Quantitative Design and Implementation of an Induction Cooker for a Copper Pan

The nonferromagnetic pans with a low equivalent resistance are desired to generate sufficient power for heating by larger eddy current. First, Maxwell 3D is used to estimate the equivalent heating resistance of a copper pan and select the optimal number of turns for a induction coil by Litz wire according to its size limitations and efficiency. Furthermore, the optimal resonant frequency is determined by maximizing the heating efficiency. Finally, the electric parameters are obtained to construct a simulation environment for the design of control strategies. A full-wave rectifier, buck converter, and half-bridge resonant converter are cascaded to construct the converter. Because of low equivalent resistance and high quality factor of the copper pan, a high slope ratio of the resonant current to the frequency is obtained. Therefore, the resonant converter is operated at a fixed switching frequency to reduce low-frequency oscillations of the resonant current. The buck converter is used to control the DC link voltage with third-harmonic injection, which enables heating power control, increases heating power and satisfies the standard, IEC-61000-3-2 Class A. Moreover, a resonant frequency estimator is developed to detect the resonant frequency for various positions of the pan on the induction coil to determine the optimal heating frequency. Finally, TMS320F28075-based converter with 100 A of peak resonant current is built. The heating effect and power loss on a copper pan is then measured, and the maximum heating efficiency is 69%. The measurement results verify the effectiveness of the proposed induction cooker and exhibits excellent agreement with the simulated results.


I. INTRODUCTION
Induction heating (IH) has become popular in domestic cooking because of its high efficiency, fast heating, accurate power control, and safety [1], [2]. Because induction cookers are flame-free, they are a convenient replacement for gas cooktops in tall buildings in earthquake-prone countries [3]. In induction cooking, a high-frequency magnetic flux is generated to induce high-frequency eddy current and hysteresis on a thin surface for heating a vessel. Conventional induction cookers consist of an AC-DC rectifier, a resonant converter, and an induction coil so that they can generate high-frequency magnetic flux and the coil with a pan acts as the resonant inductor of the resonant circuit [4]- [6]. Half-bridge series resonant converters are cost-effective circuits for IH and can The associate editor coordinating the review of this manuscript and approving it for publication was Bo Pu . be modeled as RLC circuits [6], and the pan and induction coil are equivalent to the resistor and inductor of RLC circuits [7]. The electric parameters of the aforementioned converters depend on the pan material, operating frequency, temperature, flux saturation of ferromagnetic materials, and relative position of the coil and pan [7]- [11]. Because current converters for IH are voltage sources in principle, adjusting the impedance of the resonant tank by changing the operating frequency with 50% duty (VF) [12] is a popular method for controlling the heating power. However, VF control cannot provide a wide range of power levels [13]. Although pulse density modulation [14] and discontinuous conduction modes can provide low power, the current harmonics may induce EMI issue.
Although technologies for heating ferromagnetic pans have matured, limited research has been conducted on the heating of nonferromagnetic materials, such as copper and aluminum. Nonferromagnetic pans cannot be heated through conventional IH because of the following reasons. The heating mechanism in IH is eddy currents. Therefore, the low heating resistance [15], [16] of nonferromagnetic materials results in insufficient heat generation. Furthermore, IH operates with low efficiency if the resistances of the induction coil and nonferromagnetic pan become close due to improper design. Typically, the heating resistance of ferromagnetic pans is more than ten times that of nonferromagnetic pans. Fig. 1 displays the measured results of equivalent resistance of pan R pan and equivalent coil inductance L eq of the non-ferromagnetic (copper) and ferromagnetic (IH stainless) pans of the same size by an impedance analyzer without considering the flux saturation. The resistance of the copper pan used in this study was 47 m , which is only 5% of the resistance of IH stainless pan at 100 kHz. Therefore, the current in the copper pan should be 4.8 times the current in the coil to yield the same heating power for IH stainless pans at 100 kHz. Table 1 displays the key characteristics of ferromagnetic and non-ferromagnetic materials for induction cooking, which includes R pan , L eq , change rate of inductance against frequency L eq f and resonant current against frequency i re f . Copper is an excellent conductor of heat, and copper pans are often used to heat sauces and dishes at strictly controlled temperatures. IH of nonferromagnetic pans can be achieved through various approaches, such as the use of an induction adapter, a thin slab [8], or a reducer plate [17], multiple induction coils [18], [19], and high current and high-frequency resonant converters [15], [20]- [22]. The first two methods involve heating the plate and then transferring the heat to nonferromagnetic pans. However, this approach poses a risk of scalding users. The effectiveness of IH depends on the shapes of both the plate surfaces and coils as well as the region coupled to the magnetic flux [23]. Although increasing the turns of the induction coil generates additional flux on the pan, the coil resistance also increases, which reduces the heating efficiency [7]. In [20], [21], the authors used a low switching frequency to generate a resonant current with a third-harmonic frequency close to the resonant frequency for achieving high heating power by changing the resonant capacitor. Because the method requires high DC link voltage, a time-sharing frequency-doubled resonant converter [22] is used for nonferromagnetic pans. In a previous study, a highfrequency transformer with a turns ratio of 17:3 is cascaded between a full-bridge circuit and a resonant tank to increase the load impedance for drastically reducing the MOSFET rated current [24]. The proposed IH system is illustrated in Fig. 2. The power stage mainly consists of a passive AC-DC rectifier, buck converter with synchronous rectifier control, and a half-bridge series resonant converter (HBSRC) in cascade. The buck converter is used to control the DC link voltage for achieving power control, increasing heating power, and satisfying the standard IEC-61000-3-2 Class A [25]. Therefore, the HBSRC operated at a fixed frequency to reduce low-frequency oscillations of the resonant current, which are caused by the insufficient resolution of the operating frequency. A resonant frequency estimator is proposed to determine the resonant frequency for various pan sizes and pan positions on the induction coil to obtain the optimal operation frequency before heating and to improve safety. The proposed design procedure is displayed in Fig. 3. First, Maxwell 3D and MATLAB are used to design the induction coil and resonant frequency to maximize efficiency. Next, the HBSRC and buck converter are constructed for heating power control with a fixed switching operating frequency. The simulation results indicate that an induction coil made of a 0.05-mm and 3200-strand Litz wire is optimal for reducing the skin effect and enhancing efficiency. The frequency characteristics of the coil resistance are measured using an impedance analyzer. Finally, a DSPbased controller (TMS320F28075) is used for implementing the control methodologies. The simulation and experimental results revealed that the operating frequency and number of turns of the induction coil influenced the heating efficiency. Furthermore, the resonant inductance and equivalent heating resistance obtained for the proposed induction cooker by using power integration and the impedance analyzer exhibited excellent agreement with the corresponding simulations obtained using Maxwell 3D. The proposed control approaches of resonant frequency estimation and increasing heating power through third-harmonic injection are verified through experimental results. This paper derived the design procedure by using simulated software for self-inductance, coupling factor, misalignment effects, and voltage gain in advance for the converter design to reach needed functions with higher efficiency.

