Introduction and Application of Constant On-Time (COT) Buck Regulators

This course is an introduction to a family of DC-DC power converters often referred to as "Constant On-Time" Buck regulators. We will exploresome of the advantages as compared to conventional "Hysteretic" Buck regulators.

You will see how a conventional Buck regulator is implemented using Hysteretic and Constant On-Time methods, then get an introduction to theparts that National offers for these applications.

Constant On-Time regulators get their name from the fact that a one-shot is used to set the on-time, which is inversely proportional to the inputvoltage. For continuous conduction mode operation the switching frequency is fairly constant, comparable to fixed frequency PWM regulators.

Course Map/Table of Contents1. Course Navigation

1.1 Course Navigation1.

2. Buck Regulator

2.1 Buck Regulator Power Stage Waveforms and Characteristics1.

3. Hysteretic Control

3.1 Conventional Hysteretic Control1.3.2 Conventional Hysteretic Regulator Waveforms2.

4. Constant On-Time

4.1 Constant On-Time (COT) Switching Regulator1.4.2 Constant On-Time Regulator Waveforms (Continuous)2.4.3 Frequency of Operation (Continuous)3.4.4 Operating Frequency vs Input Voltage (Continuous Operation)4.4.5 Constant On-Time Regulator Waveforms (Discontinuous)5.4.6 Frequency of Operation (Discontinuous)6.4.7 Operating Frequency vs Load7.4.8 Transient Response - Load Transient (100mA to 350mA)8.4.9 Transient Response - Unloading Transient (350mA to 100mA)9.4.10 COT Regulators Need Output Ripple Voltage for Stable Operation10.4.11 Methods to Reduce Output Ripple11.

5. National COT Regulators

5.1 Valley Current Limit in the LM50101.5.2 Minimum Load Current Requirement2.5.3 LM5007/8 High Voltage Step Down Switching Regulator3.5.4 LM5007 Switching Regulator Demo Board4.5.5 LM5010A High Voltage Step Down Switching Regulator5.5.6 LM5010 Switching Regulator Demo Board6.5.7 LM34910 Switching Regulator Demo Board7.5.8 Positive Input, -12V Output8.5.9 Integrated Buck Regulators Utilizing COT Control9.

Course Navigation

1.1 Course Navigation

Course Navigation

This course is organized like a book with multiple chapters. Each chapter may have one or more pages.

The previous and next arrows move you forward and back through the course page by page.

The left navigation bar takes you to any chapter. It also contains the bookmarking buttons, 'save' and 'go to.' To save your placein a course, press the 'save' button. The next time you open the course, clicking on 'go to' will take you to the page you saved orbookmarked.

The 'Go to Final Test' button on the left navigation bar takes you back to the Analog University course listing, where you started.Take the course final test by clicking on 'Test Yourself.'

The top services bar contains additional information such as glossary of terms, who to go to for help with this subject and an

in a course, press the 'save' button. The next time you open the course, clicking on 'go to' will take you to the page you saved orbookmarked.

The 'Go to Final Test' button on the left navigation bar takes you back to the Analog University course listing, where you started.Take the course final test by clicking on 'Test Yourself.'

The top services bar contains additional information such as glossary of terms, who to go to for help with this subject and anFAQ. Clicking home on this bar will take you back to the course beginning.

Don't miss the hints, references, exercises and quizzes which appear at the bottom of some pages.

Buck Regulator

2.1 Buck Regulator Power Stage Waveforms and Characteristics

Buck Regulator Power Stage Waveforms and Characteristics

The buck regulator is used to efficiently step-down and regulateusing Pulse-Width-Modulation (PWM). The output of the PWMcomparator controls the buck switch. This voltage waveform atthe SWITCH NODE has an average value of V

OUT. The

inductor and output capacitor create a two pole low pass filtersuch that a DC voltage with only a relatively small rippleappears at the output.The duty cycle, D, is defined as T

ON/T

S, and V

OUT = V

IN·D.

This is the same equation as one would use to calculate theaverage value of a square wave with a magnitude of V

IN , a

period of T and a duration of TON

. The diode allows a path for

the inductor current to flow or circulate when the buck switchopens.The buck regulator (and its variants) is the only topology thathas a direct connection between the input and the output whenthe control switch is on.

