A Simplified Design Method for Quasi Resonant Inverter Used in Induction Hob

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A Simplified Design Method for Quasi Resonant Inverter Used in Induction Hob

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A peer-reviewed article of this preprint also exists.

Metin Ozturk^*

This version is not peer-reviewed

Submitted:

28 August 2023

Posted:

29 August 2023

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Abstract

Induction heating (IH) technology is widely recognized and utilized in residential applications due to its high efficiency and safe operating characteristics. Resonant inverter circuits are widely used in IH systems because of their high efficiency and ability to perform soft-switching. Among the various resonant inverters used in IH systems, the single-switch quasi-resonant (SSQR) inverter topology is typically preferred for low-cost and low-output-power applications. Despite its cost advantage, the SSQR topology has a relatively narrow soft-switching range, which can be unstable depending on the electrical parameters of the load and the resonant converter circuit. Accurately determining the capacitance value of the resonant capacitor and the inductance value of the induction coil, which are the key circuit elements of the SSQR induction cooker, is crucial for designing a reliable, efficient, and durable cooking system. In other words, there exists a critical relationship between the resonant converter circuit parameters, load characteristics, and safe operating conditions. Additionally, when considering closed-loop control methods used for power control and safety, selecting appropriate resonant circuit elements becomes vital in ensuring both reliable and efficient operation. This paper focuses on a novel and simplified design method for the SSQR inverter utilized in household appliances. The proposed method and its advantages in terms of the safe operating area of the switch are theoretically investigated and verified through simulations and prototype circuits.

Keywords:

Subject: Engineering - Electrical and Electronic Engineering

1. Introduction

Induction heating systems have gained significant popularity in industrial, domestic, and medical applications over the past few decades due to their notable features including user safety, efficient and rapid heating, and easy maintenance [1,2,3,4]. The advancements in power electronics as well as electronics have contributed to the progress of induction technology [5,6,7,8]. In domestic induction cooking appliances, one or more induction coils are positioned beneath a vitro ceramic glass surface to heat up pans placed on top of it [9,10,11]. The induction coil is supplied with an alternating current, generating a magnetic field at the same frequency as the coil current in order to heat the pan. This heating process occurs through the induction surface by inducing eddy currents in the pan [2,12]. The main components of induction heating systems consist of a rectifier unit for AC-DC conversion and resonant inverter units [13,14]. Figure 1 illustrates a general power-transfer loop for domestic appliances.

Power converters, which are a crucial component of Induction heating systems, employ either single-stage or double-stage structures [15]. Double-stage systems involve both AC to DC and DC to AC conversions within IH systems [13,14]. In contrast, single-stage AC to AC systems lack a rectifier stage. These systems can be categorized into two groups: those that directly convert the input AC voltage and those that boost it.

Furthermore, Induction heating systems are composed of either single or multiple loads/coils. In the past years, single coil systems have been extensively utilized in both industrial and domestic induction applications. Recent advancements in multiple output induction heaters suggest enhancing performance through adjustable cooking surfaces [16,17,18]. The selection of different coil models depends on factors such as design requirements, cost, output power, and hob geometry. Various approaches are employed to configure cooking surfaces based on the pan size and coil design [16,19]. While pans made of ferromagnetic material are commonly used as loads, recent studies have also explored heating pans made of all metal materials [20,21,22,23,24].

Different resonant inverter topologies have been proposed based on the trade-off between cost and performance, which needs to be evaluated for each specific application. The most common inverter topologies in induction heating (IH) systems are half-bridge series resonant (HBSR) [25,26,27,28] and single-switch quasi-resonant (SSQR) [29,30,31] inverters. The SSQR inverter topology provides a reliable solution for low-power and low-cost IH applications. However, the main drawback of the quasi-resonant inverter circuit is its inability to control the power transferred to the load in a frequency-controlled manner, as in HBSR inverter circuits. This limitation stems from the fact that the working modes of the SSQR inverter switch between

R L

and

R L C

circuits [11,32]. Consequently, closed-loop control algorithms are employed to determine the turn-on and turn-off times of the semiconductor switch.

In IH systems utilizing SSQR inverters, a significant correlation exists among the resonant converter circuit, load parameters, current and voltage limits of the semiconductor switch, turn-on and turn-off times of the semiconductor switch, and closed-loop power control methodologies. Furthermore, when assessed in conjunction with the closed-loop control techniques employed for power regulation and safety purposes, the selection of resonant circuit elements assumes critical importance in guaranteeing a reliable and efficient operation.

Coil equivalent inductance and resistance values, which form the electrical model of the system comprising the coil and the pan, are challenging to determine during the modeling of resonant circuit elements. Additionally, these values are subject to variations based on factors such as the operating frequency of the resonant circuit, ambient temperature, and air gap between the pan and the coil. As a result, there exists a wide range of academic research focusing on pan and load recognition [11,29,33,34,35,36]. However, the design of the coil itself necessitates a comprehensive academic investigation. Numerous studies have been conducted on coil design, particularly in the context of magnetic fields [37,38,39].

The wide range of electrical loads associated with pans used in domestic induction hob applications with SSQR inverters allows for customization of the electrical circuit parameters based on user preferences. Furthermore, the heat generated in the pan affects the values of circuit variables such as resistance and inductance, and potential variations due to the electrical network necessitate certain assumptions to be made in the design of the heating system with SSQR inverter.

In [40,41], a Class E inverter design utilizing one inductor and one capacitor is presented. During the initial stages of the design, semiconductor losses are disregarded, and it is assumed that the pan resistance remains constant. Additionally, the coil design precedes the circuit design, and the equivalent inductance (

L

) and equivalent resistance (

R

) values are determined based on the operating frequency (

f

). Similarly, in [42], prior to the implementation of the related design, the input voltage (

V_{S}

), work coil parameters (

Q, R_{L}, L_{R}

), water mass (

m

), and required boiling time (

t

) must be defined. In [43], the design process requires the specification of inverter output power (P), DC input voltage (

U_{D C}

), resonant frequency (

f

), as well as various other load and coil parameters. In [44], the inductance value is calculated based on the number of turns N, wire diameter W, and space S between consecutive turns. In [45], the finite-element method is employed, utilizing the coil's geometry. It is noted that the inductance value varies due to the physical interaction between the coil and the ferromagnetic pan; however, there is no provided data regarding the specific inductance value for the pan.

As a result, the studies briefly mentioned above require that critical information such as coil geometry, coil design and coil inductance value must be defined before starting the circuit design, by making some assumptions. However, while designing the SSQR inverter system, it is very important to determine the coil inductance value, as in other converter designs. In other words, the purpose of the design is to determine the coil inductance value to be used in the SSQR inverter. Defining a certain value for coil inductance before starting the design will complicate the circuit design process and prolong the process of obtaining output values such as current, voltage and power at desired values.

Also, in practical circuit design applications, using the inductance value as an input parameter may not be as practical as described in the references provided. From this point of view, the proposed method provides a feasible design approach for initial conditions where the critical circuit parameters of the resonant circuit, namely coil inductance

L_{E Q}

, equivalent circuit resistance

R_{E Q}

and resonant circuit capacitor value

C_{R E S}

are not known, by utilizing the energy desired to be transferred to the coil inductor.

Input parameters such as the mains input voltage

V_{A C}

, the output power P to be transferred to the pot and the switching times of the semiconductor are determined before the design phase. Then all circuit parameters including

L_{E Q}

R_{E Q}

and

C_{R E S}

can be determined using the proposed calculation method. In this way, it is aimed to create a reference method especially for practitioners who are new to SSQR design.

The rest of the manuscript is structured as follows: In Section II, the circuit description of the SSQR inverter converter is explained. In Section III, the detailed proposed design method of SSQR inverter is summarized. Section IV shows the calculation, simulation, and experimental results, respectively. The conclusion of this study is outlined in Section V.

2. Circuit Description

The circuit diagram and schematic of the single-switch quasi-resonant inverter, along with its primary operational waveforms, are presented in Figure 2 and Figure 3, respectively. The circuit schematic comprises a semiconductor switch denoted as

T

, a freewheeling diode labeled

D

, an equivalent resistance represented by

R_{E Q}

, an equivalent inductance designated as

L_{E Q}

, and a resonance capacitor denoted as

C_{R E S}

. Upon the activation of the T switch, the circuit behaves analogously to a series

R L

circuit. During this phase, the coil accumulates energy through the resistance

R_{E Q}

over a duration labeled as

t_{O N}

. Throughout the turn-on time, the coil accumulates energy provided by the primary voltage source

V_{D C}

When the

T

switch is closed, the circuit starts to work as a series

R L C

circuit. In this configuration, resonance is established between the coil and the capacitor, facilitating energy exchange. The resonance capacitor,

C_{R E S}

, charges to the peak voltage,

V_{C E M A X}

, and eventually discharges to zero. A short time after the capacitor has completely discharged, the switch is promptly reactivated, in accordance with references [1,46,47].

