SLVSHI9 Data sheet

SLVSHI9A March 2025 – September 2025 TPS7H5020-SEP , TPS7H5020-SP

PRODMIX

8.2.2.5 Transformer Design

The turns ratio and primary inductance of the transformer are determined based on the target specifications of the converter. The turns ratio is calculated based on a maximum duty cycle of 35% targeted for the design.

Equation 39.

N_{P S_M A X} = \frac{V_{I N_M I N} \times D_{M A X}}{(V_{O U T} + V_{D}) \times (1 - D_{M A X})}

Equation 40.

N_{P S_M A X} = \frac{22 V \times 0.35}{(5 V + 0.7) \times (1 - 0.35)} = 2.08

A turns ratio of 2 is selected for the design. Based on the actual turns ratio, the minimum and maximum duty cycle can be calculated.

Equation 41.

D_{M I N} = \frac{(V_{O U T} + V_{D}) \times N_{P S}}{(V_{O U T} + V_{D}) \times N_{P S} + V_{I N_M A X}}

Equation 42.

D_{M I N} = \frac{(5 V + 0.7 V) \times 2}{(5 V + 0.7 V) \times 2 + 22 V} = 0.241

Equation 43.

D_{M A X} = \frac{(V_{O U T} + V_{D}) \times N_{P S}}{(V_{O U T} + V_{D}) \times N_{P S} + V_{I N_M I N}}

Equation 44.

D_{M A X} = \frac{(5 V + 0.7 V) \times 2}{(5 V + 0.7 V) \times 2 + 22 V} = 0.341

The primary inductance was calculated based on a 20% current ripple.

Equation 45.

L_{P} = \frac{{V_{I N_M A X}}^{2} \times {D_{M I N}}^{2}}{V_{O U T} \times I_{O U T} \times f_{S W} \times %_{R I P P L E}}

Equation 46.

L_{P} = \frac{{36 V}^{2} \times {0.24}^{2}}{5 V \times 4 A \times 500 k H z \times 0.2} = 37.3 μ H

The primary inductance selected for the actual design was 30µH, which results in an actual ripple of approximately 25%. The following equations detail how to calculate transformer primary and secondary currents that are critical for proper design of the transformer. These equations are useful for defining the physical structure of the transformer.

Equation 47.

I_{R I P P L E} = \frac{V_{O U T} \times I_{O U T} \times %_{R I P P L E}}{V_{I N_M A X} \times D_{M I N}}

Equation 48.

I_{R I P P L E} = \frac{5 V \times 4 A \times 0.25}{36 V \times 0.24} = 0.58 A

Equation 49.

I_{P R I_P E A K} = \frac{V_{O U T} \times I_{O U T}}{V_{I N_M I N} \times D_{M A X} \times η} + \frac{I_{R I P P L E}}{2}

Equation 50.

I_{P R I_P E A K} = \frac{5 V \times 4 A}{22 V \times 0.35 \times 0.85} + \frac{0.58 A}{2} = 3.35 A

Equation 51.

I_{P R I_R M S} = \sqrt{D_{M A X} \times {(\frac{V_{O U T} \times I_{O U T}}{V_{I N_M I N} \times D_{M A X}})}^{2} + \frac{{I_{R I P P L E}}^{2}}{3}}

Equation 52.

I_{P R I_R M S} = \sqrt{0.35 \times {(\frac{5 V \times 4 A}{22 V \times 0.35})}^{2} + \frac{{0.58 A}^{2}}{3}} = 1.57 A

Equation 53.

I_{S E C_R M S} = \sqrt{(1 - D_{M A X}) \times {I_{O U T}}^{2} + \frac{{(I_{R I P P L E} \times N_{P S})}^{2}}{3}}

Equation 54.

I_{S E C_R M S} = \sqrt{(1 - 0.35) \times {4 A}^{2} + \frac{{(0.58 A \times 2)}^{2}}{3}} = 3.29 A