Non-Isolated and Isolated DC–DC Converters

Introduction and Context

A DC–DC converter is a power-electronic circuit that converts one level of direct voltage to another while controlling voltage, current, power flow, or electrical isolation. Converters are central to switched-mode power supplies, renewable-energy systems, electric vehicles, battery storage, telecommunications, industrial drives, aircraft power systems, and data-centre power supplies.

The essential function is achieved by rapidly switching semiconductor devices and using inductors, capacitors, transformers, and control systems to obtain a controlled average output. Unlike a linear regulator, which dissipates excess voltage mainly as heat, a switched converter can achieve high efficiency because the semiconductor ideally operates either with nearly zero voltage or nearly zero current.

Converters are classified as:

• Non-isolated converters, in which input and output share an electrical reference or conductive path.
• Isolated converters, in which a transformer provides galvanic separation and often changes the voltage ratio.

The choice between these families involves more than voltage conversion. It also depends on safety, grounding, electromagnetic interference, transient response, bidirectional power flow, efficiency, power density, and control complexity.

Learning Objectives

After studying this chapter, the reader should be able to:

1. Explain the operating principles of major non-isolated and isolated DC–DC converters.
2. Derive ideal voltage-conversion relationships using inductor volt–second and capacitor charge balance.
3. Distinguish continuous-conduction mode (CCM), discontinuous-conduction mode (DCM), and boundary conduction.
4. Select converter topologies for practical voltage, power, isolation, and regulation requirements.
5. Calculate approximate component stresses, ripple, duty ratio, and efficiency.
6. Explain transformer reset, leakage inductance, soft switching, and control considerations.
7. Evaluate a converter design against thermal, EMI, safety, reliability, and regulatory constraints.

1. Fundamental Principles of Switched DC–DC Conversion

1.1 Ideal switching and averaging

A switch alternates between states at switching frequency f_s, with period T_s = 1/f_s. The duty ratio is

where t_on is the interval for which the main switch is on. In an ideal circuit, switch and diode losses are neglected, passive components are lossless, and steady-state periodic operation is assumed.

Two balance principles are particularly important:

Inductor volt–second balance. In steady state, the average voltage across an inductor over one switching period is zero:

Capacitor charge balance. In steady state, the average capacitor current is zero:

These relationships are exact for periodic steady state. The familiar conversion ratios derived from them generally assume ideal components and a specified conduction mode.

1.2 CCM, DCM, and boundary conduction

In CCM, inductor current never reaches zero during a switching period. In DCM, it reaches zero for part of the period. Boundary conduction is the limiting condition between the two. Conversion ratios, device stresses, and control characteristics differ substantially between CCM and DCM.

For an inductor,

Thus, for an approximately constant inductor voltage over an interval,

where L is inductance in henries, v_L is volts, and ∆t is seconds. The result has units of amperes.

1.3 Practical non-idealities

Real converters include switch on-resistance, diode forward voltage, inductor winding resistance, capacitor equivalent series resistance (ESR), transformer copper and core losses, finite switching times, parasitic capacitance, and leakage inductance. Consequently,

where η is efficiency and P_out and P_in are output and input power. A useful engineering loss model is

where the terms represent conduction, switching, magnetic, capacitor, and control losses. This is a bookkeeping approximation; each term requires a technology-specific model.

2. Non-Isolated Converters

2.1 Buck converter

The buck converter produces an output lower than the input in its normal operating range. During switch ON, the input is connected to the inductor and the inductor current rises. During switch OFF, the freewheeling diode or synchronous MOSFET provides the inductor-current path.

For ideal CCM operation, inductor volt–second balance gives

where V_in is input voltage and V_o is output voltage. The ideal duty ratio is therefore D = V_o/V_in.

For a switching period with approximately constant voltages, the peak-to-peak inductor ripple is

Using V_o = DV_in, an equivalent expression is

The approximate output-voltage ripple caused by an ideal capacitor is

This assumes triangular capacitor current, negligible ESR, and sufficiently small ripple. ESR adds an approximate ripple component ∆i_L × ESR.

The critical inductance separating CCM and DCM for an ideal buck converter is approximately

where R = V_o/I_o is the load resistance. This expression assumes a resistive load and ideal operation.

Synchronous rectification replaces the diode with a controlled MOSFET. It reduces conduction loss at low output voltage but requires dead-time control to prevent shoot-through.