2.1. Circuit Operating Modes – Waveform Equations

The operational modes of the single-switch resonant inverter, depicted in Figure 4, are examined across four primary operational stages. The conduction period of the

T

semiconductor, denoted as

t_{6} < t < t_{0}

, is mathematically modeled as a series

R L

circuit incorporating components

R_{E Q}

and

L_{E Q}

. Simultaneously, the time interval

t_{0} < t < t_{5}

, characterized by resonance interactions between

L_{E Q}

and

C_{R E S}

, is subjected to analysis as a series RLC circuit. Lastly, the conduction duration of the

D

freewheeling diode,

t_{5} < t < t_{6}

, is depicted through a series

R L

circuit model. Owing to the behavior of the single-switch resonant inverter as a series

R L C

circuit during states 2 and 3 among the four operational states, and as a series

R L

circuit during states 1 and 4, the associated circuit is evaluated in the time domain as opposed to the frequency domain.

Throughout the analysis, particular attention is directed towards steady-state analysis, with a focus on the initial operational stage. Potential phenomena like resonance capacitor discharge current and analogous transient states are deliberately disregarded for the sake of analytical simplicity.

Stage I

(t_{6} - t_{0}) :

This interval commences with the initiation of the

T

semiconductor under zero voltage conditions (ZVT) and persists until the

T

switch deactivates. Regarding the operation of the

R L

circuit, the subsequent equations can be formulated as illustrated in equations (1)-(3).

i_{L E Q} (t_{6}) = 0

(1)

i_{L E Q} (t) = i_{T} (t) = \frac{V_{D C}}{R_{L E Q}} \cdot (1 - e^{- \frac{R_{E Q}}{L_{E Q}} \cdot t})

(2)

V_{D C} = V_{L E Q} + V_{R E Q}

(3)

Stage II-III

(t_{0} - t_{5}) :

This interval initiates with the deactivation of the

T

semiconductor, and the resonance phenomenon between

L_{E Q}

and

C_{R E S}

is scrutinized through analysis as a series

R L C

circuit. Furthermore, the subsequent equations can be established to characterize the current

I_{L E Q}

, as depicted in equations (4)-(7).

i_{L E Q} (t) = e^{- α t} {(B}_{1} c o s (⍵_{d} t) + B_{2} s i n (⍵_{d} t))

(4)

d i_{L E Q} (t) / d t = {- e}^{- α t} {[(B}_{1} ⍵_{d} + B_{2} α) s i n (⍵_{d} t) + {(B}_{1} α - B_{2} ⍵_{d}) c o s (⍵_{d} t)]

(5)

i_{L E Q} (t_{0}) ⟹ B_{1} = I_{0}

(6)

d i_{L E Q} (t_{0}) / d t ⟹

B_{2} = ((V_{D C} - R_{E Q} I_{0})) / (L_{E Q} ⍵_{d}) + (α I_{0}) / ⍵_{d}

(7)

Furthermore, the mentioned equations, along with the circuit equations (8)-(11), can be employed to compute the switch collector-emitter voltage

V_{C E}

as illustrated in Figure 3.

v (t) = V_{D C} + e^{- α t} {(A}_{1} c o s (⍵_{d} t) + A_{2} s i n (⍵_{d} t))

(8)

d v (t) / d t = {- e}^{- α t} {[(A}_{1} ⍵_{d} + A_{2} α) s i n (⍵_{d} t) + {(A}_{1} α - A_{2} ⍵_{d}) c o s (⍵_{d} t)]

(9)

v (t_{0}) ⟹ A_{1} = - V_{D C}

(10)

d v (t_{0}) / d t ⟹ A_{2} = (I_{0} / C_{R E S} - α V_{D C}) / ⍵_{d}

(11)

Stage IV

(t_{5} - t_{6}) :

This interval initiates with the activation of the

D

diode, which is connected in anti-parallel to the

T

power switch. As depicted in Figure 3, the dissipation of current or energy through the source is managed by a

D

power diode. Regarding the operation of the

R L

circuit, the ensuing equations can be formulated as demonstrated in equations (12)-(15). The duration of diode current conduction,

t_{D} (t_{6} - t_{5})

, and the peak diode current are denoted as

I_{D m a x}

i_{L E Q} (t) = \frac{V_{D C}}{R_{E Q}} + (I_{D m a x} - \frac{V_{D C}}{R_{E Q}}) e^{- \frac{R_{E Q}}{L_{E Q}} \cdot t}

(12)

i_{L E Q} (t_{D}) = 0 = \frac{V_{D C}}{R_{E Q}} + (I_{D m a x} - \frac{V_{D C}}{R_{E Q}}) e^{- \frac{R_{E Q}}{L_{E Q}} \cdot t_{D}}

(13)

t_{D} = l n [\frac{V_{D C} / R_{E Q}}{V_{D C} / R_{E Q} - I_{D m a x}}] (- \frac{L_{E Q}}{R_{E Q}})

(14)

t_{D} = - \frac{L_{E Q}}{R_{E Q}} \cdot \ln (1 + \frac{I_{D m a x}}{V_{D C} / R_{E Q} - I_{D m a x}})

(15)

2.2. Safe Operating Area for Quasi Resonant Inverter

From the provided first- and second-order circuit equations, it is evident that the precise determination of

R_{E Q}, L_{E Q} a n d C_{R E S}

values hold paramount importance for ensuring the secure operational conditions of quasi-resonant induction heating applications. The chief threats to safe functionality within power electronic circuits encompass both elevated voltage and current surpassing the maximum operational thresholds of the employed semiconductors. Although all constituents of electronic circuits can be influenced by overcurrent and overvoltage stress, semiconductor switches stand out as the most vulnerable elements in inverter applications. Even if excess heat generated by excessive current can be mitigated through enforced cooling methodologies, semiconductors subjected to voltages surpassing their breakdown thresholds can promptly render them non-operational. By employing the PSpice simulation program, variations in the collector-emitter voltage (

V_{C E}

) of the semiconductor switch are assessed across diverse resonant circuit parameter configurations, as visually depicted in Figure 5.

Similarly, discharge currents of the

C_{R E S}

capacitor, frequently observed within quasi-resonant inverter circuits, pose a threat to the reliable operational conditions of both semiconductors and power electronics circuits. These instantaneous currents, also referred to as light load currents, can exceed the nominal maximum current of the semiconductor (or coil current

I_{L E Q}

) by three to four times, resulting in issues such as overheating, stress, and similar challenges. Just like the

V_{C E}

voltage example, the semiconductor switch current

I_{T}

is derived using the PSpice simulation program, contingent upon resonant circuit parameters, as depicted in Figure 6.

Nonetheless, closed-loop power control techniques and the assessment of input parameters play a pivotal role in ensuring dependable operational conditions. When scrutinizing the quasi-resonant inverter, it becomes evident that its operating modes oscillate between

R L

and

R L C

circuits. Consequently, the implementation of closed-loop control methodologies to ascertain the turn-on and turn-off timings of semiconductor switches emerges as indispensable. Depending on the material characteristics, AC supply conditions, and parameters of inverter circuit elements, miscalculations in semiconductor switch turn-on or turn-off times exceeding

1 μ s

can swiftly escalate switching losses. This outcome can render the switch inoperative due to either overheating or overvoltage occurrences.

In the next section, a new simplified design method for SSQR inverter used in household appliances is examined.

3. Proposed Design Method For Quasi Resonant Inverter

Before starting the inverter design, the circuit variables that we use as input variables and known before the design should be defined correctly and the related design should be guided by using known circuit variables. In this study, the dc source voltage

V_{D C}

that obtained as a result of rectified of ac mains voltage, the average input power

P_{A V G}

drawn from the main source, the semiconductor switch turns on time

T_{O N}

and turn off time

T_{O F F}

variables are used as the initial conditions. The method to be followed in the design can be summarized as follows:

The dc source voltage $V_{D C}$ , the average input power $P_{A V G}$ , the switch turns on time $T_{O N}$ and the switch turn off time $T_{O F F}$ variables are defined.
The maximum value of the coil current $I_{L E Q M A X}$ is calculated with the help of the relevant circuit equations.
By detecting the 1st harmonic component of the voltage applied to the resonant circuit, the load resistance $R_{L E Q}$ is calculated.
After calculating the load resistance $R_{L E Q}$ , the equivalent inductance value $L_{E Q}$ is calculated with the help of the $R L$ circuit equations.
It is determined the $α, ⍵_{0} a n d ω_{d}$ of the series $R L C$ circuit with the help of calculated variables.
The resonant capacitor value $C_{R E S}$ is calculated with the help of resonant frequency $⍵_{0}$ and inductance value $L_{E Q}$ .
The design is verified by calculating the coil current and capacitor voltage boundary conditions.

3.1. Defining of the Time Intervals $T_{O N}$ and $T_{O F F}$ , the Source Voltage $V_{D C}$ and the Input Power $P_{A V G}$ :

In order not to operate at the audible frequency value, the operating frequency values of household induction hobs are not preferred below the

20 k H z

threshold frequency value [48,49,50]. On the other hand, to increase the switching frequency will increase the switching losses of the used semiconductors [4,48,51].

