1. 1 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

2. 2 Contents Objectives of the study Equivalent circuit model of capacitor connecting to the planes Derivation of effective decoupling radius R eff Examples

3. 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. 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 E 0. Decap brings in fluctuation and damps the noise voltage. Effectiveness can be measured by the range within which the noise is sufficiently reduced. power E0E0 ground

5. 5 E 0 : noise field before the decap is added E S : 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 Equivalent Circuit power E0E0 ground h Vs = hE 0 JESES Zs E0E0 Zc +V+V -

6. 6 Scattering Field The scattering field is given by : current density on the surface of the via post where : circumference of the via is the two-dimensional Green’s function

7. 7 Zs 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 = hE 0 JESES Zs E0E0 Zc +V+V - Zs depends on the plane separation and dielectric property

8. 8 Total Voltage with Capacitor 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 = hE 0 J ESES Zs E0E0 Zc +V+V -

9. 9 Effective Decoupling Radius R eff Radius of the circle within which the noise voltage is damped 50% or more is defined as R eff 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 ;

10. 10 What Is the Best A Capacitor Can Do? Maximum R eff 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 ;

11. 11 R eff as A Function of Frequency Zs Zc R eff Effective frequency range a = 200  m, h = 200  m, er = 4.0 ESL = 0.2 nH; ESR = 100 m  ; cap = 2 n F ;

12. 12 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 ;

13. 13 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 = 0.1 nH ;

14. 14 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 = 0.1 nH ; cap = 10  F ;

15. 15 Capacitance (  F) ESR (m  ) ESL (nH) mounting inductance (nH) AVX06030.1500.80.13 AVX08051.0200.950.14 AVXIDC 05081.0200.110.02 R eff of 3 Types of Capacitors

16. 16 Conclusions Quantitative measure of the effective range of the decap, R eff. R eff is related to frequency of interest, parameters of the plane pair and capacitor parameter. Examples are shown to illustrate some useful properties.