2.2 Boost converter

The boost converter raises voltage above the input. During ON time, the inductor is connected across the source and stores energy. During OFF time, the inductor releases energy through the diode to the output.

For ideal CCM operation,

The switch voltage stress is ideally approximately V_o, and diode reverse-voltage stress is also of this order. As D approaches unity, the theoretical gain becomes very large, but conduction loss, current stress, control sensitivity, and parasitic effects become severe.

The input or inductor current ripple is

The output capacitor supplies the load during the ON interval, giving the approximate ripple

neglecting ESR. Unlike the buck converter, the boost converter has a right-half-plane zero in its CCM control-to-output transfer function. This limits achievable control bandwidth because increasing duty ratio initially reduces delivered output energy before the stored inductor energy arrives at the output.

2.3 Buck–boost and related converters

The classical inverting buck–boost converter can produce an output magnitude either below or above the input, but its output polarity is reversed. In ideal CCM,

The switch and diode experience relatively high voltage stress, approximately equal to V_in + |V_o| in the idealized circuit.

The Ćuk converter and SEPIC converter use capacitive energy transfer. The Ćuk converter normally inverts polarity and can provide relatively continuous input and output currents. The SEPIC converter is non-inverting and can maintain regulation when the input crosses the output voltage, making it useful in battery and automotive systems. These advantages are accompanied by additional capacitors, inductors, component stress, and control complexity.

2.4 Four-quadrant and bidirectional converters

A synchronous buck converter operated with controlled reverse current can form a bidirectional buck–boost stage. Such converters are used for battery charging and regenerative braking. The power direction is controlled by the relative voltage of the two ports and the average inductor current.

A bidirectional converter must address:

• current-sensor offset and polarity;
• dead-time and body-diode conduction;
• transition between charging and discharging;
• battery protection and state-of-charge limits;
• fault isolation and pre-charge requirements.

3. Isolated DC–DC Converters

Galvanic isolation prevents direct conductive current between input and output. The transformer transfers energy magnetically and can provide voltage scaling, multiple outputs, grounding flexibility, and safety separation. Isolation is especially important when the source is connected to a hazardous mains system or when different system grounds must be separated.

A high-frequency transformer is much smaller than a line-frequency transformer because transformer volume is strongly related to volt–seconds and operating frequency. However, increasing frequency raises core loss, proximity effect, skin effect, switching loss, and electromagnetic interference.

3.1 Transformer relationships

For an ideal transformer,

where N_p and N_s are primary and secondary turns. Current ratio is inversely related:

The transformer must not receive a nonzero average voltage over repeated cycles. A dc component causes flux walking and possible core saturation. The core flux change follows Faraday’s law:

where ∆B is flux-density change in teslas, A_e is effective core area in square metres, and the integral is primary volt–seconds.

3.2 Flyback converter

A flyback converter stores energy in a magnetizing inductance while the switch is ON and transfers that energy to the output while the switch is OFF. The transformer is therefore better understood as a coupled inductor than as an ordinary continuously transferring transformer.

For an ideal flyback in CCM, with turns ratio n = N_s/N_p and output magnitude V_o,

The output diode conducts during the OFF interval. The switch must withstand approximately the input voltage plus the reflected output voltage, with additional overshoot caused by leakage inductance. An RCD clamp, active clamp, or dissipative/energy-recovery snubber is commonly required.

Flyback converters are attractive below approximately several tens of watts to a few hundred watts, depending on design objectives, because one magnetic component performs energy storage and isolation. Their limitations include high ripple, high peak currents, leakage-energy problems, and difficult electromagnetic compatibility at higher power.

3.3 Forward converter

In a forward converter, energy is transferred to the secondary while the primary switch is ON. An output inductor smooths the secondary current. Because the transformer does not normally reset through the output path, a reset winding, reset clamp, or active-clamp mechanism is required.

For an ideal single-switch forward converter in CCM,

where n = N_s/N_p. The duty ratio is limited by the reset requirement. In the classical reset-winding arrangement, the maximum duty ratio is commonly near 0.5 when the reset winding has the same turns ratio and reset voltage magnitude, although other reset schemes change this limit.

Compared with a flyback converter, a forward converter generally has lower output ripple and lower peak energy-storage requirements, but it uses more magnetic components and a more involved reset circuit.

