Enhancement of electric field uniformity using 3-phase circular electrodes in RF heating applications

Abstract

This paper introduces a novel electrode structure designed to enhance electric field uniformity in radio frequency heating applications, such as food processing. The proposed 3-phase circular electrode structure, the top electrode, consists of innermost, middle, and outermost electrodes, with each electrode supplied with a voltage of a different phase. By utilizing relative phase differences between the top electrodes, the electric field distribution between the top and bottom electrodes can be effectively modified to apply a uniform electric field on the food sample. A 3D computational simulation model was used to analyze the electric field uniformity at an operating frequency of 13.56 MHz and compared it with conventional single-phase rectangular electrodes. Both simulations and experimental measurements were conducted at 16 points on a plane 1 mm above a ham sample to evaluate the electric field strength. The results showed that the 3-phase circular electrodes effectively concentrated the electric field at the sample’s center while mitigating electric field strengths at the edges and corners. Consequently, electric field uniformity was significantly improved from 75.31% with conventional single-phase rectangular electrodes to 91.89% with the proposed 3-phase circular electrodes. This 3-phase circular electrode structure demonstrates promising potential for enhancing electric field uniformity in RF heating systems.

Introduction

Throughout history, food consumption has primarily aimed to provide energy for survival. However, it has transformed into a source of pleasure and enjoyment in modern times. Nowadays, people have a desire for scrumptious and high-quality food at any time of the day. This craving has led to the increasing popularity of instant and frozen foods that can be quickly distributed and heated. Although these foods allow for efficient consumption, they do not possess the same quality as freshly prepared foods. Research has been conducted on heating methods that can improve the after-heating quality of instant and frozen foods. In particular, radio frequency (RF) heating research is being actively conducted. The RF heating system uses a pair of parallel rectangular electrodes to transmit RF waves from one electrode to the other¹, as depicted in Fig. 1a. RF electric field (E-field) is formed between these electrodes. Due to its long wavelength, this RF E-field can penetrate deeply into the material being heated, causing polar molecules and ions within the dielectric to respond to the E-field^2,3. The RF E-field exhibits rapid polarity reversal characteristics, inducing vibrations and rotations in polar molecules and ions, thereby generating heat through friction. Additionally, because the RF E-field distributes throughout the entire dielectric, it simultaneously heats both the exterior and interior of the dielectric material, inducing molecular motion across all parts of the material. As a result, it enables efficient heating across the entire material.

Before RF heating can be widely adopted for commercial applications, a critical issue must be addressed: the uneven heating that occurs at the edges and corners of the product⁴. This is primarily due to the fringing effect of the E-field, which bends towards the dielectric material between the electrodes, influenced by the dielectric’s relative permittivity⁵. In cubical samples, as shown in Fig. 1b, the edges and corners experience concentrated bending of E-fields, leading to higher localized heating. To enhance heating uniformity by minimizing the impact of E-fields on samples, researchers have explored various methods to reduce the impact of these concentrated E-fields. They experimented with adjusting the position and size of samples between electrodes⁶ and modifying container materials and thickness^7,8,9,10. Additionally, implementing partitions to prevent E-field deflection has been shown to enhance heating uniformity¹¹. In one study, rotating the sample at a controlled speed and angle significantly improved overall heating uniformity¹². While these strategies show promise, applying them in practical industrial settings remains a challenge. By modifying the shape of the electrodes, rather than altering the sample itself, the temperature distribution across the sample can be effectively adjusted through changes in the E-field distribution. For instance, varying the electrode size has been shown to significantly impact temperature uniformity¹³. Some studies have explored the physical bending sections of electrodes or adding additional electrodes to modify the power density distribution^14,15. Adjusting the angles and spacing of these electrodes helped achieve more uniform heating across the sample. However, physically adjusting the electrodes to achieve the desired E-field distribution can be cumbersome and challenging.

