o converter stability metrics -...
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TITLE
Overview and Comparison of Power Converter Stability Metrics
Joseph ‘Abe’ Hartman, OracleAlejandro ‘Alex’ Miranda, OracleKavitha Narayandass, OracleAlexander Nosovitski, OracleIstvan Novak, Oracle
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SPEAKERS
Joseph ‘Abe’HartmanPrinciple Hatrdware Engineer, [email protected] | www.oracle.com
Image Istvan Novak
Senior Principle Hatrdware Engineer, [email protected] | www.oracle.com
2
Introduction Gain-phase plots
– Traditional gain-phase plots– Gain-phase plot approximations and non-invasive measurements
Nyquist plots and Stability margin Other metrics What can go wrong?
– Wrong test signal level– Spurious signals– Impact of test equipment and load circuit– Measurement location
Summary and Conclusions
Agenda
3
Introduction Gain-phase plots
– Traditional gain-phase plots– Gain-phase plot approximations and non-invasive measurements
Nyquist plots and Stability margin Other metrics What can go wrong?
– Wrong test signal level– Spurious signals– Impact of test equipment and load circuit– Measurement location
Summary and Conclusions
Agenda
4
Basic Buck Converter and its Loop Model
Non-isolated buck converter block schematic
Simplified feedback loop
EACFMloopopen GGGGG =−
5
Bode Plot, Phase and Gain Margins
Crossover Frequency –frequency where gain magnitude equals 0 dB
Phase Margin – phase at the crossover frequency
Gain Margin – gain where phase equals 0 degrees
6
Nyquist Plot
Plots imaginary vs. real
component of loop gain
Frequency parameter
Point of instability is -1,0
-2.00
-1.50
-1.00
-0.50
0.00
0.50
1.00
1.50
2.00
-2.00 -1.00 0.00 1.00 2.00
Nyquist diagram
Gopen-loop)(1)(
)(fGfZ
fZIV
loopopen
loopopenoutloopclosedout
load
out
−
−−−− +
==∆∆
Real
Imaginary
Increasing frequency
Phase Margin
7
GainMargin
Characteristic Expression Magnitude and Its Inverse
1E+3 1E+4 1E+5 1E+61.00E-03
1.00E-02
1.00E-01
1.00E+00
1.00E+01
1.00E+02
1.00E+03
Frequency [Hz]
Mag
nitu
de
Characteristic expression and its inverse [-]
Stability Margin
Plots {1+Gopen-loop(f)} and its
inverse, the stability margin
Provides the vector magnitude
from the instability point
Characteristic Expression
8
Introduction Gain-phase plots
– Traditional gain-phase plots– Gain-phase plot approximations and non-invasive measurements
Nyquist plots and Stability margin Other metrics What can go wrong?
– Wrong test signal level– Spurious signals– Impact of test equipment and load circuit– Measurement location
Summary and Conclusions
Agenda
9
Gain-Phase Measurement Connection
Requires floating source
Injection level is important
Invasive connectionVt
𝐺𝐺𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜−𝑙𝑙𝑜𝑜𝑜𝑜𝑜𝑜 =𝑉𝑉𝑎𝑎𝑉𝑉𝑏𝑏
Va
Vb
Vt
10
Introduction Gain-phase plots
– Traditional gain-phase plots– Gain-phase plot approximations and non-invasive measurements
Nyquist plots and Stability margin Other metrics What can go wrong?
– Wrong test signal level– Spurious signals– Impact of test equipment and load circuit– Measurement location
Summary and Conclusions
Agenda
11
123.4736238
101.1575927
NISM: PM45.98 Deg
-250
-200
-150
-100
-50
0
50
100
150
200
250
1.E+3 1.E+4 1.E+5 1.E+6
Frequency (Hz)
PID Peaky - Phase
3Wire Back Calc. NISM: PM
COF:29 kHz
-20
-15
-10
-5
0
5
10
15
20
25
30
1.E+3 1.E+4 1.E+5 1.E+6
Ga
in (
dB
)
Frequency (Hz)
PID Peaky - Gain
3Wire Back Calc.
Gain-Phase Measurement Based on Impedance (1) Open-loop output impedance can be approximated
by OFF impedance ‘Peaky’ example
0.0001
0.001
0.01
0.1
1
1.E+2 1.E+3 1.E+4 1.E+5 1.E+6 1.E+7
Impe
danc
e (O
hms)
Frequency (Hz)
Impedance Profile - PID Peaky
ON OFF
1)()(
)( −=−−
−−− fZ
fZfG
loopclosedout
loopopenoutloopopen
12
Steve Sandler, "Killing the Bode Plot," DesignCon 2016, January 19-21, 2016, Santa Clara, CA.
