Complete Guide to Inductor Design and Selection in Switching Power Supplies

Basic Functions of Inductors in Switching Power Supplies

Switching power supplies, as the core power supply units of modern electronic devices, largely depend on the design and selection of inductors for their performance. Inductors play crucial roles in energy storage, current smoothing, and voltage conversion in switching power supplies, serving as core components for achieving efficient energy conversion.

Energy Storage and Transfer Function

In the operation of switching power supplies, the primary function of inductors is to store and transfer energy. When the switching transistor is conducting, the inductor stores energy from the input power source; when the switching transistor is turned off, the inductor releases the stored energy to the load. This periodic energy storage and release achieves voltage step-up and step-down conversion.

Energy Storage Mechanism

The magnetic field energy stored in an inductor can be expressed by the following formula:

W = (1/2)LI²

Where:

• W is the stored magnetic field energy (joules)
• L is the inductance value (henries)
• I is the current through the inductor (amperes)

This formula indicates that the energy stored in an inductor is proportional to the inductance value and the square of the current. In switching power supply design, by controlling the conduction and turn-off time of the switching transistor, the charging and discharging process of the inductor can be precisely controlled, thereby achieving stable output voltage.

Energy Transfer Process

In a typical Buck step-down circuit, the energy transfer process is divided into two phases:

1. Charging Phase (Switching Transistor Conducting):

• Input voltage is applied across the inductor
• Inductor current increases linearly: dI/dt = (Vin - Vout)/L
• Inductor stored energy increases
• Part of the energy is directly transferred to the load

2. Discharging Phase (Switching Transistor Off):

• Inductor discharges to the load through the freewheeling diode
• Inductor current decreases linearly: dI/dt = -Vout/L
• Stored magnetic field energy converts to electrical energy for the load
• Maintains stable output voltage

Voltage Conversion Function

In different topologies of switching power supplies, inductors achieve different voltage conversion functions:

Buck Step-Down Converter

• Voltage Relationship: Vout = Vin × D
• Inductor Function: Energy storage and output current smoothing
• Design Key Points: Select appropriate inductance value to control current ripple

Boost Step-Up Converter

• Voltage Relationship: Vout = Vin / (1 - D)
• Inductor Function: Energy storage and current continuity
• Design Key Points: Inductance value affects input current ripple

Buck-Boost Step-Up/Step-Down Converter

• Voltage Relationship: Vout = -Vin × D / (1 - D)
• Inductor Function: Energy transfer station
• Design Key Points: Inductor carries the entire load current

Current Continuity and Smoothing Function

Another important function of inductors is maintaining current continuity and smoothness. Due to the characteristic of inductors to resist current changes, they can effectively suppress current pulsations generated by switching actions, providing relatively smooth current to the load.

Continuous Conduction Mode (CCM)

In continuous conduction mode, the inductor current remains positive throughout the entire switching cycle and does not drop to zero. This operating mode has the following characteristics:

• Small Current Ripple: ΔI = (Vin - Vout) × D × T / L
• Stable Output Voltage: Output voltage is mainly determined by duty cycle
• Low Conduction Losses: Relatively small current RMS value
• Good EMI Characteristics: Relatively gentle current changes

Where D is the duty cycle and T is the switching period.

Discontinuous Conduction Mode (DCM)

Under light load conditions, the inductor current may drop to zero within the switching cycle, entering discontinuous conduction mode:

• Large Current Ripple: Higher peak current
• Changed Output Voltage Regulation Characteristics: Output voltage is load-dependent
• Potentially Increased Switching Losses: Due to higher peak current
• Fast Dynamic Response: But stability may decrease

Filtering and EMI Suppression Function

Inductors also undertake important filtering functions in switching power supplies, suppressing high-frequency noise and electromagnetic interference (EMI) generated by switching actions.

Output Filtering

Inductors and output capacitors form LC low-pass filters, effectively suppressing switching frequency and its harmonic components:

• Cutoff Frequency: fc = 1/(2π√LC)
• Attenuation Characteristics: -40dB/decade (second-order filter)
• Ripple Suppression: Output voltage ripple = Output current ripple × ESR

EMI Suppression

Properly designed inductors can effectively suppress conducted and radiated EMI:

• Common-Mode Noise Suppression: Use common-mode inductors to suppress common-mode noise
• Differential-Mode Noise Suppression: Output inductors suppress differential-mode noise
• Magnetic Field Shielding: Shielded inductors reduce magnetic field leakage

High-Frequency Switching Power Supply Inductor Selection Case Analysis

To better understand the application of inductors in switching power supplies, the following analyzes the inductor selection process in high-frequency switching power supplies through specific design cases.

