Computer system and printed circuit board manufactured in accordance with a quasi-Monte Carlo simulation technique for multi-dimensional spaces

• US 6,968,300 B2
• Filed: 01/26/2001
• Issued: 11/22/2005
• Est. Priority Date: 01/26/2001
• Status: Expired due to Term

• Current Assignee: Dell Products LP (Dell Technologies Inc.)
• Original Assignee: Dell Products LP (Dell Technologies Inc.)
• Inventors: Wallace, Douglas Elmer Jr.
• Primary Examiner(s): Thomson, W.
• Assistant Examiner(s): CRAIG, DWIN M
• Application Number:
  US09/771,049
• Publication Number:
  US 20020103555A1
• Time in Patent Office: 1,761 Days
• Field of Search: 703/2, 703/6, 703/13, 705/36, 711/5, 716/15
• US Class Current: 703/2
• CPC Class Codes: G06F 17/10 Complex mathematical operations function generation by table look-up G06F1/03; evaluation of elementary functions by calculation G06F7/544
• CPC Class Codes: G06F 30/367 Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods
• CPC Class Codes: H05K 1/0237 High frequency adaptations H05K1/0216 takes precedence
• CPC Class Codes: H05K 3/0005 for designing circuits by computer

Abstract

A computer system includes a printed circuit board manufactured in accordance with simulated trace impedances and topologies. The printed circuit board includes trace impedances characterizing at least three dimensions of a multi-dimensional space of the printed circuit board. The printed circuit board design includes trace impedances and topologies obtained with the use of a quasi-Monte Carlo simulation methodology.

Claims

1. A method for simulating trace impedance for application to manufacture a printed circuit board using a quasi-Monte Carlo model comprising:

generating a sequence of pseudo-random numbers according to a prescribed quasi-Monte Carlo model;

mapping each pseudo-random number R of the sequence of random numbers into multiple variables of unique values for the multi-dimensional space, the multi-dimensional space including D dimensions, where D is a number, the mapping providing a substantially even hard-coded point-cloud to define a grid of quasi-Monte Carlo points to provide some regularity in the point cloud over the multi-dimensional space; and

selecting a value of S according to a desired accuracy of a final simulation value, wherein the value of S defines a grid for use in conjunction with the mapping of the pseudo-random numbers into the multiple variables of the multi-dimensional space, wherein each of the multiple variables of the multi-dimensional space represents a corresponding D dimension value and wherein each dimension is characterized by a minimum and a maximum value, further wherein each dimension is characterized by a prescribed resolution S, and wherein S is the resolution of each dimension, and a ratio r, as defined by r=S^D/P^N can be predetermined to be a prime number so that the value for S can be derived from the equation for r, whereby, the simulation value in the multi-dimensional space is reduced to provide an increased accuracy within a reduced time, the simulation value being applicable for simulations of trace impedance in circuit board manufacture.

2. The method of claim 1, wherein the D dimension values are further characterized by a first dimension D0 that includes minimum and maximum values defined as D0.min and D0.max, respectively, a second dimension D1 that includes minimum and maximum values defined as D1.min and D1.max, etceteras, up to a Dth dimension.

3. A method for simulating trace impedance for application to a printed circuit board design using a quasi-Monte Carlo model comprising:

generating a sequence of pseudo-random numbers according to a prescribed quasi-Monte Carlo model;

mapping each pseudo-random number R of the sequence of random numbers into multiple variables of unique values for the multi-dimensional space, the multi-dimensional space including D dimensions, where D is a number, wherein each of the multiple variables of the multi-dimensional space represents a corresponding D dimension value and wherein each dimension is characterized by a minimum and a maximum value, the D dimension values further being characterized by a first dimension D0 that includes minimum and maximum values defined as D0.min and D0.max, respectively, a second dimension D1 that includes minimum and maximum values defined as D1.min and D1.max, etceteras, up to a Dth dimension, further wherein each dimension is characterized by a prescribed resolution S, the mapping providing a substantially even hard-coded point-cloud to define a grid of quasi-Monte Carlo points to provide some regularity in the point cloud over the multi-dimensional space; and

selecting a value of S according to a desired accuracy of a final simulation value, wherein the value of S defines a grid for use in conjunction with the mapping of the pseudo-random numbers into the multiple variables of the multi-dimensional space, wherein S is the resolution of each dimension and a ratio r, as defined by r=s^D/P^N, can be determined to be a prime number so that the value for S can be derived from the equation for r, whereby, the simulation value in the multi-dimensional space is reduced to provide an increased accuracy within a reduced time, the simulation value being applicable for simulations of trace impedance in circuit board design.

4. A method for simulating trace impedance for application to a printed circuit board design using a quasi-Monte Carlo model, said method comprising:

generating a sequence of pseudo-random numbers according to a prescribed quasi-Monte Carlo model;

mapping each pseudo-random number R of the sequence of random numbers into multiple variables of unique values for the multi-dimensional space, the multi-dimensional space including D dimensions, where D is a number, the mapping providing a substantially even hard-coded point-cloud to define a grid of quasi-Monte Carlo points to provide some regularity in the point cloud over the multi-dimensional space; and

selecting a value of S according to a desired accuracy of a final simulation value, wherein the value of S defines a grid for use in conjunction with the mapping of the pseudo-random numbers into the multiple variables of the multi-dimensional space, wherein each of the multiple variables of the multi-dimensional space represents a corresponding D dimension value and wherein each dimension is characterized by a minimum and a maximum value, further wherein each dimension is characterized by a prescribed resolution S, and wherein S is the resolution of each dimension, and a ratio r, as defined by r=s^D/P^N can be predetermined to be a prime number so that the value for S can be derived from the equation for r, whereby, the simulation value in the multi-dimensional space is reduced to provide an increased accuracy within a reduced time, the simulation value being applicable for simulations of trace impedance in circuit board design.