To achieve a uniform E-field distribution that is shown in Fig. 1c without physical adjustment of the electrodes, we propose a novel 3-phase circular electrode structure by utilizing 3-phase voltage principles. The decision to use multiple electrodes in the setup was inspired by a study that discovered the E-field uniformity could be further improved by sequentially applying the E-field to electrode pairs oriented in different directions¹⁶. This system features top three circular electrodes without edges or corners, as shown in Fig. 2a. The E-field distribution is influenced by both the amplitude and phase of the applied alternating current (AC) voltage. Amplitude refers to the peak value of the AC voltage waveform, while phase represents the temporal offset within the same frequency. By using multiple electrodes, we can adjust the phase of the RF waves in various combinations. In a 3-phase system, three AC voltages with the same frequencies but differing phases are applied, creating a continuously varying and rotating E-field vector. This allows for diverse E-field distributions based on phase differences could focus or relax the E-field at specific locations¹⁷. Our study aims to show how to significantly enhance the uniformity of the E-field by applying three-phase AC voltages of different phases, Ф₁, Ф₂, and Ф₃, to each circular electrode. By comparing this method with conventional rectangular electrodes in Fig. 2b, we highlight the advantages of the 3-phase circular RF heating system in achieving precise control and optimization of the E-field distribution flat surfaces. Through empirical validation and comparative analysis, we seek to demonstrate the advantages of our proposed system in delivering precise and uniform E-field distributions, thereby advancing the field of RF heating technology.

Fig. 1

Schematic diagrams of (a) conventional RF heating system, (b) existing non-uniform electric field distribution, and (c) uniform electric field desired to be applied at the top of the sample.

Fig. 2

Geometry design of (a) proposed 3-phase circular electrodes and (b) conventional rectangular electrodes.

Results

Effect of using 3-phase circular electrode structure about E-field distribution and uniformity

To evaluate the enhancement in E-field uniformity with 3-phase circular electrodes, it was compared to conventional rectangular electrodes. A 3-phase voltage (innermost 45°, middle 90°, and outermost 0°) was applied to the circular electrodes, while a single-phase voltage was applied to the rectangular electrodes. Figure 3 shows the E-field distribution from both side and top views. The 3-phase circular electrodes reduced concentration at the edges and corners. In contrast, the rectangular electrodes exhibited higher E-field concentrations in these areas, consistent with previous studies^6,11,18. More specifically, Fig. 4 compares the simulated and experimental E-field strength increased ratio (IR) values at each observation point on the sample’s top surface. For the 3-phase circular electrodes, the simulated IR ranged from 1.0 to 1.10, and the experimental IR ranged from 1.0 to 1.09. The maximum IR values were close: 1.10 in the simulation and 1.09 in the experiment. The E-field distribution uniformity index (EDUI) was high, reaching 90.77% in the simulation and 91.89% in the experiment. With conventional rectangular electrodes, the simulated IR ranged from 1.0 to 1.33, with the experiment IR also ranging from 1.0 to 1.33, as shown in Fig. 5. The difference between maximum and minimum IR values was 0.33, more than three times higher than with the 3-phase circular electrodes. The EDUI decreased to 75.46% in the simulation and 75.31% in the experiment, indicating reduced E-field uniformity.

Fig. 3

Electric field distribution simulated results of using proposed 3-phase circular electrodes and conventional rectangular electrodes.

Fig. 4

2D array table and 3D color map graph of E-field strength IR values observed in simulation and experiment using the proposed 3-phase circular electrodes.

Fig. 5

2D array table and 3D color map graph of E-field strength IR values observed in simulation and experiment using the conventional rectangular electrodes.

Figure 6 presents a comparison of the experimental IR values obtained using the proposed 3-phase circular electrodes with those obtained using the conventional rectangular electrodes, depicted as a 3D color map over the entire top surface of the sample. IR values were significantly reduced at the edges and corners of the sample when using 3-phase circular electrodes. Moreover, the colors of the IR values at different observation points were similar, indicating a uniform distribution of E-field strength across all observation points of the sample compared to when using conventional rectangular electrodes. Consequently, to achieve uniform heating, reducing the maximum IR value by minimizing E-field strength at the edges and corners is crucial. These results are summarized in Table 1.

Fig. 6

Comparison of E-field strength IR values of 3D color map graphs of the entire top surface of the sample using proposed 3-phase circular electrodes and conventional rectangular electrodes.

Table 1 Comparison of electrode structure used in simulations and experiments.

