SLVUBB4 User guide | TI.com

SLVUBB4B November 2017 – February 2023

12.2.4 Transfer Function CMC Boost Power Stage

Equation 68.

\frac{{\hat{v}}_{o u t}}{{\hat{v}}_{c}} = \frac{K_{m} \times (1 - D) \times (1 - \frac{Z_{L}}{{(1 - D)}^{2} \times R_{o u t}})}{{(1 - D)}^{2} + \frac{Z_{L}}{Z_{o u t}} + K_{m} \times R_{i} \times H (s) \times (\frac{1}{R_{o u t}} + \frac{1}{Z_{o u t}}) + K \times K_{m} \times (1 - D) \times (1 - \frac{Z_{L}}{{(1 - D)}^{2} \times R_{o u t}})}

Duty cycle:

Equation 42.

D = \frac{V_{o u t} - V_{i n}}{V_{o u t}}

DC-Gain:

Equation 43.

K_{m} = \frac{1}{{(0.5 - D) \times R}_{s} \times A_{s} \times \frac{1}{f_{s w i t c h} \times L} + \frac{V_{s l o p e}}{V_{i n}}}

Equation 44.

K = {0.5 \times R}_{s} \times A_{s} \times \frac{1}{f_{s w i t c h} \times L} \times D \times (1 - D)

Sampling Gain Pole:

Equation 45.

ω_{L} = π \times f_{s w i t c h}

Equation 46.

R_{i} = A_{s} \times R_{s}

Equation 47.

H (s) = 1 + \frac{s}{Q_{L} \times ω_{L}} + \frac{s^{2}}{{ω_{L}}^{2}}

With V_slope:

Equation 48.

s_{e} = V_{s l o p e} \times f_{s w i t c h}

With SLM:

s_{e} = \frac{S L M \times V_{o u t} \times A_{s} \times R_{s}}{L}

s_{n} = \frac{V_{i n} \times A_{s} \times R_{s}}{L}

Equation 49.

Q_{L} = \frac{1}{π \times [(1 + \frac{s_{e}}{s_{n}}) \times (1 - D) - 0.5]}