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**Power Electronics Notes 07A Introduction to DC/DC Converters**

Marc T. Thompson, Ph.D. Thompson Consulting, Inc. 9 Jacob Gates Road Harvard, MA Phone: (978) Fax: (888) Web: 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 Other notes © Marc Thompson, 2008

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**Summary Non-isolated (i.e. no transformer) DC/DC converters**

Step down (buck) Step up (boost) Buck-boost Cuk converter SEPIC Full-bridge Comparison of DC/DC converters

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

Typically, a power supply front end has uncontrolled full-wave diode rectifier, followed by a bus (“hold-up”) capacitor, followed by a DC/DC converter with active feedback control

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**Offline Flyback Converter**

Reference:

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**Some Real-World Design Issues that We’ll Get to Later On in the Term**

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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, the fraction of the total switching cycle that the switch is ON

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**Frequency Spectrum of Vo**

The output voltage contains switching harmonics Vo = Vd D fs= 1/Ts

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**Adding a Lowpass Filter to the Buck Converter**

The goal of the lowpass filter LC is to pass the DC component, while attenuating the switching components As frequency increases, XL increases and XC decreases 8

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**Adding a Lowpass Filter to the Buck Converter**

Corner frequency: -40 dB/decade The corner frequency must be lower than the switching frequency to attenuate the switching harmonics. 9

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**Step-Down (Buck) Converter**

Diode needed to provide current path for output current when switch is OFF

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**Buck Converter in Continuous Conduction**

In periodic steady state, inductor current flows continuously Waveform here are for buck in continuous conduction mode; note that inductor current never decays to zero In discontinuous conduction mode, there are 3 states

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**Buck Converter: PSPICE Circuit**

Circuit shown: fsw = 200 kHz, D = 0.5

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**Buck Converter: Startup Waveforms**

These waveforms are shown for a constant duty cycle of D = 0.5 during startup Note large overshoot on output voltage and inductor current

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**Same Circuit --- PSIM Simulation**

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**Same Circuit --- PSIM Simulation**

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**Analysis for DC/DC Converters 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. For instance, output voltage ripple is small compared to the DC value

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**Inductor Voltage and Current**

Remember that in an inductor:

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**Buck Converter in Continuous Conduction**

In continuous conduction, buck converter has 2 states --- switch OPEN and switch CLOSED. We can solve for output voltage by focusing on inductor Volt-second balance

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**Buck Converter in Continuous Conduction**

Switch closed (for time DT) Switch open (for time (1-D)T)

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**Buck Converter in Continuous Conduction**

The inductor ripple current UP equals ripple DOWN We already knew this result by inspection, but this methodology of inductor Volt-second balance can be used to evaluate other more complicated DC/DC converters, such as the boost, buck-boost, etc.

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**Buck Converter in Continuous Conduction --- Idealized Switching Waveforms**

Idealized because we assume that switches and diodes turn on and off with zero risetime

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

ILB = critical current below which inductor current becomes discontinuous

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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

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**Buck Converter: Capacitor Current Ripple**

Continuous conduction mode

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**Buck Converter: Output Voltage Ripple**

ESR is assumed to be zero; continuous conduction mode

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**Buck Converter: Output Voltage Ripple**

ESR is assumed to be zero

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**Example 1: Buck Converter Calculations**

Shown for SPICE example with fsw = 200 kHz, D = 0.5, L = 33 µH, C = 10 µF, Io = 1A

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**Example 1: Buck in Periodic Steady State**

Analysis shows inductor ripple = 0.38 A-pp, output voltage ripple = 24 mV-pp, confirmed by SPICE

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

Output voltage is greater than the input, with the same polarity

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**Boost Converter Waveforms in CCM**

Continuous conduction mode (CCM) Switch closed: Switch open: Inductor Volt-second balance:

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**Boost Converter: Discontinuous Conduction**

Occurs at light loads

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**Boost Converter: Effect of Parasitics**

The duty-ratio D is generally limited before the parasitic effects become significant As D gets big, input current gets very large (think about power balance….); the voltage drop in inductor and switch cause efficiency to suffer

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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

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**Boost Converter --- PSIM Simulation**

What is the output voltage?

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**Boost Converter --- PSIM Simulation**

Vo = Vi/(1-D) in continuous conduction Output voltage during startup

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**Boost Converter --- PSIM Simulation**

Note that inductor current I(RL1) never decays to zero, so we’re in continuous conduction

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**Example 2: Boost Converter Example**

Mohan, Example 7-1 Boost converter on the edge of discontinuous conduction Vi = 12V, D = 0.75, Vo = 48V, Po = 120W

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**Example 2: Boost Converter Example**

Output voltage ripple Inductor ripple current

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

The output voltage can be higher or lower than the input voltage

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**Buck-Boost Converter: Waveforms**

Continuous conduction mode Switch closed: Switch open: Inductor Volt-second balance:

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

The output voltage is held constant

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**Buck-Boost: Discontinuous Conduction**

This occurs at light loads

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

The duty-ratio is limited to avoid these parasitic effects from becoming significant

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

ESR is assumed to be zero

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**Example 3: Buck-Boost Converter: Simulation**

Vo should be -10V after startup transient dies out

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**Example 3: Buck-Boost Converter: Simulation**

Vo should be -10V in steady-state after startup transients die out Output voltage during startup

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**Buck-Boost Converter: Simulation**

The ripple is pretty big (0.5 V pp) Let’s increase the size of the filter capacitor by 10 --- what will happen?

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**Buck-Boost Converter: Simulation**

With larger C What has happened? Output voltage during startup

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**Buck-Boost Converter: Simulation**

Note that ripple is smaller, but startup transient is slower (makes sense); LC is larger Output voltage during startup

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Cuk DC-DC Converter The output voltage can be higher or lower than the input voltage Capacitor C1 stores and transfers 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

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**Cuk DC-DC Converter: Waveforms**

The capacitor voltage is assumed constant (very large) Note phase inversion at the output

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**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 This circuit is useful for lithium battery powered equipment

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**SEPIC Converter Circuits for 2 different switching states**

Reference: National Semiconductor, Application Note AN-1484, “Designing a SEPIC Converter”

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**SEPIC Converter --- Example**

Example from application note Reference: National Semiconductor, Application Note AN-1484, “Designing a SEPIC Converter”

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SEPIC Converter

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SEPIC Converter Output voltage ripple

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**Converter for DC-Motor Drives**

Four quadrant operation is possible For: DC motor drives DC to AC inverters for UPS

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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

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**Equivalent Circuits in DC-DC Converters**

Replacing inductors and capacitors by current and voltage sources, respectively

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