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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 1 Contents Objectives of the study Equivalent circuit model of capacitor connecting to the planes Derivation of effective decoupling radius Reff Examples 2 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 3 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 4 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 5 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 | ' | 4 is the two-dimensional Green’s function V : circumference of the via 6 Zs Assume the current density J is uniform on the via surface. On the via surface, the scattering field becomes E S a 4 J 2 a H 0[2] (ka) Let the total E field on the via surface equal to zero S E ( ) E0 4 a 0 J 2 a H (ka) E0 0 [2] 0 E0 h h H 0[2] (ka) ZS 2 a J 4 Zc E0 ES J Zs + V - Vs = hE0 Zs depends on the plane separation and dielectric property 7 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 8 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; 9 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 10 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; 11 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; 12 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; 13 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; 14 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 15 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. 16