power-ground plane transient impedance … transmission line model from 2d fieldgenerated...

REV. B 12/5/07

POWER-GROUND PLANETRANSIENT IMPEDANCE

ROCKY MOUNTAIN CHAPTER IEEE EMC SOCIETY

December 4 2007December 4, 2007 O.R. Buhler [email protected]

Power-Ground Plane Transient Impedance

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• Note: Much of this presentation is basedNote: Much of this presentation is based on the accompanying paper: Power-Ground Plane Transient Impedance TheGround Plane Transient Impedance. Thebulk of that work was done in April 2005 while the author was employed at Storagewhile the author was employed at Storage Technology Corporation, Louisville, CO.


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OUTLINEOUTLINEWhat is impedance?

S d SSteady-StateTransientTime vs Frequency Response

How does current flow in ground-power plane?Steady-StateTransientTransient

How close does decoupling capacitor have to be?

Effective Inter-plane capacitance.p p

Capacitor placement.


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Outline (continued)Out e (co t ued)What power disturbance does.

Inter-plane inductance.

Characteristic impedanceCharacteristic impedance.

PSpice simulation.

Vias.

Conclusions.


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What is impedance?What is impedance?• Z = V/I

Rg

I

ZVg Generator V

Z

Typically Z is measured under steady-state sinusoidal conditions.Typically Z is measured under steady state sinusoidal conditions.

Z has phase as well as magnitude.


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What is transient impedance?What is transient impedance?

• Transient impedance can be illustrated byTransient impedance can be illustrated by way of example. Lossless line.

50 OhmZo = 50 Ohm

Z=>TD

1V,

1 MHz

TD

In all cases, the transient impedance will be = Zo for the first 2TD.

The transient impedance is 50 Ohms resistive.


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Transient Impedance Example (continued):p p ( )

TD Wavelength Switch Z, Steady Stateg , y

250 ns ¼ closed infinite

500 ns ½ closed zero500 ns ½ closed zero

750 ns ¾ closed infinite

250 ns ¼ open zero

500 ns ½ open infinite

750 ns ¾ open zero

The steady state impedance differs significantly from the transient impedance.


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Time vs Frequency ResponseTime vs Frequency Response

• For logic supply PDN we are interested in theFor logic supply PDN we are interested in the time response.

• Sometimes we use frequency response methods to design for time response requirements.g p q

• S-Parameters and some behavioral models S a a ete s a d so e be a o a ode swhen applied to time response can violate causality and/or passivity.


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Time vs Frequency Response (continued)q y p ( )

• Behavioral: To model skin effect theBehavioral: To model skin effect, theLaPlace operator s is sometimes used

| 1/2| br = a|s1/2| + b

This works fine for swept-frequency a.c.response but produces bizarre effects inresponse but produces bizarre effects intransient simulation.


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● Generated transmission line model from 2D field● Generated transmission line model from 2D field simulator.

I Pedestal size is aboutInput

Output

Pedestal size is about2 – 3 % of step amplitude.

Output

Td


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• DesignCon 2006: Time and Frequency Domain Analysis g q y yof Decoupling Capacitor Distance on Printed Circuit Boards - by Bruce Archambeault, Samuel Connor, and Joseph (Jay) DiepenbrockJoseph (Jay) Diepenbrock.

This paper makes the point that frequency domain analysis does NOT clearly show the effects of discrete capacitor placement. Time domain rather than frequency domain analysis is required due to the short current burst of the I Ccurrent burst of the I.C.


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• DesignCon 2007: Comparing Time-Domain and g p gFrequency Domain Techniques for Investigation on Charge Delivery and Power-Bus noise for High-Speed Printed Circuit Boards by James L Drewniak BrucePrinted Circuit Boards – by James L. Drewniak, Bruce Archambeault, James Knighten, and Giuseppe Selli.

They contend that some of the PDN analysis is easier to understand when analyzed in the time domain.

Thi i t t th t f d i l i i● This is not to say that frequency domain analysis is without merit … you just have to be careful how you interpret the data.


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p

HOW DOES CURRENT FLOW IN THE GROUND POWER PLANE?THE GROUND-POWER PLANE?

STEADY STATESOURCE SHORT

STRANSIENTSOURCE

Current expands outward

in concentric circles. Radius

proportional to time.


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How Does Current Flow In The G d P Pl ? (C ti d)Ground-Power Plane? (Continued)

• More on Steady StateMore on Steady StateSheet Inductance (uniform current distribution) will be lower than the actualdistribution) will be lower than the actual spreading inductance.

L (32 H)( b f )(d)Lsheet = (32 pH)(number of squares)(d)where d = plane separation in mils

For spreading inductance consider a 3Dmodeler and lots of luck


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modeler and lots of luck.