P_{S W} = f_{s} . E_{o f f}

(16)

For these reasons mentioned above, SSQR inverters used in induction cookers are operated in the range of

20 - 40 k H z

. It should also be noted that SSQR inverter circuits cannot be operated directly with frequency control as with half-bridge inverters.

T_{O F F}

time is determined by controlling the resonance oscillation of the energy transferred to the load during the

T_{O N}

time. The predefined values for starting in this design study are

T_{O N} = 15 μ S

and

T_{O F F} = 25 μ S

. The source voltage

V_{D C}

is obtained by rectifying the

A C

mains voltage, as shown in Figure 7.

The purpose of the capacitor used at the output of the rectifier is to provide the instantaneous currents demanded by the inverter circuit and act as a filter. Therefore, the

D C

voltage obtained follows the form of the main. In order to make the calculations easy and understandable, first of all,

V_{D C}

voltage will be accepted as a

D C

voltage source, and then the calculation values will be updated for the case where

V_{D C}

voltage follows the mains voltage form. The case where the source voltage

V_{D C}

is the

D C

voltage source is shown in Figure 7, and the case where

V_{D C}

follows the mains voltage form is shown in Figure 8. Finally, the predefined average source power for this design study is defined as

P_{A V G} = 1250 W

3.2. Calculation of the Maximum Coil Current $I_{L E Q M A X}$ :

In the case of quasi resonant inverter circuit operating in

R L

operating mode, the coil current

i_{L E Q} (t)

equals the semiconductor switch current

i_{T} (t)

(

i_{L E Q} (t) = i_{T} (t)

). When the operating states of the quasi-resonant inverter circuit are examined, finding the maximum value of the switch current

i_{T} (t)

means finding the approximate maximum value of the coil current

i_{L E Q} (t)

I_{L E Q M A X} \approx I_{T M A X}

(17)

When the source voltage

V_{D C}

is considered constant as the

D C

voltage source, the power-time graph becomes the multiplier of the current-time graph. The switch current

i_{T} (t)

and input power

P (t)

graphs as a function of time

t

are shown in Figure 9 and Figure 10 respectively. The variation of

R L

circuit switch current

i_{T} (t)

with time

t

depends on the values of

R

and

L

and is defined by equation (18) in case

i_{L E Q} (0) = 0

i_{L E Q} (t) = i_{T} (t) = \frac{V_{D C}}{R_{L E Q}} \cdot (1 - e^{- \frac{R_{E Q}}{L_{E Q}} \cdot t})

(18)

From equation (18) it is clear that the graphs of

i (t) - t

and

P (t) - t

cannot be linear and will behave variably depending on the

R L

circuit values. However, since the resistance values created by the pots used in induction heated cookers in the primary circuits are in the range of

1 Ω - 5 Ω

, accepting these graphs as linear will be very useful for finding the

I_{T M A X}

current. For the case where the average power transferred to the

R L

circuit is defined as

P_{A V G}

and the instantaneous maximum power is defined as

P_{M A X}

, the following equation is obtained with the help of Figure 10.

P_{A V G} = \frac{P_{M A X} . T_{O N}}{2 . (T_{O N} + T_{O F F})} = \frac{V_{D C} . I_{T M A X} . T_{O N}}{2 . (T_{O N} + T_{O F F})}

(19)

As a result of equation (19),

I_{T M A X}

value can be easily calculated (20).

I_{T M A X} = \frac{P_{A V G} . 2 . (T_{O N} + T_{O F F})}{V_{D C} . T_{O N}} = \frac{P_{M A X}}{V_{D C}}

(20)

On the other hand, for the case where the source voltage

V_{D C}

follows the mains voltage form, let's define the switch current and power variables as shown below:

I_{T M A X}

→

I_{T M A X 2}

P_{M A X}

→

P_{M A X 2}

P_{A V G}

→

P_{A V G 2}

V_{D C}

→

V_{D C 2}

Equation (21) is written for the case where the average power drawn from the source during the

π / 2

interval is accepted as

P_{A V G 2}

, and the average power drawn from the source only at the time of π/2 is accepted as

P_{A V G 2 - M A X}

P_{A V G 2} = \frac{1}{π} \int_{0}^{π} P_{A V G 2 - M A X} . \sin ω t d (ω t)

(21)

And then the equation (21) is simplified, equation (22) is obtained.

P_{A V G 2} = P_{A V G 2 - M A X} . \frac{2}{π}

(22)

When the equations (19) and (20) are rearranged,

P_{A V G 2 - M A X} = \frac{P_{M A X 2} . T_{O N}}{2 . (T_{O N} + T_{O F F})} = \frac{V_{D C 2} . I_{T M A X 2} . T_{O N}}{2 . (T_{O N} + T_{O F F})}

(23)

I_{T M A X 2} = \frac{P_{A V G} . 2 . (T_{O N} + T_{O F F})}{V_{D C 2} . T_{O N}} . \frac{π}{2}

(24)

As can be easily seen from the equations (23) and (24), the switch current

I_{T M A X 2}

and the instantaneous maximum power value

P_{M A X 2}

to be obtained for the case where the source voltage follows the mains voltage will increase by

π / 2

compared to the case where the source voltage is

D C

. This is because the same

P_{A V G}

value is desired to be drawn from the source, regardless of the source voltage form.

3.3. Calculation of $R_{L E Q}$ Value by Determining the 1st Harmonic Component of The DC Voltage:

Assuming that the resonant circuit current

i_{L E Q} (t)

is sinusoidal, the 1st harmonic component of the voltage applied to the resonant circuit is obtained. In this way, the value of resistance

R

is reached by using the maximum value of the resonant circuit current. According to the Fourier theorem, any practical periodic function with an angular frequency of

ω_{0}

can be expressed as an infinite sum of sine or cosine functions that are integer multiples of

ω_{0}

[52]. Thus,

f (t)

can be expressed as:

f (t) = a_{0} + a_{1} \cos ω_{0} t + b_{1} \sin ω_{0} t

(25)

The value

a_{0}

is the mean value of the function

f (t)

and is indicated by the below equation.

a_{0} = \frac{1}{T} \int_{0}^{T} f (t) d t

(26)

The variation of

V_{D C}

voltage applied to the quasi-resonant circuit as a function of time is shown in Figure 11. The value of

a_{0}

is found with the help of equation (26) so that the

T_{O N} + T_{O F F}

value is the period of the function.

a_{0} = \frac{1}{T} \int_{0}^{T} f (t) d t = \frac{1}{T} \int_{0}^{T_{O N}} V_{D C} d t = \frac{V_{D C} . T_{O N}}{T_{O N} + T_{O F F}}

And then,

a_{1}

and

b_{1}

values of the related

V_{D C}

voltage waveform will be found respectively.

a_{1} = \frac{2}{T} \int_{0}^{T} f (t) \cos ω_{0} t d t

(27)

a_{1} = \frac{2}{T} \int_{0}^{T} f (t) \cos ω_{0} t d t = \frac{2}{T} \int_{0}^{T_{O N}} V_{D C} \cos ω_{0} t d t

a_{1} = \frac{2 V_{D C}}{T ω_{0}} {|\sin ω_{0} t|}_{0}^{T_{O N}} = \frac{V_{D C}}{π} \sin (\frac{2 π . T_{O N}}{T_{O N} + T_{O F F}})

b_{1} = \frac{2}{T} \int_{0}^{T} f (t) \sin ω_{0} t d t

(28)

b_{1} = \frac{2}{T} \int_{0}^{T} f (t) \sin ω_{0} t d t = \frac{2}{T} \int_{0}^{T_{O N}} V_{D C} \sin ω_{0} t d t

b_{1} = \frac{2 V_{D C}}{T ω_{0}} {|- \cos ω_{0} t|}_{0}^{T_{O N}} = \frac{V_{D C}}{π} (1 - \cos (\frac{2 π . T_{O N}}{T_{O N} + T_{O F F}}))

It is also possible to represent the equation in (25) in amplitude-phasor form [52].

f (t) = a_{0} + A_{1} \cos (ω_{0} t + ϕ)

(29)

A_{1} = \sqrt{a_{1}^{2} + b_{1}^{2}}

(30)

In (30)

A_{1}

is the amplitude value of the 1st harmonic component of the

f (t)

function. And so, the next steps are to find the amplitude, in other words, the peak value of the 1st harmonic component of the

V_{D C}

voltage applied to the quasi-resonant circuit, and to reach the

R_{E Q}

value by proportioning this value to the maximum value of the coil current

I_{L E Q M A X}

A_{1} = \sqrt{{(\frac{V_{D C}}{π} \sin (\frac{2 π . T_{O N}}{T_{O N} + T_{O F F}}))}^{2} + {(\frac{V_{D C}}{π} (1 - \cos (\frac{2 π . T_{O N}}{T_{O N} + T_{O F F}})))}^{2}}

i_{L E Q M A X} \approx I_{T M A X} = \frac{P_{A V G} . 2 . (T_{O N} + T_{O F F})}{V_{D C} . T_{O N}}

R_{E Q} = \frac{A_{1}}{i_{L E Q M A X}}

(31)

3.4. Calculation of the Equivalent Inductance Value $L_{E Q}$ :

In order to calculate the

L_{E Q}

inductance value, 3 different methods are used, and the results are compared with each other and verified. The first of these is to use the current equation of the series RL circuit, the second is to use the voltage at the inductor ends, and the third is to calculate the inductance value by using the energy accumulated in the inductor.

