# Induction Coil Design Considerations for High-Frequency Domestic Cooktops
## 2 Equivalent Circuit of Induction Heating
After the manipulation of the reflected impedance equation shown in (4), the effects of reflected impedance on both resistance and inductance are shown mathematically in (5) and (6). In domestic induction cookers, the increasing resonance frequency affects the equivalent inductance and resistance formed on the primary side. The equivalent inductance value formed decreases with the increasing resonance frequency, while the equivalent resistance increases. The important point here is that the equivalent inductance value determines the switching frequency together with the resonant capacitor, while the equivalent resistance value determines the value of the power to be transferred to the load. If the equivalent resistance value is too high, it limits the power to be transferred to the load, while if it is too low, it causes very high current to  
Figure 3: Switching node voltage and equivalent circuit input voltage (\(\rm V_{pri}\)). pass through the induction coil and high switching losses to transfer the desired power to the load. Therefore, these equivalent inductance and resistance values are very important. \[Z_{\text{ref}}=\frac{\omega^{2}\text{M}^{2}}{\left(\text{R}_{\text{pan}}+\text{ j}\omega\text{L}_{\text{pan}}\right)} \tag{4}\]  
Figure 2.0  
Figure 2.1  
The mutual inductance between the primary and secondary sides is determined by the air gap. The mathematical representation of mutual inductance is shown in (7). Increasing the air gap used in the induction coil decreases the equivalent resistance and increases the equivalent inductance. Decreasing the air gap increases the equivalent resistance and decreases the equivalent inductance. In induction heating systems, the power to be transferred to the metal is determined by the equivalent resistance, while the switching frequency is determined by the equivalent inductance. Decreasing the air gap will generally increase the equivalent resistance and limit the power transfers, while increasing the air gap will decrease the equivalent resistance and make the power transfer inefficient. However, decreasing the air gap in metals such as cast-iron pots makes power transfer more difficult, while in aluminum pots it makes power transfer more efficient. Figure 2.2  
After an equivalent circuit is constructed, all electrical parameters can be obtained as shown in Figure 2.3  
Figure 2.4 All electrical parameters: (**a**) input power; (**b**) input current; (**c**) equivalent resistance; (**d**) equivalent inductance. All calculations are implemented under \(\text{C}_{\text{eq}}=\) 1360 nF, \(\text{L}_{\text{eq}}=\) 65 uH, and \(\text{V}_{\text{DC}}=\) 325 V conditions. The material of the pot used in induction cookers directly affects the amount of power to be transferred and the performance. If pots that respond to the magnetic field, such as cast-iron pots, are used, the equivalent resistance and inductance values on the primary side increase. If metals that do not respond to the magnetic field, such as aluminum, are used, the equivalent resistance and inductance on the primary side will decrease significantly. The decrease in equivalent inductance requires high switching frequencies, while low equivalent resistance causes high switching losses. Figure 5 shows the actual LCR (inductance capacitance resistance) meter measurements with a cast-iron pan on a 210 mm induction coil. An induction coil with an inductance value of 65 uH is used. The coil consists of a sectional winding. While the inner windings are 13 turns, the value windings are 10 turns. An induction heating application is quite difficult to model since it contains many non-linear components. In applications, current and voltage measurements taken from the power converter circuit are used to find the values reflected on the primary side.