How Close Does The Decoupling C ?Capacitor Have To Be?

Depends on logic signal rise-time.p g g

Logic VoltagePlacing capacitor this far away in time

Shoot-thru currentdoesn’t do much good.

0 tr

Howard Johnson uses the criteria of tr/6 as maximum capacitor placement distance to be effective. That results in a round trip

delay of tr/3. Reference: Interplane Capacitance, Dr. Howard

Johnson On Line Newsletter Vol 3 Issue 21Johnson, On-Line Newsletter, Vol. 3 Issue 21,

http://www.sigcon.com


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Effective Inter-plane CapacitanceEffective Inter plane Capacitance

• Velocity of propagation (vp) = c/(er)1/2y p p g ( p) ( r)c = speed of light = 3 x 108 m/s = 1.18 x 1010in/s

• Effective radius of decoupling (re)p g ( e)re = vptr/6 = ctr/(6•er

1/2 ) er = relative dielectric constant

• Parallel plate capacitance equationCpF = (225•er•A)/d p

A = area of either plate in square inchesd = distance between plates in mils


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Effective Inter-plane Capacitance (cont’d.)ect e te p a e Capac ta ce (co t d )

• Effective plate area (AE) for decoupling is a circle p ( E) p gwith radius re. AE = πre

2

• Effective capacitance (CE): CE-pF = (225•er•π•re

2)/dCE-pF = [(225•er•π)/d][(c2tr2)/(36•er)] CE-pF = (19.6/d)(c•tr)2

● CE-pF = (2730•tr2)/di i i i dtr is risetime in nanoseconds

d is separation of gnd-pwr planes in mils


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Effective Inter-plane Capacitance (cont’d.)ect e te p a e Capac ta ce (co t d )

• The effective inter-plane capacitance isThe effective inter-plane capacitance is independent of the relative dielectric constant! It depends only on rise-timeconstant! It depends only on rise-time and distance between planes. This is the reason high dielectric constantthe reason high dielectric constant materials have not lived up to the hope that all ceramic decoupling capacitorsthat all ceramic decoupling capacitors would be eliminated.


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Effective Inter-plane Capacitance (Cont’d)ect e te p a e Capac ta ce (Co t d)

• Dielectric constant too high: Not enoughDielectric constant too high: Not enough time to get to the decoupling capacitor to do any gooddo any good.

Di l t i t t t l H t h• Dielectric constant to low: Have to share the limited amount of planar capacitance

ith t th I C ’with too many other I.C.’s.


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Capacitor PlacementCapacitor Placement

Package

b d

preferred

boundary

preferred

Package

boundary


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Denotes power pin

What power disturbance doesWhat power disturbance does

• Extends out equally in all directions suckingExtends out equally in all directions sucking charge till first discontinuity reached.

100 psp80 ps

60 ps40 ps

20 ps

The old pebble in a lake analogy.


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Capacitance Per Unit Length at Radius rCapacitance Per Unit Length at Radius r

. ℓr >> ℓ then the red . ℓarea A ≈ 2πrℓ

CpF = (0.225k)(2πrℓ)/d

rr = radius, inches

ℓ = inches

k = relative dielectric constant

d = pwr/gnd separation, inches


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Capacitance / unit length (cont’d)p g ( )

• With ℓ = 1 inch:With ℓ = 1 inch:CpF/inch = 0.45kπr/d

For vacuum, k = 1 and: CpF/inch = 0.45πr/dp

Now for a diversionNow for a diversion.


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Some Transmission Line StuffSome Transmission Line Stuff

• For a lossless line: t d = (LC)1/2 For a lossless line: tpd = (LC)tpd = prop. delay per unit length

84 723 /i h i= 84.723 ps/inch in vacuumL = inductance per unit lengthC = Capacitance per unit length

From which: L = tpd2/C


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Inter-plane InductanceInter plane InductancePlugging in per inch values for vacuum we get:Plugging in per inch values for vacuum we get:L = (84.723 x 10-12)2/[(0.45πr•10-12)/d]

LpH/inch = 5,077d/r independent of k

d in mils, r in inches


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Characteristic ImpedanceCharacteristic Impedance

• We have a relationship for capacitance perWe have a relationship for capacitance per unit length.

• We have a relationship for inductance per it l thunit length.

• Combining the two, we get characteristicimpedance


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impedance.

Characteristic Impedance (continued)Characteristic Impedance (continued)

Characteristic Impedance (Z0):Characteristic Impedance (Z0):

Z (L/C)1/2Z0(Ohms) = (L/C)1/2

L = inductance, Henries per unit length

C = capacitance, Farads per unit length


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The transient impedance of the power-The transient impedance of the powerground plane can be represented by a t d t i i litapered transmission line.

