AN892 Datasheet, PDF (3/16 Pages) Silicon Laboratories – DESIGN GUIDE FOR ISOLATED DC/DC USING THE

AN892
2.1. S1 Closed, S2 Open
V_IN is applied to the series combination of C1 and inductance L_m + L_lkg. As a result, current flows through
inductance Lm + L_lkg in a linear fashion.
V_IN – V_C1 = L_m + L_lkg  -^l-^m----^--^R--_t--_SI--^P-₁--^P----^L---^E-
Equation 1.
Where I_m,RIPPLEis the magnetizing current ramp during t_S1 and t_S1 is the time that S1 is closed.
2.2. S1 Open, S2 Closed
In this mode, a resonant tank circuit formed by C1, L_m, and L_lkg, and -V_C1 is applied across L_m + L_lkg. The resonant
tank causes the current through leakage inductance to rise as a sinusoid while the voltage at the secondary
impressed on the primary causes the current through the primary to reduce in a linear fashion. When l_lkg  l_m, the
difference current (I_m-I_lkg) flows out of the dot on the primary side of the ideal transformer. Therefore current must
flow into the dot on the secondary side and through the diode. Governing current equations are
l_{--m------R--t-S-I--P-2--P----L---E- =} –---_L-V_{---m-O---N-U----T-}
Equation 2.
I_Llkgt = I_m  sin _rt
Equation 3.
_r
=
-------------¹---------------
L_lkg  C1
Equation 4.
where N and t_S2 are primary to secondary turns ratio and time that S2 is closed respectively. _r is the resonance
tank frequency in rads/s.
The current through the diode in the secondary can be written as the difference of l_lkg and l_m scaled by the
transformer turns ratio.
I_D1 = -^l-^l-^m------–_N----^I--^l--^k--^g-
Equation 5.
As the sinusoidal current returns to match the magnetizing current, the resonance ceases and consequently no
current will flow from the dot on the primary or through the secondary into the diode.
2.3. Voltage Transfer
Let duty cycle D be defined as the ratio of time S1 is closed over the complete switching period T_SW:
D = -_t-_S----₁--^t--^S_+---¹--_t--_S---₂-
Equation 6.
Rev. 0.1
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