1

Effective Decoupling Radius of Decoupling Capacitor

Huabo Chen, Jiayuan Fang, Weiming Shi*

Dept. of Electrical EngineeringUniversity of California, Santa Cruz, CA 95064

Oct. 30, 2001

2

Contents

Objectives of the study Equivalent circuit model of capacitor

connecting to the planes Derivation of effective decoupling

radius Reff

Examples

3

Objective of Study

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

4

Approach Introduction 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

5

E0: noise field before the decap is addedES: scattering field induced by the current JVs: voltage difference between the power and ground planeZs: impedance contributed by the via and power ground

plane pairZc: impedance of the capacitor

Equivalent Circuit

power

E0

ground

h

Vs = hE0

JES

ZsE0

Zc

+

V

-

6

Scattering Field

The scattering field is given by

| ' ' ' (1)V

SE j G J d

[2]0| ' | ' |

4

jG H k

'J : current density on the surface of the via post

where

: circumference of the via Vis the two-dimensional Green’s function

7

Zs

[2]02 ( )

4S

aE J a H ka

0( ) 0S

aE E

[2]0 0 ( )

2 4S

E h h H kaZ

a J

Let the total E field on the via surface equal to zero

Assume the current density J is uniform on the via surface.

On the via surface, the scattering field becomes

Vs = hE0

JESZs

E0

Zc+

V

-

[2]0 02 ( ) 0

4J a H ka E

Zs depends on the plane separation and dielectric property

8

Total Voltage with Capacitor

2 S

C S

VJ a

Z Z

0 (2)SV E E h

Once J is found, then at any point can be found by (1)

Total voltage between the plane pair is

The current through the via

Vs = hE0

J

ESZs

E0

Zc+

V

-

SE

9

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 structuref = 200MHz, a = 200 m, h = 200 m, er = 4.0ESL = 0.1 nH;ESR = 10 m;cap = 10 F;

10

What Is the Best A Capacitor Can Do?

Maximum Reff

Parameter of the structuref = 200MHz, a = 200 m, h = 200 m, er = 4.0ESL = 0.1 nH;ESR = 10 m;cap = 10 F;

11

Reff as A Function of Frequency

Zs

Zc

Reff

Effective frequency range

max maxeff

ZcR

Zc Zs

a = 200 m, h = 200 m, er = 4.0ESL = 0.2 nH;ESR = 100 m;cap = 2 nF;

12

Effects of ESL - Increasing ESL quickly diminish the effectiveness

Parameter of the structurea = 200 m, h = 200 m, er = 4.0ESR = 10 m;cap = 10 F;

13

Effects of Capacitance for Same ESL and ESR- Different Capacitance changes effective frequency range

Parameter of the structurea = 200 m, h = 200 m, er = 4.0ESR = 10 m;ESL = 0.1nH;

14

Effects of Plane Separation h- For thin dielectrics, the main contribution for reducing noises is from planes.

Parameter of the structurea = 200 m, er = 4.0ESR = 10 m;ESL = 0.1nH;cap = 10 F;

15

Capacitance(F)

ESR(m)

ESL(nH)

mounting inductance

(nH)

AVX0603 0.1 50 0.8 0.13

AVX0805 1.0 20 0.95 0.14

AVXIDC 0508 1.0 20 0.11 0.02

Reff of 3 Types of Capacitors

16

Conclusions

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.