 # 7. Introduction to DC/DC Converters

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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

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

Block Diagram of Typical AC Input, Regulated DC Output System
Power Electronics Chapter 7 Introduction to DC/DC Converters

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

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

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

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

Buck Converter: Startup Waveforms
Power Electronics Chapter 7 Introduction to DC/DC Converters

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

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

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

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

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

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

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

Buck Conv.: Output Voltage Ripple
ESR is assumed to be zero; continuous conduction mode Power Electronics Chapter 7 Introduction to DC/DC Converters

Buck Conv.: Output Voltage Ripple
ESR is assumed to be zero Power Electronics Chapter 7 Introduction to DC/DC Converters

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

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

Pulse-Width Modulation (PWM) in DC-DC Converters
Power Electronics Chapter 7 Introduction to DC/DC Converters

Step-Up (Boost) DC-DC Converter
Output voltage must be greater than the input Power Electronics Chapter 7 Introduction to DC/DC Converters

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

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

Boost Converter: Discont. Conduction
Occurs at light loads Power Electronics Chapter 7 Introduction to DC/DC Converters

Boost: Limits of Cont./Discont. Conduction
The output voltage is held constant Power Electronics Chapter 7 Introduction to DC/DC Converters

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

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

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

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

Buck-Boost: Limits of Cont./Discont. Conduction
The output voltage is held constant Power Electronics Chapter 7 Introduction to DC/DC Converters

Buck-Boost: Discontinuous Conduction
This occurs at light loads Power Electronics Chapter 7 Introduction to DC/DC Converters

Buck-Boost Converter: Limits of Cont./Discont. Conduction
The output voltage is held constant Power Electronics Chapter 7 Introduction to DC/DC Converters

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

Buck-boost Converter: Output Voltage Ripple
ESR is assumed to be zero Power Electronics Chapter 7 Introduction to DC/DC Converters

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

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

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

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

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

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

Output Ripple in Converters for DC-Motor Drives
Bi-polar and uni-polar voltage switching Power Electronics Chapter 7 Introduction to DC/DC Converters

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

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

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

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

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