Hysteretic Control

3.1 Conventional Hysteretic Control

3.2 Conventional Hysteretic Regulator Waveforms

Conventional Hysteretic Control

Conventional hysteretic control is the simplestarchitecture available for a switching regulator. Themodulator is simply a comparator with input hysteresisthat compares the feedback voltage to a referencevoltage. When the feedback voltage exceeds thereference hysteresis voltage, the comparator outputtransitions low, turning off the switch. The switch willremain off until the feedback voltage falls below thereference hysteresis voltage, at which point, thecomparator output transitions high, turning on theswitch and allowing the output voltage (and feedbackvoltage) to rise again.This simple topology provides several benefits. It isextremely fast at reacting to load and line transients. Ithas a very wide bandwidth control loop that doesn't usean error amplifier, and doesn't require frequencycompensation. Thus, total component count isreduced, and output capacitance can be reduced.Unlike a PWM regulator, switching frequency isn't set

This simple topology provides several benefits. It isextremely fast at reacting to load and line transients. Ithas a very wide bandwidth control loop that doesn't usean error amplifier, and doesn't require frequencycompensation. Thus, total component count isreduced, and output capacitance can be reduced.Unlike a PWM regulator, switching frequency isn't setby an oscillator, but is dependant on several variables.

Hysteretic control is the simplest architecture for a switchingregulator.

Conventional Hysteretic Regulator Waveforms

The waveforms for a hysteretic buck regulatorare shown. The inductor ripple currentgenerates an AC voltage across the outputcapacitor's Equivalent Series Resistance(ESR). This results in a triangle-shapedwaveform superimposed upon the DC level atV

OUT. The buck switch alternates on and off

as the output waveform ramps beyond theupper and lower thresholds set by V

HYS at the

feedback node.The frequency of operation is a function of theinput and output voltage, the inductor, ESRand ESL of the output cap, the comparator'shysteresis and the feedback ratio. Whendesigning a regulator, we can assume thatV

OUT, V

HYS, the resistor feedback ratio, and t

dare constants. As a result, we select L andESR for a desired frequency. However, thefrequency will vary with input voltage andESR. In most cases, the output capacitor'sESR will dominate in determining bothfrequency and output ripple. Therefore, it is recommended that a low ESR ceramic output capacitor be used in series with a resistor toprovide a stable ESR. Hysteretic regulators implemented with a comparator as described, operate over a wide frequency range as theline and load conditions are varied. This varying frequency imposes filtering and noise challenges since the filtering components cannotbe optimized due to the varying frequency.

For hysteretic control, the modulator is simply a comparator with inputhysteresis.

Constant On-Time

4.1 Constant On-Time (COT) Switching Regulator

4.2 Constant On-Time Regulator Waveforms (Continuous)

4.3 Frequency of Operation (Continuous)

4.4 Operating Frequency vs Input Voltage (Continuous Operation)

4.5 Constant On-Time Regulator Waveforms (Discontinuous)

4.6 Frequency of Operation (Discontinuous)

4.7 Operating Frequency vs Load

4.8 Transient Response - Load Transient (100mA to 350mA)

4.9 Transient Response - Unloading Transient (350mA to 100mA)

4.10 COT Regulators Need Output Ripple Voltage for Stable Operation

4.11 Methods to Reduce Output Ripple

Constant On-Time (COT) Switching Regulator

Constant On-Time (COT) Switching Regulator

Shown in the figure is a block diagram of aConstant On-Time (COT) regulator. Ratherthan using a dual level comparator, the COTregulator uses a circuit which turns on thebuck switch for a time (T

ON) inversely

proportional to the input voltage (VIN

). The two

main blocks within this regulator are the ONtime one-shot and the Regulation Comparator.The Regulation Comparator monitors theoutput voltage. When the output voltage fallsbelow the regulation comparator threshold(V

REF), the comparator triggers the one-shot.

The one-shot monitors the input voltage. Oncetriggered it enables the buck switch for aperiod of time inversely proportional to theinput voltage. The larger the input voltage thesmaller the on-time. This regulator does notcontain a clock oscillator, yet operates at afixed frequency even as the input voltage isvaried.