3.4 Push–pull converter

A push–pull converter alternately applies opposite voltage polarities to a transformer primary, usually using two switches and a centre-tapped primary. Ideally, the transformer flux is reset by the alternating excitation. The topology can achieve good transformer utilization but is vulnerable to unequal switch timing or unequal voltage drops, which can cause flux imbalance and saturation.

3.5 Half-bridge and full-bridge converters

Half-bridge converters apply alternating positive and negative voltage to a transformer primary using two switches and a split or capacitive dc bus. Full-bridge converters use four switches and apply approximately +V_in or −V_in to the transformer primary. They are suitable for medium- and high-power applications.

Phase-shift full-bridge converters regulate power by changing the phase displacement between bridge legs. Transformer leakage inductance and device output capacitances can be used to achieve zero-voltage switching (ZVS), reducing turn-on loss. However, circulating current, duty-cycle loss, light-load performance, and control timing require careful optimization.

3.6 Resonant isolated converters

LLC resonant converters use an inductance–inductance–capacitance network to shape current and achieve soft switching over a useful load range. Frequency modulation, rather than simple fixed-frequency duty-ratio control, is commonly used. At resonance, circulating energy can be efficiently transferred; away from resonance, gain changes but reactive current and control sensitivity may increase.

Resonant converters provide high power density and low switching loss, particularly in electric-vehicle chargers and server power supplies. Their design requires accurate treatment of magnetizing inductance, leakage inductance, resonant frequency, transformer parasitics, gain curves, and control-region boundaries.

4. Control, Modelling, and Stability

A regulated converter compares a measured output with a reference and adjusts duty ratio or switching frequency. Voltage-mode control uses output-voltage error directly; current-mode control adds an inner current loop and improves dynamic response and current limiting.

A small-signal averaged model linearizes the converter around an operating point. The control-to-output transfer function depends on topology, conduction mode, load, parasitics, and compensation. In CCM boost and buck–boost converters, the right-half-plane zero imposes a bandwidth limitation. A practical design generally places the crossover frequency substantially below the right-half-plane-zero frequency and below one-half of the switching frequency.

Digital controllers provide adaptive dead time, telemetry, fault logging, nonlinear control, and predictive algorithms. Nevertheless, sampling delay, quantization, computational latency, software failure, and cyber-security must be included in the engineering assessment. AI-based control can assist parameter estimation or fault diagnosis, but it does not remove the need for deterministic protection, validated models, and hardware shutdown paths.

5. Design Methodology and Component Stress

A robust design begins with a specification: input-voltage range, output voltage, power, allowable ripple, transient limits, isolation rating, operating temperature, efficiency target, lifetime, and standards.

A typical sequence is:

1. Select an appropriate topology based on voltage ratio, power, isolation, and power-flow direction.
2. Determine the worst-case duty ratio and current conditions over the complete input and load range.
3. Select switching frequency considering efficiency, size, EMI, and control bandwidth.
4. Select inductance from allowable ripple and verify CCM/DCM boundaries.
5. Select capacitors from ripple current, capacitance, ESR, voltage, lifetime, and bias effects.
6. Select semiconductor voltage and current ratings with transient margin, not merely nominal values.
7. Design magnetic components for flux-density, copper-loss, insulation, thermal, and creepage requirements.
8. Design gate drive, dead time, snubbers, clamps, current sensing, and protection.
9. Validate conducted and radiated EMI, thermal performance, dynamic response, and abnormal operation.

For a buck converter, if the desired ripple ratio is r = ∆i_L/I_o, the inductance estimate is

The selected value must be checked at bias and temperature because real inductors lose inductance as current increases.

Semiconductor selection must consider:

• static voltage and current ratings;
• switching energy and gate charge;
• reverse-recovery behaviour;
• short-circuit withstand time;
• thermal resistance and junction temperature;
• avalanche and repetitive transient capability.

6. Worked Example: CCM Buck Converter

An ideal buck converter supplies 24 V at 120 W from a 48 V dc source. The switching frequency is 100 kHz, and the desired inductor ripple is limited to 20% of the output current. Determine the duty ratio, load current, and approximate inductance.

The duty ratio is

The load current is

The allowed ripple is

Using the buck ripple equation,

Thus, an ideal first estimate is 120 µH. A practical design must account for tolerance, dc-bias inductance reduction, winding loss, thermal rise, capacitor ripple, switch loss, and the fact that actual duty ratio exceeds 0.5 because of conduction losses.

