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

2.11.1 Crossover Frequency (fcross) Selection

The crossover frequency of the loop can be either selected to be 1/10 the switching frequency or 1/5 the right-half plane zero frequency, whichever is lower. Equation 19 shows the calculation for 1/10 the switching frequency. Equation 20 and Equation 21 show how to calculate the 1/5 the right half plane zero frequency at full load and half load conditions.

Equation 19. fcross=fsw10=2.1MHz10=210kHz
Equation 20. fCROSS_1= fZ_RHP 5=RLOAD∙D'25∙2∙π∙LM= 7.5Ω∙0.525∙2∙π∙1.5µH=39.8kHz
Equation 21. fCROSS_2= 15Ω∙0.2525∙2∙π∙1.5µH=19.9kHz

where

  • D' is (1 -D) a the minimum supply voltage
  • RLOAD is the load resistance equal to VLOAD / ILOAD

To give some margin, the crossover frequency is selected to be 16.6kHz, a little less than 1/5 the right half plane zero frequency at half load condition. In this design example, the performance under the full load condition is more important and needs to be optimized. Therefore, the full load condition with the input voltage from 6 V to 9 V is used for the following calculations. After the design and selection of the compensation loop, the stability of the half load condition can be checked with the equations in Section 4.