Adding a one-shot helps to maintain constant frequencyoperation.

Constant On-Time Regulator Waveforms (Continuous)

The waveforms for a COT buck regulator areshown. The inductor ripple current generatesan AC voltage across the output capacitor'sEquivalent Series Resistance (ESR). Thisresults in a triangle-shaped waveformsuperimposed upon the DC level at V

OUT. The

buck switch turns on when the output voltage(as sensed at the feedback pin) falls to theV

ON threshold. The buck switch remains on for

a period of time determined by the on-timeone-shot. The addition of the on-time one-shotgreatly reduces the variation in operationalfrequency as we will see.

The inductor ripple current into the ESR creates the ripple voltage for the feedbackcomparator.

Frequency of Operation (Continuous)

The following equations illustrate how a relatively constant operating frequency is obtained using a constant on-time hysteretic regulator. Thebasic Buck regulator equation for any Buck regulator operating in continuous conduction mode defines the duty cycle D of the Buck switch.

Frequency of Operation (Continuous)

The following equations illustrate how a relatively constant operating frequency is obtained using a constant on-time hysteretic regulator. Thebasic Buck regulator equation for any Buck regulator operating in continuous conduction mode defines the duty cycle D of the Buck switch.

D = VOUT

/ VIN

= TON

· FS

, where TON

is the on-time and FS is the operating frequency. The constant on-time controller sets the

on-time of the Buck switch.

TON

= K · RON

/ VIN

, where K is a constant and RON

is a programming resistor. VIN

is in the denominator as expected, setting the

on-time inversely proportional to VIN

.

Rearranging and substituting TON

into the first equation, then solving for FS yields: F

S = V

OUT / (K · R

ON).

Since VOUT

, K and RON

are all constants, the operating frequency will also be a constant. In practice the actual operating frequency will vary

slightly (<10%) due to nonlinearities in the one-shot, propagation delays, and non-ideal switch voltage drops.

Operating Frequency vs Input Voltage (Continuous Operation)

Shown in this graph are actual operating frequencymeasurements of a COT regulator with a varying input voltageand a constant load.The small change in operating frequency is due to second ordereffects such as non-linearity of the COT one-shot and voltagedrops of the internal buck switch and the external free-wheeldiode.

For continuous conduction mode, the operating frequency is nearlyconstant.

Constant On-Time Regulator Waveforms (Discontinuous)

For a COT regulator, the constant frequencyrelationship holds true provided the inductorcurrent remains continuous. At light loadingconditions the current in the inductor willbecome discontinuous. Shown here are theswitching waveforms for a Buck regulator

For a COT regulator, the constant frequencyrelationship holds true provided the inductorcurrent remains continuous. At light loadingconditions the current in the inductor willbecome discontinuous. Shown here are theswitching waveforms for a Buck regulatorcontrolled with constant on-time control in thediscontinuous conduction mode, which meansthe ramping inductor current returns to zeroevery cycle. The inductor current indiscontinuous conduction mode has threestates: ramp up, ramp down, and zero. Similarto continuous conduction mode, the Buckswitch turns on at a predetermined V

ONthreshold and the Buck switch remains on foran on-time of K/V

IN. Following the on-time, the

switch turns off and the inductor current rampsdown to zero. V

OUT ramps down to the V

ONthreshold with a slope inversely proportional to the load resistance. A large load resistance requires a longer time for V

OUT to decay

back to the VON

threshold. The operating frequency will decrease with increasing load resistance while operating in discontinuous

conduction mode. This characteristic is actually desirable to maintain the conversion efficiency at light load, due to the reduction inswitching losses with decreasing operating frequency.

For discontinuous conduction mode, the operating frequency will decrease with increasing loadresistance.

Frequency of Operation (Discontinuous)

The switching frequency at discontinuous mode can be predicted as follows:

Peak Inductor Current:

For high input, lower output voltage applications the discontinuous mode peak inductor current can be simplified to:

Output Power:

Solving for FS:

Note that the switching frequency will vary inversely to the output load resistance (RLOAD

) since all of the other parameters in the above

equation are constants.

Decreasing frequency at light load decreases switching losses, maintaining low powerefficiency.

equation are constants.