7. Illustrative Case: Isolated Auxiliary Supply for an Industrial Drive

Background. An industrial motor drive requires a 15 W isolated auxiliary supply producing 15 V for control electronics from a 300–400 V dc link. The control board must remain separated from the power-stage reference.

Problem. The supply must operate over a wide input range, meet reinforced-isolation requirements, limit conducted EMI, and survive start-up and output short circuit.

Analysis. A flyback topology is suitable because the power is modest and isolation is essential. At the minimum input voltage, the designer selects a nominal duty ratio that leaves adequate regulation range. The transformer is designed as a coupled inductor, with magnetizing inductance chosen from allowable peak current and stored energy. Leakage inductance is measured or estimated because it determines clamp energy and switch-voltage overshoot.

Approach. The design uses an isolated feedback signal, such as an optocoupler or isolated amplifier, and a primary-side controller with cycle-by-cycle current limiting. A clamp limits leakage-induced voltage. Creepage and clearance are established from the applicable insulation category, working voltage, pollution degree, and material group. Y-capacitor selection is made only after leakage-current and EMI limits are verified. Thermal testing is performed at minimum and maximum input voltage and at enclosure worst-case temperature.

Outcome. The topology meets the power and isolation requirement with relatively few components, but its high peak currents require careful transformer construction, snubber optimization, and EMI filtering. The case demonstrates that topology selection is a system decision rather than a choice based only on conversion ratio.

Learning points. Isolation affects magnetics, feedback, safety, layout, testing, and fault behaviour. A nominally efficient converter can fail compliance because of insulation, leakage current, common-mode noise, or inadequate transient protection.

8. Limitations, Safety, and Professional Practice

Non-isolated converters cannot by themselves provide protective separation. Their output may be hazardous if the input is hazardous, even when the output voltage is numerically low. Isolated converters also require verified insulation systems; a transformer symbol does not automatically imply safety isolation.

Important practices include controlled creepage and clearance, reinforced insulation where required, fusing, over-voltage and over-current protection, safe discharge of capacitors, interlocks, thermal shutdown, and fault testing. Standards depend on the application and jurisdiction; designers must consult the applicable product, insulation, EMC, and environmental standards rather than relying on generic voltage rules.

Layout is part of the circuit. High-di/dt loops must be compact, gate-drive returns must be controlled, power and signal grounds must be intentionally connected, and shielding or common-mode filtering must not compromise safety isolation. Measurement requires appropriately rated differential probes and current probes; an oscilloscope ground clip connected incorrectly can create a lethal short circuit.

Contemporary developments include gallium-nitride and silicon-carbide switches, planar magnetics, integrated power modules, digital active-clamp control, synchronous rectification, hybrid switched-capacitor converters, and wide-bandgap devices operating at higher frequency. These technologies can improve power density, but their fast transitions increase layout sensitivity and EMI risk.

Chapter Summary

DC–DC converters regulate voltage and power by controlled switching and energy storage. Inductor volt–second balance and capacitor charge balance provide the foundation for ideal conversion-ratio derivations. Buck, boost, buck–boost, Ćuk, SEPIC, and bidirectional converters are non-isolated topologies whose suitability depends on voltage range, polarity, ripple, and power-flow requirements.

Isolated converters use high-frequency transformers to provide galvanic separation and voltage scaling. Flyback converters store and then transfer energy, while forward, push–pull, half-bridge, full-bridge, and resonant converters transfer energy through transformer action in different ways. Transformer reset, flux balance, leakage inductance, insulation, and common-mode EMI are central design issues.

Practical design requires analysis of CCM and DCM, semiconductor and magnetic stresses, control-loop stability, thermal behaviour, EMI, protection, safety standards, and manufacturing variation. Efficiency and power density must never be pursued independently of reliable protection and verified isolation.

Key Terms

DC–DC converter: Circuit that converts one dc voltage or current level to another.

Duty ratio: Fraction of a switching period for which a switch is commanded on.

CCM: Conduction mode in which inductor current remains above zero.

DCM: Conduction mode in which inductor current reaches zero.

Volt–second balance: Zero average inductor voltage in periodic steady state.

Charge balance: Zero average capacitor current in periodic steady state.

Buck converter: Step-down non-isolated converter.

Boost converter: Step-up non-isolated converter.

Buck–boost converter: Converter capable of step-up or step-down magnitude, usually with polarity inversion.

Galvanic isolation: Absence of a direct conductive path between two electrical circuits.