Effect of using 3-phase circular electrode structure about temperature

To confirm whether the differences in the E-field distribution based on the electrode structure also appeared similarly in the temperature distribution on the sample’s top surface, a power of 95 W was applied. This power was applied to both the 3-phase circular electrodes and the conventional rectangular electrodes using power amplifiers. Figure 7 shows the initial temperature distribution of the sample surface before heating and the temperature distribution after heating the sample for 1 h using two electrode structures. Comparing the images after heating for 1 h, the temperature bars were observed to be similar, but there was a clear difference in the temperature distribution. As a result of heating with 3-phase circular electrodes, the center, edges, and corners of the sample surface showed a yellow color close to the highest temperature of 26.2 ℃, confirming that the sample was heated evenly. When heated using conventional rectangular electrodes, the corners and edges of the sample surface took on a yellow color and were close to the highest temperature of 25.5 ℃. However, the center of the sample was purple, close to the lowest temperature of 21.5 ℃, confirming that the sample surface was heated unevenly. This difference in temperature distribution appeared similar to the E-field uniformity comparison results in Fig. 6. Since the temperature value is also an indicator of the surface of the sample, the highest and lowest temperature values were substituted into the EDUI equation. It was found that the surface temperature uniformity increased by 16% when using the proposed 3-phase circular electrodes compared to the conventional rectangular electrodes. This value is equivalent to the 16% increase in E-field uniformity previously analyzed.

Fig. 7

Comparison of temperature distribution of the entire top surface of the sample using 3-phase circular electrodes and conventional rectangular electrodes.

Fig. 8

Comparison electric field distribution simulation results of using circular electrodes with each electrode input voltage phase variation. (a) Innermost, (b) middle, (c) outermost electrode.

Phase controllability to adjust E-field uniformity

To evaluate the E-field control effect by changing the phase of the applied voltage for the proposed 3-circular electrode structure, we set a consistent amplitude of 1,000 V across all electrodes while varying the phase of each electrode individually. During the phase adjustment of each electrode, it was found that when the phase difference between electrodes exceeded 90°, the E-field was concentrated at the electrodes, preventing sufficient field applied to the sample (Supplementary Fig. S1). Based on this, the maximum phase difference for controlling the E-field was set to 90°, and the phase change was displayed up to 60° to effectively show the variation in the E-field with phase variation at each electrode without redundant images.

Figure 8a shows the E-field distributions as the phase of the innermost electrode was varied from 0° to 60°, while the middle and outermost electrodes maintained a fixed phase of 90°. As the phase of the innermost electrode increased, the E-field gradually extended from the inner electrode to the top of the sample, as indicated by the black round line. When the phase of the innermost electrode was varied from 0° to 60°, the E-field strength at the edge increased by 982 V/m from 16,049 V/m to 17,031 V/m, and the corner increased by 313 V/m from 19,394 V/m to 19,707 V/m. However, the center experienced a substantial increase of 3,167 V/m from 10,921 V/m to 14,088 V/m, approaching the edge of 17,031 V/m. This adjustment led to a 15.18% increase in EDUI from 56.31% at 0° to 71.49% at 60°. Figure 8b illustrates E-field distributions with the phase of the middle electrode was varied from 30° to 60°, while the innermost and outermost electrodes maintained a fixed phase of 0°. As the phase of the middle electrode increased, the E-field became more concentrated on the middle electrode as indicated by the black round line, reducing the excessive E-field applied to the edges and corners of the sample. When the phase of the middle electrode was varied from 30° to 60°, the E-field strength at the edge decreased by 1,443 V/m from 16,680 V/m to 15,237 V/m, and the corner decreased by 1,957 V/m from 19,086 V/m to 17,129 V/m. The center also decreased by 1,347 V/m from 14,056 V/m to 12,709 V/m. To achieve better E-field uniformity, the E-field strength of the center must be similar to that of the edge or corner. Adjusting the phase of the innermost and middle electrodes to 30° and 60°, respectively, increased the E-field strength at the center from 12,709 V/m to 13,834 V/m and more closely approached 15,527 V/m at the edge. Considering EDUI, there was no significant difference between 73.65% and 74.20% when the middle electrode phase was 30° and 60°, respectively. However, when the phase of the middle electrode was 60° and the phase of the innermost electrode varied to 30°, EDUI increased up to 80.50%. By simultaneously changing the phase of the middle and innermost electrodes, the E-field at the edge and corner of the sample were weakened, and the E-field was concentrated in the center. Lastly, Fig. 8c shows the E-field distributions with the phase of the outermost electrode was varied from 60° to 10°, while the innermost and middle electrodes maintained a fixed phase of 90°. As the phase of the outermost electrode decreased, the E-field around the outermost electrode became more concentrated as indicated by the black round line, resulting in a decrease in the E-field within the sample. When the phase of the outermost electrode was varied from 60° to 10°, the E-field strength of the edge decreased by 2,395 V/m from 16,753 V/m to 14,358 V/m, and the center decreased by 528 V/m from 14,419 V/m to 13,891 V/m. In contrast, the corner experienced a substantial decrease of 3,887 V/m from 19,090 V/m to 15,203 V/m, approaching the E-field strength value of 14,358 V/m at the edge and 13,891 V/m at the center. This adjustment increased the EDUI by 12.99%, from 75.53% at 60° to 88.52% at 10°.