Decreasing frequency at light load decreases switching losses, maintaining low powerefficiency.

Operating Frequency vs Load

The operating point where the mode (continuous ordiscontinuous) of the power converter changes depends uponon the chosen inductor value and the input/output voltages.Shown on this chart is the operating frequency of a 48V input,10V output regulator designed with a 100µH inductor. Theregulator operates in continuous conduction mode for all loadcurrents greater than 50mA with a relatively constant operatingfrequency as predicted. For output loading less than 50mA theregulator operates in discontinuous mode and the operatingfrequency decreases with decreasing load as shown.

Transient Response - Load Transient (100mA to 350mA)

Another attribute of both hysteretic and COT controlled regulators is inherently fast transient response. Regulators that provide control utilizingconventional Pulse Width Modulation (PWM) techniques require an error amplifier and associated compensation. This compensation is necessaryfor stable operation, but imposes a bandwidth limitation and a subsequent limit on the transient response of the regulator. A hysteretic regulatordoes not require an error amplifier or associated compensation. This feature allows almost instantaneous response to transient load changes.

Shown in this chart is the transient responseof a constant on-time hysteretic regulator for aload step from 100mA to 350mA. The threewaveforms are: output voltage (AC coupled),load current and switching node voltage. Therecovery time for this transient is less than5µs.

Transient Response - Unloading Transient (350mA to 100mA)

Shown in this chart is the transient responseof a constant on-time hysteretic regulator for aload step from 350mA to 100mA. The threewaveforms are: output voltage (AC coupled),load current, and switching node voltage. Therecovery time for this transient is less than5µs.It can be noted that Buck regulators with lowvoltage outputs have longer recovery times

load step from 350mA to 100mA. The threewaveforms are: output voltage (AC coupled),load current, and switching node voltage. Therecovery time for this transient is less than5µs.It can be noted that Buck regulators with lowvoltage outputs have longer recovery timesduring unloading transients since the inductorvoltage is lower (-V

OUT) during unloading

transients.

COT Regulators Need Output Ripple Voltage for Stable Operation

The response time of the regulationcomparator depends on the amount ofoverdrive at the inverting input, and on thespeed at which it is applied (dv/dt) at the endof the off-time. If the ripple at V

OUT is reduced,

that means less ripple amplitude at FB, and alower dv/dt. The comparator's response timeis longer. This disrupts the totalon-time/off-time duty cycle, and the circuitoperation may be erratic.The ripple voltage at V

OUT, and consequently

at FB, is created by the inductor’s ripplecurrent acting on R

ESR (assuming the intrinsic ESR of C2 is negligible).

The LM5007, LM5008, LM5010, and LM34910 buck regulators require a minimum of 25 mV p-p ripple at the FB pin for properoperation. The required ripple at V

OUT is higher than that at FB due to the attenuation from the feedback resistors. The minimum ripple

occurs at minimum VIN

, when the duty cycle is highest.

Ceramic capacitors need additional ESR for stableoperation.

Methods to Reduce Output Ripple

In Figure A, the ripple at VOUT

is fed to FB through CR

. Therefore the ripple at VOUT

can be

less than in the standard circuit since it is not attenuated as much by the feedback resistors.

In Figure B, taking the output right from COUT

provides an output with less ripple, but load

regulation (and efficiency) is degraded since the load current passes through RESR

. If the

application requires low ripple voltage but is tolerant of degraded load regulation this is agood solution.

In Figure C, RESR

can be removed, resulting in low ripple at VOUT

. The ripple required at FB

is produced by R1/C1/C2. Since VOUT

is an AC ground, and SW switches between VIN

and

ground, a sawtooth is generated at the R1/C1 junction. C2 then couples that ripple to FB.

is produced by R1/C1/C2. Since VOUT

is an AC ground, and SW switches between VIN

and

ground, a sawtooth is generated at the R1/C1 junction. C2 then couples that ripple to FB.

