Download Effective Decoupling Radius of Decoupling Capacitor

Effective Decoupling Radius of
Decoupling Capacitor
Huabo Chen, Jiayuan Fang, Weiming Shi*
Dept. of Electrical Engineering
University of California, Santa Cruz, CA 95064
Oct. 30, 2001
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Contents
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Objectives of the study
Equivalent circuit model of capacitor
connecting to the planes
Derivation of effective decoupling radius
Reff
Examples
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Objective of Study
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Adding decaps is a common approach to maintain
power integrity
Decaps are usually added by experience and lack a
quantitative measure of effectiveness
Some people suggest a effective range of /10, where
 is the wavelength at the series resonance frequency
To provide a quantitative measure to assess the
effectiveness
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Approach Introduction
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Assume the power ground plane pair is infinite large.
Noise is uniformly distributed along the plane. The electric
field before adding the capacitor is E0.
Decap brings in fluctuation and damps the noise voltage.
Effectiveness can be measured by the range within which
the noise is sufficiently reduced.
power
E0
ground
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Equivalent Circuit
Zc
+
power
E0
ground
h
E0
ES
J
Zs
V
-
Vs = hE
0
E0: noise field before the decap is added
ES: scattering field induced by the current J
Vs: voltage difference between the power and ground plane
Zs: impedance contributed by the via and power ground
plane pair
Zc: impedance of the capacitor
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Scattering Field
The scattering field is given by
E S      j  G   |  ' J   ' d  '
where
(1)
V
J   ' : current density on the surface of the via post
 j  [2]
G   |  ' 
H 0  k |    ' |
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is the two-dimensional Green’s function
V : circumference of the via
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Zs
Assume the current density J is uniform on the via surface.
On the via surface, the scattering field becomes
E
S
    a  

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J  2 a  H 0[2] (ka)
Let the total E field on the via surface equal to zero
S
E
 (  )  E0 

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 a
0
J  2 a  H (ka)  E0  0
[2]
0
E0 h
h H 0[2] (ka)
ZS 

2 a  J
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Zc
E0 ES
J
Zs
+
V
-
Vs = hE0
Zs depends on the plane separation and dielectric property
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Total Voltage with Capacitor
The current through the via
J  2 a 
Once J is found, then E S    at any
point can be found by (1)
Total voltage between the plane pair is
V      E S     E0  h
(2)
VS
ZC  Z S
Zc
E0 ES
J
+
Zs
V
-
Vs = hE0
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Effective Decoupling Radius Reff
Radius of the circle within which the noise voltage is
damped 50% or more is defined as Reff
Parameter of the structure
f = 200MHz, a = 200 m,
h = 200 m, er = 4.0
ESL = 0.1 nH;
ESR = 10 m;
cap = 10 F;
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What Is the Best A Capacitor Can Do?
Parameter of the structure
f = 200MHz, a = 200 m,
h = 200 m, er = 4.0
ESL = 0.1 nH;
ESR = 10 m;
cap = 10 F;
Maximum Reff
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Reff as A Function of Frequency
Reff
max Reff
Zc
max
Zc  Zs
Zs
Zc
Effective frequency range
a = 200 m,
h = 200 m, er = 4.0
ESL = 0.2 nH;
ESR = 100 m;
cap = 2 nF;
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Effects of ESL
- Increasing ESL quickly diminish the effectiveness
Parameter of the structure
a = 200 m,
h = 200 m, er = 4.0
ESR = 10 m;
cap = 10 F;
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Effects of Capacitance for Same ESL and ESR
- Different Capacitance changes effective frequency range
Parameter of the structure
a = 200 m,
h = 200 m, er = 4.0
ESR = 10 m;
ESL = 0.1nH;
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Effects of Plane Separation h
- For thin dielectrics, the main contribution for reducing
noises is from planes.
Parameter of the structure
a = 200 m, er = 4.0
ESR = 10 m;
ESL = 0.1nH;
cap = 10 F;
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Reff of 3 Types of Capacitors
AVX0603
Capacitance ESR ESL mounting
(F)
(m) (nH) inductance
(nH)
0.1
50
0.8
0.13
AVX0805
1.0
20
0.95
0.14
AVXIDC 0508
1.0
20
0.11
0.02
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Conclusions
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Quantitative measure of the effective range
of the decap, Reff.
Reff is related to frequency of interest,
parameters of the plane pair and capacitor
parameter.
Examples are shown to illustrate some useful
properties.
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