# Induction Coil Design Considerations for High-Frequency Domestic Cooktops
## 2 Equivalent Circuit of Induction Heating  
Domestic induction cooking systems basically consist of a power converter, which produces high-frequency oscillating voltage, and induction coils. An induction coil produces a magnetic field due to the high-frequency current flowing through it. This changing magnetic field induces eddy currents at the base of the ferromagnetic pan. The basic structure of a domestic induction cooking system is shown in Figure 1.  
In Figure 1, a full-bridge rectifier is used to obtain DC voltage from the AC network. An IGBT (insulated gate bipolar transistor) is used as a semiconductor power switch. The switches are positioned in a half-bridge configuration. 'HS IGBT' represents the upper switch, while 'LS IGBT' represents the lower switch. 'Snubber Cap' represents the film capacitor used in the passive snubber cell. In contrast, 'Resonance Cap' represents the resonance capacitors used to create high-frequency sinusoidal oscillation, and film capacitors are generally preferred. A 'DC Bus Cap' capacitor is used to suppress high-frequency noises that will occur in the rectified AC voltage, and low-value (3-5 \(\mu\)F) film capacitors are preferred. When industrial and domestic induction heating systems are analyzed, the pan-induction coil structure is modeled as an equivalent series inductance and resistance. In the literature, induction heating systems are modeled as magnetically coupled circuits. The primary side consists of a power circuit and a resonance tank. The power circuit applies a square wave to the resonance tank. The fundamental harmonic of this voltage is calculated by using the first harmonic approximation method. The resonance tank consists of an equivalent resonance capacitor and an induction coil. The secondary side consists of the inductance and resistance of the pot used. The electrical equivalent circuits are shown in Figure 2.  
V\({}_{\text{pri}}\) voltage is the first harmonic component of the switching node voltage, as shown in Figure 3. It is produced by rectifying the main voltage after it is modulated by the half-bridge converter. This modulated voltage is directly applied to the resonant tank, which consists of C\({}_{\text{eq}}\) and L\({}_{\text{coil}}\). Figure 1: Domestic induction heating system structures. Figure 2: Electrical equivalent circuit of induction heating systems. The capacitor \(\rm C_{eq}\) represents the equivalent of the resonant capacitors used in the power converter. The inductance \(\rm L_{coil}\) represents the inductance value of the induction coil used, while the inductance \(\rm L_{pan}\) represents the inductance of the pot used. The resistance \(\rm R_{pan}\) represents the resistance of the pot used. The current on the primary side is represented as \(\rm I_{coil}\), while the current induced in the pot base is represented as \(\rm I_{pan}\). The mutual inductance in these two magnetically coupled circuits is represented as \(\rm M\). The primary and secondary side circuit equations are shown in (1) and (2), respectively. \[-\rm V_{pri}+\rm Z_{pri}\rm I_{pri}+\rm j\omega L_{pri}\rm I_{pri}-\rm j\omega M _{sec}=0 \tag{1}\]  
\[\rm Z_{sec}\rm I_{sec}+\rm j\omega L_{sec}\rm I_{sec}-\rm j\omega M_{pri}=0 \tag{2}\]  
To analyze the circuit, secondary side impedances are reduced to the primary side to analyze the equivalent circuit, as shown in (3). \[\rm V_{pri}-\rm I_{pri}\left(\left(Z_{pri}+\rm j\omega L_{pri}\right)+\frac{ \omega^{2}M^{2}}{\left(Z_{sec}+\rm j\omega L_{sec}\right)}\right) \tag{3}\]  
As can be seen in (3), the equivalent primary side impedance consists of the primary side self-impedance and the reflected impedance. The reflected impedance is determined by switching frequency, electrical characteristics of the pan, and magnetic coupling between them. The switching frequency determines the resistance of the ferromagnetic pan due to the skin effect phenomenon. \(\rm L_{pan}\) depends on the material used at the base of the pan. The magnetic coupling is determined by the air gap.