II. OPTIMAL DESIGN OF AN IH SYSTEM THROUGH SIMULATION
The software-assisted procedure for designing an IH system is as follows. First, Ansys Maxwell 3D is used to analyze the eddy current heating phenomenon in the copper pan through electromagnetic induction. Then, a pan size is selected and as a nominal value, and the Litz wire is used as the induction coil. Moreover, the AC resistance of the coil is measured using an impedance analyzer. Furthermore, the number of turns of the induction coil and the operating frequency of IH are selected using Maxwell 3D to obtain high efficiency for the required specification. The equivalent heating resistance of the selected pan and the inductances of the induction coil with and without the pan are simulated by Maxwell 3D.  Finally, the capacitance of the resonant capacitor is selected to model the HBSRC for IH. The IH characteristics, such as high quality factor Q and high slope of the resonant current versus frequency, of the copper pan obtained through quantitative prediction can be used to develop control methodologies.

A. COILS AND LITZ WIRE SELECTIONS
The IH specifications are presented in Table 2. Fig. 4 displays the equivalent circuit model of the induction cooker with the pan. The other design baselines of the induction coil are as follows: (i) The gap between the coil and pan is 2 mm. (ii) The copper pan is located at the center of the induction coil. (iii) The coil comprised an equivalent #6 AWG (4 mm) 3200-strand #AWG 44 Litz wire to reduce the skin effect. The resistance per unit length of the stranded Litz wire is measured using the impedance analyzer because the Litz wire is too complex for simulating the resistance using Maxwell 3D [26], [27]. (iv) The simulation temperature of environment is set as 25 • C.
To conduct accurate simulation of the pan resistance, the thickness of each layer of the bottom side of the pan was set as 0.073 mm, which is less than half of the skin depth of copper at 200 kHz. The other simulated parameters are presented in Table 3. Fig. 4 displays the equivalent circuit model of the induction cooker. If the resonant circuit loss is neglected, the heating efficiency can be expressed as follows: where R pan : equivalent resistance of the pan. R coil : equivalent resistance of the coil. P loss (= P circuit + P coil ) : power loss of the resonant circuit. R eq = R pan + R coil : equivalent resistance of induction coil with a pan.
R circuit ( R eq ) : resonant circuit resistance, which includes the ESR of the resonant capacitor and current sensor as well as the power trace of the printed circuit board (PCB).

