1. Buck Converter (Step-Down)
Output Voltage:
\[ V_o = D \cdot V_s \]
Where \( D \) is the duty cycle, \( 0 \leq D \leq 1 \)
Duty Cycle:
\[ D = \frac{t_{on}}{T} = \frac{V_o}{V_s} \]
Output Current (Continuous Conduction Mode):
\[ I_o = \frac{I_L}{1} = I_L \]
Inductor Ripple Current:
\[ \Delta I_L = \frac{V_o(1-D)}{f_s L} = \frac{(V_s - V_o)D}{f_s L} \]
Critical Inductance (CCM/DCM Boundary):
\[ L_{crit} = \frac{(1-D)R}{2f_s} \]
Output Voltage Ripple:
\[ \Delta V_o = \frac{\Delta I_L}{8f_s C} = \frac{V_o(1-D)}{8L C f_s^2} \]
Key Characteristics:
- Type: Step-down converter (\(V_o < V_s\))
- Switch ON: Inductor charges, energy stored
- Switch OFF: Diode conducts, inductor releases energy to load
- Efficiency: Typically 85-95%
- Applications: Voltage regulators, battery-powered devices
2. Boost Converter (Step-Up)
Output Voltage:
\[ V_o = \frac{V_s}{1-D} \]
Duty Cycle:
\[ D = 1 - \frac{V_s}{V_o} = \frac{V_o - V_s}{V_o} \]
Input Current (CCM):
\[ I_s = \frac{I_o}{1-D} \]
Inductor Ripple Current:
\[ \Delta I_L = \frac{V_s D}{f_s L} \]
Critical Inductance:
\[ L_{crit} = \frac{D(1-D)^2 R}{2f_s} \]
Output Voltage Ripple:
\[ \Delta V_o = \frac{V_o D}{R C f_s} \]
Key Characteristics:
- Type: Step-up converter (\(V_o > V_s\))
- Switch ON: Inductor charges from source
- Switch OFF: Inductor voltage adds to source, charging capacitor
- Voltage Gain: Theoretically infinite as \(D \rightarrow 1\)
- Applications: LED drivers, power factor correction, renewable energy
3. Buck-Boost Converter (Inverting)
Output Voltage:
\[ V_o = -\frac{D}{1-D} V_s \]
Negative sign indicates polarity inversion
Voltage Gain (Magnitude):
\[ M = \left|\frac{V_o}{V_s}\right| = \frac{D}{1-D} \]
Duty Cycle:
\[ D = \frac{|V_o|}{V_s + |V_o|} \]
Inductor Ripple Current:
\[ \Delta I_L = \frac{V_s D}{f_s L} \]
Critical Inductance:
\[ L_{crit} = \frac{D(1-D)^2 R}{2f_s} \]
Key Characteristics:
- Type: Step-up/down with polarity inversion
- Can produce: \(|V_o| < V_s\) or \(|V_o| > V_s\)
- Switch ON: Energy stored in inductor
- Switch OFF: Energy transferred to load with reversed polarity
- Applications: Bipolar supplies, automotive systems
4. Ćuk Converter
Output Voltage:
\[ V_o = -\frac{D}{1-D} V_s \]
Capacitor Voltage (C1):
\[ V_{C1} = \frac{V_s}{1-D} \]
Energy Transfer:
\[ P = \frac{1}{2} C_1 V_{C1}^2 f_s \]
Key Characteristics:
- Topology: Two inductors, two capacitors
- Advantage: Continuous input and output currents (low ripple)
- Energy Transfer: Through capacitor C1
- Polarity: Inverted output
- Applications: Low-noise power supplies, battery applications
5. SEPIC Converter (Single-Ended Primary Inductor Converter)
Output Voltage:
\[ V_o = \frac{D}{1-D} V_s \]
Coupling Capacitor Voltage:
\[ V_C = V_s \]
Key Characteristics:
- Polarity: Non-inverting (same as input)
- Topology: Two inductors (can be coupled), one capacitor for energy transfer
- Feature: True shutdown capability
- Advantage: Input-output isolation possible
- Applications: Battery-powered systems, automotive
6. Zeta Converter
Output Voltage:
\[ V_o = \frac{D}{1-D} V_s \]
Key Characteristics:
- Polarity: Non-inverting
- Topology: Similar to SEPIC but different arrangement
- Feature: Continuous input current
- Advantage: Low input current ripple
7. Converter Comparison Table
| Converter | Voltage Gain | Polarity | Type |
|---|---|---|---|
| Buck | \(M = D\) | Non-inverting | Step-down |
| Boost | \(M = \frac{1}{1-D}\) | Non-inverting | Step-up |
| Buck-Boost | \(M = -\frac{D}{1-D}\) | Inverting | Step-up/down |
| Ćuk | \(M = -\frac{D}{1-D}\) | Inverting | Step-up/down |
| SEPIC | \(M = \frac{D}{1-D}\) | Non-inverting | Step-up/down |
