Capacitors are passive electronic components found in various shapes and using different materials [1]. Numerous ceramic capacitors, especially multilayer ceramic capacitors (MLCC), are used on a modern printed circuit board (PCB). They have a major role in resonant circuits, power supply bypass, and filters [2]. This makes them indispensable in all modern electronic devices, including but not limited to wearable smart sensors, environmental monitoring, agriculture, and food control, to name a few. Due to their popularity, the global market of MLCCs was valued at USD 5315 million in 2017 and it is predicted to increase to USD 7833 million by 2024 ^[3][4][3,4].

As presented in Figure 1, MLCCs are composed of three main elements: inner electrode, outer electrode, and ceramic dielectric material, mainly made of nickel, silver, and palladium [5].

The main advantages of the MLCCs are their small size and price [6]. Despite their small size, they have large capacitance and favorable electrical characteristics. These characteristics are small equivalent series inductance (ESL), small equivalent series resistance (ESR), good frequency response, a wide range of capacitance value, and their ability to be used for long periods at high temperature or in high-voltage applications ^[7][8][9][7,8,9].

All of these MLCCs advantages are due to the high-level permittivity dielectric material, Barium Titanate (BaTiO₃), they are made of ^[10][11][12][10,11,12]. Ironically, the two main electro-mechanical properties of the BaTiO₃  cause one of the newest problems in electronic devices: the singing capacitors phenomenon [13]. These properties are piezoelectricity and electrostriction. When an AC voltage is applied to the MLCC, the capacitor starts to vibrate due to the piezoelectricity. At the same time, the electric field generated between the inner electrodes creates electrostrictive vibration whose level is similar to the piezoelectric vibration level. Furthermore, the nonlinear phenomenon of the electrostriction also makes a second harmonic frequency vibration of the applied voltage [13]. In recent years, the thickness of the hundreds of dielectric layers present in an MLCC has decreased to achieve a large capacitance in a small package size [1]. Therefore, both properties must be taken into consideration, as the vibration generated by the piezoelectric effect is proportional to the electric field, and the vibration generated by the electrostriction is proportional to the square of the electric field [8]. Besides the piezoelectric and electrostrictive effects, the converse magnetoelectric effect also influences the MLCCs behavior. An induced electric polarization that appears under an applied magnetic field characterizes the magnetoelectric effect. On the contrary, the converse magnetoelectric effect is characterized by an induced magnetization under an external electric field [14]. When driven near resonance frequency, the converse magnetoelectric coefficient reaches the maximum [15]. The resonance frequency of the MLCC vibration is in the range of MHz, therefore pweople should not be able to hear anything. However, as the MLCCs are surface-mount devices (SMD), the induced vibration is transferred to the PCB via solder joint ^[1][16][1,16]. When an AC voltage is applied to the MLCC, the dielectric material expands in the direction of the electric field and contracts in the direction perpendicular to the electric field, causing the deformation of the board, as shown in Figure 2 ^[4] [4]. Therefore, the PCB starts to vibrate with the MLCC, and the frequency can reach the audible range of 20 Hz–20 kHz [10]. ResWearchers can conclude that the singing capacitor phenomenon is caused by three major factors [2]:

• the MLCC itself—the capacitor acts as an excitation source;
• the mounting situation—the solder joint is the vibration transfer path;
• the PCB—the board is the acoustic noise resonator.

2. The Acoustic Noise Caused by MLCCs

DueIn to the piezoelectric and electrostrictive effects of BaTiO₃, this pape MLCCs’ inter electrodes vibrate(https://doi.org/10.3390/s22103869), causing a chain reaction. The vibration is transferred from the inter electrodes to the capacitor terminals, from the terminals to the solder joint, and finally from the solder joint to the PCB, causing the singing review of the literature information about the singing capacitors phenomenon. Therefore, to eliminate the audible noise caused by MLCC, researchers must interrupt the vibratio is presented. In transfer.

TheSection 2, first solution would be to use capacitors with a low dielectric constant. These capacitors would solve the singing capacitor phenomenon from the root cause.

For e will show how to detecthe vibration transfer from MLCC to the solder joint, many alternatives are available. The component suppliers offer low acoustic noise capacitors, such as metal terminals or metal plate capacitors, interposer or alumina substrate MLCCs, thicker dielectric layer capacitors, and dipped radial leads capacitors. The most effective commercial solution is the metal terminal capacitor, which attenuates the noise by 25 dB. Some authors suggest increasing the cover layer thickness to reduce the transmitted vibration.

For the vibration transfer to the PCBthe problematic MLCCs on a PCB. In Section 3, some authors suggested decreasing the solder joint. Unfortunately, to date, this has not been demonstrated to be efficient. Other authors suggested placing the MLCC in a vertical orientation on PCB to increase the resonating frequency. Of course, the layout geometry has a big impact on the PCB acoustic noise. The mirror or back-to-back configuration is considered the best solution ie solutions for singing capacitors found in the literature.

As mentwioned before, it is better to prevent than to correct. By simulating the designll be presented, while in Section 4, reswearchers can avoid the apparition of the singing capacitor phenomenon. To simulate the acoustic behavior, researchers need a harmonic analysis. The simulation is more precise if researchers also implement a statistical sim will present types of simulation and a parameter sensitivity annalysis. Some authors recommend a three-dimensional FEM simulation and a vibration analysis ^[17].

Th to prevent audible two mnost popular methods found in the literature to measure the acoustic noise caused by MLCCs are SPL measurement and LDV measurement. These two can be correlated with a linear equation. Other methods to investigate the singing capacitor phenomenon are the optical sensor fiber, piezoelectric accelerometer, active excitation method, and vibration and rail voltage coherence method.

