Power Electronics Notes 07A Introduction to DC/DC Converters

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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

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

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

Offline Flyback Converter
Reference:

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

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

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

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

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

Step-Down (Buck) Converter
Diode needed to provide current path for output current when switch is OFF

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

Buck Converter: PSPICE Circuit
Circuit shown: fsw = 200 kHz, D = 0.5

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

Same Circuit --- PSIM Simulation

Same Circuit --- PSIM Simulation

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

Inductor Voltage and Current
Remember that in an inductor:

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

Buck Converter in Continuous Conduction
Switch closed (for time DT) Switch open (for time (1-D)T)

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.

Buck Converter in Continuous Conduction --- Idealized Switching Waveforms
Idealized because we assume that switches and diodes turn on and off with zero risetime

Buck Converter: Waveforms at the Boundary of Cont./Discont. Conduction
ILB = critical current below which inductor current becomes discontinuous

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

Buck Converter: Capacitor Current Ripple
Continuous conduction mode

Buck Converter: Output Voltage Ripple
ESR is assumed to be zero; continuous conduction mode

Buck Converter: Output Voltage Ripple
ESR is assumed to be zero

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

Example 1: Buck in Periodic Steady State
Analysis shows inductor ripple = 0.38 A-pp, output voltage ripple = 24 mV-pp, confirmed by SPICE

Step-Up (Boost) DC-DC Converter
Output voltage is greater than the input, with the same polarity

Boost Converter Waveforms in CCM
Continuous conduction mode (CCM) Switch closed: Switch open: Inductor Volt-second balance:

Boost Converter: Discontinuous Conduction

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

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

Boost Converter --- PSIM Simulation
What is the output voltage?

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

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

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

Example 2: Boost Converter Example
Output voltage ripple Inductor ripple current

Step-Down/Up (Buck-Boost) Converter
The output voltage can be higher or lower than the input voltage

Buck-Boost Converter: Waveforms
Continuous conduction mode Switch closed: Switch open: Inductor Volt-second balance:

Buck-Boost: Limits of Cont./Discont. Conduction
The output voltage is held constant

Buck-Boost: Discontinuous Conduction

Buck-Boost Converter: Effect of Parasitics
The duty-ratio is limited to avoid these parasitic effects from becoming significant

Buck-Boost Converter: Output Voltage Ripple
ESR is assumed to be zero

Example 3: Buck-Boost Converter: Simulation
Vo should be -10V after startup transient dies out

Example 3: Buck-Boost Converter: Simulation
Vo should be -10V in steady-state after startup transients die out Output voltage during startup

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?

Buck-Boost Converter: Simulation
With larger C What has happened? Output voltage during startup

Buck-Boost Converter: Simulation
Note that ripple is smaller, but startup transient is slower (makes sense); LC is larger Output voltage during startup

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

Cuk DC-DC Converter: Waveforms
The capacitor voltage is assumed constant (very large) Note phase inversion at the output

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

SEPIC Converter Circuits for 2 different switching states
Reference: National Semiconductor, Application Note AN-1484, “Designing a SEPIC Converter”

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

SEPIC Converter

SEPIC Converter Output voltage ripple

Converter for DC-Motor Drives
Four quadrant operation is possible For: DC motor drives DC to AC inverters for UPS

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

Equivalent Circuits in DC-DC Converters
Replacing inductors and capacitors by current and voltage sources, respectively