Quasi Resonant Inverter Load Recognition Method

Induction heating (IH) technology is very popular in domestic applications because of its efficiency and safe operating properties. Resonant inverter circuits are widely used in IH systems owing to their high efficiency and soft-switching capability. Among the resonant inverters used in IH systems, the single-switch quasi-resonant inverter topology is generally preferred for low-cost and low-output-power applications. Despite the low-cost advantage of the quasi-resonant inverter, the soft-switching range is quite narrow, and it is not stable depending on the electrical parameters of the load that is desired to be heated. In other words, there is a critical relationship between the electrical characteristics of the pan, turn-on, and turn-off times, which are the control parameters of the semiconductor switch, and the safe working conditions. In addition, when the importance of closed-loop control methods is evaluated together with the selection of resonant circuit elements, it is essential to determine whether the load is suitable for heating, and to determine the electrical properties of the load to provide both reliable and efficient operating conditions. This study focuses on a new load-detection method based on circuit analysis for quasi-resonant induction hobs. After determining the load parameters, the turn-on and turn-off times of the semiconductor switch were determined to obtain the lowest possible switching loss. Therefore, the boundary conditions of the semiconductor switch are maintained within these limits. The proposed method and its advantages for the switch safe operating area were theoretically examined and proved through simulations and prototype circuits.


I. INTRODUCTION
Induction heating systems are mainly used in industrial, domestic, and medical applications owing to their user safety, efficient heating, easy cleaning, and fast heating features [1], [2], [3]. Domestic induction cooking apparatuses comprise at least one induction coil placed beneath the in vitro ceramic glass surface to heat up pans placed on top of the surface [4], [5], [6], [7], [8], [9]. To heat the pan, the induction coil is The associate editor coordinating the review of this manuscript and approving it for publication was Chi-Seng Lam .
supplied with an alternating current that generates a magnetic field at the same frequency as the coil current. This induces eddy currents that cause heating through the pan disposed on the induction surface [4], [6], [10]. The main components of induction heating systems are the rectifier unit, which is used for AC-DC conversion, and resonant inverter units [1], [11], [12]. A general power-transfer loop for domestic appliances is shown in Fig. 1.
Depending on the balance between cost and performance, which must be evaluated for each application, different resonant inverter topologies have been proposed [13], [14]. The most common inverter topologies in IH systems are half-bridge and single-switch quasi-resonant inverters. The single-switch quasi-resonant inverter topology offers a reliable solution for low-power, low-cost IH applications. The main disadvantage of the quasi-resonant inverter circuit is that it cannot control the power transferred to the load as frequency-controlled, as in half-bridge inverter circuits. The main reason for this is that the working modes of the quasiresonant inverter switch between RL and RLC circuits. Therefore, closed-loop control algorithms are used to determine the turn-on and turn-off times of the semiconductor switch.
In IH systems that use quasi-resonant inverters, there is an important relationship among the load parameters, current and voltage limit values of the semiconductor switch, turn-on and turn-off times of the semiconductor switch, and closedloop power control methods. When the importance of closedloop power control methods is evaluated together with the selection of resonant circuit elements, it is essential to determine whether the load is suitable for heating and the electrical properties of the load to ensure both reliable and efficient operation conditions. Although common induction heaters are designed to heat ferromagnetic pans, determining the load conditions for every working case is challenging [15], [16], [17]. Because of the relationship between the inverter circuit parameters and the induction loads, load identification methods are critical in induction hob applications, not only for accurate power control but also for reliable design [18], [19], [20], [21], [22], [23], [24], [25], [26], [27].

II. CIRCUIT DESCRIPTION
The circuit diagram and schema of the single-switch quasiresonant inverter and its main operation waveforms are presented in Fig. 2 and 3, respectively. The circuit schema includes a semiconductor switch T , freewheeling diode D, equivalent resistance R EQ , equivalent inductance L EQ and resonance capacitor C RES . When the switch T is turned on, the circuit acts as a serial RL circuit. The coil stores energy through the resistance R EQ for the t ON . The coil stores the energy supplied by the main V DC throughout the turn-on time. When the switch T was turned off, the circuit acted as a serial RLC circuit. The coil and capacitor resonate and exchange energy. The resonance capacitor C RES charges the peak voltage V CEMAX and eventually discharges it to zero. The switch was turned on again shortly after the capacitor was fully discharged [28], [29], [30].

