Beat Frequency Analysis of
Multiphase Voltage Regulators
Ken Boyden
Oct 2012
1
Agenda
• 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
2
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
Simple dual phase buck voltage regulator – phases are separated by 180°
5
Non-Linear Control for Transient
6
2 Phase switching waveform- 180° separation
Steady State FET Drive Waveforms
Control FET
Phase 1
Sync FET
Phase 2
Control FET
Sync FET
7
Transient at switching frequency
Phase 1 responds by trying to sink current
Phase 1 Response – Closed Down
Current Transient
Phase 2 is in position to source current to the load
Phase 2 Response – full open
8
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
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 2 pulse width shrinking
Phase 1 pulse width starting to grow
Phase 1 moves from a cut-off response to start sourcing current
10
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
Actual representation of Beat components from 2 phases at 385KHz with a
400KHz switching frequency. 2 phases of a 4 phase system are shown
12
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
•
•
•
Current Waveform
Load frequency
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 1,3,5,...

1
n1/2

n
1
4 1,3,5,... n
2
Sin(i t)
Sin(i t)
Triangle Wave
Square Wave
t
tr
f
A

τ
T

tr
sin(n

)

)
sin(n

T
T
 n  2A

t
T n 
n r
T
T
Quadrature Mixer Model simplifies analysis
1
1
Cos(A)* Sin(B)  Cos(A  B)  Cos(A  B)
2
2
Source
1
1
Cos( s   l )  Cos( s   l )
2
2
Load
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
Bessel Integral
Load switching component
cos(l t )
Bessel Integral
Source with clock frequency modulation
sin(ct  m sin(nmt ))
J n (m) 
1


cos(nt  m sin(t ))dt
0
‘Beat’ switching component
cos((c  l )t  m sin(mt ))
J1
J3
J2
J1
J2
J0
J3
F (kHz)
19
Frequency Modulating the switching
period
FM
A *Cos( ct  mSin( mt))
Modulating the switching frequency
A *Cos(( s   l )t  mSin( mt))
Modulated Beat component
This leads to
A *Cos(( s   )lt)*Cos(mSin( mt))  A * Sin(( s   )lt)* Sin(mSin( mt))
Cos(mSin( mt))  J 0 
1
1
mCos(2 mt)  J 4mCos(4 mt)...
J
2
2
2
Modulation Index
m
f
f
max
mod
Where f
max
is the maximum bandwidth for communication and f
mod
is the actual modulation frequency
f max
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
Linear time FM Clock Modulation
3.4
Output Ripple
Vout (V) 3.3
3.2
0.6
LISN Output
(V)
–0.5
0.8
OSC Ramp
(V)
0.1
8
Switch Node
(V)
–0.5
1.1
Error Amplifier
Output (V)
0.9
3.40
From: Rice, Gehrke, Segal
3.45
Time
(ms)
3.51
22
Spectral Peak Reduction from Linear FM
From: Rice, Gehrke, Segal
23
FSK Modulation
m
f
max
m
f
f
max
mod
 .25 f
f
f
max
mod
 .25
mod
We can see that just moving the
Clock 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
24
PSM(Pulse Skip Modulation)
PFM pulse train with skipped pulses
m
f
f
max
mod
m
f
f


f
f
max
mod
nf
s
2
f
max
mod
s

n
2
Pseudo Random Sequencing of the Clock
From: Rice, Gehrke, Segal
26
Improved High Speed Phase Balance Algorithm
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)
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