3.4.1. $L_{E Q}$ calculation using series $R L$ circuit switch current $i_{T}$ value:

As mentioned earlier, the series

R L

circuit switch current

i_{T} (t)

as a function of time

t

, depends on the

R_{E Q}

and

L_{E Q}

values and is defined by equation (32) for

i_{L E Q} (0) = 0

i_{L E Q} (t) = i_{T} (t) = \frac{V_{D C}}{R_{L E Q}} \cdot (1 - e^{- \frac{R_{E Q}}{L_{E Q}} \cdot t})

(32)

Since the source voltage

V_{D C}

, equivalent resistance

R_{E Q}

, maximum value of coil current

I_{L E Q M A X}

and time information

T_{O N}

are now known,

L_{E Q}

value can be found by using equation (33).

L_{E Q} = - \frac{R_{L E Q} . T_{O N}}{L n (1 - \frac{R_{L E Q} . I_{L E Q M a x}}{V_{D C}})}

(33)

3.4.2. $L_{E Q}$ calculation using inductor voltage $V_{L E Q}$ value:

Equation (34) is obtained by using Kirchhoff’s voltage law in series

R L

circuit.

V_{D C} = V_{L E Q} + V_{R E Q}

(34)

And also, the voltage

V_{L E Q}

at the inductor ends is presented by the below equation (35).

v_{L E Q} = L_{E Q} \frac{d i_{L E Q} (t)}{d t}

(35)

We will also make the linearity assumption that we used when finding the

I_{T M A X}

current in the series

R L

circuit. The inductance value for this range where the semiconductor switch and coil currents are equal to each other indicated by the below equation.

L_{E Q} = V_{L E Q} . \frac{∆ t}{∆ i_{L E Q}} = (V_{D C} - V_{R E Q}) \frac{T_{O N}}{I_{T M A X}}

(36)

Although the

V_{D C}

voltage is constant, the

V_{R E Q}

voltage is expressed as (37) for the case where the current is considered linear.

V_{R E Q} = \frac{I_{T M A X} . R_{E Q}}{2}

(37)

When this expression is substituted in (36), the equation (38) is reached.

L_{E Q} = (V_{D C} - \frac{I_{T M A X} . R_{E Q}}{2}) \frac{T_{O N}}{I_{T M A X}}

(38)

3.4.3. $L_{E Q}$ calculation using inductor energy $W_{L E Q}$ value:

The energy accumulated in the inductor is expressed by the equation (39) in terms of inductance and inductor current.

W_{L E Q M A X} = \frac{1}{2} L_{E Q} . {I_{L E Q M A X}}^{2}

(39)

When the area under the

P (t) - t

graph shown in Figure 10 is integrated, the total energy transferred to the series

R L

circuit is found. Assuming the

P (t) - t

graph as linear (40) is found.

W_{M A X} = \frac{P_{M A X} . T_{O N}}{2}

(40)

To find the total energy transferred to the inductor, the energy dissipated in the resistor is subtracted from the total energy transferred to the series

R L

circuit.

W_{L E Q M A X} = W_{M A X} - W_{R E Q M A X}

(41)

Equation (42) is obtained as a result of equations (40) and (41).

W_{L E Q M A X} = \frac{P_{M A X} . T_{O N}}{2} - {(\frac{I_{T M A X}}{2})}^{2} . R_{E Q}

(42)

After the energy accumulated in the inductor is reached, equation (43) is used to arrive at the

L_{E Q}

equivalent inductance.

\frac{1}{2} L_{E Q} . {I_{L E Q M A X}}^{2} = \frac{P_{M A X} . T_{O N}}{2} - {(\frac{I_{T M A X}}{2})}^{2} . R_{E Q}

(43)

And finally, it is getting the equation (44) by the help of equations (39) and (43).

L_{E Q} = \frac{2}{{I_{T M A X}}^{2}} (\frac{P_{M A X} . T_{O N}}{2} - {(\frac{I_{T M A X}}{2})}^{2} . R_{E Q})

(44)

3.5. Determination The Series RLC Circuit Parameters:

Since the

T_{O F F}

time, which is the turnoff time of the semiconductor switch, is defined and known before the design, and the

L_{E Q}

and

R_{E Q}

values are calculated, the damping coefficient

α

, resonant frequency

⍵_{0}

and damped resonant frequent

⍵_{d}

values of the series

R L C

circuit can be calculated easily. First, the damped resonant frequency

⍵_{d}

is calculated by using the relationship between the

T_{O F F}

time and the resonant frequency

T_{R E S}

of the series

R L C

circuit.

T_{R E S} \approx T_{O F F} . \frac{4}{3}

(45)

f_{R E S} = f_{d} = \frac{1}{T_{R E S}}

(46)

ω_{d} = 2 π f_{d} = \frac{2 π}{T_{R E S}}

(47)

ω_{d} = \frac{2 π}{T_{O F F}} . \frac{3}{4}

(48)

And then, the damping coefficient

α

of the series

R L C

circuit is found by the equation (49).

α = \frac{R_{E Q}}{2 L_{E Q}}

(49)

Finally, the resonant frequency

⍵_{0}

is calculated with the help of the equation (51).

⍵_{d} = \sqrt{{⍵_{0}}^{2} - α^{2}}

(50)

⍵_{0} = \sqrt{{⍵_{d}}^{2} + α^{2}}

(51)

3.6. Calculation of the Resonant Circuit Capacitor Value Inductance Value $C_{R E S}$ :

After calculating the resonant frequency

⍵_{0}

and the equivalent inductance

L_{E Q}

values, the resonant circuit capacitance value

C_{R E S}

is found by using equation (52).

⍵_{0} = \frac{1}{\sqrt{L_{E Q} C_{R E S}}}

(52)

C_{R E S} = \frac{1}{L_{E Q} {(⍵_{0})}^{2}}

(53)

3.7. Calculation of Current and Voltage Boundary Conditions of Semiconductor Switch:

Defining boundary conditions for the single switch inverter design is very important. In working stage II and stage III (series

R L C

circuit mode) the coil current

I_{L E Q}

and switch voltage

V_{C E}

values reach their maximum values. Knowledge about these two parameters is very important and valuable for the designer not only for reliable working conditions but also to control system parameters such as power. As it can be seen from Figure 3 that when the coil current

I_{L E Q}

reach its maximum value

I_{L E Q M A X}

, the derivation of the

I_{L E Q}

current is zero (

t = t_{1}

). As result of this the maximum coil current

I_{L E Q M A X}

can be derived by the help of (54)-(56).

d i_{L E Q} (t_{1}) / d t = 0 ⟹ i_{L E Q} (t_{1}) = I_{L E Q M A X}

(54)

t_{1} = \tan^{- 1} [- {(B}_{1} α - B_{2} ⍵_{d}) / {(B}_{1} ⍵_{d} + B_{2} α)]) / ⍵_{d}

(55)

I_{L E Q M A X} = i_{L E Q} (t_{1}) = e^{- α t_{1}} {(B}_{1} c o s (⍵_{d} t_{1}) + B_{2} s i n (⍵_{d} t_{1}))

(56)

Single switch induction cooker’s maximum power level is limited by power switch maximum breakdown voltage level. When the switch voltage

V_{C E}

reach its maximum value

V_{C E M A X}

, the

I_{L E Q}

current is zero (

t = t_{3}

). As result of this the maximum switch voltage

V_{C E M A X}

can be derived by the help of (57)-(59).

i_{L E Q} (t_{3}) = 0 ⟹ v (t_{3}) = V_{C E M A X}

(57)

t_{3} = \tan^{- 1} (- B_{1} / B_{2}) / ⍵_{d}

(58)

V_{C E M A X} = v (t_{3}) = V_{D C} + e^{- α t_{3}} {(A}_{1} c o s (⍵_{d} t_{3}) + A_{2} s i n (⍵_{d} t_{3}))

(59)

3.8. The Flowchart of the Proposed Design Method

The flowchart shown in Figure 12 is developed to understand the determining of the

L_{E Q}

and

R_{E Q}

more clearly. It determines the boundary conditions of the semiconductor switch with the help of the same flow chart. If the boundary conditions are not within the defined safe limit values of the semiconductor, the design is started from the beginning.

4. Verification of Proposed Analysis Method

In order to prove the accuracy of the proposed design method, first of all, critical circuit parameter values are calculated using predefined input parameters depending on the design requirements. By using the circuit parameters obtained as a result of the calculation, simulation studies are carried out and the boundary conditions required to ensure reliable operation of the inverter circuit are measured.

