SLVAE09B July   2018  – August 2021 TPS560430

 

  1.   Trademarks
  2. 1Introduction
  3. 2Peak Current Mode Loop Modeling
    1. 2.1 Overall Control Block Diagram and Transfer Function Derivation
    2. 2.2 Inside Current Loop Model
    3. 2.3 Overall Loop Model
    4. 2.4 Inductor and Output Capacitor Design Limits
    5. 2.5 The Equation to Calculate Bandwidth and Phase Margin
  4. 3Inductor and Output Capacitor Design
    1. 3.1 Inductor Design
    2. 3.2 Output Capacitor Design
    3. 3.3 Simulation and Bench Verification
  5. 4Summary
  6. 5References
  7. 6Revision History

2.2 Inside Current Loop Model

Based on Equation 3 to Equation 5 and Figure 2-2, the transfer function from control to inductor current is Gci(s):

Equation 8. GUID-C8DEC941-C35A-4B37-AB67-EA47681B7FF4-low.gif

For PCM buck converter, the crossover frequency is much smaller than half switching frequency, so around crossover frequency Equation 8 can be simplified as Equation 9. The inside current loop is simplified as a single pole, which is very helpful for the loop response analysis of PCM buck converter.

Equation 9. GUID-C7CE9242-7CAC-41E8-81D9-D99D60ADE5B2-low.gif

If the inside current loop Gci(s) is not stable, subharmonic oscillation occurs. A system is stable as long as each of the poles of the closed loop transfer function lies in the left half plane. The minimum inductor value is calculated to prevent subharmonic oscillation:

Equation 10. GUID-09255E4F-D2D5-43BB-861E-1B29FE91076C-low.gif