Case 1: 5V/3A Buck Converter Design

Design Requirements

• Input voltage: 12V±10%
• Output voltage: 5V±2%
• Output current: 3A
• Switching frequency: 500kHz
• Efficiency requirement: >90%
• Output ripple: <50mV

Inductance Value Calculation

1. Basic Parameter Determination:

• Duty cycle: D = Vout/Vin = 5/12 = 0.417
• Switching period: T = 1/500kHz = 2μs
• Current ripple rate selection: 30%
• Inductor current ripple: ΔI = 0.3 × 3A = 0.9A

2. Inductance Value Calculation:
   L = (Vin - Vout) × D × T / (2 × ΔI)
   L = (12 - 5) × 0.417 × 2×10⁻⁶ / (2 × 0.9)
   L = 3.24μH

3. Standard Value Selection: Select 3.3μH standard value

Inductor Specification Determination

1. Current Specifications:

• Average current: 3A
• Peak current: 3 + 0.9/2 = 3.45A
• Saturation current requirement: >4.5A (1.3× safety factor)
• Rated current requirement: >3.5A

2. Other Specifications:

• DCR requirement: <20mΩ (efficiency consideration)
• Self-resonant frequency: >5MHz (10× switching frequency)
• Operating temperature: -40°C~+125°C

Inductor Selection Result

Based on the above requirements, select shielded power inductor:

• Inductance value: 3.3μH±20%
• Saturation current: 5.2A
• Rated current: 4.0A
• DCR: 15mΩ
• Size: 5×5×3mm
• Shield type: Ferrite shielded

Case 2: 12V/1A Boost Converter Design

Design Requirements

• Input voltage: 3.3V±5%
• Output voltage: 12V±1%
• Output current: 1A
• Switching frequency: 1MHz
• Efficiency requirement: >85%
• Input ripple: <100mA

Inductance Value Calculation

1. Basic Parameter Determination:

• Duty cycle: D = 1 - Vin/Vout = 1 - 3.3/12 = 0.725
• Switching period: T = 1MHz = 1μs
• Input current: Iin = Iout × Vout / (Vin × η) = 1 × 12 / (3.3 × 0.85) = 4.28A
• Input current ripple rate: 20%
• Input current ripple: ΔIin = 0.2 × 4.28 = 0.86A

2. Inductance Value Calculation:
   L = Vin × D × T / (2 × ΔIin)
   L = 3.3 × 0.725 × 1×10⁻⁶ / (2 × 0.86)
   L = 1.39μH

3. Standard Value Selection: Select 1.5μH standard value

Special Considerations

Special considerations for Boost circuits include:

1. Continuous Conduction Boundary:
   Lcrit = Vin × (Vout - Vin) × T / (2 × Vout × Iout_min)
   CCM must be maintained even at 10% load

2. Input Capacitor Requirements:
   Due to large input current pulsation, sufficient input capacitance is needed

3. Output Diode Selection:
   Fast recovery diodes or synchronous rectification are required

Case 3: Multi-Phase Interleaved Buck Converter

Design Requirements

• Input voltage: 48V
• Output voltage: 12V
• Output current: 20A
• Number of phases: 4
• Switching frequency: 200kHz (per phase)
• Efficiency requirement: >95%

Multi-Phase Design Advantages

1. Current Sharing: Each phase carries 5A current
2. Ripple Cancellation: 4-phase interleaving significantly reduces output ripple
3. Heat Distribution: Power losses distributed across 4 inductors
4. Dynamic Response: Equivalent switching frequency of 800kHz

Inductance Value Calculation

1. Single-Phase Inductance Value:

• Current per phase: 5A
• Current ripple rate: 40% (can be higher due to ripple cancellation effect)
• Single-phase current ripple: 2A
• Single-phase inductance value: L = (48-12) × (12/48) × (1/200kHz) / (2 × 2) = 2.25μH

2. Total Ripple Calculation:

• Ripple cancellation coefficient for 4-phase interleaving is approximately 0.25
• Total output current ripple: 2A × 0.25 = 0.5A
• Ripple rate: 0.5/20 = 2.5%

Inter-Phase Matching Requirements

1. Inductance Value Matching: Within ±5%
2. DCR Matching: Within ±10%
3. Saturation Characteristic Matching: Ensure simultaneous saturation
4. Temperature Characteristic Matching: Avoid imbalance due to temperature drift

Through these case analyses, it can be seen that inductor selection requires comprehensive consideration of circuit topology, performance requirements, cost constraints, and other factors, making it a systematic engineering decision process.