1) LITZ WIRE SELECTION
Because R pan and R coil are the key factors influencing the heating efficiency, the R pan and R coil values for the 15-turn and 4800-strand #AWG 44 Litz wire are compared with those for the 21-turn and 3200-strand #AWG 44 Litz wire and the 29-turn and 1600-strand #AWG 44 Litz wire shown in Fig. 5 under the same coil diameter with the same copper pan shown in Table 1. Fig. 6 and Table 3 present a comparison of the parameters and efficiency of the aforementioned three Litz wire coils obtained using (1). R pan is proportional to the square-root of frequency due to the skin effect, but the R coil is nonlinear function of frequency because of the proximityeffect on Litz wires [28]. Although Table 3 indicates that the 15-turn Litz wire has the lowest R coil , the R pan of the 21-turn Litz wire is larger than that of the 15-turn wire. Therefore, the heating efficiency of the 21-turn Litz wire is 4.3% higher than that of the 15-turn Litz wire. Consequently, the 21-turn induction coil is selected for the developed IH system. Fig. 7 illustrates the measured resistance of the Litz wire spiral coils for various turns. The results indicate that the resistance of the spiral coil is proportional to the length of coil at various frequencies. Therefore, these results can be used to estimate the resistance of the Litz coil. The aforementioned  approach can replace complex and time-consuming software simulation for the calculation of the Litz wire resistance. The following results are obtained from the simulations of the pan power and efficiency for various turns of the 3200-strand Litz wire shown in Fig. 8:

2) INFLUENCE OF THE COIL TURN ON HEATING POWER AND THE HEATING EFFICIENCY
(i) The pan power is highly proportional to the number of coil turns at various frequencies. Although an increase in the number of turns can increase the output power, the size limitation of the coil diameter should be considered. (ii) Due to the higher resistance of the induction coil in higher operating frequency, the heating efficiency and power at 100 kHz operating frequency will be higher than 200 kHz. 5108 VOLUME 9, 2021  (iii) The maximal efficiency is 80.1% for 21 turns at 100 kHz (same value as in Table 3).

B. CHARACTERISTICS OF THE HBSRC FOR THE COPPER PAN 1) INDUCTANCE ANALYSIS WITH AND WITHOUT THE COPPER PAN
According to the design process, the 21-turn and 3200-strand Litz wire is used as the induction coil. The coil inductance without and with the copper pan can be expressed as follows: where L coil and L eq : coil inductance without and with the copper pan, respectively. φ coil : total flux generated by the coil without the pan. : MAGNETIC RESISTANCE. The equivalent inductance with the copper pan L eq is smaller than the coil inductance L coil without a pan by (2) and (3), because of the negative flux of eddy current. The field simulation software Maxwell 3D is used to simulate L eq and the magnetic flux distribution with and without the copper pan on the induction coil is shown in Fig. 9. The simulation results are briefly described as follows: (i) The magnetic flux generated by the induction coil without the pan is naturally and symmetrically distributed on both sides of the coil, as displayed in Fig. 9(a). However, when the copper pan is placed on the coil, the magnetic flux decreased and most of the magnetic flux is concentrated between the coil and the bottom of the copper pan, as displayed in Fig. 9(b). This phenomenon occurred mainly due to the eddy current generated by the penetration of the magnetic flux into the pan bottom. (ii) The L eq values displayed in Fig. 9(c) are 10.5µH and with and 36.4µH (= L coil ) without the copper pan on the coil, respectively.
where δ(= ρ π f µ ) : penetration depth of the flux. µ : permeability. ρ : conductivity. D : thickness of bottom of the copper pan. Fig. 11 illustrates the influence of the operating frequency on the heating efficiency, R pan , and R coil of the 21-turn and 3200-strand Litz wire. In this study, (i) R pan is simulated using Maxwell 3D and increased with an increase in the frequency; (ii) R coil is calculated using the method displayed in Fig. 7; (iii) the heating efficiency η decreased due to the higher increase in R coil than in R pan under increasing frequency. The maximal heating efficiency is 80% at 130 kHz. Therefore, the resonant frequency is selected near 130 kHz.

