TIDUF73 September   2024

 

  1.   1
  2.   Description
  3.   Resources
  4.   Features
  5.   Applications
  6.   6
  7. 1System Description
  8. 2System Overview
    1. 2.1 Block Diagram
    2. 2.2 Design Considerations
      1. 2.2.1 Design Theory
      2. 2.2.2 Resistor Selection
        1. 2.2.2.1 Transistor and Diode Selection
      3. 2.2.3 Overcurrent Detection – Short-Circuit Protection
    3. 2.3 Highlighted Products
      1. 2.3.1 TPSI3100-Q1
      2. 2.3.2 INA180-Q1
      3. 2.3.3 TPSI2140-Q1
  9. 3Hardware, Software, Testing Requirements, and Test Results
    1. 3.1 Hardware Requirements
      1. 3.1.1 External Hardware Requirements
    2. 3.2 Test Setup
    3. 3.3 Test Results
  10. 4Design and Documentation Support
    1. 4.1 Design Files
      1. 4.1.1 Schematics
      2. 4.1.2 BOM
    2. 4.2 Tools
    3. 4.3 Documentation Support
    4. 4.4 Support Resources
    5. 4.5 Trademarks
  11. 5About the Author

2.2.1 Design Theory

At a high level, a passive precharge circuit is a simple RC circuit that can be represented as an exponentially decaying function. The voltage on the capacitor is calculated using Equation 1:

Equation 1. V C =   V S   × ( 1 - e - t τ )

where

  • VS is the system voltage
  • The time constant τ, or Tau, determines the rate of charge

For this system, the precharge cycle is considered complete when the 5τ has passed. Some systems can require longer than 5τ to charge to maintain that the voltage drop across the main contactors meets the contactor switching requirements. The desired system resistance is calculated from the time constant equation (Equation 2):

Equation 2. 5 × τ = 5 × R × C = 0.5   s e c o n d s

Substituting the DC-Link capacitance and solving for R, the system resistance is 50Ω. Of all the components in the power path, the precharge power resistor dissipates the most power. This component is not sized with the peak or average power in mind, however. To size the resistor, the pulse energy and length are the most important. The energy can be calculated through two ways: as an integral of power over time (Equation 3) and as a function of the capacitor (Equation 4):

Equation 3. E =   ∫ 0 0.5 20,000 × e - 2 × t 0.1 d t ≈ 1000   J
Equation 4. E =   1 2 C V 2 = 1000   J