This is a valid model for twice the propagation time to the first discontinuitypropagation time to the first discontinuity(decoupling capacitor).


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v = (1 inch/84 723 ps)/k1/2vp = (1 inch/84.723 ps)/kradius r from point of entry at time t:

r = vpt = t/[(84.723 ps)(k1/2)], inchesp

Z0 = (5 075•d•10-12)/tZ0 (5,075 d 10 )/t


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With t in picoseconds and d in mils:With t in picoseconds and d in mils:Z0 = 5.075d/t, Ohms

The power-ground plane can be represented by a cascade of transmission line sections.


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The ModelThe Model

Three mil ground-power plane ImpedanceThree mil ground power plane. Impedanceat some radius r at time t.

Impedance versus Time

1.400001.60000

s)

0.400000.600000.800001.000001.20000

peda

nce

(Ohm

s

0.000000.20000

0 100 200 300 400 500 600

Time (picoseconds)

Imp


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The ModelThe Model

Tapered transmission line:Tapered transmission line:

Td = 10 ps

Zo = 1.5225

Td = 10 ps

Zo = 0.76125Section 52

Td = 10 ps

Zo = 0.02928Source Can add discrete resistor at each section output if board resistance modeling is desired


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resistance modeling is desired.

The Model (continued)The Model (continued)

• 1 amp peak current source used:1 amp peak current source used:

SignalVoltage

Supply Current

Tr/2tr


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Spice SimulationSpice Simulation

250 ps Signal Rise Time250 ps Signal Rise Time


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Spice Simulation (continued)Spice Simulation (continued)

500 ps Signal Rise Time


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ViasVias

• Inductance of a round rod with radius rInductance of a round rod with radius r and length ℓ:

L = 5 08ℓ{ln(2ℓ/r) 0 75} nHL = 5.08ℓ{ln(2ℓ/r) – 0.75}, nHr = inches, ℓ = inches

Reference: Bogatin, Eric, Signal Integrity Simplified, Prentice Hall,g , , g g y p , ,2004, ISBN 0-13-066946-6, pg 159.


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Vias (continued)Vias (continued)

• Ground & Power Via Close Together:Ground & Power Via Close Together:

r1 r2

ℓ

s


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Gnd-Pwr Via close together (continued):g ( )

ℓ{ 2/( ) }Ltotal = 5.08ℓ{ln[s2/(4r1r2)] + 0.5}, nH

Dimensions in inches

Reference: Waddel, Brian C.,Transmission Line Design Handbook, Artech House, 1991Line Design Handbook, Artech House, 1991

ISBN 0-89006-436-9, pg 411.


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• Pwr-Gnd vias close together (continued):Pwr Gnd vias close together (continued):We can model this via pair as a transmission linesection:section:

Z0 = (L/C)1/2 tpd = (LC)1/2

Z0 = L/tpd0 pd

Calculate tpd from ℓ•(84.723 ps/inch)•(k1/2)


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ConclusionsConclusions

• There is a non-zero time required for aThere is a non zero time required for a power disturbance to travel from the integrated circuit to the first decouplingintegrated circuit to the first decoupling capacitor.

• The time required for a disturbance to• The time required for a disturbance to propagate in a circuit board is determined by the dielectric constant of the circuitby the dielectric constant of the circuit board.


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Conclusions (continued)Conclusions (continued)

• This non-zero time limits the amount of effectiveThis non zero time limits the amount of effective capacitance of the power-ground plane of the circuit board.

• For a large circuit board, the effective capacitance depends only on the signal rise-time and the separation between power plane and ground plane. The effective capacitance is independent of the relative dielectric constant ofindependent of the relative dielectric constant of the circuit board.


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• If the relative dielectric constant of theIf the relative dielectric constant of the circuit board is too high, the effectiveness of discrete decoupling capacitors may beof discrete decoupling capacitors may be negated.

• A tapered transmission line model may be• A tapered transmission line model may be used to evaluate voltage transients prior to the round trip time of the first decouplingthe round trip time of the first decoupling capacitor.


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• More accurate simulation can be obtainedMore accurate simulation can be obtained from huge RLCGM circuits but at the cost of complexity and simulation timeof complexity and simulation time.

• More accurate simulation can be obtained from field modeling software but requiresfrom field modeling software but requires lots of resources and time. In addition they may not model transientsthey may not model transients.


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• The transmission line model can add aThe transmission line model can add a resistor at the output of each section if desired to model plane resistancedesired to model plane resistance.

• The transmission line model does notmodel board resonances that aremodel board resonances that are important in swept-frequency a.c. analysis.


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• QUESTIONS• QUESTIONS• COMMENTS• COMMENTS• THANKS FOR YOUR TIMETHANKS FOR YOUR TIME


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power-ground plane transient impedance … transmission line model from 2d fieldgenerated...

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