AN2450 datasheet(13/35 Pages) STMICROELECTRONICS

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DocID12784 Rev 6

13/35

AN2450

Voltage gain and input impedance

Figure 5. Normalized input impedance magnitude

The ac analysis can also help to estimate converter's efficiency

and predict how this

changes with the load. Considering the generic model similar to the one in Figure 2 on

page 7, where the resonant tank includes also the dissipative elements (i.e. series resistors

for magnetic components winding losses and capacitor's ESR, and parallel resistors for

magnetic losses of inductors and transformer), we can compute the transfer function

HLOSS(j) and the input impedance Zin.LOSS(j). By calculating input and output power in

terms of HLOSS and Zin.LOSS, we get:

Equation 29

where Yin.LOSS is the admittance (reciprocal of Zin.LOSS) and the input and output power are

expressed as:

Equation 30

Equation 31

The region on the left-hand side of the diagram in Figure 5, i.e. for a normalized frequency

lower than fno, is the capacitive region, where the tank current leads the half-bridge square

voltage; at normalized frequency higher than the resonance frequency fnr (= 1), on the right-

hand side region, the input impedance is inductive, and the resonant tank current lags the

input voltage. In the region between the two resonance frequencies the impedance can be

either capacitive or inductive, depending on the value of the impedance phase angle.



Pout

-----------

HLOSS j



RoacRe YinLOSS j





-----------------------------------------------------------

ViFHAIrt



cos

ViFHA

2Re

ZinLOSS j



--------------------------------

Pout

VoFHA



Irect

oFHA



Roac



-----------------------

iFHA

Roac



------------------

 H

LOSS j



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