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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. Contents. Objectives of the study Equivalent circuit model of capacitor connecting to the planes

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Effective Decoupling Radius of Decoupling Capacitor

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  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. 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. power E0 ground 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.

  5. Zc + V Zs E0 ES J - Vs = hE0 power E0 h ground Equivalent Circuit 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

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

  7. Zc + V Zs E0 ES J - Zs Assume the current density J is uniform on the via surface. On the via surface, the scattering field becomes Let the total E field on the via surface equal to zero Vs = hE0 Zs depends on the plane separation and dielectric property

  8. Zc + V E0 ES Zs J - Vs = hE0 Total Voltage with Capacitor The current through the via Once J is found, then at any point can be found by (1) Total voltage between the plane pair is

  9. Effective Decoupling Radius ReffRadius 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;

  10. 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

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

  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. 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;

  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 = 0.1nH; cap = 10 F;

  15. 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.

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