COF:29 kHz
-20
-15
-10
-5
0
5
10
15
20
25
30
1.E+3 1.E+4 1.E+5 1.E+6
Ga
in (
dB
)
Frequency (Hz)
PID Optimized - Gain
3Wire Back Calc.
Gain-Phase Measurement Based on Impedance (2)
0.0001
0.001
0.01
0.1
1
1.E+2 1.E+3 1.E+4 1.E+5 1.E+6 1.E+7
Impe
danc
e (O
hms)
Frequency (Hz)
Impedance Profile - PID Optimized
ON OFF
Open-loop output impedance can be approximated by OFF impedance
Optimized example1
)()(
)( −=−−
−−− fZ
fZfG
loopclosedout
loopopenoutloopopen
13
62.74829761
54.1844861
NISM:PM57.55 Deg
-250
-200
-150
-100
-50
0
50
100
150
200
250
1.E+3 1.E+4 1.E+5 1.E+6
Frequency (Hz)
PID Optimized - Phase
3Wire Back Calc. NISM: PM
Steve Sandler, "Killing the Bode Plot," DesignCon 2016, January 19-21, 2016, Santa Clara, CA.
Gain-Phase Measurement Based on Impedance (3)
DC bias for OFF impedance is important
14
NISM Example on Low-Noise DUT
NISM is noninvasive
Estimates phase
margin based on
second order model
of output impedance
Output impedance
Group delay
15
Steve Sandler, "Killing the Bode Plot," DesignCon 2016,
January 19-21, 2016, Santa Clara, CA.
NISM Example on High-Noise DUT
Output impedance
Group delay
16
Steve Sandler, "Killing the Bode Plot," DesignCon 2016, January 19-
21, 2016, Santa Clara, CA.
Introduction Gain-phase plots
– Traditional gain-phase plots– Gain-phase plot approximations and non-invasive measurements
Nyquist plots and Stability margin Other metrics What can go wrong?
– Wrong test signal level– Spurious signals– Impact of test equipment and load circuit– Measurement location
Summary and Conclusions
Agenda
17
Impedance, Gain-Phase on Unstable Converter
18
1.0E-4
1.0E-3
1.0E-2
1.0E-1
1.0E+0
1.E+3 1.E+4 1.E+5 1.E+6Frequency [Hz]
Impedance magnitude ON, OFF [ohm]
-250-200-150-100-50050100150200250
-60-50-40-30-20-10
010203040
1.E+3 1.E+4 1.E+5 1.E+6Frequency [Hz]
Measured gain magnitude, phase [dB, deg]
Nyquist and Stability Plots on Unstable Converter
19
0
1
2
3
1.E+03 1.E+04 1.E+05 1.E+06
Mag
nitu
de
Frequency [Hz]
Modulus (Stability) Margin
Stability Margin: 0.41 @ 152.21 kHz
1
23
23
-2
-1
0
1
2
-2 -1 0 1 2
Imag
inar
y
Real
Nyquist Plot1: Phase Margin: 84.11° @ 2.52 kHz2: Gain Margin: 5.01 dB @ 159.88 kHz
3: Stability Margin: 4.59 dB @ 152.21 kHz
1
23
Characteristic Equation
Impedance, Gain-Phase on Stable Converter
20
1.E-4
1.E-3
1.E-2
1.E-1
1.E+0
1.E+2 1.E+3 1.E+4 1.E+5 1.E+6 1.E+7Frequency [Hz]
Impedance magnitude, ON, OFF [ohm]
-250
-200
-150
-100
-50
0
50
100
150
200
250
-50
-40
-30
-20
-10
0
10
20
30
40
1.E+2 1.E+3 1.E+4 1.E+5 1.E+6 1.E+7Frequency [Hz]
Measured gain magnitude, phase [dB, deg]
-2
-1
0
1
2
-2 -1 0 1 2
Imag
inar
y
Real
Nyquist Plot
1
2
3
0
1
2
3
1.E+03 1.E+04 1.E+05 1.E+06 1.E+07
Mag
nitu
de
Frequency [Hz]
Stability Margin
Stability Margin: 0.82 @ 13.34 kHz
1 23
Nyquist and Stability Plots on Stable Converter
21
Characteristic Equation
Introduction Gain-phase plots
– Traditional gain-phase plots– Gain-phase plot approximations and non-invasive measurements
Nyquist plots and Stability margin Other metrics What can go wrong?
