AN2450 datasheet(5/35 Pages) STMICROELECTRONICS

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DocID12784 Rev 6

5/35

AN2450

FHA circuit model

whose fundamental component vi.FHA(t) (in phase with the original square waveform) is:

Equation 2

where fsw is the switching frequency. The rms value Vi.FHA of the input voltage fundamental

component is:

Equation 3

As a consequence of the above mentioned assumptions, the resonant tank current irt(t) will

be also sinusoidal, with a certain rms value Irt and a phase shift  with respect to the

fundamental component of the input voltage:

Equation 4

This current lags or leads the voltage, depending on whether inductive reactance or

capacitive reactance dominates in the behavior of the resonant tank in the frequency region

of interest. Irrespective of that, irt(t) can be obtained as the sum of two contributes, the first

in phase with the voltage, the second with 90° phase-shift with respect to it.

The dc input current Ii.dc from the dc source can also be found as the average value, along

a complete switching period, of the sinusoidal tank current flowing during the high-side

MOSFET conduction time, when the dc input voltage is applied to the resonant tank:

Equation 5

where Tsw is the time period at switching frequency.

The real power Pin, drawn from the dc input source (equal to the output power Pout in this

ideal case) can now be calculated as both the product of the input dc voltage Vdc times the

average input current Ii.dc and the product of the rms values of the voltage and current's first

harmonic, times cos

 :

Equation 6

the two expressions are obviously equivalent.

The expression of the apparent power Papp and the reactive power Pr are respectively:

Equation 7

viFHA t



---Vdc

f

swt



sin

viFHA



-------Vdc

irt t

2Irt

f

swt



–



sin

2Irt



cos

f

swt



2Irt

–

sin



f

swt



cos



sin

Iidc

Tsw

---------

irt t t



-------Irt



cos

Tsw

---------



VdcIidc ViFHAIrt



cos

Papp

ViFHAIrt



sin

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