Discussion

The primary issue with conventional RF heating methods lies in the uneven heating of food products, particularly the excessive heating that occurs at the edges and corners due to the fringing effect of the E-field⁵. While various studies have sought to address this problem by modifying container properties^7,8,9,10,11 or physically altering the electrodes^13,14,15, these approaches are cumbersome and difficult to implement in commercial applications. We have proposed a novel 3-phase circular electrode structure that achieves uniform E-field distribution across the entire sample surface without physical modifications. We compared this structure with conventional rectangular electrodes to demonstrate its effectiveness. Although comparing the single circular electrodes with the 3-phase circular electrodes is valid, as shown in Supplementary Fig. S2, the E-field distribution, strength increased ratio (IR), and E-field uniformity index (EDUI), as well as the higher values at the edges and corners, exhibited similar patterns to those of conventional rectangular electrodes. This suggests that the single circular electrodes do not differ significantly from the rectangular electrodes. Given the widespread use of rectangular electrodes in similar studies, we believe that comparing the 3-phase circular electrodes with the conventional rectangular electrodes will be more beneficial for the advancement of RF heating research. Conventional RF heating systems with single-phase rectangular electrodes struggle to alter the E-field distribution. However, our 3-phase circular electrodes allow precise adjustment by varying the phase differences between input voltages of each electrode, concentrating or weakening the E-field in targeted areas of the sample’s surface. This approach improved EDUI by 16%, achieving over 90% compared to conventional electrodes. When power was applied, the 3-phase circular electrodes achieved uniform heating across the sample’s top surface. In contrast, conventional rectangular electrodes caused excessive heating at the edges and corners while providing minimal heating at the center. This pattern of temperature distribution corresponds with the E-field distribution, highlighting the link between the E-field and temperature. Previous studies confirmed the relationship between E-field and temperature distribution using simulations that matched the experimental temperature distributions without directly measuring the E-field^{7,11,19,20,21}. Due to the difficulty of accurately measuring the E-field in the sample, these studies utilized simulations. In contrast, our study directly measured the E-field on the sample surface. Despite minor discrepancies caused by the influence of the probe (Supplementary Fig. S3), the E-field distribution obtained from our measurements was consistent with the E-field distribution predicted by the simulation and temperature distribution from measurements. Therefore, we demonstrate that our results show that the 3-phase circular electrode structure effectively enhances both E-field and temperature uniformity. It addresses issues such as localized overheating and non-uniform heating, overcoming the limitations of conventional RF heating systems.

However, because power was applied to the electrodes for proof-of-concept purposes, the ability to achieve high power output was limited. Given that temperature is proportional to power, the uniform temperature distribution observed at low power suggests that similar uniformity can be achieved with a higher power in future studies. Additionally, the 3-phase circular electrode structure uses three power amplifiers to apply power. Each amplifier handles only 1/3 of the total 95 W, allowing the system to operate at a lower rated voltage compared to the conventional rectangular electrode structure, where a single amplifier would handle the full 95 W. This 3-phase circular structure significantly reduces the burden on the power supply, enabling more stable heating.

