SNVA940 November   2021 LM5157 , LM5157-Q1 , LM51571-Q1 , LM5158 , LM5158-Q1 , LM51581 , LM51581-Q1

 

  1.   Trademarks
  2. 1LM5157 Boost Design Example
  3. 2Calculations and Component Selection
    1. 2.1  Switching Frequency
    2. 2.2  Inductor Calculation
    3. 2.3  Slope Compensation Check
    4. 2.4  Inductor Selection
    5. 2.5  Diode Selection
    6. 2.6  Output Capacitor Selection
    7. 2.7  Input Capacitor Selection
    8. 2.8  UVLO Resistor Selection
    9. 2.9  Soft-Start Capacitor Selection
    10. 2.10 Feedback Resistor Selection
    11. 2.11 Control Loop Compensation
      1. 2.11.1 Crossover Frequency (fcross) Selection
      2. 2.11.2 RCOMP Selection
      3. 2.11.3 CCOMP Selection
      4. 2.11.4 CHF Selection
    12. 2.12 Power Loss and Efficiency Estimation
  4. 3Implementation Results
  5. 4Small Signal Frequency Analysis
    1. 4.1 Boost Regulator Modulator Modeling
    2. 4.2 Compensation Modeling
    3. 4.3 Open Loop Modeling

2.2 Inductor Calculation

The inductance value of the boost converter can be calculated with the inductor current ripple ratio (RR, defined as the peak to peak ripple current over the average inductor current). There are three main considerations dominating the selection of the inductance value: the power loss, the falling slope of the inductor current and the right-half plane (RHP) zero frequency (ωZ_RHP) of the control loop.

  • As the inductance value increases, the inductor core loss and the RMS current becomes smaller but also note that the DCR of the inductor could be higher.
  • The inductance value should be large enough so that the falling slope of the inductor current is small enough to prevent the sub-harmonic oscillation in the peak current mode control of the LM5157x/LM5158x.
  • In a boost converter, the RHP zero usually sets the bandwidth limit of the design. Therefore, the RHP zero frequency should be high enough to allow a higher crossover frequency of the control loop. As the relative inductance value decreases the RHP zero frequency increases.

A maximum ripple ratio between 30% and 70% results in a good balance between the considerations above. In this example, the maximum ripple ratio of the inductor current is set to 60%. In the continuous conduction mode (CCM) operation, the maximum ripple ratio occurs at a duty cycle of 33% (DmaxΔIL=0.33) and Equation 2 is used to calculate the supply voltage at 33% duty cycle.

Equation 2. V SUPPLY _ max Δ IL = V LOAD ∙ 1 - D max Δ IL = 12 ∙ 1 - 0.33 = 8 V

where

  • DmaxΔIL is the duty cycle where the maximum inductor ripple current occurs

Knowing VSUPPLY_maxΔIL, the desired ripple ratio, and the switching frequency, Equation 3 is used to calculate the inductance value at 1.6A load (VSUPPLY = 6V to 9V).

Equation 3. L M _ calc _ 1 = V SUPPLY I SUPPLY ∙ RR ∙ f sw ∙ D = 8 V 2.4 A ∙ 0.6 ∙ 2.1 MHz ∙ 0.33 = 0.88 μH

where

  • D is the duty cycle where the maximum inductor ripple current occurs
  • RR is the inductor current ripple ratio

In the 0.8A load case (VSUPPLY = 3V to 6V) where it does not result in a duty cycle of 33% the maximum supply voltage (6V, duty cycle = 0.5) is used to calculate the maximum ripple ratio. Equation 4 is used to calculate the inductor value.

Equation 4. L M _ calc _ 2 = 6 V 1.6 A ∙ 0.6 ∙ 2.1 MHz ∙ 0.5 = 1.49 μH

A standard inductance of 1.5µH is selected for the value of LM to cover the requirement of both regions. The maximum peak inductor current occurs when the supply voltage is at the minimum value, VSUPPLY_min, and the maximum load current ILOAD_max. The peak inductor current is calculated using Equation 5 and Equation 6. Again, two regions are calculated separately and the maximum is the larger one.

Equation 5. I L peak _ MAX _ 1 = V LOAD ∙ I OUT V SUPPLY ∙ η + 1 2 ∙ V SUPPLY ∙ D L M ∙ f sw = 12 V ∙ 1.6 A 6 V ∙ 0.9 + 1 2 ∙ 6 V ∙ 0.5 1.5 μH ∙ 2.1 MHz = 4.03 A
Equation 6. I L peak _ MAX _ 2 = 12 V ∙ 0.8 A 3 V ∙ 0.9 + 1 2 ∙ 3 V ∙ 0.75 1.5 μH ∙ 2.1 MHz = 3.91 A

where

  • η is the estimated efficiency

The peak inductor current is used to properly select the device among LM5158, LM51581, LM5157, and LM51571. Please refer to the data sheets for their current limits. Due to component tolerances and power loss of the regulator, the peak current limit should be selected with some margin above the calculated peak inductor current. In this example, a margin of 15% is used and the LM5157 device is selected.