5. The method of claim 4, wherein the D dimension values are further characterized by a first dimension D0 that includes minimum and maximum values defined as D0.min and D0.max, respectively, a second dimension D1 that includes minimum and maximum values defined as D1.min and D1.max, etceteras, up to a Dth dimension.

6. Apparatus for simulating trace impedance for application to a printed circuit board design using a quasi-Monte Carlo model, said apparatus comprising:

a random number generator for generating a sequence of pseudo-random numbers according to a prescribed quasi-Monte Carlo model;

a mapping processor for mapping each pseudo-random number R of the sequence of random numbers into multiple variables of unique values for the multi-dimensional space, the multi-dimensional space including D dimensions, where D is a number, wherein each of the multiple variables of the multi-dimensional space represents a corresponding D dimension value and wherein each dimension is characterized by a minimum and a maximum value, the D dimension values further being characterized by a first dimension D0 that includes minimum and maximum values defined as D0.min and D0.max, respectively, a second dimension D1 that includes minimum and maximum values defined as D1.min and D1.max, etceteras, up to a Dth dimension, further wherein each dimension is characterized by a prescribed resolution S, the mapping providing a substantially even hard-coded point-cloud to define a grid of quasi-Monte Carlo points to provide some regularity in the point cloud over the multi-dimensional space; and

a value selector for selecting a value of S according to a desired accuracy of a final simulation value, wherein the value of S defines a grid for use in conjunction with the mapping of the pseudo-random numbers into the multiple variables of the multi-dimensional space, wherein S is the resolution of each dimension and a ratio r, as defined by r=s^D/P^N, can be determined to be a prime number so that the value for S can be derived from the equation for r, whereby, the simulation value in the multi-dimensional space is reduced to provide an increased accuracy within a reduced time, the simulation value being applicable for simulations of trace impedance in circuit board design.

7. A method of designing a printed circuit board by simulating trace impedance using a quasi-Monte Carlo model comprising:

characterizing the printed circuit board by at least three dimensions of a multi-dimensional space; and

manufacturing the printed circuit board in accordance with a simulated trace impedance, the simulated trace impedance obtained by;

generating a sequence of pseudo-random numbers according to a prescribed quasi-Monte Carlo model;

mapping each pseudo-random number R of the sequence of random numbers into multiple variables of unique values for the multi-dimensional space, the multi-dimensional space including D dimensions, where D is a number, wherein each of the multiple variables of the multi-dimensional space represents a corresponding D dimension value and wherein each dimension is characterized by a minimum and a maximum value, the D dimension values further being characterized by a first dimension D0 that includes minimum and maximum values defined as D0.min and D0.max, respectively, a second dimension D1 that includes minimum and maximum values defined as D1.min and D1.max, etceteras, up to a Dth dimension, further wherein each dimension is characterized by a prescribed resolution S, the mapping providing a substantially even hard-coded point-cloud to define a grid of quasi-Monte Carlo points to provide some regularity in the point cloud over the multi-dimensional space; and

selecting a value of S according to a desired accuracy of a final simulation value, wherein the value of S defines a grid for use in conjunction with the mapping of the pseudo-random numbers into the multiple variables of the multi-dimensional space, wherein S is the resolution of each dimension and a ratio r, as defined by r=s^D/P^N, can be determined to be a prime number so that the value for S can be derived from the equation for r, whereby, the simulation value in the multi-dimensional space is reduced to provide an increased accuracy within a reduced time, the simulation value being applicable for simulations of trace impedance in circuit board design.

8. A computer system, including a printed circuit board designed by simulating trace impedance using a quasi-Monte Carlo model comprising:

the printed circuit board including impedance traces that characterize at least three dimensions of a multi-dimensional space of said printed circuit board, wherein said impedance traces include trace impedances obtained by;

generating a sequence of pseudo-random numbers according to a prescribed quasi-Monte Carlo model;

mapping each pseudo-random number R of the sequence of random numbers into multiple variables of unique values for the multi-dimensional space, the multi-dimensional space including D dimensions, where D is a number, wherein each of the multiple variables of the multi-dimensional space represents a corresponding D dimension value and wherein each dimension is characterized by a minimum and a maximum value, the D dimension values further being characterized by a first dimension D0 that includes minimum and maximum values defined as D0.min and D0.max, respectively, a second dimension D1 that includes minimum and maximum values defined as D1.min and D1.max, etceteras, up to a Dth dimension, further wherein each dimension is characterized by a prescribed resolution S, the mapping providing a substantially even hard-coded point-cloud to define a grid of quasi-Monte Carlo points to provide some regularity in the point cloud over the multi-dimensional space; and

selecting a value of S according to a desired accuracy of a final simulation value, wherein the value of S defines a grid for use in conjunction with the mapping of the pseudo-random numbers into the multiple variables of the multi-dimensional space, wherein S is the resolution of each dimension and a ratio r, as defined by r=s^D/P^N, can be determined to be a prime number so that the value for S can be derived from the equation for r, whereby, the simulation value in the multi-dimensional space is reduced to provide an increased accuracy within a reduced time, the simulation value being applicable for simulations of trace impedance in circuit board design.