The 3-phase circular electrodes offer phase control, allowing for precise adjustment of the E-field distribution and more efficient operation. Supplementary Fig. S4 shows the simulated results of optimized EDUI for the three-electrode and four-electrode systems. The optimized EDUI for the four-electrode system is similar to that of the three-electrode system, despite providing more degrees of freedom for E-field control with the addition of an extra power amplifier, which increases the system’s complexity. This indicates that the three-phase electrode system already provides sufficient degrees of freedom for effective E-field control to achieve good EDUI. However, some areas of the top electrodes exhibited high E-field values. Although power consumption did not increase when using the same power levels as with conventional rectangular electrodes. This indicates that the energy efficiency of the overall setup can be inferred from the similar temperature increase observed on the sample’s top surface after RF heating at 95 W. When applying the E-field, impedance matching was carefully implemented to minimize power reflection and ensure effective power transfer. Consequently, as seen in Fig. 7, both the 3-phase circular electrodes and the conventional rectangular electrodes exhibited a maximum temperature increase of 17.5 °C on the sample’s top surface. This similarity in temperature rise indicates that the power delivery efficiency of the two electrode structures was comparable. Furthermore, in both cases, the temperature distribution patterns closely followed the corresponding E-field distribution of Fig. 6, suggesting that the heating efficiency was not significantly different between the two electrode structures. However, potential electrode damage due to the high E-field between the top electrodes must be considered. Future improvements should focus on reducing the high E-field in these areas. Therefore, various solutions, such as increasing the gap between the top electrodes or changing the shape of the electrodes to a curved design, are needed. If these adjustments are made, both temperature and E-field values can be used as indicators of heating uniformity, which will be helpful in research on RF heating methods using E-fields.

Methods

Ham sample information

Ham, a packaged processed meat, was purchased from a local supermarket in Seongdong-gu, Seoul, Korea. The ham was made from ground pork shoulder and had a relative permittivity of 100–1,000i and an electric conductivity of 0.53 S/m at 25 ℃^22,23. Ham has been used as a sample in experiments comparing RF heating with other heating methods^24,25,26. The ham was cut into 140 × 140 × 30 mm³ and weighed 643 g.

Physical model for computer simulation of RF heating

Geometry generation and E-field distribution analysis simulations were performed using the commercial finite element method (FEM) software, COMSOL Multiphysics version 6.1. (Burlington, MA, USA). To simplify the modeling procedure, only a pair of parallel electrodes, the sample, and the air cavity were implemented in the simulation^15,19,20. The distance between the top and bottom electrodes was set to 100 mm, and the sample was positioned at the center of the bottom electrode. The air cavity was set to a size of 1000 × 800 × 700 mm³, which was large enough to sufficiently surround the electrodes and sample. The relative permittivity of the air cavity was 1, and the electric conductivity was 0 S/m, as referenced from the COMSOL material library. The electrodes, made of copper, had a relative permittivity of 1 and an electric conductivity of 5.99 × 10⁷ S/m, also referenced from the COMSOL material library.

Electrode structures

This study proposed a new electrode structure named 3-phase circular electrodes, depicted in Fig. 2a. The circular top electrode consisted of a central circle and two peripheral donut shapes spaced apart. The central circle was named the innermost electrode, the first donut was called the middle electrode, and the second donut was called the outermost electrode. The diameter of the innermost electrode was set to 60 mm, the width of the middle electrode was set to 67 mm, and the width of the outermost electrode was set to 39.5 mm. The spacing between the innermost and middle electrodes was set to 6 mm, and the spacing between the middle and outermost electrodes was set to 15 mm. The width and spacing of the electrodes were set to minimize parasitic capacitance, which impacts power consumption. This was achieved by considering the coupling and capacitance between individual electrodes to ensure that the capacitance values were similar to those of the conventional rectangular electrodes. The bottom electrode was modeled in a square shape with an area of 315 × 315 mm². Each of the 3-phase circular top electrodes was connected to an individual RF signal generator and received voltages V₁, V₂, and V₃ with the same amplitude as A₁ but different phases of Ф₁, Ф₂, and Ф₃. For comparative purposes, a rectangular top electrode was implemented, consistent with the design utilized in previous studies, as shown in Fig. 2b. The rectangular top and bottom electrodes were set to a size of 303 × 200 mm², reflecting the size of a commercial microwave oven. The rectangular electrode received a voltage V₄ with a single phase of Ф₄ and an amplitude of A₂ from a single RF signal generator. The thickness of all electrodes was standardized at 2 mm.

