AN892 Datasheet, PDF (10/16 Pages) Silicon Laboratories – DESIGN GUIDE FOR ISOLATED DC/DC USING THE

AN892
Typically, R_LOAD << (R5 + R6) and gm_p is approximately 3/N. The DC gain in P-mode simplifies to:
A_DC·_{ P}  –⁵----⁰---^x----¹---⁰-_R---³--₅--^---_--³---_NR-----^L---^O----^A---^D--
Equation 31.
Notice that the DC gain of P mode is proportional to R_LOAD and inversely proportional to R5. At heavy loads (small
R_LOAD), a very large R5 could significantly increase the output voltage error as the DC gain reduces. Conversely, a
very small R5 increases power consumption and gm_fb variability due to higher dependency on gm_ea, which can
significantly vary more than 1/(R5||R6) over temperature or from part to part. The total duration of this mode is
approximately 7ms.
3.3. Proportional Integral Mode
After P-mode, the controller switches to PI-mode, the steady state and final operation mode. During this mode of
operation, the error amplifier drives an impedance that consists of the series combination of resistor R7 and
capacitor C11. To achieve a smooth transition between P and PI modes, it is recommended to set R7 to match
R_INT R7 and C11 are connected to the COMP pin.
.
R7 = R_INT  50x10³
In PI-mode, the loop transfer is given by:
Equation 32.
where
H_PIs = A_{DC PI}---₁-----+------_------^-_s-p----¹--₁----_-+---_--^{-------}_^s--^z---₁^---1----^-+-----_{-------s}--_p------₂----_-
Equation 33.
_p1  -_R----_o---_--_g---_m--¹--_f--_b---_C----₁----₁--
Equation 34.
_z1  _R-----₇----^1C-----₁---₁--
Equation 35.
_p2  -_R----_L---_O----_A--¹-_D----_C-----₁---₀--
Equation 36.
A_{DC PI} = –^R-----^o---^--^g---^m----^f--^b---^gR---^m--₅----^p---^R----^L---^O----^A----^D-
Equation 37.
Notice that the loop transfer function in PI-Mode has an additional pole-zero pair when compared with P-Mode. In
addition, the loop DC-gain is much higher in PI-Mode than in P-Mode due to R_o,gmfb>>R_INT.
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