– Wrong test signal level– Spurious signals– Impact of test equipment and load circuit– Measurement location
Summary and Conclusions
Agenda
22
Impedance Profile and Characteristic Expression Impedance plot has peaks
The lows of the Characteristic Expression occur at the same frequency points
Direct correlation between impedance profile peaks and instability
23
0.0
0.5
1.0
1.5
2.0
2.5
3.0
1.E-4
1.E-3
1.E-2
1.E-1
1.E+0
1.E+3 1.E+4 1.E+5 1.E+6
Mag
nitu
de
Ohm
sFrequency [Hz]
Impedance [OFF, ON] and SM
)(1)(
)(fGfZ
fZloopopen
loopopenoutloopclosedout
−
−−−− +
=
Chr. Eq
Introduction Gain-phase plots
– Traditional gain-phase plots– Gain-phase plot approximations and non-invasive measurements
Nyquist plots and Stability margin Other metrics What can go wrong?
– Wrong test signal level– Spurious signals– Impact of test equipment and load circuit– Measurement location
Summary and Conclusions
Agenda
24
Gain-Phase Curves vs. Injection Level
Loop gain varies several orders of magnitude over frequency
Improper signal level can lead to saturation or noisy results
25
Introduction Gain-phase plots
– Traditional gain-phase plots– Gain-phase plot approximations and non-invasive measurements
Nyquist plots and Stability margin Other metrics What can go wrong?
– Wrong test signal level– Spurious signals– Impact of test equipment and load circuit– Measurement location
Summary and Conclusions
Agenda
26
Impedance and Gain-Phase vs. DC Load Current
-250
-200
-150
-100
-50
0
50
100
150
200
250
0.0001
0.001
0.01
0.1
1
1.E+2 1.E+3 1.E+4 1.E+5 1.E+6 1.E+7Frequency [Hz]
Impedance magnitude and phase [ohm, deg]0.8A
54.43
-25
-20
-15
-10
-50
0
50
100
150
200
250
-80
-60
-40
-20
0
20
40
60
1.E+2 1.E+3 1.E+4 1.E+5 1.E+6Frequency [Hz]
Gain magnitude and phase [dB, deg]0.8A
-40
-20
0
20
40
60
80
100
0.0001
0.001
0.01
0.1
1
1.E+2 1.E+3 1.E+4 1.E+5 1.E+6 1.E+7Frequency [Hz]
Impedance magnitude and phase [ohm, deg]1.2A
97.34
-200
-150
-100
-50
0
50
100
150
-80
-60
-40
-20
0
20
40
60
1.E+2 1.E+3 1.E+4 1.E+5 1.E+6Frequency [Hz]
Gain magnitude and phase [dB, deg]1.2A
Measured small signal output impedance can be a significant function of load current
At the same time, measured gain-phase also changes
27
Periodic Output Disturbance
At the operating point of
sudden change, a
periodic, uncorrelated
ripple appears
28
Impedance vs. Injection Level
At the operating point of
sudden change, the
measured output
impedance linearly varies
with injection level
29
Introduction Gain-phase plots
– Traditional gain-phase plots– Gain-phase plot approximations and non-invasive measurements
Nyquist plots and Stability margin Other metrics What can go wrong?
