Patent Application
20070276641
Aspects of the present disclosure are best understood from the following detailed description when read with the accompanying figures. It is emphasized that, in accordance with the standard practice in the industry, various features are not drawn to scale. In fact, the dimensions of the various features may be arbitrarily increased or reduced for clarity of discussion.
For purposes of this disclosure, an IHS may include any instrumentality or aggregate of instrumentalities operable to compute, classify, process, transmit, receive, retrieve, originate, switch, store, display, manifest, detect, record, reproduce, handle, or utilize any form of information, intelligence, or data for business, scientific, control, entertainment, or other purposes. For example, an IHS may be a personal computer, a PDA, a consumer electronic device, a network server or storage device, a switch router or other network communication device, or any other suitable device and may vary in size, shape, performance, functionality, and price. The IHS may include memory, one or more processing resources such as a central processing unit (CPU) or hardware or software control logic. Additional components of the IHS may include one or more storage devices, one or more communications ports for communicating with external devices as well as various input and output (I/O) devices, such as a keyboard, a mouse, and a video display. The IHS may also include one or more buses operable to transmit communications between the various hardware components.
In one embodiment, IHS 100,
In step 144, a 3D solid modeling step is performed to extract data from the 3D circuit geometry input and configure or transform the extracted data into data having a format that is useful for the analysis to be performed in step 146. The 3D solid modeling process in step 144 generates a 3D solid of the circuit traces and interconnects from the 3D circuit geometry input. Examples of commercially available 3D modeling software tools include ALIBRE DESIGN from Alibre, Inc., DESIGNING MODELING from CoCreate Software, Inc., and SOLID EDGE from UGS.
In step 146, a non-Fourier numerical analysis step is performed on heat conduction through the circuit geometry. Heat propagation in isotropic media is usually governed by Fourier's law of heat conduction. However, when the excitation has the profile of high current and short pulse duration, non-Fourier behavior is common. Therefore, a non-Fourier hyperbolic scheme to analyze heat dissipation as a function of high amplitude and short duration transient pulses is used to determine potential high ampacity risk locations in the circuit layout. To arrive at the solution, Equation 2) below is solved numerically using an incomplete Cholesky conjugate gradient (ICCG) method optionally combined with a modified successive over-relaxation scheme (mSOR). As set forth below, Equation 1) is the Fourier's law of heat conduction:
where Q is the heat flow, A is the transversal surface area, Δx is the thickness of the conductors through which the heat is passing, K is a conductivity constant dependent on the nature of the conductor material and its temperature, and ΔT is the temperature difference through which the heat is being transferred. Equation 1) is a partial differential equation of parabolic type. Unlike the classical Fourier heat conduction equation represented in Equation 1), Equation 2) is a non-Fourier equation that also describes heat conduction:
where α is the thermal diffusivity, and τ is the thermal relaxation time. Unlike the Fourier equation, Equation 2) is a partial differential equation of hyperbolic type.
The non-Fourier numerical analysis of Equation 2) described herein uses incomplete Cholesky conjugate gradient (ICCG) method optionally combined with a modified successive over-relaxation scheme (mSOR) in an iterative process to solve the linear equation:
Ax=b, 3)
where x is the solution vector, A is a real, sparse, positive-finite, and symmetric n×n matrix containing data representative of the 3D solid of the circuit layout, and b is a given n-vector of complex n-space. Matrix A is sparse because the number of zero elements therein is sufficiently large. An iterative method is contemplated herein until convergence on a solution is achieved. The conjugate gradient is an iterative method that starts from the residual,
r
0
=b−Ax
0, 4)
where k is an iteration index, and X0 is an initial estimate for the solution. An orthogonal basis for the Krylov subspace span {Akr0}, for k=0, 1, . . . , is generated by means of three-term recurrence relations. A sequence of symmetric tri-diagonal matrices {Tk} is also generated. The resulting symmetric tri-diagonal systems of equations are usually more easily solved than the original problem. A sequence of solution iterates {xk} is thus generated such that the sequence of the norms of the residuals {∥rk∥} converges to a required tolerance.
Incomplete Cholesky is a preconditioner for the iterative conjugate gradient method to achieve faster convergence. The incomplete Cholesky factorization is represented in the following equation:
M=PLDL
T
P
T
=A−R, 5)
wherein P is a permutation matrix, L is the lower triangular with unit diagonal elements, D is diagonal, and R is a remainder matrix.
Modified successive over-relaxation or mSOR is another preconditioner that may be alternatively or additionally used for the iterative conjugate gradient method to achieve faster convergence. The preconditioner mSOR is a two parametric method that weights the diagonal of the positive-definite matrix. Consider the matrix, A, in the following form:
where D1 and D2 are square non-singular matrices. This may be rewritten as:
where ω is used for the equations corresponding to D1 and ω′ is used for the equations corresponding to D2. Therefore, the iteration matrix B(ω, ω′) is defined by:
where F=−D1−1M and G=−D2−1.
In step 148, a determination is made as to whether convergence has been achieved in the non-Fourier heat conduction numerical analysis performed in step 146. If the numerical analysis has converged to a solution, then the results are generated and the process ends in step 150. However, if convergence has not occurred, then a determination is made as to whether the assumptions made about the boundary conditions or the 3D circuit geometry are incorrect or should be modified in step 152. If the assumptions about the 3D circuit geometry should be modified, then the process proceeds to step 154 to revise one or more of these assumptions. The revised 3D geometry assumptions are provided to step 144 where the 3D solid modeling is performed, and execution then proceeds to step 146 for the numerical analysis. Alternatively, a determination may be made that boundary conditions should be modified, and in step 156 the boundary conditions are revised, and the revised boundary conditions are provided to step 146 to perform the heat conduction numerical analysis. This process is repeated until a convergence to a solution has been achieved.
The solution from the process described above and shown in
Accordingly, the embodiments described herein may be incorporated into a design cycle of any system having one or more electrical circuits embodied in a printed circuit board. The system and method described herein are operable to reliably analyze the ampacity of a DC net under DC and AC transient pulse excitation, and therefore identify locations of ampacity risk. A numerical analysis method using incomplete Cholesky conjugate gradient and optionally modified successive over-relaxation scheme is described herein to converge on a solution given assumptions on the 3D circuit geometry, the boundary conditions, and the excitation to the circuit.
Although illustrative embodiments have been shown and described, a wide range of modification, change and substitution is contemplated in the foregoing disclosure and in some instances, some features of the embodiments may be employed without a corresponding use of other features. Accordingly, it is appropriate that the appended claims be construed broadly and in a manner consistent with the scope of the embodiments disclosed herein.
