1

Beat Frequency Analysis of Multiphase Voltage RegulatorsKen BoydenOct 2012

Agenda

2

• Switching Regulators and transient requirements• Origin and illustration of Beat Frequency

• Why does it happen• Scope Shots• Mathematical Model

• How do we beat the beat?• Some initial Algorithms from EMC analysis• Most used Algorithm• Phase Balancing

Multiphase Voltage Regulator Requirements

• Low Voltage levels and High current levels dominate the requirements of power for Server CPUs

• CPU utilization comes in bursts causing transients to follow • Intel requires a testing regime that emulates these dynamic requirements

• Dynamic current transients are tested over the frequency range starting at 1KHz to 1MHz with varying duty cycles

• Testing at frequencies close to the switching frequency of the regulators has caused the most problem.

• Current imbalance between phases poses the greatest danger to the regulator.

• Standard PWM regulation allows Pulse Width separation during transient events

• New Control techniques are needed to limit Current imbalance during Transient

• Response is not limited to PWM Topologies

3

Phase Current Imbalance Example

4

Simple 2 Phase PWM Buck Regulator Model

5

Simple dual phase buck voltage regulator – phases are separated by 180°

Non-Linear Control for Transient

6

2 Phase switching waveform- 180° separation

7

Phase 1

Phase 2

Steady State FET Drive Waveforms

Control FET

Sync FET

Control FET

Sync FET

Transient at switching frequency

8

Current Transient

Phase 2 Response – full open

Phase 1 Response – Closed Down

Phase 2 is in position to source current to the load

Phase 1 responds by trying to sink current

High Rep Rate Transient results

Transients near the switching frequency actually cause phase alignment between those phases sourcing and those phases sinking current. Most non-linear transient algorithms support this.

9

Transient near Switching Frequency

10

Current Transient near Switching Frequency

Phase 2 is in the best position to source current to the load, but the slightly higher load step frequency causes a truncated response

Phase 1 moves from a cut-off response to start sourcing current

Phase 1 pulse width starting to grow

Phase 2 pulse width shrinking

Dynamics with load switching near the regulator switching frequency

If we look across the inductor for each phase it is possible to see the effect of the pulsed load near the switching frequency

•Phase 2 shrinks as it adjusts to the slightly higher frequency of the load but still is sourcing most of the current needed

•Phase 1 is now starting to supply more current but is still sinking current for most of the cycle.

•As phase and frequency of the load matches against the synchronous switching frequency we begin to see a sinusoidal decrease in phase 2 current and a sinusoidal increase in phase 1 current

•This becomes a low frequency sinusoidal response

11

Phase response during beat condition

12

Actual representation of Beat components from 2 phases at 385KHz with a 400KHz switching frequency. 2 phases of a 4 phase system are shown

Consequences of Large Current Imbalances

• Modes exist where phases source current to both the load and those phases sinking current. • This puts extra strain on power stage components and inductors

• Extra stress is put on Input Capacitors

• Beats may even cause mechanical vibration in the system

• Some transients may cause system shut down or power stage destruction

13

Simple Math Model of one of the phases

switching frequency Load frequencyCurrent Waveform

• This is basically a sampling system• In normal regulation the switching frequency is much

higher than the load frequency• ‘Mixing effects become evident’

Transient Fourier spectrum

8

n1/212n1,3,5,...

Sin(it)

4

1

n1,3,5,... Sin(it)

Triangle Wave

Square Wave

A

T

tr t f

τ

n 2A T

sin(n T

)

n T

sin(n tr

T)

n tr

T

Quadrature Mixer Model simplifies analysis

12

Cos( s l ) 12

Cos( s l )

Cos(A)*Sin(B) 12

Cos(A B) 12

Cos(A B)

Load

Source

Understanding the phenomena

• A simple 1 phase model is that of an analog mixer where the load and the source waveforms mix at the output

• The output of this mixer would be a beat component plus higher frequency mixing components

• The beat component posses the most problem for switching regulators

• These components can have large current imbalances• This may lead to operation near or beyond inductor saturation limits

resulting in possible hard damage• The beat components are usually with in the audio range and can make

inductors ‘sing’• Component vibration is also a worry

17

How can we diminish or eliminate beat components?• Lowering the output impedance will also lower the amplitude of

the beat but will not solve other issues related to current imbalance

• In order to solve current related issues we must find a way to lower the actual beat fundamental frequency component

• We can borrow techniques from many years of effort to build power supplies that limit EM noise.