C. RESONANT CAPACITOR AND CURRENT 1) RESONANT CAPACITANCE
According to the specifications in Table 2, the induction coil made of a 21-turn and 3200-strain Litz wire exhibits its maximum efficiency at 130 kHz. The required resonant capacitance is calculated to be 142.7 nF when L eq = 10.5µH .

2) RESONANT CURRENT
The characteristics of the resonant current are key factors for calculating the heating power, performing pan detection, and developing control algorithms for the copper pan. For the HBSRC converter displayed in Fig. 2, the peak resonant current can be derived using the following expression: where v Req (s) (= 2V dc π R eq |Z re | ) : voltage amplitude of the R eq derived using the first-harmonic method.
C r (if one neglects the R circuit due to R circuit R eq ) The simulated RMS resonant current i rs,rms for various R eq values is displayed in Fig. 12. The following conclusions were obtained: (i) The parameter i rs,rms increased rapidly when the operating frequency is close to the resonant frequency because the R eq value of the copper pan is smaller than that of the ferromagnetic pan.
(ii) To reduce the switching loss of the MOSFET in the half-bridge, the operating frequency is set to be higher than f r for reaching the ZVS.
(iii) The derivative of i re by frequency, d df i re,rms , at the operating frequency 135 kHz is 40A rms /kHz. Thus, the HBSRC 5110 VOLUME 9, 2021  should provide a high-resolution operating frequency to reduce low-frequency oscillations for heating power control.

D. RESONANT FREQUENCY ESTIMATION
The high Q factor of the copper pan, misalignment of the pan position, and variation of the copper pan size caused variations in the operation frequency shown in Fig. 13. The proposed function for the estimation of the resonant frequency is used to determine the optimal operation frequency range. Because of the low resistance of the copper pan, the impedance of the resonant tank (Z re ) can be simplified as follows when the operating frequency is higher than the resonant frequency shown in Fig. 14: Assume the resonant current i re (t) is dominated by the fundamental component i re (t), the following expression is obtained: Therefore, the estimated inductance L r,est and resonant frequency ω r,est are expressed as follows: According to (8) and (9), the estimated resonant frequency f r,est can be calculated using the given operating frequency, known resonant capacitance, and given amplitude of the resonant current.

E. BUCK CONVERTER
The proposed specifications of the buck converter are presented in Table 1. The DC link voltage is controlled from 35 V to 70 V to satisfy various heating power demands. Moreover, a SiC MOSFET and synchronous control are adopted on Q1 and Q2 to achieve high efficiency. The key component selection are described in the following text:

1) INDUCTANCE
The inductor current ripple is designed to be 25% of the peak DC link current. The calculated inductor current ripple was 100 µH, and TDK ferrite core ETD 59 is used to construct the inductor.

2) DC LINK CAPACITORS
To achieve passive power factor correction, and proposed DC link voltage control method, the small capacitance is designed to be 33 µF and a low-ESR film capacitor with high RMS current capacity is selected.  frequency estimator for initialization to determine the operating frequency, and heating power control for cooking. The proposed schemes are described in the following text.

A. RESONANT FREQUENCY ESTIMATION
It is used to estimate the resonant frequency of pans of various sizes or to detect misalignment. According to (9), f r,est can be expressed as follows: For a given C r , f s , sensing peak value of the resonant current I rep , and DC link voltage v dc , the on-line calculation of f r,est by using a look-up table is convenient. The flowchart of the process for searching the resonant frequency is displayed in Fig. 15. First, the initial values and searching resonant frequency are set according to I rep . If the size of the pan is larger than maximal size, I rep is larger than I re,est at the initial frequency f s,max , and the system ends frequency searching. When I rep reaches the default value I re,est , the estimated resonant frequency f r,est can be obtained using (10). The maximal and minimal operating frequencies f s,max and f s,min can be determined from the simulated results obtained using Maxwell 3D and MATLAB. The maximal and minimal frequencies are dependent on the maximal pan size and without pan on the induction coil, respectively.

B. HEATING POWER CONTROL WITH PFC
To control the heating power and satisfy harmonics requirements simultaneously, the proposed control schemes are used shown in Fig. 16. These schemes are described in the following text.