A. CIRCUIT OPERATING MODES -WAVEFORM EQUATIONS
The working modes of the single-switch resonant inverter shown in Fig. 4 were examined in four main operation stages. The conduction time of the T semiconductor t 6 < t < t 0 is modeled as a series RL circuit that consists of R EQ and L EQ , while the time interval t 0 < t < t 5 where resonance occurs between L EQ and C RES is analyzed as a series RLC circuit. Finally, the conduction time of the D freewheeling diode t 5 < t < t 6 is modeled as a series RL circuit. As a result of the single-switch resonant inverter working as a series RLC circuit for states 2 and 3 out of 4 operating states and as a series RL circuit for operating states 1 and 4, the related circuit is analyzed with the time domain instead of the frequency domain.
Stage I (t 6 − t 0 ) : This interval starts with the T semiconductor's turn-on under zero voltage (ZVT) and continues until the T switch turns off. For the RL circuit operation, the VOLUME 10, 2022 following equations can be defined as in (1)-(3): : This interval starts with the turn-off of the T semiconductor, and resonance occurs between L EQ and C RES were analyzed as a series RLC circuit. In addition, the following equations can be defined for I LEQ current, as in (4)- (7).
In addition, the above equations and circuit equations (8)- (11) can be used to calculate the switch collector-emitter voltage V CE shown in Fig. 3.
Stage IV (t 5 − t 6 ) : This interval starts with the turning on D diode, which is connected anti-parallel to T power switch. As shown in Fig. 3, the freewheeling of current or energy through the source is handled by a D power diode. For the RL circuit operation, the following equations can be defined as in (12)-(15): The diode current conduction time t D (t 6 − t 5 ) and the diode peak current are expressed I Dmax .

B. SAFE OPERATING AREA FOR QUASI RESONANT INVERTER
From the first-and second-order circuit equations given above, it is determined that the optimum determination of R EQ , L EQ and C RES values is highly important for safe operating conditions of quasi-resonant induction heating applications. The two main factors that threaten safe working conditions in power electronic circuits are higher voltage and current than the maximum working conditions of the semiconductors used. Although all electronic circuit elements are affected by the overcurrent and overvoltage stresses, semiconductor switches are the most sensitive components in inverter applications. Even if overheating caused by excessive current can be eliminated by forced cooling methods, semiconductors exposed to voltages higher than the breakdown voltage can become inoperable within a very short time. Using the PSpice simulation program, the variances of the semiconductor switch collector-emitter voltage V CE values were obtained for different resonant circuit parameters, as shown in Fig. 5.
In the same manner, C RES capacitor discharge currents, which are frequently observed in quasi-resonant inverter circuits, threaten the reliable operation conditions of both semiconductors and power electronics circuits. These instantaneous currents, also called light load currents, can be three to four times larger than the nominal maximum current of the semiconductor (or coil current I LEQ ), and they cause overheating, stress, and similar problems. As in the V CE voltage example, the semiconductor switch current I T is obtained with the help of the PSpice simulation program, depending on different resonant circuit parameters, as shown in Fig. 6.
However, closed-loop power control techniques and the evaluation of input parameters are important for reliable working conditions. When the quasi-resonant inverter is analyzed, it can be observed that the working modes switch between RL and RLC circuits. Therefore, closed-loop control techniques used to determine the turn-on and turn-off times of semiconductor switches are essential. Depending on the material characteristics, AC supply conditions, and inverter circuit element parameters, calculating the semiconductor switch turn-on or turn-off times with an error greater than 1µs can rapidly increase switching losses. As a result, the switch is inoperable owing to overheating or overvoltage.
In the next section, a new analysis method is proposed for the identification of the load to be heated.

III. QUASI RESONANT INVERTER ANALYSIS FOR PROPOSED LOAD RECOGNITION METHOD
Similar to other inverter topologies, it is necessary to have knowledge of certain predefined circuit parameters to start the analysis of a quasi-resonant power inverter. By the help of these predefined circuit parameters, and using equations (1)-(54), different inverter analysis methods can be iteratively improved. In this section, a new analysis methodology for calculating the circuit parameters and a new load identification method are proposed. The remainder of this paper is organized as follows.
First, the equations for the time intervals t 0 to t 6 shown in Fig. 3, are defined. Afterwards the damping coefficient α and damped resonant frequency ω d are obtained from time interval values. Subsequently, the resonant frequency ω 0 is derived from α and ω d values (50). Then, with the help of ω 0 and C RES , equivalent inductance L EQ is calculated (51). Finally, the equivalent resistance R EQ was calculated using the L EQ and α (52).

