AN2450 datasheet(4/35 Pages) STMICROELECTRONICS

4 / 35 page

FHA circuit model

AN2450

4/35

DocID12784 Rev 6

FHA circuit model

The FHA approach is based on the assumption that the power transfer from the source to

the load through the resonant tank is almost completely associated to the fundamental

harmonic of the Fourier expansion of the currents and voltages involved. This is consistent

with the selective nature of resonant tank circuits.

Figure 1. LLC resonant half-bridge converter

The harmonics of the switching frequency are then neglected and the tank waveforms are

assumed to be purely sinusoidal at the fundamental frequency: this approach gives quite

accurate results for operating points at and above the resonance frequency of the resonant

tank (in the continuous conduction mode), while it is less accurate, but still valid, at

frequencies below the resonance (in the discontinuous conduction mode).

It is worth pointing out also that many details of circuit operation on a cycle-to-cycle time

base will be lost. In particular, FHA provides only a necessary condition for MOSFETs' zero-

voltage switching (ZVS) and does not address secondary rectifiers' natural ability to work

always in zero-current switching (ZCS). A sufficient condition for Power MOSFETs' ZVS will

be determined in Section 3: ZVS constraints on page 16 still in the frame of FHA approach.

Let us consider the simple case of ideal components, both active and passive.

The two Power MOSFETs of the half-bridge in Figure 1 are driven on and off symmetrically

with 50% duty cycle and no overlapping. Therefore the input voltage to the resonant tank

vsq(t) is a square waveform of amplitude Vdc, with an average value of Vdc/2. In this case the

capacitor Cr acts as both resonant and dc blocking capacitor. As a result, the alternate

voltage across Cr is superimposed to a dc level equal to Vdc/2.

The input voltage waveform vsq(t) of the resonant tank in Figure 1 can be expressed in

Fourier series:

Equation 1

Rout

Vdc

n:1

Input source

Resonant

tank

Ideal

transformer

Uncontrolled

rectifier

Low-pass

filter

Load

Cout

Controlled

Switch Network

Vout

Irt

vsq t

Vdc

---------



---Vdc

---

135.





f

swt



sin

.…

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