1) POWER CONTROL OF THE COPPER PAN
To achieve power control, a simple heating power estimator is developed. The estimated heating power of pan P pan can be expressed as follows: where η HB : efficiency of the HBSRC caused by switching and conduction loss.
i rep : peak current of i re . R misc : miscellaneous resistance in the resonant tank, which consists of a current sensor, main power path of the PCB, and ESR of the resonant capacitor.
The power controller is constructed using a PI-type regulator, which generates a peak fundamental voltage command V * dcp1 to reach the required DC link voltage for the HBSRC. Due to the MOSFETs operating in the ZVS region, the switching losses of the HBSRC and η HB can be expressed as follows: 2

) THIRD-HARMONIC INJECTION OF THE DC LINK VOLTAGE COMMAND
To satisfy the IEC-61000-3-2 standard, a voltage pattern generator with third-harmonic injection was used to produce the waveform g(t) of the DC link voltage command v * dc . The maximal permissible third-harmonic current should be less than 2.3A rms according to IEC-61000-3-2-2014 Class A for household appliances. Therefore, the proposed v * dc is expressed as follows: where K v : ratio of third DC link voltage harmonic If the line voltage v ac is sinusoidal and f s is fixed, then the DC link power p dc is expressed as follows: 5112 VOLUME 9, 2021 where Z SRC : equivalent input impedance of the HBSRC under a fixed operating frequency.
η buck : efficiency of the buck converter. v ac (t) = V p sin ω 1 t : line voltage. Let i ac (t) = I 1 sin ω 1 t + I 3 sin 3ω 1 t By substituting (15) into (16), the following expression is obtained: where K v can be calculated according to (18)  To maintain the same power factor for various heating power conditions, we fix K v as 0.12 in the proposed control loop. Fig. 17 displays the simulated result for the thirdharmonic current under various loads. The aforementioned figure indicates that the K v value enabled the third-harmonic current to satisfy the IEC-61000-3-2-2014 Class A standard.

3) DC LINK VOLTAGE CONTROL
If excellent DC link voltage control is achieved using (15), the heating power of the pan P pan can be expressed as follows: where |Z re | = R 2 re + (X L r − X C r ) 2 R re = R pan +R coil +R circuit Thus, P pan can be controlled by V * dcp1 and K v under a fixed operating frequency to replace the traditional variable frequency method, as displayed in Fig. 16. Consequently, the low-frequency oscillations caused by inaccurate operating frequencies are reduced. Moreover, the PI voltage controller and a voltage feedforward controller G 1 are adopted to obtain excellent voltage command tracking. On the basis of (15), G 1 can be derived by voltage gain of buck converter expressed as follows:

4) COMPARISON OF THE POWER CONTROL METHODS
The peak voltage of the proposed method determined from the differential of (15), which yields V dc.peak = 0.881V dcp1 at 3.54ms when K V = 0.12. Therefore, the peak current of the proposed method was 0.881 times the I re.peak of the traditional method (K V = 0). The power expansion ratio between the proposed and traditional method derived from (19) under the same V dc.peak and I re.peak is expressed as follows: Fig. 18 displays the simulated DC link voltage of the proposed method. For the same limitations of I re.peak =100A, and V dcp = 70 V, the simulation results presented in Table 4 and Fig. 19 indicates the proposed control method can provide 31% higher power than the traditional control method.  Table 2. VOLUME 9, 2021

A. COIL CONSTRUCTION AND PARAMETER MEASUREMENT
The coil winding is selected according to the results of the aforementioned analysis. The selected coil winding is a 21-turn, 0.05-mm, and 3200-strand Litz wire with a diameter of approximately 200 mm. Moreover, the thermoset plastics Epoxy is used to fix coils and assist heat dissipation. The procedure of constructing the coil winding and measurement setup are displayed in Fig. 21. Fig. 22 displays the simulated and measured parameters of the proposed IH system with copper pan. Because no magnetic saturation occurred, we use an impedance analyzer (WK 6500B) to measure the equivalent parameters of IH with the copper pan. The results reveal that the maximal difference between measurement and simulation is less than 7%.  Fig. 23 illustrates the measured efficiency of the buck converter at various output voltages. The output power is proportional to the output voltage v dc , and the equivalent impedance of IH with the copper pan is lower than that with the ferromagnetic pan. The rated power is set as 1 kW at a 70-V output voltage. The efficiency of the proposed approach is more than 97.5% when the output power is larger than 18% of the rated power.

