beat frequency analysis of multiphase voltage regulators · pdf file1. beat frequency analysis...
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Beat Frequency Analysis of Multiphase Voltage RegulatorsKen BoydenOct 2012
Agenda
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• 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
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Phase Current Imbalance Example
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Simple 2 Phase PWM Buck Regulator Model
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Simple dual phase buck voltage regulator – phases are separated by 180°
Non-Linear Control for Transient
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2 Phase switching waveform- 180° separation
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Phase 1
Phase 2
Steady State FET Drive Waveforms
Control FET
Sync FET
Control FET
Sync FET
Transient at switching frequency
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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.
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Transient near Switching Frequency
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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
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Phase response during beat condition
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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
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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
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n1/212n1,3,5,...
Sin(it)
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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
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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
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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
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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
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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
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From: Rice, Gehrke, Segal
FSK Modulation
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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
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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
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4 Phase Data with HSPB disabled – 385KHz
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4 Phase Data with HSPB enabled – 385KHz
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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.
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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
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