A. DEFINING TIME INTERVAL EQUATIONS
In working stages II-III, the coil current I LEQ and switch turnoff voltage V CE reach their maximum values. Knowledge of these two parameters and their boundary conditions is very important and useful for designers not only for reliable working conditions but also for controlling system parameters such as the magnitude of the power transfer to the load. Moreover, the maximum current and voltage values of these quantities are functional in determining the time intervals that are used for the load identification method.
As shown in Fig. 3, when the coil current I LEQ reached its maximum value I LEQmax , the derivation of the I LEQ current VOLUME 10, 2022 was zero (t = t 1 ). Consequently, the maximum coil current I LEQmax can be derived using (16)- (18).
The maximum power level of a single-switch induction cooker is limited by the maximum breakdown voltage level of the power switch. When the switch voltage V CE reaches its maximum value V CEmax , the I LEQ current is zero (t = t 3 ). Consequently, the maximum switch voltage V CEmax can be derived as (19)-(21).
When serial resonance occurs between L EQ and C RES , the switch voltage V CE passes the DC bus voltage V DC twice (t 2 and t 4 ). Using (22)-(25), T RES and ω d can be derived as follows: In addition to the above equations, an approximate approach should be used to calculate t 5 . Referring to (8) Following transformations are applied according to Pythagoras theorem.
According to (27), (28) can be rewritten as following. where, Equation (45) can be obtained by organizing Equation (29) with the transformations defined in Equation (30). Cosine theorem can be used to obtain a compact representation as follows.
Following variable is defined to study on frequency analysis.
The period of f 1 (t 5 ) is exactly equal to the period of cos (θ − ω d t 5 ). Owing to the nature of the cosine term, the x-axis intersection points can be defined as follows: To obtain an appropriate solution, f 1 (t 5 ) is linearized around x 1 point as follows.
The intersection points with the x-axis of f lin (t 5 ) term can be defined as t * 5 and are derived as follows: Because the descending edge of f 1 (t 5 ) is sharp, an approximate solution of t * 5 is appropriate to satisfy the design requirements. Fig. 7 shows the approximate t * 5 calculation. For the proposed method, it was appropriate to assume t 5 = t * 5 .
89380 VOLUME 10, 2022 Then, using (4) and (42), the diode current peak value I Dmax and diode conduction time interval t D can be determined, respectively.
B. DEFINING RLC CIRCUIT PARAMETERS α,ω d and ω 0 The time intervals obtained from circuit operation modes such as t 2 , t 3 and t 4 can be determined using digital measurement methods. For this purpose, it is useful and practical to use microcontrollers or similar digital circuit components. In addition, provided that the resonant capacitor C RES is known, the unknown circuit parameters can be calculated using Equations (49)-(52). The resonant period T RES value can be found using with t 2 and t 4 time intervals.
By the help of the equation (46), the damped resonant frequency ω d value is obtained from t 2 and t 4 time intervals (47).
It is not easy to measure the t 1 time intervals practically. Fortunately, from the circuit equations mentioned previously, it is clear that the t 1 value can be obtained from the t 3 and the t 4 time intervals.
Alpha can also be found using the following equations: One of these equations can be selected according to the controller abilities.
For the serial RLC circuit, α and ω d values are very beneficial for finding unknown circuit parameters, such as equivalent resistance R EQ and equivalent inductance L EQ . The resonant frequency ω 0 is derived from α and ω d values (50).
The equivalent inductance L EQ is calculated by using ω 0 and C RES .
And the equivalent resistance R EQ is calculated with using the L EQ and α (52).
Finally, t 6 − t o time interval can be found by the help of (2).