4.1. Calculation Results

As a result of the proposed method and calculation tools, a standard design example has been carried out and the calculated results are listed in Table 1. Firstly, the initial values are defined and then the critical circuit elements’ values are calculated. As previously mentioned, the average source power for this design study is defined as the

P_{A V G} = 1275 W

. And also, the switch turn-on and turn-off times are defined as the

T_{O N} = 15 μ S

and

T_{O F F} = 25 μ S

. The source voltage

V_{D C}

is obtained by rectifying the

A C

mains voltage.

The critical circuit elements values are calculated as

R_{E Q} = 5, 83 Ω

L_{E Q} = 98, 5 μ H

, and

C_{R E S} = 278, 86 n F

. In addition to circuit parameters

L_{E Q}

and

R_{E Q}

, the current and voltage boundary conditions of the semiconductor switch are calculated to check design reliability. As can be seen from Table 1, depending on the input values defined for this study, the maximum value of the switch voltage

V_{C E M A X}

is calculated as

834, 49 V

, and the maximum value of the switch current

I_{L E Q M A X}

is calculated as

33, 57 A

4.2. Simulation Results

A simulation prototype circuit has been developed using the predefined and calculated circuit parameters from Table 1, and it is shown in Figure 13. The OrCAD PSpice software program has been used for the simulation, with a particular emphasis on ensuring that the maximum coil current (

I_{L E Q M A X}

) and maximum switch voltage (

V_{C E M A X}

) values align with the values calculated in the previous section.

When the critical circuit element values obtained from measurement results were directly used in the designed circuit for simulation, some deviations were observed in the

I_{L E Q M A X}

and

V_{C E M A X}

values. The measured switch voltage was found to be

760 V

instead of the expected

835 V

, resulting in an error of approximately

9 %

. Similarly, the maximum coil current, which should have been

33.57 A

, was measured as

30.85 A

, indicating an error of approximately

8 %

Although the deviation values might be acceptable for many designers, the root cause of the discrepancy has been investigated to continue the simulation studies. It was hypothesized that the deviation arose from the proposed design method, which assumed a linear current-time graph by neglecting the resistance value in the RL operating mode of the SSQR inverter. Based on this assumption, a sweep analysis method has been employed in the relevant simulation program, scanning

R_{E Q}

resistance values between

4 Ω

and

6 Ω

with a precision of

0,1 Ω

. The resistance value that yielded the same current and voltage values as the calculated ones has been determined. Figure 14 illustrates the graph of the obtained current and voltage values from the scanning process. It has been observed that when a resistance value of

4,3 Ω

was used instead of the calculated resistance value of

5,83 Ω

, the calculated values matched exactly with the simulation results. All the results obtained from the scanning process are presented numerically in Table 2.

To compare the results from the simulation circuit with the application circuit under the same conditions, the coil current (

I_{L E Q}

) and switch voltage (

V_{C E}

) graphs are separately presented over a 20ms time interval in Figure 15 and Figure 16. The primary advantage of this representation is to provide a comprehensive and detailed understanding of how these variables change over time for those examining the study. By placing the simulation and application circuit results side by side, researchers can directly compare them and assess the accuracy or deviation between the simulated and actual circuit performance. This comparative analysis allows for a better understanding of the similarities and differences, enabling researchers to gain insights into potential factors that may affect the circuit's behavior. Furthermore, by examining the variation of coil current and switch voltage over time, researchers can gain valuable insights into the dynamic behavior of the circuit. This information can be used to optimize the circuit's performance, identify potential issues such as transient spikes or oscillations, and make informed design decisions to ensure the circuit operates within desired parameters.

4.3. Experimental Results

Once the theoretical calculations and simulation studies developed for the calculation of critical circuit parameters are completed, the outputs of the proposed calculation method are tested using a practical application circuit. Before examining the results of the application circuit, it is beneficial to review the technical specifications of the induction coil and the heated pans used in the application circuit. This will facilitate the interpretation of deviations between the practical application results and the theoretical calculations and simulation circuit results.

As described in detail in the introduction of the study, a wide range of pan types are used in household induction cooktops. The electrical effects of these pans on the electronic circuitry are particularly critical due to their ability to change the equivalent resistance and equivalent inductance values. However, it is not feasible to test all possible pan models in practical applications. Therefore, in the experimental implementation of the proposed method, three different pan models with different electrical and magnetic characteristics, as shown in Figure 17, have been used. These pan models include cast iron, stainless steel, and specially designed alloy pans for induction heating.

On the other hand, Table 3 provides the physical and electrical characteristics of the induction coil used in the practical application circuit, as well as the measured equivalent inductance and resistance values when using three different types of pans. In practical application, although an exact match of the calculated resistance and inductance values obtained through the proposed calculation method is not achieved, the feasibility of the proposed method has been demonstrated.

The coil current, the switch voltage and the output power values obtained when using three different pan models are presented in Table 4. In addition, in Table 5, the output results obtained using the calculation, simulation and application circuit for similar conditions are compared. Upon closer examination of Table 5, it is evident that the values obtained through the calculation method closely match the nearest capacitor value used.

However, the different electrical characteristics of the pans used in practical applications make it challenging to directly compare the calculation and application circuits. In practical implementation, a coil current

(I_{L E Q M A X})

42,4 A

and a switch voltage

(V_{C E M A X})

928 V

have been measured for a resistance of

4,21 Ω

, while in theoretical calculations and simulation circuit, these values were

33,6 A

and

835 V

, respectively. The deviation is approximately

20 %

for current and

10 %

for voltage. The main reason for this discrepancy is the change in the resistance and inductance values measured at the initial conditions when the pan is heated. As a result of these studies, considering the variety of pans used in practical applications, the proposed calculation method is proven to be reliable for initiating the design process.

To compare the results from the simulation circuit with the application circuit under the same conditions, the coil current (

I_{L E Q}

) and switch voltage (

V_{C E}

) graphs are separately presented over a 20ms time interval in Figure 18 and Figure 19. When comparing these graphs with the results obtained from the simulation circuit in Figure 15 and Figure 16, it is evident that very similar results can be achieved. Also, the detailed waveforms of the coil current and switch voltage are shown in Figure 20. Finally, the experimental setup is shown in Figure 21.

5. Conclusions

This paper is focused on a new design method for SSQR inverter used in household appliances. Before starting the inverter design, the circuit variables that we use as input variables and known before the design should be defined correctly and the related design should be guided by using known circuit variables. In this study, the dc source voltage

V_{D C}

that obtained as a result of rectified of ac mains voltage, the average input power

P_{A V G}

drawn from the main source, the semiconductor switch turns on time

T_{O N}

and turn off time

T_{O F F}

variables are used as the initial conditions. In order to prove the accuracy of the proposed design method, first of all, critical circuit parameter values are calculated using predefined input parameters depending on the design requirements. By using the circuit parameters obtained as a result of the calculation, simulation studies are carried out and the boundary conditions required to ensure reliable operation of the inverter circuit are measured.

After the completion of the theoretical background and simulation studies developed for use in critical circuit parameter calculation studies, the outputs of the relevant design method are run with the help of a practical application circuit. The results obtained from the experimental circuit are also compatible with the simulation results. The reliability of the proposed design and calculation method is proven by comparing the data obtained as a result of the simulation and experimental with the data obtained as a result of the calculation.

Author Contributions

Conceptualization, M.O.; methodology, M.O.; validation, M.O.; investigation, M.O.; writing—original draft preparation, M.O.; writing—review and editing, M.O. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

No new data were created.

Acknowledgments

This work was supported by the Scientific and Technological Research Council of Turkey and co-financed by the Mamur Technology Systems Research and Development Center under Project 3210188.

Conflicts of Interest

The authors declare no conflict of interest.