National COT Regulators

5.1 Valley Current Limit in the LM5010

5.2 Minimum Load Current Requirement

5.3 LM5007/8 High Voltage Step Down Switching Regulator

5.4 LM5007 Switching Regulator Demo Board

5.5 LM5010A High Voltage Step Down Switching Regulator

5.6 LM5010 Switching Regulator Demo Board

5.7 LM34910 Switching Regulator Demo Board

5.8 Positive Input, -12V Output

5.9 Integrated Buck Regulators Utilizing COT Control

Valley Current Limit in the LM5010

In Normal Operation (Low Load Current) theinductor current increases during the on-timeand decreases during the off-time. The p-pamplitude (ΔI) is determined by V

IN, V

OUT, and

the inductor value. The load current is theaverage I

O.

In Normal Operation (High Load Current), theaverage I

O is higher, but the ripple waveform

is the same as at the low load current. It hassame p-p amplitude and timing. In the figurethe average exceeds the LM5010's currentlimit threshold. That is OK as long as the lower peak falls below the threshold during the normal off-time. V

OUT is regulated at its correct

value by the Regulation Comparator.In Normal Operation, the Regulation Comparator controls the input to the On Timer based on the voltage at FB.

Current limiting occurs when the waveform is increased such that thecurrent's lower peak would be above the threshold. As long as thecurrent in R

SENSE is above the threshold, the Current Limit Comparator

prevents the next on-time from starting, even if the voltage at FB is low.The off-time is extended until the current reduces to the threshold. Thenthe next on-time starts. V

OUT and the frequency are reduced, and the

circuit operates in a constant current mode (IOCL

). The transition in and

out of current limit mode is smooth with no foldback or abrupt changes.As the load current is reduced, V

OUT and the frequency increases, and

the waveforms return to normal.The LM5010 and LM34910 use a Valley Current Limit technique whichmonitors the load current during the off-time rather than during theon-time. This method allows the average load current to exceed thecurrent limit threshold as long as the lower peak of the inductor currentwaveform does not exceed the threshold (1.25A). When the lower peak"tries" to exceed the threshold (as load current is increased) the off-timeincreases to allow the inductor current to ramp down to the threshold.The next on-time does not start until the current reduces to the threshold.Output voltage, power, and input current are reduced in this mode, aswell as the frequencyThe LM5007/LM5008 current limit implementation differs in that the buck switch peak current is monitored instead of the valley currentmonitor of the LM5010. When the LM5007/8 detects an over-current condition, the buck switch remains off for a user programmableoff-time before a new on-time is allowed.

Valley Current LimitFor valley current limiting, which of the following are true?

1.There is no foldback.

Valley Current LimitFor valley current limiting, which of the following are true?

1.There is no foldback.

2.The transition in and out of current limit is smooth.

3.The operating frequency is reduced.

1 Answer: They are all true.

Minimum Load Current Requirement

The bootstrap capacitor (C4) provides the voltage to power the driver,and the current to charge the switch's gate each on-time. C4 isrecharged each off-time when the SW pin is at ground. The rechargecurrent flows from V

CC through the internal diode, C4, L1, and through

R1/R2 and the load.If the recharge current through C4 is too small, C4 will not rechargesufficiently, the switch will not turn on, and the circuit will shutdown. Thisoccurs if the load current is too low AND R1 and R2 are too high invalue.The minimum current to keep C4 properly charged has been determinedexperimentally to be about 200µA.If the application is such that the load current will be zero at times, theminimum required current for C4's recharge can be provided by makingR1 and R2 small enough. This is why the data sheet recommends thosetwo resistors be in the range of 1k to 10k ohms.

A minimum load is required to keep the bootstrap capacitorcharged.

LM5007/8 High Voltage Step Down Switching Regulator

There is a family of highvoltage constant on-timeregulators available fromNational Semiconductor.The LM5007 contains a 75Vrated Buck switch with acurrent limit set to 725mAnominal. The LM5008contains a 100V rated Buckswitch with a current limit setto 500mA nominal. Very fewexternal components (1Diode, 1 Inductor, 10discrete components) arenecessary to realize acomplete regulator solution.

RON

sets the on-time and

resulting operatingfrequency.R

CL sets the off time following an over-current event.

R1 and R2 sets the output voltage.R3 sets the output voltage ripple, necessary for stable operation. The recommended output ripple is approximately 25mV at the FB pin.

The LM5007/8 integrates the following features:

Integrated 75V (LM5007) or 100V (LM5008) N-Channel Buck Switch

RCL

sets the off time following an over-current event.