– Wrong test signal level– Spurious signals– Impact of test equipment and load circuit– Measurement location
Summary and Conclusions
Agenda
30
Impedance of Electronic Load
-150
-100
-50
0
50
100
150
0.1
1
10
100
1000
1.E+2 1.E+3 1.E+4 1.E+5 1.E+6 1.E+7Frequency [Hz]
Impedance magnitude, phase [ohm, deg]
0.0E+0
5.0E-7
1.0E-6
1.5E-6
2.0E-6
2.5E-6
3.0E-6
0.0E+0
5.0E-6
1.0E-5
1.5E-5
2.0E-5
1.E+2 1.E+3 1.E+4 1.E+5 1.E+6 1.E+7Frequency [Hz]
Extracted capacitance, inductance [F, H] High current electronic
loads have capacitors
across their input
The extra capacitance
can change the DUT
behavior
31
-100
-80
-60
-40
-20
0
20
40
60
0.0001
0.001
0.01
0.1
1
1.E+2 1.E+3 1.E+4 1.E+5 1.E+6 1.E+7Frequency (Hz)
With eload caps - Impedance mag. and phase [ohm, deg]
Effect of Electronic Load
Measured output
impedance and gain-
phase plots with and
without extra capacitance
in electronic load
32
-100
-80
-60
-40
-20
0
20
40
60
0.0001
0.001
0.01
0.1
1
1.E+2 1.E+3 1.E+4 1.E+5 1.E+6 1.E+7Frequency (Hz)
No eload caps - Impedance mag. and phase [ohm, deg]
-50
0
50
100
150
200
-30
-20
-10
0
10
20
30
40
1.E+3 1.E+4 1.E+5 1.E+6 1.E+7Frequency (Hz)
No eload caps - Gain phase calculated [dB, deg]
-200
-150
-100
-50
0
50
100
150
200
-50
-40
-30
-20
-10
0
10
20
30
40
1.E+2 1.E+3 1.E+4 1.E+5 1.E+6 1.E+7Frequency (Hz)
With eload caps - Gain phase calculated [dB, deg]
Impact of Secondary Output Filter
33
0.0001
0.001
0.01
0.1
1
1.E+2 1.E+3 1.E+4 1.E+5 1.E+6 1.E+7Frequency [Hz]
OFF Impedance with, without filter [Ohm]
0.0001
0.001
0.01
0.1
1
1.E+2 1.E+3 1.E+4 1.E+5 1.E+6 1.E+7Frequency [Hz]
On Impedance with, without filter [Ohm]
Geometry for Plane R-C Filtering
16 - 1000uF D-size bulk capacitors populated
Configurations target various cases of extra phase shift in voltage transfer function Remote
sense connection
DC-DCconverter
34
“Impact of Regulator Sense-point Location on PDN Response,” DesignCon 2015, Santa Clara, CA, January 27 - 30, 2015
Plane R-C Filtering
0.1
1
1.E+4 1.E+5 1.E+6Frequency
Voltage Transfer magnitude [-]
1.E+3 1.E+4 1.E+5 1.E+6-75
-65
-55
-45
-35
-25
-15
-5
5
Frequency
Voltage Transfer phase [deg]
35
Introduction Gain-phase plots
– Traditional gain-phase plots– Gain-phase plot approximations and non-invasive measurements
Nyquist plots and Stability margin Other metrics What can go wrong?
– Wrong test signal level– Spurious signals– Impact of test equipment and load circuit– Measurement location
Summary and Conclusions
Agenda
36
Effect of Measurement Location
`
-60
-40
-20
0
20
40
60
80
1.E+3 1.E+4 1.E+5 1.E+6Frequency [Hz]
Calculated and measured gain magnitude [dB]
-200
-150
-100
-50
0
50
100
150
200
1.E+3 1.E+4 1.E+5 1.E+6Frequency [Hz]
Calculated and measured gain phase [deg]
1.E-5
1.E-4
1.E-3
1.E-2
1.E-1
1.E+0
1.E+2 1.E+3 1.E+4 1.E+5 1.E+6 1.E+7Frequency [Hz]
Impedance magnitude [ohm]
37
CPU Socket
1730mi ls
VR
Control ler
IC Pin 15mi ls CPU PIN
Sense Point
Test Point PCB
Effect of Measurement Location
Green Sense: 1, Measure: 2
BlueSense: 2, Measure: 2
RedSense: 2, Measure: 1
DC-DC
Capacitors1
2
38
Introduction Gain-phase plots
– Traditional gain-phase plots– Gain-phase plot approximations and non-invasive measurements
Nyquist plots and Stability margin Other metrics What can go wrong?
– Wrong test signal level– Spurious signals– Impact of test equipment and load circuit– Measurement location
Summary and Conclusions
Agenda
39
Phase and gain margins are useful metrics only in special cases Nyquist plot, Characteristic expression and Stability margin plots provide
specific views of DUT stability conditions Direct loop gain measurement is invasive but most robust NISM is noninvasive, works well with low-noise peaky impedance profiles Loop gain calculated from OFF and ON impedances is minimally invasive,
but measurement location matters Measuring the loop gain function requires careful setting of injection power Frequency-domain measurements are invalid if uncorrelated tracking
spurious signals are generated by the DUT
Summary and Conclusions
40
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QUESTIONS?
Thank you!
41