IV. PROPOSED LOAD RECOGNITION METHOD
After analyzing the time intervals of the quasi-resonant inverter operation, a new load recognition method is proposed using the relevant time intervals, which are the outputs of the analysis studies. In the proposed method, t 2 , t 3 and t 4 time intervals were considered sufficient for the load recognition method. However, considering that the time intervals obtained with the help of the analyses in the first chapter will shed light on different studies on the subject, all the equations obtained in the study are preserved.
In quasi-resonant inverter circuits used in domestic induction heating hobs, the determination of the turn-on and turnoff times of the semiconductor switch is important for operation under soft-switching conditions. Because the load to be heated is variable and unknown, the electrical parameters of the load should first be determined correctly, and then the turn-on and turn-off times suitable for these characteristics should be determined. For this purpose, a small amount of energy is transferred to the coil by turning the semiconductor switch on so that the inverter circuit can operate safely and the time intervals required by the proposed method can be determined. In practice, the initial turn-on time of the switch is of the order of 2µs. Depending on the resonance that will occur between the coil and capacitor, the time intervals t 2 , t 3 and t 4 are measured. The electrical parameters of the load to be heated were determined using the proposed analytical method. Finally, with the help of the proposed analysis method, the turn-on and turn-off times (t ON and t OFF ) of the switch are determined, and operation under soft-switching conditions is ensured.
The visual algorithm, shown in Fig. 8, was developed to understand the process more clearly. At the end of the process, which starts with the input pulse signal, both load parameters are determined, and the semiconductor switch turn-on and turn-off times that provide the soft switching positions are determined.
The quasi-resonant inverter analysis method, which is analyzed in detail in this section, is verified by simulation and induction hob implementation in the next section. Although the proposed analysis method to determine the equivalent resistance R EQ and equivalent inductance L EQ with the help of the time intervals is very useful for practical implementation, the accurate determination of α and ω d is very important.

V. VERIFICATION OF PROPOSED LOAD RECOGNITION METHOD
The results obtained from the analysis are confirmed by simulation and application studies in this section. After the completion of the theoretical background studies developed for VOLUME 10, 2022 use in load identification studies, the outputs of the relevant analysis methods were first run in the simulation environment and then applied with the help of a practical application circuit.
To make an accurate comparison, four different ferromagnetic pans were used as loads in the simulation and experimental studies. When Table 1 is examined in detail, it can be observed that each pan has different ferromagnetic characteristics. The pans used were selected from different points in the ferromagnetic spectrum. Thus, we attempted to prove that the proposed method is suitable for all pans used in practice. The values obtained from the simulation and application were compared, and the reliability of the analysis was proved.

A. SIMULATION RESULTS
The simulation circuit application achieved using the PSIM program is shown in Fig. 9-a. It includes the AC main source, induction hob resonant tank, related current and voltage measurement tools, and a circuit parameter calculator. As shown in Fig. 9-b, the logic gates and flip-flop circuits are used to determine the t 2 , t 3 and t 4 time intervals. As described above section, time intervals are used as input values to calculate other circuit parameters such as α, ω 0 , R EQ and L EQ . As an output of this simulation circuit, V Gate is the semiconductor switch gate voltage, V DC is the DC bus voltage, V CE

B. EXPERIMENTAL VERIFICATIONS
The circuit scheme of the induction cooktop with quasiresonant topology is shown in Fig. 11. The experimental circuit prototype is shown in Fig. 12. The main supply voltage V AC = 230 VAC and rectified DC bus voltage V DC = 320V. A GSIB2560 bridge rectifier was used in the rectifier circuit. Because the IHW20N135R5 IGBT with the body diode is used as a switch, an additional diode is not used in the circuit and C RES = 270 nF. An advanced ARM-based 32-bit MCU STM32F100R8 microprocessor is used in the prototype application circuit. The operating frequency of the processor was 16MHz. The I LEQ coil current readings were made using a 10m shunt resistor and an op-amp circuit. The switch turn-off voltage, I LEQ coil current, and defined time interval values are shown in Fig. 10.
Voltage readings are obtained with the help of the voltage divider resistor circuit and the ADC channel of the processor. The coil current and switch voltages are read in multiples of 10ms and placed in the array, the highest and lowest values are   eliminated, and the average value of eight current and voltage data is used. The experimental prototype circuit results are shown in Fig. 13 and 14. The results were measured   using simulations, and the prototype circuits are compared in Table 1 for four different ferromagnetic pans. When a visual algorithm is used to determine the L EQ and R EQ load parameters, the quadratic circuit parameters are determined. Afterwards the load parameters L EQ and R EQ are found with VOLUME 10, 2022  the help of the obtained circuit parameters. The same method is valid in both simulation and experimental studies. However, we cannot easily provide these details in the simulation and experimental result tables. Therefore, we directly obtained the final load parameter results. As a result, when the differences between the simulation and experimental results were examined, the equivalent inductance deviation was less than %6. Although the equivalent resistance deviation was not as low as the equivalent inductance, the comparison results were sufficient for the proposed load identification method.

