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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






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






Agenda

9

Gain-Phase Measurement Connection

Requires floating source

Injection level is important

Invasive connectionVt

𝐺𝐺𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜−𝑙𝑙𝑜𝑜𝑜𝑜𝑜𝑜 =𝑉𝑉𝑎𝑎𝑉𝑉𝑏𝑏

Va

Vb

Vt

10






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.






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


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


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






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






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






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


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


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






Agenda

30

Impedance of Electronic Load

-150

-100

-50

0

50

100

150

0.1

1

10

100

1000


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


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


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


With eload caps - Gain phase calculated [dB, deg]

Impact of Secondary Output Filter

33

0.0001

0.001

0.01

0.1

1


OFF Impedance with, without filter [Ohm]

0.0001

0.001

0.01

0.1

1


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






Agenda

36

Effect of Measurement Location

`

-60

-40

-20

0

20

40

60

80


Calculated and measured gain magnitude [dB]

-200

-150

-100

-50

0

50

100

150

200


Calculated and measured gain phase [deg]

1.E-5

1.E-4

1.E-3

1.E-2

1.E-1

1.E+0


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






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


40

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QUESTIONS?

Thank you!

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