POWER-GROUND PLANE Transient Impedance … transmission line model from 2D fieldGenerated...
Transcript of 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]
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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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Time vs Frequency Response (continued)q y p ( )
● 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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Time vs Frequency Response (continued)q y p ( )
• 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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Time vs Frequency Response (continued)q y p ( )
• 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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Characteristic Impedance (continued)Characteristic Impedance (continued)
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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Characteristic Impedance (continued)Characteristic Impedance (continued)
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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Characteristic Impedance (continued)Characteristic Impedance (continued)
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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Vias (continued)Vias (continued)
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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Vias (continued)Vias (continued)
• 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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Conclusions (continued)Conclusions (continued)
• 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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Conclusions (continued)Conclusions (continued)
• 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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Conclusions (continued)Conclusions (continued)
• 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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