C. BOUNDARY CONDITION ANALYSIS
Despite the benefits of the quasi-resonant inverter, there is a critical relationship between the load parameters and the current and voltage limits of the semiconductor switch. After defining the load parameters using the proposed method, the simulation and experimental results are compared in terms of the boundary condition. As a result of obtaining L EQ and R EQ values using the proposed analysis method, semiconductor switch boundary conditions were also analyzed. The coil current I LEQ and switch turn-off voltage V CE are very important  and useful for the designer not only for reliable working conditions, but also for controlling system parameters such as the magnitude of the power transfer to the load. The visual algorithm developed to determine the I LEQmax and V CEmax values is shown in Fig. 15. While determining the circuit parameters with the help of the proposed method, the relevant time intervals and other circuit parameters were first determined. When the proposed method is used, the circuit is maintained within safe operating limits, and a satisfactory difference is measured between the simulation and application results. For this purpose, simulation and application results are presented. For this purpose, a comparative study was conducted for the safe operating limits listed in Table 2. The boundary conditions obtained with the boundary conditions obtained with the help of the measured results from the simulation and prototype circuits are compared in Table 2 for four different ferromagnetic pans. When the differences between the simulation and experimental results were examined, it was observed that the maximum semiconductor current deviation was <%3 and the maximum semiconductor collector voltage deviation is less than %7. Similar to previous results, the comparison results were sufficient for the proposed load identification method.
Some experimental results are shown in Fig. 16 for the stainless-steel pan and in Fig. 17 for the iron pan. When the experimental results were examined, it was observed that the quasi-resonant inverter remained in the safe operating area when the load detection parameters obtained using the proposed method were used.

VI. CONCLUSION
The proposed method focuses on a new load detection method based on circuit analysis for quasi-resonant induction hobs. The time intervals obtained from circuit operation modes such as t 2 ,t 3 and t 4 can be determined using digital measurement methods. As a result of obtaining L EQ and R EQ values with the help of the proposed analysis method, the turn-on and turn-off times of the semiconductor switch, as well as the boundary conditions, are analyzed. For this purpose, it is useful and practical to use microcontrollers or similar digital circuit components. In addition, if the resonant capacitor C RES is known, unknown circuit parameters can be calculated. Although the proposed analysis method to determine the equivalent resistance R EQ and equivalent inductance L EQ with the help of time intervals is very useful for practical applications, the accurate determination of α and ω d is very important.
After the completion of the theoretical background studies developed for use in load identification studies, the outputs of the relevant analysis methods were first run in the simulation environment and then applied with the help of a practical application circuit. The results measured from the simulation and the prototype circuits are compared in terms of circuit parameters, such as the equivalent resistor, inductor, and boundary conditions for four different ferromagnetic pans. The values obtained from the simulation and application were compared, and the reliability of the analysis was proved. He has authored or coauthored three conference papers in the area of power electronics. He also engaged in three research projects involving power electronics. His current research interests include power factor correction, switching power supplies, high-frequency power conversion, induction heating, and active and passive snubber cells in power electronics.
BURHANEDDIN EMRE was born in Malatya, Turkey, in 1994. He received the B.S. degree in electrical and electronics engineering from Istanbul University, Istanbul, Turkey, in 2019, where he is currently pursuing the M.S. degree in electrical and electronics engineering.
Since 2020, he has been an Electronics Engineer at the Research and Development Department, Mamur Technology Inc. His current research interests include power supply switching, high-frequency power conversion, and induction heating.
BARIS OZ was born in Istanbul, Turkey, in 1988. He received the B.Sc. degree in electrical engineering from Yildiz Technical University, and the M.Sc. degree in mechanical engineering from Istanbul Technical University. He is currently pursuing the Ph.D. degree in control and automation engineering with Yildiz Technical University. He has been working with the Research and Development Center, Mamur Technology Inc., as a Research and Development Project Manager. His current research interests include control systems, machine vision, industrial image-processing applications, optimization, and dynamical system modeling.