References

W. P. W. KOMATSU, “A simple and reliable class E inverter for induction heating applications,” Int. J. Electron., vol. 84, no. 2, pp. 157–165, Feb. 1998. [CrossRef]
H. OMORI and M. NAKAOKA, “New single-ended resonant inverter circuit and system for induction-heating cooking apparatus,” Int. J. Electron., vol. 67, no. 2, pp. 277–296, Aug. 1989. [CrossRef]
T. Tanaka, “A new induction cooking range for heating any kind of metal vessels,” IEEE Trans. Consum. Electron., vol. 35, no. 3, pp. 635–641, 1989. [CrossRef]
Lucía, P. Maussion, E. Dede, and J. M. Burdío, “Induction heating technology and its applications: Past Developments, current Technology, and future challenges,” IEEE Trans. Ind. Electron., vol. 61, no. 05, pp. 2509–2520, 2014. [CrossRef]
Lucia, D. Navarro, P. Guillen, H. Sarnago, and S. Lucia, “Deep Learning-Based Magnetic Coupling Detection for Advanced Induction Heating Appliances,” IEEE Access, vol. 7. pp. 181668–181677, 2019. [CrossRef]
U. Has and D. Wassilew, “Temperature control for food in pots on cooking hobs,” IEEE Trans. Ind. Electron., vol. 46, no. 5, pp. 1030–1034, 1999. [CrossRef]
C. Ekkaravarodome, P. Charoenwiangnuea, and K. Jirasereeamornkul, “The simple temperature control for induction cooker based on class-E resonant inverter,” in 2013 10th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology, May 2013, pp. 1–6. [CrossRef]
M. K. Kazimierczuk and S. Wang, “Frequency-domain analysis of series resonant converter for continuous conduction mode,” IEEE Trans. Power Electron., vol. 7, no. 2, pp. 270–279, Apr. 1992. [CrossRef]
Lucia, H. Sarnago, and J. M. Burdio, “Soft-stop optimal trajectory control for improved operation of the series resonant multi-inverter,” IECON Proc. (Industrial Electron. Conf., pp. 3283–3288, 2014. [CrossRef]
D. Paesa, C. Franco, S. Llorente, G. Lopez-Nicolas, and C. Sagues, “Adaptive Simmering Control for Domestic Induction Cookers,” IEEE Trans. Ind. Appl., vol. 47, no. 5, pp. 2257–2267, Sep. 2011. [CrossRef]
M. Ozturk, F. Zungor, B. Emre, and B. Oz, “Quasi Resonant Inverter Load Recognition Method,” IEEE Access, vol. 10, no. August, pp. 89376–89386, 2022. [CrossRef]
V. Crisafulli and C. V. Pastore, “New control method to increase power regulation in a AC/AC quasi resonant converter for high efficiency induction cooker,” in Proceedings - 2012 3rd IEEE International Symposium on Power Electronics for Distributed Generation Systems, PEDG 2012, 2012, pp. 628–635. [CrossRef]
H. Sarnago, O. Lucia, A. Mediano, and J. M. Burdio, “A Class-E Direct AC–AC Converter With Multicycle Modulation for Induction Heating Systems,” IEEE Trans. Ind. Electron., vol. 61, no. 5, pp. 2521–2530, May 2014. [CrossRef]
H. Sarnago, O. Lucia, A. Mediano, and J. M. Burdio, “Direct AC–AC Resonant Boost Converter for Efficient Domestic Induction Heating Applications,” IEEE Trans. Power Electron., vol. 29, no. 3, pp. 1128–1139, Mar. 2014. [CrossRef]
P. Vishnuram and G. Ramachandiran, “Capacitor-less induction heating system with self-resonant bifilar coil,” International Journal of Circuit Theory and Applications, vol. 48, no. 9. pp. 1411–1425, 2020. [CrossRef]
H. P. Park, M. Kim, J. H. Jung, and H. S. Kim, “Load adaptive modulation method for all-metal induction heating application,” Conf. Proc. - IEEE Appl. Power Electron. Conf. Expo. - APEC, vol. 2018-March, pp. 3486–3490, 2018. [CrossRef]
H. Sarnago, O. Lucia, and J. M. Burdio, “Multiple-output ZCS resonant inverter for multi-coil induction heating appliances,” Conf. Proc. - IEEE Appl. Power Electron. Conf. Expo. - APEC, pp. 2234–2238, 2017. [CrossRef]
Lucia, C. Carretero, D. Palacios, D. Valeau, and J. M. Burdío, “Configurable snubber network for efficiency optimisation of resonant converters applied to multi-load induction heating,” Electron. Lett., vol. 47, no. 17, pp. 989–991, 2011. [CrossRef]
M. S. Huang, C. C. Liao, Z. F. Li, Z. R. Shih, and H. W. Hsueh, “Quantitative Design and Implementation of an Induction Cooker for a Copper Pan,” IEEE Access, vol. 9. pp. 5105–5118, 2021. [CrossRef]
S. H. Jeong, J. Il Jin, H. P. Park, and J. H. Jung, “Enhanced load adaptive modulation of induction heating series resonant inverters to heat various-material vessels,” J. Power Electron., vol. 22, no. 6, pp. 1020–1032, 2022. [CrossRef]
W. Han, K. T. Chau, W. Liu, X. Tian, and H. Wang, “A Dual-Resonant Topology-Reconfigurable Inverter for All-Metal Induction Heating,” IEEE J. Emerg. Sel. Top. Power Electron., vol. 10, no. 4, pp. 3818–3829, 2022. [CrossRef]
S. R. Ramalingam, C. S. Boopthi, S. Ramasamy, M. Ahsan, and J. Haider, “Induction heating for variably sized ferrous and non-ferrous materials through load modulation,” Energies, vol. 14, no. 24, 2021. [CrossRef]
J. Jin, M. Kim, J. Han, K. Kang, and J. H. Jung, “Input voltage selection method of half-bridge series resonant inverters for all-metal induction heating applications using high turn-numbered coils,” J. Power Electron., vol. 20, no. 6, pp. 1629–1637, 2020. [CrossRef]
E. Jang, S. M. Park, D. Joo, H. M. Ahn, and B. K. Lee, “Analysis and Comparison of Topological Configurations for All-Metal Induction Cookers,” J. Electr. Eng. Technol., vol. 14, no. 6, pp. 2399–2408, 2019. [CrossRef]
H. Sarnago, Ó. Lucía, A. Mediano, and J. M. Burdío, “Analytical Model of the Half-Bridge Series Resonant Inverter for Improved Power Conversion Efficiency and Performance,” IEEE Trans. Power Electron., vol. 30, no. 8, pp. 4128–4143, 2015. [CrossRef]
H. I. Hsieh, C. C. Kuo, and W. Te Chang, “Study of half-bridge series-resonant induction cooker powered by line rectified DC with less filtering,” IET Power Electron., 2023. [CrossRef]
H. Sarnago, P. Guillén, J. M. Burdío, and O. Lucia, “Multiple-Output ZVS Resonant Inverter Architecture for Flexible Induction Heating Appliances,” IEEE Access, vol. 7, pp. 157046–157056, 2019. [CrossRef]
H. W. Koertzen, J. D. van Wyk, and J. A. Ferreira, “Design of the half-bridge, series resonant converter for induction cooking,” PESC Rec. - IEEE Annu. Power Electron. Spec. Conf., vol. 2, pp. 729–735, 1995. [CrossRef]
N. Altintas, M. Ozturk, and U. Oktay, “Performance evaluation of pan position methods in domestic induction cooktops,” Electr. Eng., 2023. [CrossRef]
Hirota, H. Omori, K. A. Chandra, and M. Nakaoka, “Practical evaluations of single-ended load-resonant inverter using application-specific IGBT and driver IC for induction-heating appliance,” in Proceedings of 1995 International Conference on Power Electronics and Drive Systems. PEDS 95, pp. 531–537. [CrossRef]
Sheikhian, N. Kaminski, S. Voß, W. Scholz, and E. Herweg, “Optimisation of Quasi-resonant Induction Cookers,” 2013 15th Eur. Conf. Power Electron. Appl. EPE 2013, 2013. [CrossRef]
M. Ozturk and N. Altintas, “Multi-output AC–AC converter for domestic induction heating,” Electr. Eng., vol. 105, no. 1, pp. 297–316, Feb. 2023. [CrossRef]
J. Villa, D. Navarro, A. Dominguez, J. I. Artigas, and L. A. Barragan, “Vessel Recognition in Induction Heating Appliances - A Deep-Learning Approach,” IEEE Access, vol. 9. pp. 16053–16061, 2021. [CrossRef]
E. Spateri, F. Ruiz, and G. Gruosso, “Modelling and Simulation of Quasi-Resonant Inverter for Induction Heating under Variable Load,” Electron., vol. 12, no. 3, 2023. [CrossRef]
Zheng-Feng Li, Jhih-Cheng Hu, Ming-Shi Huang, Yi-Liang Lin, Chun-Wei Lin, and Yu-Min Meng, “Load Estimation for Induction Heating Cookers Based on Series RLC Natural Resonant Current.” doi: 10.3390/en15041294.
H. Sarnago, O. Lucía, and J. M. Burdio, “A Versatile Resonant Tank Identification Methodology for Induction Heating Systems,” IEEE Trans. Power Electron., vol. 33, no. 3, pp. 1897–1901, Mar. 2018. [CrossRef]
J. Acero, J. M. Burdío, L. A. Barragán, and R. Alonso, “A model of the equivalent impedance of the coupled winding-load system for a domestic induction heating application,” IEEE Int. Symp. Ind. Electron., no. 1, pp. 491–496, 2007. [CrossRef]
J. Acero, O. Lucia, C. Carretero, I. Lope, and C. Diez, “Efficiency improvement of domestic induction appliances using variable inductor-load distance,” in 2012 Twenty-Seventh Annual IEEE Applied Power Electronics Conference and Exposition (APEC), Feb. 2012, pp. 2153–2158. [CrossRef]
H. Okuno, H. Yonemori, and M. Kobayashi, “Relation of gap length and resonant frequency about a double-coil drive type IH cooker,” in 2008 15th IEEE International Conference on Electronics, Circuits and Systems, Aug. 2008, pp. 65–68. [CrossRef]
P. Charoenwiangnuea, C. Ekkaravarodome, I. Boonyaroonate, P. Thounthong, and K. Jirasereeamornkul, “Design of domestic induction cooker based on optimal operation class-E inverter with parallel load network under large-signal excitation,” J. Power Electron., vol. 17, no. 4, pp. 892–904, 2017. [CrossRef]
P. Charoenwiangnuea, S. Wangnipparnto, and S. Tunyasrirut, “Design of A Class-E Direct AC-AC Converter with Only One Capacitor and One Inductor for Domestic Induction Cooker,” in 2021 18th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology (ECTI-CON), May 2021, pp. 679–682. [CrossRef]
S. Yilmaz, B. S. Sazak, and S. Cetin, “Design and implementation of web-based training tool for a single switch induction cooking system using PHP,” Elektron. ir Elektrotechnika, no. 3, pp. 89–92, 2010, [Online]. Available: https://www.semanticscholar.org/paper/Design-and-Implementation-of-Web-Based-Training-for-Yilmaz-Sazak/d44d3831c3d6722cf80422afd7a4eabaf1f091f9.
B. S. Sazak, “Design of a 500W Resonant Induction Heater,” Pamukkale Univ. J. Eng. …, pp. 1–12, 2011, [Online]. Available: https://www.researchgate.net/publication/267858491_DESIGN_OF_A_500W_RESONANT_INDUCTION_HEATER.
H. Zeroug, T. M. Leulmi, M. M. Lograda, and N. Tadrist, “Design and development of IGBT resonant inverters for domestic induction heating applications,” in 6th IET International Conference on Power Electronics, Machines and Drives (PEMD 2012), 2012, pp. F22–F22. [CrossRef]
L. Meng, K. Wai, E. Cheng, S. Member, and K. W. Chan, “Systematic Approach to High-Power and Energy-Efficient Industrial Induction Cooker System : Circuit Design , Control Strategy , and Prototype Evaluation,” vol. 26, no. 12, pp. 3754–3765, 2011.
H. Terai et al., “Comparative Performance Evaluations of IGBTs and MCT in Single-Ended Quasi-Resonant Zero Voltage Soft Switching Inverter,” no. 1, pp. 2178–2182.
H. Omori, H. Yamashita, M. Nakaoka, and T. Maruhashi, “A novel type induction-heating single-ended resonant inverter using new bipolar Darlington-Transistor,” in 1985 IEEE Power Electronics Specialists Conference, Jun. 1985, pp. 590–599. [CrossRef]
Millán, D. Puyal, J. M. Burdío, O. Lucía, and C. M. De Luna, “IGBT Selection Method for the Design of Resonant Inverters for Domestic Induction Heating Keywords Method to measure the power losses,” vol. 1.
J. Acero et al., “The domestic induction heating appliance: An overview of recent research,” in 2008 Twenty-Third Annual IEEE Applied Power Electronics Conference and Exposition, Feb. 2008, pp. 651–657. [CrossRef]
T. Nishida, S. Moisseev, E. Hiraki, and M. Nakaoka, “Duty Cycle Controlled Soft Combutation High Frequency Inverter for Consumer Induction Cooker and Steaimer,” pp. 1846–1851, 1846.
V. Crisafulli and M. Antretter, “Design considerations to increase power density in induction cooking applications using the new Field stop II technology IGBTs,” PCIM Eur. 2015; Int. Exhib. Conf. Power Electron. Intell. Motion, Renew. Energy Energy Manag. Proc., no. May, pp. 19–21, 2015.
M. N. O. S. Charles K. Alexander, Fundamentals of Electric Circuits, 7th Editio. McGraw-Hill Education,.

