Coil design for induction cooking system

Question

I am designing an induction heating circuit using a half bridge, series resonant circuit. Wildly simplified schematic follows (will use IGBTs instead of MOSFETs for the final design, but they were not available in the schematic editor):

^{simulate this circuit – Schematic created using CircuitLab}

L1 will be the induction heating coil, using a spiral geometry similar to this:

The basic theory is explained in lots of materials around the web such as this old ST application note.

Given a value for L1, and a desired switching frequency \$f\$ (say 20-30 kHz), one can calculate a value for C using $$ f = \frac{1}{2 \pi \sqrt{L_1 C}} $$

From there we can take \$C_2 = C_3 = C/2\$. The actual switching frequency should be safely above resonance so as to ensure the circuit works in the inductive area.

Of course, all of this assumes that a value of \$L_1\$ is given, and this is the part where I am stuck. I've been searching the internet as well as academic papers, but so far I haven't found a design procedure detailing how to select \$L_1\$ so as to achieve the desired heating power.

In principle I could just build an inductor of the desired physical size (say 20 cm of diameter), measure it with an LCR meter, and then select \$C_2\$ and \$C_3\$ according to the procedure above. However, say I build this circuit and it doesn't achieve the desired heating power; then what should I do next? Increase the physical size of the inductor? Increase/decrease inductance (with a corresponding adjustment in the capacitor to maintain the switching frequency constant)?

In summary: how should I go about actually designing/engineering the induction heating coil, rather than just applying blind trial and error?

Answer 1

You should use one additional inductor Lr (L resonant) in series, both capacitor C2 and C3 could be also marked as Cr. Then, in your formula L1C becomes LrCr.

L1 should have just minimum effect on resonant frequency L1 << Lr.

However if you don't want to use additional Lr, then the resonant frequency is dependant of the load applied. The inductor acts like a tranformer N:1, where the N is the equvalent number of primary turns (coli) and 1 is the secondary single turn (the pot). The load (resitance of the pot) is connected to the secondary. Depending of the load applied (different pot) also the resonating frequncy will change, therefore you need to have a switching device capable of measuring phase difference between voltage and current and adapt the frequency. If you want to stay above resonating frequency then you could acheive this by having a setpoint in a phase angle, this is done with PLL. Some induction heating devices use PLL, you can also check tesla coil builders forum as they alsu use this self resonant (quasi resonant) techniques.