to provide further insights to the sensor design.
The equivalent circuit of the sensor is shown in Fig. 9 (a), where L s and R s are the equivalent inductance and resistance of the sensor besides the capacitance, C cr and C tip that were introduced previously, R vna is the output impedance of the VNA that equals to 50 ohms, and E 1 is the signal source from the VNA. When the sensor tip is placed near the DUT, additional capacitive coupling is induced between the sensor tip and the DUT (with and without defects), thus more detailed circuit models are proposed for different situations which are used to replace C tip .
A. OPEN DEFECT CASE Fig. 9 (b) and (c) show the detailed circuit model in the situation when the proposed sensor is placed on top of a trace of DUT (i.e. the reference case for open defect) and in the situation when there is a open defect, respectively. These two situations with the capacitive coupling between the sensor tip and the DUT are shown in Fig. 9 (d) and (e), respectively. Fig. 9 (f) shows a side view of Fig. 9 (e). for open reference, the subscript B, t, St, and i, denote the correspondence to branch, trace, surrounding trances, and the i th branch arm, respectively. As shown in Fig. 9 2) are the capacitance between the two branches of the sensor tip, that between the i th branch and the trace underneath (labelled with trace), and that between the i th branch and all the other surrounding DUT traces except the one underneath the sensor. With the extracted capacitance value of all the components and equivalent circuits shown in Fig. 9 (b) and (c), f r can be   1) and (2). When the f r calculated from the model is compared with the simulation results as shown in Fig. 3 (a), (b) and (c). the variation was found to be less than 50 ppm in the ROI. Thus, the accuracy of these circuit models is verified.
The 2D plot patterns caused by the open defect as shown in Fig. 3 (b) and (c) are explained with the help of the equivalent circuits. Due to the symmetry of the DUT and sensor in the reference case, To further simplify the analysis, the capacitance components in the open defect condition are normalized to the open reference condition as follows, where k i > 0 (i = 1,. . . 6), k 5 indicates the coupling between the trace underneath the sensor tip and the surrounding traces, k 6 reflects the change in the peripheral capacitance due to the open defect, and In Eq. (6), owing to the physical configuration between the sensor tip, the DUT, and the open defect, 0 < k 1 , k 2 , k 3 , k 4 < 1, k 1 + k 2 < 1. When an open defect was introduced, the capacitance between one of the branches to the trace, for example, for branch 1, C o-ref B1-t is split into two parts, C o B1-t1 and C o B1-t2 , and C o-ref B1-t > C o B1-t1 +C o B1-t2 due to an increase in the distance introduced by the opening, therefore, k 1 + k 2 < 1. With the same token, k 3 + k 4 < 1. When there are no surrounding traces, k 5 = 0.
In Fig. 3 and Fig. 8, f r is increased dramatically near the open defect, forming a bright patch for the detection. The increase in f r is caused by a decrease in C tip which is denoted as C tip-o where the subscript o indicates an open defect.
Based on the proposed circuits shown in Fig. 9 (b) and (c), and expressions in Eq. (6), C tip-o can be approximately expressed as follows, where M = k 1 k 3 k 1 +k 3 , N = k 2 k 4 k 2 +k 4 , and P is expressed in Eq. (8) below, As C tip-o < 0, M + N + P + k 6 < 0.5. Within this range, an increase in (M + N + P + k 6 ) leads to a decrease in | C tip-o | which lower f r . Moreover, M corresponds to the contribution along the path from C o B1-t1 to C o B2-t1 , and N corresponds to the other one from C o B1-t2 to C o B2-t2 in Fig. 9 (c), while P is closely related to the coupling between the trace underneath the sensor tip and the surrounding traces (i.e. k 5 ). It is noted that when the traces have a higher pitch (i.e. they are far apart), k 5 decreases, and so is P. When the traces are shorted, C ti-St is replaced by short circuits, and k 5 → ∞, P becomes P = (k 1 k 4 −k 2 k 3 ) 2 (k 1 +k 3 )(k 2 +k 4 )(k 1 +k 2 +k 3 +k 4 ) which is an increase compared to the value in Eq. (8). An increase in P leads to an drop in | C tip-o |, thus resulting in a lower shift in f r when the traces are shorted compared to those in the case when they are open. The circuit model helps to explain the size of the bright patch that is used for defect detections. Fig. 10 (a) and (b) show the changes of M, N, P, and k 6 when the sensor tip moves along the y-and the x-direction, respectively. When the sensor tip is moving along the y-direction, C o-ref B-t stays constant. In Fig. 10 (a), the horizontal axis y represent the the distance between the center of the tip to that of the open defect along the y-direction. Comparing all the curves, N and k 6 are relatively small and decrease slowly when y increases. P in the case when the traces are shorted (the purple curve) is higher than that in the case when the traces are open (the yellow curve), as explained in the previous paragraph. Moreover, it is observed that P dominates when y < 0.125 mm and beyond y = 0.125 mm, M dominates. M increases as y increases, which decreases | C tip-o | based on Eq. (7) and lowers f r . Therefore, the knee of the slope of M decides the boundary of the patch which is directly related to the resolution of detection. In this case, beyond y ≈ 0.4 mm, M becomes more than 0.42, | C tip | < 0.1 fF, and no obvious shift of f r is observed.
When the sensor tip is moving along the x-direction, C o-ref varies. In Fig. 10 (b), due to the symmetry with respect to the x-axis, N = M, thus 2M is plotted. Besides, it shows the variation of P, k 6 , and C o-ref B-t with respect to x where x is defined as the distance between the center of the tip to that of the open defect along the x-direction. For the reference capacitance, C o-ref B-t decays as x increases. Comparing the curves for 2M, P, and k 6 , similar to the case along the y-direction, k 6 are relatively small and decrease slowly when y increases, and P in the case when the traces are shorted is higher than that in the case when the traces are open. Both P curves decays as x increases whereas the curve for 2M increases. At point x ≈ 0.2 mm and beyond, | C tip | < 0.1 fF and no obvious shift of f r is observed. It decides the boundary of the patch along this direction.

