SNVA991 October   2022 LM5123-Q1

 

  1.   How to Design a Boost Converter Using LM5123
  2.   Trademarks
  3. 1Design Example
  4. 2Calculations and Component Selection
    1. 2.1  Switching Frequency
    2. 2.2  Initial Inductor Calculation
    3. 2.3  Current Sense Resistor Selection
    4. 2.4  Inductor Selection
    5. 2.5  Output Capacitor Selection
    6. 2.6  Input Capacitor Selection
    7. 2.7  Feedback Resistor Selection
    8. 2.8  UVLO Resistor Selection
    9. 2.9  Soft-Start Capacitor Selection
    10. 2.10 Control Loop Compensation
      1. 2.10.1 Crossover Frequency (fcross) Selection
      2. 2.10.2 RCOMP Selection
      3. 2.10.3 CCOMP Selection
      4. 2.10.4 CHF Selection
    11. 2.11 MOSFET selection
  5. 3Implementation Results
  6. 4Small Signal Frequency Modeling
    1. 4.1 Boost Regulator Modulator Modeling
    2. 4.2 Compensation Modeling
    3. 4.3 Open Loop Modeling
  7. 5Resources

2.3 Current Sense Resistor Selection

The LM5123 has a fixed internal slope compensation ramp of 45 mV and a sensed peak current limit of 60 mV referenced to the input of the current sense amplifier. The current sense resistor is sized to prevent sub-harmonic oscillation as the slope compensation is a fixed value and to allow maximum power delivery. The selection process is an iterative process. Analyzing these two separate boundary conditions allow for the correct resistor value to be calculated.

The maximum current sense resistor value is calculated based on the adequate slope compensation to prevent sub-harmonic oscillation in Equation 7. The maximum current sense resistor value is calculated at the maximum duty cycle which occurs at the minimum supply voltage, and the maximum target load voltage.

Equation 7. R C S s l o p e ≤ 1.5 ∙ L M ∙ V S L ∙ f S W V L O A D - V S U P P L Y = 1.5 ∙ 2.6 µ H ∙ 45 m V ∙ 440 k H z 35 V - 8 V = 2.86   m Ω

Based on the calculation, the final selection of the current sense resistor must be less than 2.86 mΩ to prevent sub-harmonic oscillation at the highest duty cycle. Note the RCSmax value is proportional to the selected inductance value.

The peak inductor current calculated in Section 2.2, is used to size the current sense resistor for maximum output power. Due to component tolerances and power loss, the peak current limit is selected with some margin above the calculated peak inductor current. Typically, a range of 5% to 20% is used. In this example, a margin of 20% is selected. The calculated peak inductor current limit is estimated using Equation 8.

Equation 8. I L P E A K l i m i t s e t = 1 + M L I M I T ∙ I L P E A K m a x = 1 + 0.2 ∙ 27.67 A = 33.2 A

where

  • MLIMIT is the select margin above the calculated peak inductor current

The minimum peak current limit set by the current sense resistor must be greater than 33.2 A. The ideal resistor value is calculated using Equation 9

where

Equation 9. R C S p o w e r ≤ V C L I L P E A K l i m i t s e t = 60 m V 33.2 A = 1.8   m Ω
  • VCL is the fixed 60 mV current limit of the device.

To allow for maximum power the resistor value must be less than 1.8 mΩ.

Sub-harmonic oscillation can occur in a design where the RCSslope value is greater then than the RCSpower value. If this condition occurs, the ripple ratio of the inductor needs to be decreased and the procedure in Section 2.2 should be revisited. By decreasing the ripple ratio the effective slope compensation is increased. The slope compensation is adequate for this design example, and current sense resistor value is selected as a standard value of 1.5 mΩ. Rearranging Equation 9 to Equation 10, the peak inductor current limit is calculated.

Equation 10. I L P E A K l i m i t = V C L R C S = 60 m V 1.5 m Ω = 40   A

The selected value of 1.5 mΩ, results in a peak inductor current limit of 40 A.