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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 6, DECEMBER 2007

Design of the L-LC Resonant Inverter for Induction Heating Based on Its Equivalent SRI
José M. Espí Huerta, Member, IEEE, Enrique J. Dede García Santamaría, Member, IEEE, Rafael García Gil, and Jaime Castelló Moreno

Abstract—This paper presents the new L-LC induction heating generator and probes that, inresonance, are equivalent to a series resonant inverter. This equivalence is then used to compare both topologies, extracting the advantages and disadvantages of the L-LC usage. In addition, based on this equivalence, a design procedure is proposed that covers all possible L-LC configurations. Finally, some experimental results are presented, showing waveforms during normal and short-circuitoperation. Index Terms—Active transformer, hybrid series–parallel resonant inverter (L-LC), parallel resonant inverter (PRI), reactive transformer, series resonant inverter (SRI).

I. I NTRODUCTION NDUCTION heating generators are resonant inverters in which the resonant tank is formed by the heating coil and a capacitor, in a series resonant inverter (SRI) [1]–[3] or in a parallel resonant inverter (PRI)[4]–[7]. They are used to heat metals to be welded, melted, or hardened. Their mission is to create a very intense alternating current through the heating coil, where the working piece is introduced. The magnetic fields created induce surface Foucault currents on the piece that are heating it up. The loaded heating coil is equivalent to an inductance L with a series resistance R, representing theohmic losses on the piece. Previous works on induction heating reveal that the threeelement L-LC oscillator [8]–[13] can offer a better performance than the traditional SRI, particularly due to its short-circuit immunity and lower transformer secondary current. This paper reviews the most relevant L-LC properties [14] and shows that the L-LC (if it is well designed) behaves equivalently to an SRI.This equivalence is then used to compare the L-LC with the SRI, to determine the conditions under which the L-LC performs better than the SRI, as well as to design the L-LC in an intuitive manner. II. A NALYSIS OF THE L-LC R ESONANT C IRCUIT Fig. 1 shows the full-bridge configuration of the L-LC resonant inverter for induction heating. Substituting the heating coil and the piece by its equivalentL–R series network results in the L-LC oscillator, as depicted in Fig. 2.

I

Fig. 1. L-LC resonant inverter in full-bridge configuration.

Fig. 2. L-LC oscillator with isolation transformer and heating coil L–R series equivalent network.

A. L-LC Impedance The L-LC impedance Z, as seen from the secondary side of the isolation transformer (Fig. 2), is Z(s) = Lω0 (β + 1)
s ω0 3

+

1 Qs ωp

s ω0 2

2

+
1 Qp

s ω0 s ωp

+ +1

1 (β+1)Q

(1)

+

where s is the Laplace variable, β = Ls /L, and ω0 is the resonant frequency of the L-LC shown in the following: 1 ω0 = √ Le C (2)

with Le = Ls L, ωp is the resonant frequency of the parallel ending of the L-LC shown in the following:
Manuscript received September 20, 2005; revised June 26 2007. The authors arewith the Department of Electrical Engineering, University of Valencia, 46100 Valencia, Spain (e-mail: Jose.M.Espi@uv.es). Digital Object Identifier 10.1109/TIE.2007.905928 0278-0046/$25.00 © 2007 IEEE

ωp = √

1 LC

(3)

ESPÍ HUERTA et al.: DESIGN OF THE L-LC RESONANT INVERTER FOR INDUCTION HEATING

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Fig. 4. Trigonometric relationship between oscillator parameters (Q and β) andperformance (φ and Hi ).

B. Heating Power The L-LC power control is typically carried out by means of switching frequency variation above ω0 [9], where the circuit is inductive. The maximum power is delivered at ω0 with minimum switching angle φ (Fig. 3), and the power reduces as the frequency increases. The isolation transformer adapts the oscillator impedance so that the power at ω0 is set at...