Setting initial and boundary conditions based on the governing equation of the electric current module

An electric current module and frequency domain study were used to determine the E-field distribution. The electric current module was used to analyze the formation and strength of the E-field based on Eq. (1). This module, used in many RF heating simulation studies, simplifies Maxwell’s equations to Laplace’s equations based on quasi-static assumptions^{6,8,10,11,12,14,16,19,20,21}. Several studies have mentioned that the quasi-static assumption can be effectively applied when the wavelength of the RF system used in the simulation is much longer than the size of the electrodes used in the analysis^7,13,15,18.

$$\:-\nabla\:\cdot\:(\left(\sigma\:+i2\pi\:{\epsilon\:}_{0}{\epsilon\:}_{r}\right)\nabla\:V)=0$$

(1)

where $\:\sigma\:$ is the electric conductivity of the material (S/m), $\:i=\sqrt{-1}$, $\:{\epsilon\:}_{0}$ is the permittivity of free space (8.85 × 10^–12 F/m). $\:{\epsilon\:}_{r}$ is the relative permittivity of the dielectric material, and $\:V$ is the electric potential related to the E-field by $\:E=-\nabla\:V$. The top electrode was set to an electric source applying a voltage of 1,000 V at a frequency of 13.56 MHz, and the bottom electrode was configured as an electric ground (V = 0). The electric source and ground created an E-field between the electrodes. The 1,000 V used in the simulation was a relative value chosen to clearly observe the variations in the E-field. The applied voltage was proportionally adjusted from this relative value in the actual E-field and temperature measurement experiments. By setting the sample and air cavity as electric current module domain selection, the form of the E-field around the electrodes and at the sample surface.

E-field uniformity evaluation

Previous studies have defined uniformity using formulas based on values observed at various points or sections of the sample^6,12,27. To evaluate the uniformity of the E-field distribution in a symmetrical sample, 16 observation points were selected at equal distances within a 1/4 section of the sample area, each positioned 1 mm above the sample surface. These points included the center, edges, and corners. The positions of the observation points for simulation and experiment are shown in Fig. 9. A formula similar to that used to define luminance uniformity was adopted to define EDUI in terms of extreme changes in E-field strength at the sample surface. This used the method of maximum deviation of light variation from plane²⁸. It is defined by Eq. (2),

$$\:EDUI\:\left(\%\right)=\left(1-\left(\right(\left({V/m}_{MAX}\right)-\left({V/m}_{MIN}\right))/({V/m}_{MAX})\right)\times100.\:$$

(2)

The maximum observed E-field strength value is denoted as $\:{V/m}_{MAX}$ and the minimum value is denoted as $\:{V/m}_{MIN}$. Higher EDUI values improve RF heating uniformity, approaching 100%. The change in E-field strength at an observation point is evaluated by comparing the observed value with the minimum value at each point using the E-field strength value IR of Eq. (3),

$$\:IR={(V/m}_{obs})/({V/m}_{MIN}).\:\:$$

(3)

The E-field strength value at an observation point is expressed as $\:{V/m}_{obs}$, where $\:{V/m}_{MIN}$ is the minimum value of all observed E-field strength values. An IR value of 1 represents the minimum value; the higher the value, the stronger the applied E-field.

Fig. 9

16 electric field observation points on the top of the sample.

Determining the 3-phase of input voltages

To evaluate the E-field strength and EDUI of the sample surface according to the phase difference in voltage, the phase was set using the flow chart in Fig. 10. Simulations were performed using a fixed sample size of 140 × 140 × 30 mm³. The amplitudes of the voltages applied to the top electrodes, A₁ and A₂, were set to 1000 V, and the phases of the voltage applied to all electrodes were set to 90°. To investigate the effect of leading or lagging timing within the range of 0° to 180°, it was set to 90°. Next, phase Ф₃ of the outermost electrode, which focuses the most E-field on the sample at the edges and corners, was adjusted first. The Ф₃ was varied increments of ±5° (both increasing and decreasing) until the EDUI value on the sample surface exceeded 85%. After determining the Ф₃, the phase Ф₁ of the innermost electrode was adjusted using the same method. The Ф₁ was varied in increments of ±5° until the EDUI value on the sample surface exceeded 90%. Since the Ф₁ might not fall between 0° and 180°, Ф₃ was readjusted as needed to find a phase combination that achieved an EDUI value exceeding 90%. Following this flow chart, phases of 45°(Ф₁), 90°(Ф₂), and 0°(Ф₃) were ultimately applied to the innermost, middle, and outermost electrodes, respectively. This procedure requires only a single adjustment, such as setting the temperature and timer, before the heating process begins. In real-life situations, monitoring the E-field is challenging, and changes in electrical characteristics during heating can vary depending on the sample. To address this, future applications should use feedback from additional sensors, such as temperature or infrared sensors.