Figure 1. General power transfer loop.

Figure 2. Single switch inverter (a) circuit diagram (b) circuit schematic.

Figure 3. General power transfer loop.

Figure 4. Circuit operating modes of single switch inverter.

Figure 5.

V_{C E}

voltage value variances in PSpice. (a)

R_{E Q} = 3 Ω

L_{E Q} = 80 μ H

and depending on

C_{R E S}

values. (b)

C_{R E S} = 270 n F

L_{E Q} = 80 μ H

and depending on

R_{E Q}

values. (c)

R_{E Q} = 3 Ω

C_{R E S} = 270 n F

depending on

L_{E Q}

values.

Figure 5.

V_{C E}

voltage value variances in PSpice. (a)

R_{E Q} = 3 Ω

L_{E Q} = 80 μ H

and depending on

C_{R E S}

values. (b)

C_{R E S} = 270 n F

L_{E Q} = 80 μ H

and depending on

R_{E Q}

values. (c)

R_{E Q} = 3 Ω

C_{R E S} = 270 n F

depending on

L_{E Q}

values.

Figure 6.

I_{T}

current value variances in PSpice. (a)

R_{E Q} = 3 Ω

L_{E Q} = 80 μ H

and depending on

C_{R E S}

values. (b)

C_{R E S} = 270 n F

L_{E Q} = 80 μ H

and depending on

R_{E Q}

values. (c)

R_{E Q} = 3 Ω

C_{R E S} = 270 n F

depending on

L_{E Q}

values.

Figure 6.

I_{T}

current value variances in PSpice. (a)

R_{E Q} = 3 Ω

L_{E Q} = 80 μ H

and depending on

C_{R E S}

values. (b)

C_{R E S} = 270 n F

L_{E Q} = 80 μ H

and depending on

R_{E Q}

values. (c)

R_{E Q} = 3 Ω

C_{R E S} = 270 n F

depending on

L_{E Q}

values.

Figure 7.

V_{D C}

and switch current

I_{T}

as a function of time for the case where the source voltage

V_{D C}

is the

D C

voltage source.

Figure 7.

V_{D C}

and switch current

I_{T}

as a function of time for the case where the source voltage

V_{D C}

is the

D C

voltage source.

Figure 8.

V_{D C}

and switch current

I_{T}

as a function of time for the case where the source voltage

V_{D C}

follows the mains voltage form.

Figure 8.

V_{D C}

and switch current

I_{T}

as a function of time for the case where the source voltage

V_{D C}

follows the mains voltage form.

Figure 9. Switch current

i_{T} (t)

as a function of time

t

Figure 9. Switch current

i_{T} (t)

as a function of time

t

Figure 10. Input power

P (t)

as a function of time

t

Figure 10. Input power

P (t)

as a function of time

t

Figure 11. Input voltage

V_{D C}

as a function of time

t

Figure 11. Input voltage

V_{D C}

as a function of time

t

Figure 12. Flowchart of proposed method to determine

L_{E Q}

R_{E Q}

I_{L E Q M A X}

and

V_{C E M A X}

Figure 12. Flowchart of proposed method to determine

L_{E Q}

R_{E Q}

I_{L E Q M A X}

and

V_{C E M A X}

Figure 13. Prototype simulation circuit for proposed converter.

Figure 14. Coil current

I_{L E Q}

and switch voltage

V_{C E}

for sweeped

R_{E Q}

values as a function of time

t .

Figure 14. Coil current

I_{L E Q}

and switch voltage

V_{C E}

for sweeped

R_{E Q}

values as a function of time

t .

Figure 15. Coil current

I_{L E Q}

as a function of time

t

obtained using the simulation circuit.

Figure 15. Coil current

I_{L E Q}

as a function of time

t

obtained using the simulation circuit.

Figure 16. Switch voltage

V_{C E}

as a function of time

t

obtained using the simulation circuit.

Figure 16. Switch voltage

V_{C E}

as a function of time

t

obtained using the simulation circuit.

Figure 17. General pan models are used with induction cookers.

Figure 18. Coil current

I_{L E Q}

as a function of time

t

obtained using the prototype circuit.

Figure 18. Coil current

I_{L E Q}

as a function of time

t

obtained using the prototype circuit.

Figure 19. IGBT collector emitter voltage

V_{C E}

as a function of time

t

obtained using the prototype circuit.

Figure 19. IGBT collector emitter voltage

V_{C E}

as a function of time

t

obtained using the prototype circuit.

Figure 20. Detailed waveforms obtained using the prototype circuit. Blue signal: IGBT collector emitter voltage

V_{C E}

(200V/div), Purple signal: coil current

I_{L E Q}

(10A/div), Yellow signal: IGBT gate control signal (5V/div).

Figure 20. Detailed waveforms obtained using the prototype circuit. Blue signal: IGBT collector emitter voltage

V_{C E}

(200V/div), Purple signal: coil current

I_{L E Q}

(10A/div), Yellow signal: IGBT gate control signal (5V/div).

Figure 21. Experimental setup.

Table 1. Calculating circuit parameters.