In conclusion, thise on PCB. We will end with a short discussion about the pacoustic noise caused by MLCCs is a current problem in modern electronic systems. Therefore, the interest in this issue is high among the experts who study electronics in specialized literature. Unfortunately, the solution for this phenomenon is not straightforward due to the design-oriented behavior of the MLCCper’s highlights and findings.

References

1. Kim, D.; Kim, W.; Kim, W.-C. Dynamic Analysis of Multilayer Ceramic Capacitor for Vibration Reduction of Printed Circuit Board. J. Mech. Sci. Technol. 2019, 33, 1595–1601. [Google Scholar] [CrossRef]
2. Ko, B.-H.; Park, H.-G.; Kim, D.; Park, N.-C.; Park, Y.-P. Reduction of Multilayer Ceramic Capacitor Vibration by Changing the Cover Thickness. Microsyst. Technol. 2016, 22, 1375–1380. [Google Scholar] [CrossRef]
3. Johnson, W.L.; Kim, S.A.; Quinn, T.P.; White, G.S. Nonlinear Acoustic Effects in Multilayer Ceramic Capacitors. AIP Conf. Proc. 2013, 1511, 1462–1469. [Google Scholar] [CrossRef]
4. Lu, T.; Ding, M.; Wu, K. Simulation and Characterization of Singing Capacitors in Consumer Electronics. In Proceedings of the 2019 IEEE International Symposium on Electromagnetic Compatibility, Signal & Power Integrity (EMC+SIPI), New Orleans, LA, USA, 22–26 July 2019; pp. 522–526. [Google Scholar] [CrossRef]
5. Yu, D.; Dai, K.; Zhang, J.; Yang, B.; Zhang, H.; Ma, S. Failure Mechanism of Multilayer Ceramic Capacitors under Transient High Impact. Appl. Sci. 2020, 10, 8435. [Google Scholar] [CrossRef]
6. Wang, Y.-Q.; Ko, B.-H.; Jeong, S.-G.; Park, K.-S.; Park, N.-C.; Park, Y.-P. Analysis of the Influence of Soldering Parameters on Multi-Layer Ceramic Capacitor Vibration. Microsyst. Technol. 2015, 21, 2565–2571. [Google Scholar] [CrossRef]
7. Ko, B.-H.; Jeong, S.-G.; Ahn, Y.-G.; Park, K.-S.; Park, N.-C.; Park, Y.-P. Analysis of the Correlation between Acoustic Noise and Vibration Generated by a Multi-Layer Ceramic Capacitor. Microsyst. Technol. 2014, 20, 1671–1677. [Google Scholar] [CrossRef]
8. Ko, B.; Jeong, S.; Kim, D.; Park, N. Identification of the Electromechanical Material Properties of a Multilayer Ceramic Capacitor. Int. J. Appl. Ceram. Technol. 2017, 14, 424–432. [Google Scholar] [CrossRef]
9. Sun, Y.; Zhang, J.; Yang, Z.; Hwang, C.; Wu, S. Measurement Investigation on Acoustic Noise Caused by “Singing” Capacitors on Mobile Devices. In Proceedings of the 2019 IEEE International Symposium on Electromagnetic Compatibility, Signal & Power Integrity (EMC+SIPI), New Orleans, LA, USA, 22–26 July 2019; pp. 505–510. [Google Scholar] [CrossRef]
10. Sun, Y.; Wu, S.; Zhang, J.; Hwang, C.; Yang, Z. Measurement Methodologies for Acoustic Noise Induced by Multilayer Ceramic Capacitors of Power Distribution Network in Mobile Systems. IEEE Trans. Electromagn. Compat. 2020, 62, 1515–1523. [Google Scholar] [CrossRef]
11. Kim, H.; Kim, D.; Park, N.-C.; Park, Y.-P. Acoustic Noise and Vibration Analysis of Solid State Drive Induced by Multi-Layer Ceramic Capacitors. Microelectron. Reliab. 2018, 83, 136–145. [Google Scholar] [CrossRef]
12. Margielewicz, J.; Gąska, D.; Litak, G.; Wolszczak, P.; Trigona, C. Nonlinear Dynamics of a Star-Shaped Structure and Variable Configuration of Elastic Elements for Energy Harvesting Applications. Sensors 2022, 22, 2518. [Google Scholar] [CrossRef]
13. Ko, B.-H.; Kim, D.; Park, N.-C.; Park, Y.-P. Study on Effective Piezoelectric Coefficient for Finite Element Analysis of Multi-Layer Ceramic Capacitor. In Proceedings of the 2015 Joint IEEE International Symposium on the Applications of Ferroelectric (ISAF), International Symposium on Integrated Functionalities (ISIF), and Piezoelectric Force Microscopy Workshop (PFM), Singapore, 24–27 May 2015; pp. 64–66. [Google Scholar] [CrossRef]
14. Jia, Y.; Luo, H.; Zhao, X.; Wang, F. Giant Magnetoelectric Response from a Piezoelectric/Magnetostrictive Laminated Composite Combined with a Piezoelectric Transformer. Adv. Mater. 2008, 20, 4776–4779. [Google Scholar] [CrossRef]
15. Wu, Z.; Xiang, Z.; Jia, Y.; Zhang, Y.; Luo, H. Electrical Impedance Dependence on the Direct and Converse Magnetoelectric Resonances in Magnetostrictive/Piezoelectric Laminated Composites. J. Appl. Phys. 2012, 112, 106102. [Google Scholar] [CrossRef]
16. Kim, D.; Park, N.-C.; Park, Y.-P. Analysis of High-Pitched Noise from Solid-State Drives Generated by Multilayer Ceramic Capacitors. Microsyst. Technol. 2016, 22, 1367–1374. [Google Scholar] [CrossRef]