Fig. 10

Flow chart sets the optimal phase value of the voltage applied to the 3-phase circular electrodes.

Experiment setup for E-field measurement

This study used a directly configured RF heating system to apply the newly proposed top electrodes. The RF heating system included an RF signal generator (Keysight 33600 A) operating at a frequency of 13.56 MHz, a direct current (DC) supply (GP_INSTEK GPS-3303), a power amplifier, an impedance-matching circuit, and a pair of electrodes. As shown in Fig. 11a,b, the proposed 3-phase circular electrodes and the conventional rectangular electrodes were used in the E-field measurement experiments. The height between the top and bottom electrodes was maintained at 100 mm using four plastic 3D printing blocks. Sub Miniature Type A (SMA) connectors were placed on the edges of both the circular and rectangular electrodes. SMA connectors are small screw-on types used for connecting equipment such as RF signal generators and RF heating systems. The SMA connector of the bottom electrode, each SMA connector of the top electrode, and the individual signal output port of the RF signal generator were connected with an RF coaxial cable. A scaled-down AC voltage of 13.56 MHz was applied to the top electrode, and the bottom electrode was connected to the ground. Figure 11c shows the ham sample used in the experiment. The E-field strength was measured using a 100D EMC probe from Beehive Electronics. This EMC probe’s narrow tip made it easy to measure the E-field at a single point. The EMC probe was connected to a spectrum analyzer and a digital oscilloscope using the same manufacturer’s 110 A probe cable. To ensure accuracy, the EMC probe and probe cable were fixed on a non-metallic material to keep them horizontal without contact with the electrodes, minimizing hand interference during E-field measurements.

Fig. 11

Experimental structures such as (a) 3-phase circular electrodes, (b) rectangular electrodes, and (c) ham sample.

Experiment setup for applying E-field

The temperature measurement experiment setup mirrored the E-field measurement setup, using four plastic 3D-printed blocks to maintain a 6 cm gap between the top and bottom electrodes. A RF heating system for heating included a DC supply, RF signal generator, power amplifier, and impedance matching components. The schematic of this RF heating system experimental setup for applying E-field is shown in Fig. 12. The DC supply and RF signal generator drove the power amplifier, which was connected to the electrodes through impedance matching. The impedance matching was achieved using a simplest L matching network, calculated with Element 14’s impedance matching calculator. This RF heating system was configured for each electrode using SMA connectors and RF coaxial cables. A scaled-down AC voltage of 13.56 MHz was applied to the top electrode, and the bottom electrode was connected to the ground. Before being applied to each electrode, the RF signal generators were verified to produce the selected 3-phase using an oscilloscope. For the 3-phase circular electrodes, the RF heating system delivered 1/3 of the total 95 W power to each electrode. For conventional rectangular electrodes, a single electrode received the full 95 W. Before the heating experiment, the ham sample was refrigerated, and the initial temperature was set at 8 ℃. A 140 × 140 × 15 mm³ ham sample was wrapped in transparent film and placed on parchment paper to prevent direct contact with the electrodes and moisture generated from the sample during RF heating. The temperature distribution was measured after 1 h at a low output power of 95 W. The electrodes were placed inside a Faraday cage to protect the human body from the electromagnetic fields generated by the electrodes. After heating, the sample removed from the Faraday cage and captured sample’s surface temperature distribution using a FLIR thermal imaging camera by Teledyne Technologies. This ensured that the temperature distributions were obtained without any influence on the E-field distribution formed during the heating process.

Fig. 12

Schematic of RF heating system connections for applying E-field experiment.