Pre-Defined Circuit Parameters
$T_{O N}$	$15 μ S$
$T_{O F F}$	$25 μ S$
$P_{A V G}$	$1275 W$
$V_{A C}$	$230 V A C$
$V_{D C 2}$	$325,27 V D C$
Calculated Circuit Parameters
$P_{A V G 2}$	$1275 W$
$P_{A V G 2 - M A X}$	$2002,77 W$
$P_{M A X 2}$	$10681,42 W$
$I_{T M A X 2}$	$32,84 A$
$a_{0}$	$121,97$
$a_{1}$	$73,21$
$b_{1}$	$176,75$
$A_{1}$	$191,31$
$R_{E Q}$	$5,83 Ω$
$L_{E Q}$	$98,5 μ H$
$T_{R E S}$	$33,33 μ S$
$f_{R E S}$	$30 k H z$
$ω_{d}$	$188495,56$
$α$	$29570,68$
$⍵_{0}$	$190800,95$
$C_{R E S}$	$278,86 n F$
Calculated Boundary Conditions
$I_{L E Q M A X}$	$33,57 A$
$V_{C E M A X}$	$834,49 V$

Table 2. Simulation circuit results.

Input Circuit Parameters		Output Boundary Parameters		Output Power
$R_{E Q}$	$L_{E Q}$	$C_{R E S}$	$I_{L E Q M A X}$	$V_{C E M A X}$	$P_{A V G 2}$
$4,0 Ω$	$98,5 μ H$	$278,86 n F$	$34,20 A$	$852 V$	$1060 W$
$4,1 Ω$	$98,5 μ H$	$278,86 n F$	$34,00 A$	$846 V$	$1080 W$
$4,2 Ω$	$98,5 μ H$	$278,86 n F$	$33,80 A$	$842 V$	$1100 W$
$4,3 Ω$	$98,5 μ H$	$278,86 n F$	$33,60 A$	$835 V$	$1110 W$
$4,4 Ω$	$98,5 μ H$	$278,86 n F$	$33,40 A$	$832 V$	$1120 W$
$4,5 Ω$	$98,5 μ H$	$278,86 n F$	$33,30 A$	$826 V$	$1130 W$
$4,6 Ω$	$98,5 μ H$	$278,86 n F$	$33,10 A$	$821 V$	$1140 W$
$4,7 Ω$	$98,5 μ H$	$278,86 n F$	$32,90 A$	$815 V$	$1150 W$
$4,8 Ω$	$98,5 μ H$	$278,86 n F$	$32,70 A$	$810 V$	$1155 W$
$4,9 Ω$	$98,5 μ H$	$278,86 n F$	$32,50 A$	$805 V$	$1160 W$
$5,0 Ω$	$98,5 μ H$	$278,86 n F$	$32,30 A$	$800 V$	$1165 W$
$5,1 Ω$	$98,5 μ H$	$278,86 n F$	$32,10 A$	$795 V$	$1170 W$
$5,2 Ω$	$98,5 μ H$	$278,86 n F$	$31,90 A$	$790 V$	$1180 W$
$5,3 Ω$	$98,5 μ H$	$278,86 n F$	$31,75 A$	$785 V$	$1190 W$
$5,4 Ω$	$98,5 μ H$	$278,86 n F$	$31,60 A$	$780 V$	$1200 W$
$5,5 Ω$	$98,5 μ H$	$278,86 n F$	$31,45 A$	$775 V$	$1210 W$
$5,6 Ω$	$98,5 μ H$	$278,86 n F$	$31,20 A$	$770 V$	$1215 W$
$5,7 Ω$	$98,5 μ H$	$278,86 n F$	$31,05 A$	$765 V$	$1220 W$
$5,8 Ω$	$98,5 μ H$	$278,86 n F$	$30,85 A$	$760 V$	$1225 W$
$5,9 Ω$	$98,5 μ H$	$278,86 n F$	$30,70 A$	$755 V$	$1230 W$
$6,0 Ω$	$98,5 μ H$	$278,86 n F$	$30,50 A$	$750 V$	$1235 W$

Table 3. Technical specifications of the reference induction coil.

Parameter	Symbol	Value	Unit
Number of turns	$n$	28
External diameter of the coil	$a_{n}$	180	mm
Inner diameter of the coil	$a_{1}$	30	mm
Distance between coil winding and ferrite bars	$h$	4	mm
Distance between coil winding and pan	$d$	4	mm
Strand amount of a litz wire		66
Wire diameter of single strand		0,27	$m m$
Ferrite permeability	$µ_{r}$	800
Equivalent inductance with no load	$L_{E Q N o L o a d}$	110	µH
Equivalent resistance with no load	$R_{E Q N o L o a d}$	0,12	$Ω$
Equivalent inductance with cast iron pan	$L_{E Q P a n}$	89,76	µH
Equivalent resistance with cast iron pan	$R_{E Q P a n}$	4,21	$Ω$
Equivalent inductance with stainless steel pan	$L_{E Q P a n}$	81,81	µH
Equivalent resistance with stainless steel pan	$R_{E Q P a n}$	3,36	$Ω$
Equivalent inductance with silit silargan pan	$L_{E Q P a n}$	69,07	µH
Equivalent resistance with silit silargan pan	$R_{E Q P a n}$	2,48	$Ω$

Table 4. Experimental circuit results.

Input Circuit Parameters		Output BoundaryParameters		Output Power
$R_{E Q}$	$L_{E Q}$	$C_{R E S}$	$I_{L E Q M A X}$	$V_{C E M A X}$	$P_{A V G 2}$
$4,21 Ω$	$89,76 μ H$	$270 n F$	$42,4 A$	$928 V$	$1276 W$
$3,36 Ω$	$81,81 μ H$	$270 n F$	$42,8 A$	$968 V$	$1270 W$
$2,48 Ω$	$69,07 μ H$	$270 n F$	$45,6 A$	$920 V$	$1255 W$

Table 5. Comparison of the calculation, simulation, and experimental circuit results.

Input Circuit Parameters		Output BoundaryParameters		Output Power
$R_{E Q}$	$L_{E Q}$	$C_{R E S}$	$I_{L E Q M A X}$	$V_{C E M A X}$	$P_{A V G 2}$
$C a l c u l a t i o n R e s u l t s$
$5,83 Ω$	$98,5 μ H$	$278,86 n F$	$33,57 A$	$834,49 V$	$1275 W$
$S i m u l a t i o n R e s u l t s$
$4,3 Ω$	$98,5 μ H$	$278,86 n F$	$33,60 A$	$835 V$	$1110 W$
$5,8 Ω$	$98,5 μ H$	$278,86 n F$	$30,85 A$	$760 V$	$1225 W$
$E x p e r i m e n t a l R e s u l t s$
$4,21 Ω$	$89,76 μ H$	$270 n F$	$42,4 A$	$928 V$	$1276 W$
$3,36 Ω$	$81,81 μ H$	$270 n F$	$42,8 A$	$968 V$	$1270 W$
$2,48 Ω$	$69,07 μ H$	$270 n F$	$45,6 A$	$920 V$	$1255 W$

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A Simplified Design Method for Quasi Resonant Inverter Used in Induction Hob

Abstract

1. Introduction

2. Circuit Description

2.1. Circuit Operating Modes – Waveform Equations

2.2. Safe Operating Area for Quasi Resonant Inverter

3. Proposed Design Method For Quasi Resonant Inverter

3.1. Defining of the Time Intervals T O N and T O F F , the Source Voltage V D C and the Input Power P A V G :

3.2. Calculation of the Maximum Coil Current I L E Q M A X :

3.3. Calculation of R L E Q Value by Determining the 1st Harmonic Component of The DC Voltage:

3.4. Calculation of the Equivalent Inductance Value L E Q :

3.4.1. L E Q calculation using series R L circuit switch current i T value:

3.4.2. L E Q calculation using inductor voltage V L E Q value:

3.4.3. L E Q calculation using inductor energy W L E Q value:

3.5. Determination The Series RLC Circuit Parameters:

3.6. Calculation of the Resonant Circuit Capacitor Value Inductance Value C R E S :

3.7. Calculation of Current and Voltage Boundary Conditions of Semiconductor Switch:

3.8. The Flowchart of the Proposed Design Method

4. Verification of Proposed Analysis Method

4.1. Calculation Results

4.2. Simulation Results

4.3. Experimental Results

5. Conclusions

Author Contributions

Funding

Data Availability Statement

Acknowledgments

Conflicts of Interest

References

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3.1. Defining of the Time Intervals $T_{O N}$ and $T_{O F F}$ , the Source Voltage $V_{D C}$ and the Input Power $P_{A V G}$ :

3.2. Calculation of the Maximum Coil Current $I_{L E Q M A X}$ :

3.3. Calculation of $R_{L E Q}$ Value by Determining the 1st Harmonic Component of The DC Voltage:

3.4. Calculation of the Equivalent Inductance Value $L_{E Q}$ :

3.4.1. $L_{E Q}$ calculation using series $R L$ circuit switch current $i_{T}$ value:

3.4.2. $L_{E Q}$ calculation using inductor voltage $V_{L E Q}$ value:

3.4.3. $L_{E Q}$ calculation using inductor energy $W_{L E Q}$ value:

3.6. Calculation of the Resonant Circuit Capacitor Value Inductance Value $C_{R E S}$ :