JAJSQK4 データシート

JAJSQK4 November 2023 LM25185

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8.2.1.2.10 Compensation Components

Choose compensation components for a stable control loop using the procedure outlined as follows.

First, calculate the power stage transfer function with Equation 26. L_mag is the magnetizing inductance of the transformer. C_out is the output capacitance. R_load is the load resistance.

Equation 26.

G_{p w} (s) = A_{M} \times A_{C S} \times \frac{(1 - \frac{s}{ω_{z R H P}}) (1 + \frac{s}{ω_{z E S R}})}{1 + \frac{s}{ω_{p}}}

where

Equation 27.

A_{M} = \frac{R_{l o a d} \times N_{p s} \times (1 - D)}{2 \times (1 + D)}

Equation 28.

A_{C S} = \frac{1}{10 \times R_{C S}}

Equation 29.

ω_{z R H P} = \frac{{(1 - D)}^{2}}{D} \frac{R_{l o a d} \times N_{p s}^{2}}{L_{m a g}}

Equation 30.

ω_{z E S R} = \frac{1}{C_{o u t} \times R_{E S R}}

Equation 31.

ω_{p} = \frac{1 + D}{C_{o u t} \times R_{l o a d}}

Next, use Equation 32 to calculate the power stage gain at the cross-over frequency F_co which is selected to be 1 kHz for this design.

Equation 32.

G a i n (F_{c o}) = 20 \times \log (|G_{p w} (2 j \times π \times F_{c o})|)

Select R_COMP to satisfy the desired cross-over frequency.

Equation 33.

R_{C O M P} = \frac{10^{- \frac{G a i n (F_{c o})}{20}}}{g_{m}} R_{F B} \frac{100 μA}{V_{r e f}}

Select C_COMP to set the compensator zero at 2 times of the load pole.

Equation 34.

C_{C O M P} = \frac{1}{2 \times ω_{p} \times R_{C O M P}}

Select C_HF to set the compensator pole at 50 to 200 times the compensator zero.

Equation 35.

C_{H F} = \frac{C_{C O M P}}{150}

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8.2.1.2.10 Compensation Components