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**7. Introduction to DC/DC Converters**

Marc T. Thompson, Ph.D. Adjunct Associate Professor of Electrical Engineering Worcester Polytechnic Institute Thompson Consulting, Inc. 9 Jacob Gates Road Harvard, MA Phone: (978) Website: Portions of these notes excerpted from the CD ROM accompanying Mohan, Undeland and Robbins, Power Electronics Converters, Applications and Design, 3d edition, John Wiley 2003 Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Chapter 7 Introduction to DC/DC Converters**

Summary Non-isolated (i.e. no transformer) DC/DC converters Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Block Diagram of Typical AC Input, Regulated DC Output System**

Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Stepping Down a DC Voltage**

In this example, the average value of the output voltage = DVin where D is the DUTY CYCLE in PWM (pulse-width modulation) control D = ton/Ts Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Chapter 7 Introduction to DC/DC Converters**

Step-Down (Buck) DC-DC Converter Add LC filter to reduce switching ripple Flyback diode also needed Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Buck Converter: Waveforms**

Steady state; inductor current flows continuously Waveform below for buck in continuous conduction mode Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Buck Converter: SPICE Circuit**

Circuit shown: fsw = 200 kHz, D = 0.5 Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Buck Converter: Startup Waveforms**

Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Analysis for DC/DC Converter in Continuous Conduction and Steady State**

In steady state, the inductor current returns to the same value every switching cycle, or every T seconds Therefore, the inductor ripple current UP equals ripple DOWN Several assumptions to simplify analysis: Periodic steady state --- all startup transients have died out Small ripple --- ripple is small compared to average values Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Buck Converter in Continuous Conduction**

In continuous conduction, buck converter has 2 states --- switch OPEN and switch CLOSED Switch closed (for time DT) Switch open (for time (1-D)T) Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Buck Converter in Continuous Conduction**

The inductor ripple current UP equals ripple DOWN We already knew this result from first principles, but this methodology of inductor Volt-second balance can be used to evaluate other more complicated DC/DC converters Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Buck Converter: Waveforms at the Boundary of Cont./Discont. Conduction**

ILB = critical current below which inductor current becomes discontinuous Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Buck Converter: Discontinuous Conduction Mode**

Steady state; inductor current discontinuous (i.e. it goes zero for a time) Note that output voltage depends on load current Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Buck: Limits of Discontinuous Conduction**

The duty-ratio of 0.5 has the highest value of the critical current For low output current, buck goes discontinuous Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Buck: Limits of Cont./Discont. Conduction**

In regulated power supply, Vd may fluctuate but Vo is kept constant by control of D Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Buck Conv.: Output Voltage Ripple**

ESR is assumed to be zero; continuous conduction mode Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Buck Conv.: Output Voltage Ripple**

ESR is assumed to be zero Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Buck Conv.: Calculations**

Shown for SPICE example with fsw = 200 kHz, D = 0.5, L = 33 µH, C = 10 µF, Io = 1A Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Buck: SPICE Result in Periodic Steady State**

Analysis shows inductor ripple = 0.38 A-pp, output voltage ripple = 24 mV-pp, confirmed by SPICE Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Pulse-Width Modulation (PWM) in DC-DC Converters**

Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Step-Up (Boost) DC-DC Converter**

Output voltage must be greater than the input Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Boost Converter Waveforms**

Continuous current conduction mode Switch closed: Switch open: Inductor Volt-second balance: Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Boost: Limits of Cont./Discont. Conduction**

The output voltage is held constant For low load current, current conduction becomes discontinuous Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Boost Converter: Discont. Conduction**

Occurs at light loads Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Boost: Limits of Cont./Discont. Conduction**

The output voltage is held constant Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Boost Converter: Effect of Parasitics**

The duty-ratio D is generally limited before the parasitic effects become significant Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Boost Converter Output Ripple**

ESR is assumed to be zero Assume that all the ripple component of diode current flows through capacitor; DC component flows through resistor Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Step-Down/Up (Buck-Boost) Converter**

The output voltage can be higher or lower than the input voltage Note output phase inversion Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Buck-Boost Converter: Waveforms**

Continuation conduction mode Switch closed: Switch open: Inductor Volt-second balance: Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Buck-Boost: Limits of Cont./Discont. Conduction**

The output voltage is held constant Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Buck-Boost: Discontinuous Conduction**

This occurs at light loads Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Buck-Boost Converter: Limits of Cont./Discont. Conduction**

The output voltage is held constant Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Buck-Boost Converter: Effect of Parasitics**

The duty-ratio is limited to avoid these parasitic effects from becoming significant Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Buck-boost Converter: Output Voltage Ripple**

ESR is assumed to be zero Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Chapter 7 Introduction to DC/DC Converters**

Cuk DC-DC Converter The output voltage can be higher or lower than the input voltage Capacitor C1 is primary means of storing and transferring energy from input to output When switch is ON, C1 discharges through the switch and transfers energy to the output When switch is OFF, capacitor C1 is charged through the diode by energy from the input and L1 Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Cuk DC-DC Converter: Waveforms**

The capacitor voltage is assumed constant (very large) Note phase inversion at the output Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Chapter 7 Introduction to DC/DC Converters**

SEPIC Converter Single-ended primary inductance converter (SEPIC) Can buck or boost the voltage Note that output is similar to buck-boost, but without a phase inversion Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Converter for DC-Motor Drives**

Four quadrant operation is possible For: DC motor drives DC to AC inverters for UPS Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Chapter 7 Introduction to DC/DC Converters**

Converter Waveforms Bi-polar voltage switching Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Chapter 7 Introduction to DC/DC Converters**

Converter Waveforms Uni-polar voltage switching Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Output Ripple in Converters for DC-Motor Drives**

Bi-polar and uni-polar voltage switching Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Switch Utilization in DC-DC Converters**

It varies significantly in various converters PT = VTIT where VT and IT are peak switch voltage and current In direct converters (buck and boost) switch utilization is good; in indirect converter (buck-boost and Cuk) switch utilization is poor Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Equivalent Circuits in DC-DC Converters**

Replacing inductors and capacitors by current and voltage sources, respectively Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Reversing the Power Flow in DC-DC Conv.**

For power flow from right to left, the input current direction should also reverse Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Real-World Issue: Capacitor ESR**

Real-world capacitors have equivalent series resistance (ESR) This ESR may have dominant effect on output ripple Power Electronics Chapter 7 Introduction to DC/DC Converters

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**Effects of Capacitor ESR**

Without ESR, output ripple is 24 mV-pp ESR has increased ripple to approximately 30 mV-pp Power Electronics Chapter 7 Introduction to DC/DC Converters

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