SNVA994 Application note

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

3.2.1 Maximum Duty Cycle and Turns Ratio Selection

In CCM operation the duty cycle of the low side switch is calculated using Equation 2.

Equation 2.

D = \frac{\frac{N_{P}}{N_{S}} \times |V_{L O A D}|}{V_{S U P P L Y} + \frac{N_{P}}{N_{S}} \times |V_{L O A D}|}

where

N_P is the number of turns on the primary side winding and assumed to be 1
N_S is the number of turns on the secondary side winding.

The maximum duty cycle occurs when the supply voltage is at the minimum value. By selecting the maximum duty cycle, the number of turns on the secondary winding can be determined. Selecting the duty cycle to be less than 50% brings two main benefits. First, it reduces the need for slope compensation which is required for stable operation when the duty cycle is greater than 50% in CCM operation. As for some wide input voltage designs limiting the duty cycle below 50% might not be possible, the LM5157x/LM5158x provides programmable slope compensation for such designs. Second, the right-half plane zero (RHPZ) of the converter is pushed to a higher frequency when designing with a smaller duty cycle, this helps to improve the load transient response and simplifying the control loop compensation calculations. For this design the maximum duty cycle (D_MAX) is selected to be 50%. The number of turns on the secondary winding is calculated using Equation 3.

Equation 3.

N_{S_c a l c} = \frac{(|V_{L O A D}|) \times (1 - D_{M A X}) \times N_{P}}{V_{S U P P L Y_m i n} \times D_{M A X}} = \frac{(|10 V|) \times (1 - 0.5) \times 1}{8 V \times 0.5} = 1.25

Selecting N_S1 to be 1.2 turns the turns ratio to achieved in the fewest number of full turns. The other secondary windings N_Sx are selected to be:

Winding	Turns
N_S1	1.2
N_S2	2.4
N_S3	2.4
N_S4	2.4

In this example the minimum number of turns is 5 on the primary winding and 6 turns on the first secondary winding. With N_S1 selected, Equation 4 is used to calculate the maximum duty cycle.

Equation 4.

D_{M A X} = \frac{\frac{N_{P}}{N_{S}} \times |V_{L O A D}|}{V_{S U P P L Y_m i n} + \frac{N_{P}}{N_{S}} \times |V_{L O A D}|} = \frac{\frac{1}{1.2} \times 10 V}{8 V + \frac{1}{1.2} \times 10 V} = 0.51

D_MAX is calculated to be approximately 50.1%, which is a little bit above the target maximum duty cycle of 50%. The number of turns on the auxiliary winding is calculated using Equation 5.

Equation 5.

N_{S 2_c a l c} = N_{S 1} \times \frac{|V_{L O A D 2}|}{|V_{L O A D 1}|} = 1.2 \times \frac{20 V}{10 V} = 2.4

where

V_Load1 is the Load1 winding voltage