Impact of Inductor Saturation on Power Supply Performance

Inductor saturation is a critical issue that must be addressed in switching power supply design. When the operating current of an inductor exceeds its saturation current, the inductance value drops dramatically, severely affecting the performance and reliability of the power supply.

Physical Mechanism of Inductor Saturation

Inductor saturation is an inherent characteristic of magnetic materials. When the magnetic field strength exceeds the saturation magnetic field strength of the material, the magnetic permeability drops sharply.

Magnetization Curve and Saturation

The B-H curve (magnetization curve) of magnetic materials describes the relationship between magnetic flux density B and magnetic field strength H:

1. Linear Region: Constant permeability, B = μH
2. Saturation Region: Decreased permeability, dB/dH → 0
3. Saturation Flux Density Bsat: Maximum magnetic flux density the material can achieve

Relationship Between Inductance Value and Permeability

Inductance value is directly related to the permeability of the magnetic core:

L = (μ₀ × μᵣ × N² × A) / l

Where:

• μ₀ is the permeability of free space
• μᵣ is the relative permeability
• N is the number of winding turns
• A is the core cross-sectional area
• l is the magnetic path length

When the core saturates, μᵣ drops sharply, causing a significant reduction in inductance value.

EMI Considerations and Suppression Techniques for Power Inductors

Electromagnetic interference (EMI) is an important consideration in switching power supply design. Inductors are both sources of EMI generation and important means of EMI suppression. Proper inductor design and selection are crucial for meeting EMC standards.

EMI Generation Mechanisms

EMI Sources in Switching Power Supplies

EMI in switching power supplies mainly originates from:

1. Fast Switching Actions of Switching Transistors:

• Generate high-frequency harmonics
• dv/dt and di/dt produce displacement and conduction currents
• Parasitic parameters form resonant circuits

2. Magnetic Field Changes in Inductors:

• Flux changes produce induced electric fields
• Nonlinear characteristics of core materials generate harmonics
• Parasitic capacitance between windings forms high-frequency paths

3. PCB Routing and Parasitic Parameters:

• Trace inductance and capacitance create antenna effects
• Discontinuous ground planes produce common-mode noise
• Improper high-frequency return paths cause radiation

EMI Propagation Paths

EMI propagates through the following paths:

1. Conducted Propagation:

• Differential-mode conduction: Propagates through power lines
• Common-mode conduction: Propagates through power lines to ground
• Frequency range: 150kHz~30MHz

2. Radiated Propagation:

• Near-field radiation: Electromagnetic fields close to the source
• Far-field radiation: Electromagnetic waves far from the source
• Frequency range: 30MHz~1GHz

EMI Suppression Techniques

1. Inductor Selection Strategy

Selecting appropriate inductor types is crucial for EMI suppression:

• Shielded Inductors:

• Completely enclosed magnetic field, small leakage field

• Suitable for EMI-sensitive applications

• Relatively high cost

• Semi-Shielded Inductors:

• Partial magnetic field shielding

• Balance between performance and cost

• Suitable for general applications

• Unshielded Inductors:

• Low cost, high performance

• Require proper layout to reduce EMI

• Suitable for applications with less stringent EMI requirements

2. Filter Circuit Design

Proper filter circuit design is key to EMI suppression:

• Input Filters:

• Common-mode inductor + differential-mode inductor + capacitor

• Suppress conducted EMI

• Prevent internal noise from propagating to the power grid

• Output Filters:

• LC filters suppress switching ripple

• Reduce high-frequency noise at the output

• Improve EMI environment at the load end

• Multi-Stage Filtering:

• Multi-stage filtering with different cutoff frequencies

• Improve high-frequency attenuation characteristics

• Avoid limitations of single-stage filtering

3. PCB Layout Optimization

PCB layout has significant impact on EMI suppression:

• Inductor Layout:

• Keep away from sensitive circuits

• Avoid magnetic field coupling

• Consider thermal requirements

• Ground Plane Design:

• Complete ground plane

• Shortest return path

• Avoid ground plane splits

• Trace Design:

• Shortest connection paths

• Avoid forming loop antennas

• Control trace impedance

4. Shielding Techniques

Shielding techniques are effective methods for suppressing radiated EMI:

• Magnetic Shielding:

• Use high-permeability materials

• Shield low-frequency magnetic fields

• Suitable for power frequency and low-frequency applications

• Electric Shielding:

• Use conductive materials

• Shield high-frequency electric fields

• Requires good grounding

• Electromagnetic Shielding:

• Combines magnetic and electric shielding

• Full-spectrum EMI suppression

• Higher cost but better effectiveness