R1 and R2 sets the output voltage.R3 sets the output voltage ripple, necessary for stable operation. The recommended output ripple is approximately 25mV at the FB pin.

The LM5007/8 integrates the following features:

Integrated 75V (LM5007) or 100V (LM5008) N-Channel Buck SwitchPeak Switch Current Limit 0.725A (LM5007) or 0.5A (LM5008)Internal HV Start-up Vcc RegulatorAdjustable Output Voltage (2.5V to 70V)Thermal Shutdown (165°C)Packages: MSOP-8 and LLP-8

LM5007 - High Voltage (80V) Step Down Switching RegulatorLM5008 - High Voltage (100V) Step Down Switching Regulator

LM5007 Switching Regulator Demo Board

AN-1298: Application Note 1298 LM5007 Evaluation Board

LM5010A High Voltage Step Down Switching Regulator

Two additional higher current devices are alsoavailable. The LM34910 contains a 40V ratedBuck switch, while the LM5010 contains an75V rated Buck switch. Both devices arecapable of providing output currents up to 1.5Amps.

The devices are provided with an exposed metal padon the underside of the device to facilitate heatremoval. Two additional changes from the LM5007/8are:

Addition of a soft start pin to ease stressduring start-up.Valley Current Limit (set to 1.25A nominal)rather than peak current limit. The valleycurrent is monitored by connecting therecirculating diode to an internal senseresistor.

The LM5010 integrates the following features:

Integrated 40V (LM34910) or 75V (LM5010) N-Channel Buck SwitchCapable of 1.5A Output CurrentSoft StartAdjustable Output Voltage (2.5V - 70V)Thermal Shutdown (165°C)Packages: MSOP-14EP and LLP-10

Integrated 40V (LM34910) or 75V (LM5010) N-Channel Buck SwitchCapable of 1.5A Output CurrentSoft StartAdjustable Output Voltage (2.5V - 70V)Thermal Shutdown (165°C)Packages: MSOP-14EP and LLP-10

Soft start causes the output voltage to increase in a controlled manner, which limits the in-rush currentat turn-on.

LM5010A High Voltage 1A Step Down Switching RegulatorAN-1423: Application Note 1423 LM5010A Evaluation Board

LM5010 Switching Regulator Demo Board

AN-1352: Application Note 1352 LM5010 Evaluation Board

LM34910 Switching Regulator Demo Board

LM34910 High Voltage (40V, 1.25A) Step Down Switching Regulator

LM34910 High Voltage (40V, 1.25A) Step Down Switching Regulator

Positive Input, -12V Output

LM5010 Buck-Boost Application

In applications where a negative output voltage is required, any ofthe constant on-time regulators described can be reconfigured intothis buck-boost circuit. When the main switch is turned on, energyis stored in the output inductor. When the main switch is turned off,the inductor current continues to flow through the output capacitorand load, returning through the recirculating diode, creating thenegative output voltage.The transfer function for this topology is:V

OUT = V

IN · D / (1 - D)

The average inductor current is:IOUT

· (1 + VOUT

/ VIN

)

The regulator IC is referenced to the negative output to ease thedesign of the output feedback. There is a limitation that themaximum input to output voltage differential must not exceed therating of the regulator IC. Since the current delivered to the outputfrom the inductor is delivered in pulses rather than being deliveredcontinuously, the output voltage ripple of this circuit will be greaterthan a Buck regulator described previously.

A buck regulator IC can be configured as a buck-boost with its ground referenced to thenegative output.

Integrated Buck Regulators Utilizing COT Control

Shown are the available integrated buck regulators utilizing COT control. Check the current selector guide to get the latest informationas the family is constantly expanding.

COT

Constant On-Time

D

Duty Cycle

ESL

D

Duty Cycle

ESL

Equivalent Series Inductance

ESR

Equivalent Series Resistance

FSSwitching Frequency

PWM

Pulse Width Modulation

T, TSPeriod of one cycle, measured in seconds. Generally refers to the switching period.

tdDelay time

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Thank you,PowerWise Design University Team Introduction and Application of Constant On-Time (COT) Buck Regulators Copyright © 2010 by National Semiconductor All rights reserved