SNVA994A Application note

SNVA994A February 2022 – March 2023 LM5157 , LM5157-Q1 , LM51571-Q1 , LM5158 , LM5158-Q1 , LM51581 , LM51581-Q1

3.2.2 Primary Winding Inductance Selection

Three main parameters are considered when selecting the inductance value of primary winding: primary winding current ripple ratio (IL_RR), falling slope of the transformer current and the RHPZ frequency (ω_{Z_RHP}). Finding a balance between these three parameters helps to simplify the rest of the design process.

The primary winding ripple current ripple ratio is selected to balance the copper loss and core loss of the transformer. As the relative ripple current increases; the core losses increase and the copper losses decrease.
The falling slope of the transformer current should be small enough to prevent sub-harmonic oscillation in applications with a duty cycle greater than 50%. A relatively larger inductance value of the primary winding results in a smaller falling slope. The LM5157x/LM5158x provides fixed internal slope compensation as well as programmable slope compensation for these applications.
The right half plane zero should be placed at high frequency, allowing for a higher crossover frequency of the control loop. As the relative inductance value of the primary winding decreases the right half plane zero frequency increases.

A maximum ripple ratio between 30% and 70% results in a good balance of the total power loss of the transformer, matching the down slope of the transformer current to the internal slope compensation and the increasing the right half plane zero frequency. The maximum ripple ratio of the inductor current is set to 60%. In CCM operation, the maximum primary winding ripple current occurs when the supply voltage is at the maximum value. For this application we choose CCM at the minimum input voltage and DCM for the higher voltage range. The primary winding inductance value for CCM operation is calculated using Equation 6.

Equation 6.

L_{M_c a l c} = \frac{{N_{P}}^{2} \times {V_{S U P P L Y}}^{2} \times {V_{L O A D}}^{2}}{I L_{R R} \times f_{S W} \times P_{O U T_t o t a l} \times {(N_{S} \times V_{S U P P L Y} + N_{P} \times |V_{L O A D}|)}^{2}}

L_{M_c a l c} = \frac{1^{2} \times {8 V}^{2} \times {10 V}^{2}}{0.6 \times 250 k H z \times 8.5 W \times {(1.2 \times 8 V + 1 \times 10 V)}^{2}} = 13.1 µ H

where

IL_RR is the ripple ratio
V_SUPPLY is the minimum supply voltage
P_{OUT_total} is the maximum power delivered by the flyback regulator

The primary winding inductance is selected to be 8µH. The primary winding ripple current and primary winding peak current are calculated using Equation 7 and Equation 8, respectively. The peak primary winding current occurs at the minimum supply voltage.

Equation 7.

Δ {I L}_{M} = \frac{V_{S U P P L Y_m i n} \times D}{L_{M} \times f_{S W}} = \frac{8 V \times 0.51}{8 µ H \times 250 k H z} = 2.04 A

Equation 8.

{I L}_{P E A K} = \frac{P_{O U T_t o t a l}}{V_{S U P P L Y_m i n} \times D} + \frac{Δ {I L}_{M}}{2} = \frac{8.5 W}{8 V \times 0.51} + \frac{2.04 A}{2} = 3.10 A

IL_PEAK is used to properly size the current sense resistor. Table 3-1 summarizes the key parameters of selected transformer.

Table 3-1 Selected Transformer Parameters

Parameter	Value
Turns Ratio (N_P:N_S1:N_S2:N_S3:N_S4)	1:1.2:2.4:2.4:2.4 (5:6:12:12:12)
Primary winding inductance (L_M)	8 µH
Primary winding saturation current (I_SAT)	5.5 A