SLVUBB4 User guide

SLVUBB4B November 2017 – February 2023

12.2.6 Transfer Function CMC Forward Power Stage

For interleaved topologies like Push-Pull, Half-Bridge, or Full-Bridge, twice as much FET switching frequency must be used for calculations because the output inductor "sees" twice the FET switching frequency.

Equation 59.

\frac{{\hat{v}}_{o u t}}{{\hat{v}}_{c}} = \frac{K_{m} \times Z_{o u t} \times \frac{N_{s}}{N_{p}}}{Z_{L} + Z_{o u t} + K_{m} \times R_{i} \times \frac{N_{s}}{N_{p}}}

Duty cycle:

Equation 60.

D = \frac{V_{o u t} \times \frac{N_{p}}{N_{s}}}{V_{i n}}

DC-Gain:

Equation 61.

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

Sampling Gain Pole:

Equation 62.

ω_{L} = π \times f_{s w i t c h}

Equation 63.

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

Equation 64.

A_{s} = \frac{1}{N^{'}}

N' is the turns ratio between auxiliary and primary winding.

Equation 65.

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

With V_slope:

Equation 66.

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 \frac{N_{p}}{N_{s}} \times A_{s} \times R_{s}}{L \times {(\frac{N_{p}}{N_{s}})}^{2}}

s_{n} = \frac{(V_{i n} \times \frac{N_{s}}{N_{p}} - V_{o u t}) \times A_{s} \times R_{s}}{L}

Equation 67.

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