| Zeta | \(M = \frac{D}{1-D}\) | Non-inverting | Step-up/down |
8. Operating Modes
Continuous Conduction Mode (CCM)
Inductor current never reaches zero
\[ I_{L,min} > 0 \] \[ L > L_{crit} \]
Discontinuous Conduction Mode (DCM)
Inductor current reaches zero during switching period
\[ I_{L,min} = 0 \] \[ L < L_{crit} \]
Boundary Conduction Mode (BCM)
Operation at CCM/DCM boundary
\[ L = L_{crit} \]
9. Common Design Parameters
Switching Frequency:
\[ f_s = \frac{1}{T} \]
Typical range: 20 kHz - 1 MHz
Duty Cycle:
\[ D = \frac{t_{on}}{T} = t_{on} \cdot f_s \]
Average Power:
\[ P_{out} = V_o \cdot I_o \]
Efficiency:
\[ \eta = \frac{P_{out}}{P_{in}} \times 100\% = \frac{V_o I_o}{V_s I_s} \times 100\% \]
RMS Current (for component sizing):
\[ I_{rms} = \sqrt{\frac{1}{T}\int_0^T i^2(t) dt} \]
Peak-to-Peak Ripple Factor:
\[ r = \frac{\Delta I_L}{I_L} \]
Typically designed for 20-40% ripple
10. Component Selection Guidelines
Switch (MOSFET/IGBT):
- Voltage rating: \(V_{rated} \geq 1.5 \times V_{max}\)
- Current rating: \(I_{rated} \geq 1.5 \times I_{peak}\)
- Consider \(R_{DS(on)}\) for conduction losses
Diode:
- Fast recovery diode or Schottky for high frequency
- Voltage rating: \(V_{rated} \geq 1.5 \times V_{max}\)
- Average current rating: \(I_{avg} \geq I_o\)
Inductor:
- Current rating: \(I_{rated} \geq I_{L,max}\)
- Core saturation: Consider peak current
- DC resistance affects efficiency
- Select core material based on frequency
Capacitor:
- Voltage rating: \(V_{rated} \geq 1.5 \times V_{max}\)
- ESR affects ripple voltage
- RMS current rating: \(I_{rms} \geq \Delta I_L / 2\sqrt{3}\)
- Ceramic, electrolytic, or film based on application
11. Power Losses
Conduction Loss (Switch):
\[ P_{cond} = I_{rms}^2 \cdot R_{DS(on)} \]
Switching Loss:
\[ P_{sw} = \frac{1}{2} V_{ds} I_d (t_r + t_f) f_s \]
Inductor Core Loss:
\[ P_{core} = K_c f_s^\alpha B_{ac}^\beta V_{core} \]
Inductor Copper Loss:
\[ P_{copper} = I_{L,rms}^2 \cdot R_{dc} \]
Capacitor ESR Loss:
\[ P_{ESR} = I_{C,rms}^2 \cdot ESR \]
Total Loss:
\[ P_{loss} = P_{cond} + P_{sw} + P_{core} + P_{copper} + P_{ESR} + P_{diode} \]
12. Control Techniques
Voltage Mode Control
Output voltage is directly controlled
- Simple implementation
- Single feedback loop
- Slower transient response
Current Mode Control
Inner current loop, outer voltage loop
- Faster transient response
- Inherent current limiting
- Better line regulation
Hysteretic Control
Variable frequency operation
- Very fast transient
- Simple to implement
- Variable switching frequency
13. General Design Procedure
Step-by-Step Design:
- Step 1: Specify input voltage range (\(V_{s,min}\), \(V_{s,max}\))
- Step 2: Specify output voltage and current (\(V_o\), \(I_o\))
- Step 3: Choose switching frequency (\(f_s\))
- Step 4: Calculate duty cycle range
- Step 5: Select ripple current (typically 20-40% of \(I_o\))
- Step 6: Calculate inductance: \(L = \frac{V \cdot D}{f_s \cdot \Delta I_L}\)
- Step 7: Calculate capacitance: \(C = \frac{\Delta I_L}{8 f_s \Delta V_o}\)
- Step 8: Select components with appropriate ratings
- Step 9: Design control loop (compensator)
- Step 10: Verify thermal design and efficiency
14. Important Design Considerations
PCB Layout: Keep switching loops small, use ground planes, separate power and signal grounds
Thermal Management: Ensure adequate heatsinking for switches and diodes. Use thermal vias for SMD components.
EMI/EMC: Use proper filtering at input/output. Consider snubbers for voltage spikes. Shield sensitive circuits.
Protection: Implement overcurrent, overvoltage, and thermal protection circuits.
Soft-Start: Implement to limit inrush current and stress on components during startup.