TY - THES

T1 - Analysis of power ground planes

AU - Trinkle, Joe

PY - 2005

Y1 - 2005

N2 - [Truncated introduction] A major contribution of this thesis is the observation that the N port impedance parameters for the distribution planes can be modelled as simple LC series elements in the frequency range over which the interesting interactions between the loading elements and the planes occur. Loosely speaking, the C represents the inter-plane capacitance and the L is associated with a first order frequency trend of the transfer and input impedances associated with the planes. In the literature, values for L have been obtained for power ground plane structures using curve fitting techniques [38]. In this thesis, formulae are developed for L based on the modal summation expression. As for the impedance case, the approach developed in the thesis that removes the singular behaviour, results in computational efficient expressions. Preliminary results on the simple LC model were presented by the author in [42, 43] The results reported in the thesis extend this work in the light of the new impedance model proposed. The simple LC characterisation enables the development of new low frequency expression for the input and transfer impedance for ports on planes loaded with many decoupling capacitors. The expressions are based on a one off frequency independent decomposition of the inductance matrix associated with the placement of the capacitors. The eigen-mode decomposition eliminates the need for matrix inversion at each frequency point and leads to an efficient computational procedure for calculating the impedance of loaded planes. Furthermore, the interaction between the capacitors and planes is clearly seen in the analytical expressions. This has led to new insights regarding the interaction of multiple capacitors with supply planes in terms of location, resonance mechanisms, pole locations and damping. These insights are beneficial to the understanding and optimisation of printed circuit board power distribution systems.

AB - [Truncated introduction] A major contribution of this thesis is the observation that the N port impedance parameters for the distribution planes can be modelled as simple LC series elements in the frequency range over which the interesting interactions between the loading elements and the planes occur. Loosely speaking, the C represents the inter-plane capacitance and the L is associated with a first order frequency trend of the transfer and input impedances associated with the planes. In the literature, values for L have been obtained for power ground plane structures using curve fitting techniques [38]. In this thesis, formulae are developed for L based on the modal summation expression. As for the impedance case, the approach developed in the thesis that removes the singular behaviour, results in computational efficient expressions. Preliminary results on the simple LC model were presented by the author in [42, 43] The results reported in the thesis extend this work in the light of the new impedance model proposed. The simple LC characterisation enables the development of new low frequency expression for the input and transfer impedance for ports on planes loaded with many decoupling capacitors. The expressions are based on a one off frequency independent decomposition of the inductance matrix associated with the placement of the capacitors. The eigen-mode decomposition eliminates the need for matrix inversion at each frequency point and leads to an efficient computational procedure for calculating the impedance of loaded planes. Furthermore, the interaction between the capacitors and planes is clearly seen in the analytical expressions. This has led to new insights regarding the interaction of multiple capacitors with supply planes in terms of location, resonance mechanisms, pole locations and damping. These insights are beneficial to the understanding and optimisation of printed circuit board power distribution systems.

KW - Electric power distribution

KW - Mathematical models

KW - Electromagnetic compatibility

KW - Electric circuit analysis

KW - Power ground planes

KW - Power distribution

M3 - Doctoral Thesis

ER -