AN2450 datasheet(14/35 Pages) STMICROELECTRONICS

14 / 35 page

Voltage gain and input impedance

AN2450

14/35

DocID12784 Rev 6

By imposing that the imaginary part of Zn(fn, , Q) is zero (which means imposing that Zin

has zero phase angle, as Zo is real and does not affect the phase), we can find the

boundary condition between capacitive and inductive mode operation of the LLC resonant

converter.

The analytical results are the following:

Equation 32

Equation 33

where fnZ represents the normalized frequency where, for a fixed couple (- Q), the input

resonant tank impedance is real (and only real power is absorbed from the source); while

QZ is the maximum value of the quality factor, below which, at a fixed normalized frequency

and inductance ratio (fn - ) the tank impedance is inductive; hence, the maximum voltage

gain available in that condition is also found:

Equation 34

By plotting the locus of operating points [MMAX(, Q), fnZ(,Q)], whose equation on M - fn

plane is the following:

Equation 35

we can draw the borderline between capacitive and inductive mode in the region between

the two resonance frequencies, shown in Figure 6. It is also evident that the peak value of

the gain characteristics for a given quality factor Q value, already lies in the capacitive

region.

fnZ  Q





 1 



–

 1 



–



22

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

QZ fn 







1fn

–

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



----



 2

–

MMAX  Q





MfnZ  Q 

 Q







MZ fn 





2 1 

 

–

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