• Then main technique used to lower peak EM radiation was modulating the switching period such that when mixed with the load frequency peak spectral components are pushed to side bands

• There are several methods for spreading the spectrum• FM• FSK (Frequency Shift Keying)• PSM (Pulse Skip/Pulse Position Modulation)• Direct Sequence

18

19

Bessel Integral

)cos( tl

))sin(sin( tnmt mc

))sin()cos(( tmt mlc

Load switching component

Source with clock frequency modulation

‘Beat’ switching component

tdtmtnmJn

))sin(cos(1)(0

Bessel Integral

J1

J2

J1

F (kHz)

J2J3

J0J3

Frequency Modulating the switching period

FMA*Cos( c t mSin( m t))Modulating the switching frequency

A*Cos(( s l )t mSin( m t))

This leads to

A*Cos(( s l) t)*Cos(mSin( m t)) A*Sin(( s

l ) t)* Sin(mSin( m t))

Cos(mSin( m t)) 0J 12 2J mCos(2 m t) 1

2 4J mCos(4 m t)...

Modulated Beat component

Modulation Index

m maxfmod

f

Where is the maximum bandwidth for communication and is the actual modulation frequency

At a modulation index of 2.4 no energy is present in the fundamental and all energy is pushed to the side bands.At modulation indexes greater than 2 much of the fundamental frequency energy is down

f max

f max f mod

Linear time FM Clock Modulation

22

3.45Time (ms)

3.40 3.51

3.4Output Ripple

Vout (V) 3.3

3.20.6

LISN Output(V)

–0.5

0.8OSC Ramp

(V)0.1

8Switch Node

(V)–0.5

1.1Error Amplifier

Output (V)0.9

From: Rice, Gehrke, Segal

Spectral Peak Reduction from Linear FM

23

From: Rice, Gehrke, Segal

FSK Modulation

24

m maxfmodf

maxf mod.25 f

m maxfmodf

.25

We can see that just moving theClock between 2 frequencies helps, but is not enough to fix the problem. If we want to just change between finite frequency elements we need to introduce more frequencies and higher frequency random deployment

m maxfmodf

maxf n

sf2

modf sf

m maxfmodf

n2

PSM(Pulse Skip Modulation)

PFM pulse train with skipped pulses

Pseudo Random Sequencing of the Clock

26

From: Rice, Gehrke, Segal

Improvements to high speed phase balance (Patent Filed)• Compares each pulse to a filtered average of all the pulses (more consistent)• Takes into account low speed balancer offsets (no need to turn off low speed

during transients)• Only operates at high load rep rate frequencies (settable frequency and

voltage threshold to enable)• Increased resolution in the pulse width difference needed to skip (better

control)

Improved High Speed Phase Balance Algorithm

27

4 Phase Data with HSPB disabled – 385KHz

28

4 Phase Data with HSPB enabled – 385KHz

29

Summary

• Beat frequency can be defeated

• The techniques required are not easy to implement. Especially for analog systems.

• Even fixed pulse systems will exhibit Beat Frequency symptoms. Usually manifesting in a ‘limit cycle’ symptom

• IR’s digital controller eliminates these components with their proprietary High Speed Phase Balancing technique

• Combating ‘Beats’ without some type of modulation algorithm requires many more external passives and does not eliminate the ‘Beat’ but just reduces it.

30

Bibliography

Understanding Noise Spreading Techniques and their effects in Switch-Mode Power Applications

John Rice, Dirk Gehrke, Mike Segal

Transient Frequency Modulation: A new approach to Beat Frequency Current Sharing Issues in Multi-Phase Switching Regulators

Osvaldo Zambetti, Alessandro Zafarana, Andrea Cappelletti, Raimondo Vai, Emanuele Bertelli

STMicroelectronics / IP&C Division, Cornaredo, Italy

Spread spectrum switching : low noise modulation technique for PWM inverter drives

J.T. Boys, P.G. Handley

Modeling and Analysis of Pulse Skip Modulation* LUO Ping, ZHANG Bo, WANG Shun-ping, FENG Yong

School of Microelectronics and Solid-State Electronics, University of Electronic Science and Technology

31