Flyback converter: Isolated converter that stores energy in magnetizing inductance and transfers it during another switching interval.

Forward converter: Isolated converter that transfers energy to the output during switch conduction.

Flux walking: Progressive displacement of transformer operating flux caused by volt–second imbalance.

Leakage inductance: Inductance associated with magnetic flux that does not link both windings.

Soft switching: Switching with reduced voltage or current overlap, such as ZVS or ZCS.

Right-half-plane zero: Dynamic feature that can limit control bandwidth because it produces an initially adverse output response.

Creepage: Shortest path along an insulating surface between conductors.

Clearance: Shortest distance through air between conductors.

Synchronous rectification: Use of controlled semiconductor switches instead of diodes for rectification.

Review Questions

Short Answer Questions

1. State the assumptions behind the ideal CCM buck conversion ratio.
2. Why does a boost converter become difficult to regulate at very high duty ratio?
3. Distinguish a flyback transformer from a transformer used for direct energy transfer.
4. What is transformer flux walking, and why is it dangerous?
5. Define creepage and clearance.

Long Answer Questions

1. Derive the ideal CCM conversion ratios of buck, boost, and inverting buck–boost converters using inductor volt–second balance.
2. Compare flyback and forward converters in terms of energy transfer, component stress, power range, and control requirements.
3. Explain the operation and design considerations of a phase-shift full-bridge converter.
4. Discuss the influence of CCM, DCM, and boundary conduction on converter modelling and control.
5. Develop a systematic design procedure for an isolated industrial power supply, including safety and EMI considerations.

Analytical / Application Questions

1. A 48 V-to-12 V, 240 W buck converter operates at 200 kHz with a permitted inductor ripple of 25% of load current. Calculate the ideal duty ratio, load current, and first-estimate inductance.
2. An ideal CCM boost converter must raise 24 V to 60 V. Calculate its duty ratio and explain two practical reasons why the real duty ratio and efficiency will differ from the ideal result.
3. Select and justify a suitable isolated topology for a 2 kW bidirectional battery charger requiring high efficiency, galvanic isolation, and wide-range soft switching. State the principal magnetic, control, and protection risks.

Multiple Choice Questions with Answers

Question 1

For an ideal buck converter operating in CCM, the output voltage is:

A. V_in/(1−D)

B. D V_in

C. −D V_in/(1−D)

D. V_in/D

Correct Answer: B. D V_in

Question 2

The ideal CCM conversion ratio of a boost converter is:

A. D

B. 1−D

C. 1/(1−D)

D. D/(1−D) with reversed polarity

Correct Answer: C. 1/(1−D)

Question 3

Which balance condition is used to derive steady-state inductor conversion ratios?

A. Average inductor voltage is zero

B. Average inductor current is zero

C. Average capacitor voltage is zero

D. Average switch power is zero

Correct Answer: A. Average inductor voltage is zero

Question 4

A 48 V ideal buck converter produces 12 V in CCM. Its duty ratio is:

A. 0.125

B. 0.25

C. 0.50

D. 4.0

Correct Answer: B. 0.25

Question 5

Which isolated converter stores energy primarily in its magnetizing inductance during switch ON time?

A. Forward converter

B. Flyback converter

C. Half-bridge converter

D. Phase-shift full bridge

Correct Answer: B. Flyback converter

Question 6

The principal danger of transformer volt–second imbalance is:

A. Capacitor ESR reduction

B. Flux walking and core saturation

C. Lower switching frequency

D. Removal of leakage inductance

Correct Answer: B. Flux walking and core saturation

Question 7

A right-half-plane zero in a CCM boost converter generally:

A. Allows unlimited control bandwidth

B. Limits control bandwidth

C. Eliminates input current ripple

D. Provides galvanic isolation

Correct Answer: B. Limits control bandwidth

Question 8

For a 24 V, 120 W output, the output current is:

A. 0.2 A

B. 2 A

C. 5 A

D. 20 A

Correct Answer: C. 5 A

Question 9

Which feature is characteristic of synchronous rectification?

A. A controlled MOSFET replaces a rectifier diode

B. The transformer is removed

C. The converter must operate in DCM

D. Isolation is automatically provided

Correct Answer: A. A controlled MOSFET replaces a rectifier diode

Question 10

Creepage is measured:

A. Through the magnetic core

B. Along an insulating surface

C. Only across a semiconductor junction

D. As the switching period

Correct Answer: B. Along an insulating surface