AN901 Datasheet, PDF (18/25 Pages) STMicroelectronics – Electromagnetic compatibility

AN901
4.1. Transformer Design
For this example, operating in CCM was chosen. Equation 7 establishes the relationship between turns ratio n and
duty cycle D. Accounting for forward voltage drop across D1 of 0.5 V and targeting a duty cycle of 40%, Equation 7
can be solved for transformer turns ratio n:
n  _---_V----_O----_U----_T----+---^V--_V---^I-^N_f---_D-^D--₁---_---_--₁-----–----_D------_  ₅-²---_.-⁴-₅----^----⁰-₀---^..-⁴-₆--  2.91
Equation 46.
A 3:1 turns ratio was chosen.
The next parameters to choose are the switching period and primary inductance. The Si886xx has externally set
switching frequency range of 200 kHz to 900 kHz. 500 kHz was chosen for this example. C6 is set to 470 nF and
R13 is calculated by rearranging Equation 31:
R13 = ¹----⁰---²----⁵---_C.--⁵--₆--^-----^T----^s---^w-- = -¹---⁰---²--₄--⁵--₇-^.--⁵⁰----_---1--²-0---^_–---₉^{1---0---–}---⁶- = 4.36k
Equation 47.
R13 was set to 4.32 kΩ as that is the closest 1% resistor value.
To determine L_m, consider at what minimum load should the converter operate in CCM. For this design, it was
targeted to operate in CCM between 70% and full load. At the cross-over point between DCM and CCM:
Substituting,
Im_AVE = -^I--^m-----^R---^I-₂-^P----^P---^L---^E--
Equation 48.
And solving for L_m:
-⁰---^.-_n-⁷--_--^-₁----^I-–-^L---^O_D----^A-_--^D-- = -^V----^I-^N-₂---^D-_L---_m-^T----^s--^w--
Equation 49.
L_m = ⁿ----^V----^I-₁-^N--_.--_4D----^-_--¹--_I--_L-–--_O--^D--_A---^-_D-^T----^s---^w-- = ³-----^-----²---⁴-----^-----⁰---^.--⁴---₁--^--_.-₄--⁰---^.--⁶-----^----²----^---1---0---^–---⁶- = 24.7H
Equation 50.
A transformer with turns ratio of 3:1 and primary inductance of 25 μH was chosen.
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