B. SHORT DEFECT CASE
A short defect most likely happens in between two traces. Therefore, for the case with a short defect, the reference case has the sensor tip is placed above the gap between two traces, as shown in Fig. 11 (a). When there is a short introduced underneath the sensor tip, unlike the case with an open defect where more coupling capacitance are needed to be considered, the coupling capacitance stays a similar configuration as that of the reference case. Fig. 11 (c) and (d) show the circuit model of the reference case and that with a short defect, respectively. Fig. 11 (a) and (b) illustrate the source of the coupling in the setup. The superscript, s, is used to represent short defect. The rest of the content in the superscript and the subscript have the similar meaning as the open defect case in the setup. Similarly, the capacitance in Fig. 11 (d) can be expressed based on those in the reference case. They are shown as follows, where k 7 , k 8 > 1, k 9 < 0. For a short defect, in Fig. 3 and Fig. 8, f r is increased dramatically near the short defect, forming a dark patch for the detection. The decrease in f r is caused by an increase in C tip , C tip-s , where the subscript s indicates a short defect.
Based on the proposed circuits shown in Fig. 11 (c) and (d), and expressions in Eq. (9), C tip-s can be approximately expressed as follows, where Next, the circuit model in Figs. 11 (c) and (d) helps to explain the size of the dark patch for the short defect detection. Figs. 12 (a) and (b) show the changes of (Q−0.5) and k 9 when the sensor tip moves along the y-and the x-direction, respectively. When the sensor tip is moving along the y-direction, C s-ref B-t stays constant. In Fig. 10 (a), comparing all the curves, (Q−0.5) starts to decrease rapidly at y ≈ 0.2 mm, and becomes steady at the location of y ≈ 0.4 mm, which determines the boundary of the patch. While k 9 becomes steady when y > 0.2 mm, which has small effect on the patch boundary.
When the sensor tip is moving along the x-direction, C s-ref varies. As shown in Fig. 12 (b), it is noted that (Q − 0.5) dramatically decreases at the range of x < 0.2 mm, however, C s-ref B-t and k 9 almost remain constant in this range, therefore, Q is still the major parameter that determines the boundary of the patch along x direction.

C. COMPARISON TO THE EXISTING SOLUTIONS
For the existing E-field-based near-field RF NDE methods in the literature, for the methods using open-ended coaxial probing technique [14]- [17], the spatial resolution lies in the range from a few millimetres to a few centimetres, which is relatively large. While for the methods using cavity resonance technique [18], [19], SRRs [13], [20], [21], and open-ended waveguide slit [22], [23], the spatial resolution could be high but the cost will increase due to higher working frequency, complex fabrication process or measurement setup. For the H-field-based RF NDE methods mentioned in [24]- [29], recent progresses from [26], [28] could detect single thin crack with width equals to 0.1 mm on a bare metal plate, but the sensor size falls in the range of more than a few millimeters, which means the spatial resolution is not enough to distinguish errors in the complex PCBA environment.
Comparing the imaging performance of the proposed sensor with the existing near-field RF NDE methods in the literature, it can be found that the proposed sensor has sufficient spatial resolution to distinguish the open and short defects on different pins of an IC package. And the simple fabrication process and relatively low operating frequency reduce the overall cost.

V. CONCLUSION
This paper presents a compact near-field split resonator sensor for open and short defects detection on modern PCBAs. The sensor structure has been designed that strong electric field is confined at the sensor tip for defects sensing. Moreover, the sensitivity of the sensor is verified using both simulation and practical results. Therefore, the proposed sensor shows great potential for microwave imaging setup to detect defects on PCBAs in the manufacturing supply chain. Besides, detail circuit models have been made to explain the detection principle and boundary, and it helps explain how the DUT traces termination types will influence the sensitivity of the sensor. Future work involves the integration of the sensor in a sensing array that will accelerate the measurement speed.