In-Depth Notes on DC-DC Converters and Power Electronics

Linear Voltage Regulator

  • Efficiency: Low efficiency; example: Vo = 0.5 Vs, ext{ efficiency } ( ext{η}) = 50\%

Switching Converter

  • Basic Principle: Ideal switch has no losses;
    • Voltage equation: V = rac{D imes V_s}{T}

Buck Converter

  • Circuit Diagram: Shows input and output, inductor and current paths.
  • Key Relationships:
    • VL = Vs - V_o

Buck Converter Modes

  1. Mode 1: Switch closed, diode off

    • Inductor voltage: VL = L rac{diL}{dt}
    • Current change during DT: I{max}, I{min}

  2. Mode 2: Switch open, diode on

    • VL = -Vo
    • Current flow and change analysis on inductor.

Flux Balance

  • Ensure net flux change in inductor is zero:
    • ext{Flux change closed} + ext{Flux change open} = 0
    • Vs D T - Vo (1-D)T = 0

Current Ripple

  • Calculation of current ripple rac{ΔIL}{I} using switching parameters; related to (D, Vo).
    • ΔI = rac{V_o(1 - D)T}{L}

Voltage Ripple

  • Voltage ripple derived from capacitor and current through it:
    • ΔV_o = rac{ΔQ}{C} where ΔQ = I imes D imes T
    • Ripple effects managed using capacitor size C.

Example 1: Buck Converter

  • Parameters:
    • V_s = 50 V, D = 0.4, f = 20 kHz, L = 400 \mu H, C = 100 \mu F, R = 20 \Omega
  • Calculations:
    • (a) Output Voltage: V_o
    • (b) Maximum/Minimum Inductor Current
    • (c) Output Voltage Ripple

Minimum Inductance for CCM

  • For continuous conduction mode, I_{min} = 0; at boundaries:
    • Ensure I_{min} stays positive.

Example 2: Design a Buck Converter

  • Specifications: Output Voltage: 18 V, load R = 10 Ω, Ripple < 0.5\%, D = 0.375
  • Calculate:
    • (a) Duty ratio
    • (b) Inductor and Capacitor values: L = 78.1 \mu H, C = 125 \mu F
    • (c) Peak voltage ratings

Boost Converter

  • Basic Operation:
  • Mode 1: Switch ON (Inductor energy storage)
  • Mode 2: Switch OFF (Energy release)
    • Flux must balance through operation modes.

Current Ripple in Boost Converters

  • Similar analysis as Buck converters; care to observe changes in amplitude and frequency relation.

Buck-Boost Converter

  • Operating principles maintain voltage manipulation; ensures control over output and feedback.
  • Current and voltage ripple considerations for engineering design.