DC-DC Converters

Cheatsheet Content

DC-DC Converters Overview Convert a DC voltage from one level to another using switched-mode techniques. Key components: Power semiconductor switches (MOSFETs, IGBTs), energy storage elements (inductors, capacitors), diodes. Operation involves rapid switching to create a pulsed waveform, followed by filtering to achieve a stable DC output. Categorized as non-isolated (Buck, Boost, Buck-Boost, Cuk, SEPIC) or isolated (Flyback, Forward, Push-Pull, Half-Bridge, Full-Bridge). Non-Isolated Converters (CCM Operation) 1. Buck Converter (Step-Down) Circuit Diagram: Vin GND S1 D L C R Vo GND Purpose: $V_o Output Voltage: $V_o = D \cdot V_{in}$ Inductor Current Ripple: $\Delta I_L = \frac{V_o(1-D)}{f_s L}$ Output Voltage Ripple (ESR neglected): $\Delta V_o = \frac{\Delta I_L}{8 f_s C}$ Minimum Inductance for CCM: $L_{min} = \frac{(1-D) R}{2 f_s}$ Waveforms (CCM): IL t Io Imax Imin D.Ts Ts Vs t Vin 2. Boost Converter (Step-Up) Circuit Diagram: Vin GND L S1 D C R Vo GND Purpose: $V_o > V_{in}$ Output Voltage: $V_o = \frac{V_{in}}{1-D}$ Inductor Current Ripple: $\Delta I_L = \frac{V_{in} D}{f_s L}$ Output Voltage Ripple (ESR neglected): $\Delta V_o = \frac{I_o D}{f_s C}$ Minimum Inductance for CCM: $L_{min} = \frac{D(1-D)^2 R}{2 f_s}$ Waveforms (CCM): IL t Iin Imax Imin D.Ts Ts Vd t Vo-Vin 3. Buck-Boost Converter (Step-Up/Step-Down, Inverting) Circuit Diagram: Vin GND S1 L D C R Vo GND Purpose: $V_o$ can be higher or lower than $V_{in}$, but always opposite polarity. Output Voltage: $V_o = -\frac{D}{1-D} V_{in}$ Inductor Current Ripple: $\Delta I_L = \frac{V_{in} D}{f_s L}$ Output Voltage Ripple (ESR neglected): $\Delta V_o = \frac{I_o D}{f_s C}$ Minimum Inductance for CCM: $L_{min} = \frac{(1-D) R}{2 f_s} \cdot \frac{D}{(1-D)}$ Waveforms (CCM): IL t Iin Imax Imin D.Ts Ts Vs t Vin Vin+|Vo| 4. Cuk Converter Purpose: $V_o$ can be higher or lower than $V_{in}$, same polarity. Uses a series capacitor for energy transfer. Output Voltage: $V_o = \frac{D}{1-D} V_{in}$ Key Feature: Non-pulsating input and output currents (ideal). 5. SEPIC Converter (Single-Ended Primary Inductor Converter) Purpose: $V_o$ can be higher or lower than $V_{in}$, same polarity. Uses two inductors and a series capacitor. Output Voltage: $V_o = \frac{D}{1-D} V_{in}$ Key Features: Non-inverting, true shutdown (output is zero when switch is off), non-pulsating input current. Isolated Converters These converters use a transformer to provide galvanic isolation between input and output, and to allow for large step-up/step-down ratios and multiple outputs. 1. Flyback Converter Principle: Energy is stored in the transformer's magnetizing inductance during switch ON ($t_{ON}$) and transferred to the output during switch OFF ($t_{OFF}$). Output Voltage (CCM): $V_o = \frac{D}{1-D} N V_{in}$, where $N = N_s/N_p$ (turns ratio) Applications: Low to medium power (typically 2. Forward Converter Principle: Energy is transferred from input to output when the switch is ON. Requires a demagnetizing winding or reset circuit to prevent transformer core saturation. Output Voltage (CCM): $V_o = D N V_{in}$, where $N = N_s/N_p$ Applications: Medium power (typically 100W - 500W). More efficient than flyback for similar power levels. 3. Push-Pull Converter Principle: Uses two switches and a center-tapped transformer primary. Switches operate alternately, driving the transformer in both directions. Output Voltage (CCM): $V_o = 2D N V_{in}$, where $N = N_s/N_{p,half}$ (turns ratio of secondary to half primary) Advantages: Efficient use of transformer core, suitable for higher power. Disadvantage: Requires careful matching of switch characteristics to prevent core saturation. 4. Half-Bridge Converter Principle: Uses two switches in series with two capacitors across the input. The capacitor midpoint forms an AC ground for the transformer primary. Output Voltage (CCM): $V_o = D N V_{in}$, where $N = N_s/N_p$ Advantages: Good for medium to high power, lower voltage stress on switches ($V_{in}$) compared to push-pull ($2V_{in}$). 5. Full-Bridge Converter Principle: Uses four switches in a bridge configuration to drive the transformer primary with a bipolar voltage. Output Voltage (CCM): $V_o = 2D N V_{in}$, where $N = N_s/N_p$ Advantages: Highest power capability, lowest voltage stress on switches ($V_{in}$), optimal core utilization. Applications: High power applications (e.g., kW range). Key Parameters & Operating Modes Duty Cycle ($D$): Fraction of the switching period ($T_s$) during which the main switch is ON. $D = t_{ON} / T_s$. Switching Frequency ($f_s$): Reciprocal of the switching period, $f_s = 1/T_s$. Higher $f_s$ allows for smaller $L$ and $C$ but increases switching losses. Continuous Conduction Mode (CCM): Inductor current ($I_L$) never drops to zero during a switching cycle. All formulas above are for CCM. Discontinuous Conduction Mode (DCM): Inductor current drops to zero for a portion of the switching cycle. Occurs at light loads or low inductance. DCM alters the voltage conversion ratio and dynamic response. For Buck: $V_o = V_{in} \frac{2D}{1+\sqrt{1+\frac{8L}{RT_s}D^2}}$ For Boost: $V_o = V_{in} (1 + \frac{2L}{RT_s} \frac{D^2}{1-D})$ For Buck-Boost: $V_o = -V_{in} \frac{D^2}{1-D} \frac{R T_s}{2L}$ Critical Inductance ($L_{crit}$): The minimum inductance value required to maintain CCM at a given load and duty cycle. $L_{crit}$ is often half of $L_{min}$ for boundary conduction mode. Ripple Current ($\Delta I_L$): Peak-to-peak variation in inductor current. A design goal is often to keep $\Delta I_L$ within 20-40% of the average inductor current. Ripple Voltage ($\Delta V_o$): Peak-to-peak variation in output voltage. Determined by capacitor size, ESR, and ripple current. Efficiency ($\eta$): $\eta = P_{out} / P_{in}$. Losses include conduction losses (in switches, diodes, inductors, capacitors) and switching losses (in switches). Control Methods Pulse Width Modulation (PWM): The most common method. A fixed switching frequency with variable duty cycle. Voltage Mode Control: Output voltage is compared to a reference, error signal controls PWM. Current Mode Control: Inner current loop controls inductor/switch current, outer voltage loop controls current reference. Offers better transient response and inherent overcurrent protection. Pulse Frequency Modulation (PFM): Fixed pulse width with variable switching frequency. Used for light loads to maintain high efficiency (avoids switching losses at high frequency). Hysteretic Control: Output voltage is kept within a defined band by switching the converter on/off directly, without a clock. Fast transient response, but variable switching frequency.