(i)ZVS turn-on operation
Since ZVS operation is very important to reduce the switching loss of the HBSRC. Fig.24 shows that the proposed HBSRC provides ZVS turn-on under different loaded conditions.
(ii)Efficiency measurement To obtain accurate efficiency measurements, the tested copper pan is filled with 1.5 L of water, is displayed in Fig. 25(a). The copper pan is wrapped with Styrofoam for thermal insulation as displayed in Fig. 25(b). The ambient temperature is 25 • C. The average power is measured using a digital scope (RTO 1014) with 16-bit vertical resolution in the high-definition mode. The average output power and efficiency of the copper pan can be expressed as follows:   where  P circuit = i 2 re.rms × R circuit P coil = i 2 re.rms × R coil Because copper is a temperature-dependent material, the coil resistance and pan resistance at a fixed operation frequency can be expressed as follows: Fig. 26, Fig. 27 and Table 5 present the measured results of the resonant tank, the power loss distribution, and the measured power and efficiency of the proposed IH system with the copper pan, respectively. The following conclusions are obtained from the measured results:   (i) The total efficiency of the HRSRC with the copper pan is 69.8% at 93 • C. (ii) Due to the low heating resistance of the copper pan, copper losses from the coil accounted for 60% of the total losses. (iii) The measured coil efficiency [P o /(P o + P coil )] is 79.5%, which is consistent the results of the proposed calculation method (Fig. 11).

C. VERIFICATION OF THE CONTROL METHODOLOGIES 1) RESONANT FREQUENCY ESTIMATION
The proposed resonant frequency estimation method is verified for various conditions of misalignment of the copper   pan on the coil. The experimental results obtained using the impedance analyzer and the estimation results are presented in Table 6. The maximum error of the proposed estimation method was less than 3%.

2) POWER CONTROL USING THE DC LINK VOLTAGE WITH THIRD-HARMONIC INJECTION
The proposed DC link voltage control method with a fixed switching frequency exhibits a stable performance and without low frequency peak current ripple on the resonant current compared to traditional frequency modulation (FM) method as shown in Fig. 28. Wherein, the traditional FM method exists 2 kHz peak current ripple which may induce acoustic noise.
The proposed power control method by controlling the DC link voltage v dc is verified and compared to traditional control method shown in Fig.29 and Fig.30. The proposed method can reach input power P ac of 494 W and 650 W under V dc.peak = 50V, I re.peak = 70 A and V dc.peak = 50V, I re.peak = 100 A, respectively. All of the power are near 32%  higher than the traditional method at the same operating conditions, which are match to the analyzed results. Moreover, the power factor is 0.96 at 650W output power which is closed to the designed value (0.97) shown as Table 7.

V. CONCLUSION
This paper presents a Maxwell-3D-assisted IH design process for copper pans to achieve optimal efficiency. A DSP-based digitally controlled IH system for copper pan, which includes an AC-DC rectifier, a buck converter, and a HBSRC with an optimal design induction coil, is implemented to verify the proposed design process and control methods. Analysis and Maxwell 3D simulation are verified using the measured results. The key contributions of this paper can be summarized as follows: 1) The proposed IH design process involves the selection of Litz wire, determination of the optimal number of coil turns, and design of the resonant frequency to achieve the optimal efficiency by using the Maxwell-3D and the per unit coil resistance R coil . Finally, a 21-turn and 3200-strand #AWG 44 IH coil is selected, and the resonant frequency of the HBSRC is 130 kHz; thus, a coil efficiency of 80% is achieved. The performance of the selected coil is verified by obtaining experimental results.
2) The Maxwell 3D simulated results of the equivalent coil parameters L coil , L eq , and R pan are verified using an impedance analyzer, and the error between the simulated and experimental results is less than 6%.
3) A resonant frequency estimation method is proposed to provide a suitable operation frequency under non-ideal conditions, such as misalignment of the pan position and varying pan size. 4) A power control method involving DC link voltage control with third-harmonic injection is proposed to provide a stable resonant current with a fixed switching frequency and near 32% higher output power than that provided by traditional FM control methods under the same peak resonant current and peak voltage of v dc .
5) The maximal efficiency of the buck converter is 98.7% with SiC MOSFETs and synchronous rectifier control, and the efficiency of the HBSRC for copper pan is 69.7% at 93 • C.