# Patent

## Title
Layout of networks using parallel and series elements

## Abstract

Disclosed are systems, methods, and algorithms for network layout. A network layout having subnetworks of matching series and parallel elements is systematically generated to implement the network within area constraints. After the selection of the number of rows of network elements, the number of elements in each row, the sequencing of the elements, and the element locations, are systematically determined. The network layout systematically produced reduces the influence of unfavorable factors on the network such as temperature gradients, process gradients, and interference, by dispersing subnetwork elements throughout the layout.

## Background
RELATED APPLICATION
United States Patent Application of Du and Jaska, Ser. No. 10/217285, filed Aug. 12, 2002, entitled “Implementation of Networks Using Parallel and Series Elements.” is incorporated herein in its entirety for all purposes by this reference.


TECHNICAL FIELD
The present invention relates in general to systems, methods, and algorithms for layout of networks with parallel and series elements. More particularly, the invention relates to the systematic generation of a schematic or design layout for a network using combinations of matching series and parallel elements.
BACKGROUND OF THE INVENTION
In a network (M) which may be characterized by the quotient of a cross-quantity and a through-quantity, M=cross-quantity/through-quantity, it is generally known that certain relationships govern series and parallel network elements. For example, in an electrical resistor network, resistance (R) is the quotient of voltage (V) and current (i), R=V/i. It is well known that series elements are additive, e.g. Requivalent=(R1+R2+R3+ . . . RN), and that the equivalent resistance of parallel resistor elements is described by the relationship, Requivalent−1=(R1−1+R2−1+R3−1+ . . . RN−1). Such relationships hold true for other physical networks M as well.
In many engineering applications the problem of how to implement a network using multiple identical elements is encountered. Often such an implementation is sought in order to reduce the influence of unfavorable factors. In integrated circuit layout for example, the effects of an uneven temperature gradient, nonuniform distribution of process layers, and noise emissions from adjacent circuit blocks, may be alleviated by implementing a desired network value, such as resistance or capacitance, using smaller individual elements rather than using one lump-sum component.
Problems arise however, in attempting to describe a network using a combination of series and parallel elements. It is often desirable to use elements with matching physical characteristics. The use of matching network elements helps to equalize the effects of thermal gradients and material gradients and other unfavorable factors. The use of matching elements is also often desirable from a manufacturing standpoint. It is known in the arts to approach the breakdown of a network into series and parallel elements using some degree of trial and error. The problem is made more complex by concerns such as, in the example of integrated circuit and design, the desire to minimize area and the desire to minimize the count of individual network elements or to utilize elements of a particular value or size.
Techniques exist for systematically breaking down a network into series and parallel elements. See for example, the U.S. patent application Ser. No. 10/217,285 of Du and Jaska, filed Aug. 12, 2002, entitled “Implementation of Networks Using Parallel and Series Elements,” which is incorporated herein in its entirety for all purposed by this reference. However, once a network has been described in terms of subnetworks of series and parallel elements, the task of laying out the physical network remains a challenging one. In a resistor network for an integrated circuit for instance, a given element value is implemented using a resistor of the appropriate length and width. (Thickness is generally determined by the process and materials used). The network must then be implemented within area limitations. Typically a designer spends long hours attempting to determine a layout for the subnetworks of individual elements and interconnections. The task is complicated by the desirability of distributing elements of each subnetwork throughout the entire network to help alleviate the effects of unfavorable factors. Such cut-and-try layout techniques are tedious, time consuming, and error prone. Oftentimes network layouts have more than one hundred individual elements with the result that misplacement of elements detrimental to performance can go undetected. The number of possible permutations and lack of a systematic approach can lead to inconsistency from designer to designer, which can lead to further complications in circuits having numerous network blocks prepared by numerous designers.
It would be useful and advantageous in the arts to provide algorithms, systems, and methods for systematically laying out networks of parallel and series elements. Such tools could reduce tedium, error, time, cost, and inconsistency in preparing network layouts. Such tools could also be used to generate schematic diagrams describing networks in terms of series and parallel elements.
SUMMARY OF THE INVENTION
In general, the present invention provides systems, methods, and algorithms for network layout. In carrying out the principles of the present invention, in accordance with an embodiment thereof, a method of laying out a network having subnetworks of series and parallel elements includes the selection of a number of rows of network elements for layout within a particular area. The number of elements in each row, the sequencing of the elements, and the element locations are systematically determined. The subnetwork elements are dispersed within the layout.
According to a preferred embodiment of the invention, an algorithm for layout of a network having subnetworks of series and parallel elements includes steps for accepting the input of an area to be occupied by the network and the number of rows of network elements. The number of columns of elements, the number of elements to be placed in each row, sequencing of the elements, element locations, and ultimately a network layout, are determined.
According to another aspect of the invention, a schematic diagram of a network layout is generated.
According to another aspect of the invention, a system for constructing a network layout from a combination of matching series and parallel elements is provided. The system includes means for executing an algorithm to determine the physical layout of the network and means for coupling a quantity of matching series and parallel elements to assemble the network layout.
The invention provides several technical advantages including but not limited to increased efficiency and consistency in network layout, a reduction in tedium and savings in time. The potential for error in laying out a network is also reduced.



BRIEF DESCRIPTION OF THE DRAWINGS
The above and additional features and advantages of the present invention will be more clearly understood from consideration of the following detailed description in connection with the accompanying drawings in which:
FIG. 1 is a graphical representation of a network used in describing an example of the invention;
FIG. 2 is a process flow diagram illustrating the systematic layout of a network with a combination of series and parallel elements;
FIGS. 3A through 3D are block diagrams illustrating an example of the systematic layout of a network using the invention; and
FIG. 4 is a block diagram depicting an example of a system of the invention.



References in the detailed description correspond to like references in the figures unless otherwise noted. Like numerals refer to like parts throughout the various figures. The descriptive and directional terms used in the written description such as top, bottom, left, right, etc., refer to the drawings themselves as laid out on the paper and not to physical limitations of the invention unless specifically noted. The drawings are not to scale and some features of embodiments shown and discussed are simplified or exaggerated for illustrating the principles of the invention.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS
The invention provides for the systematic layout of a network in a combination of series and parallel elements. The invention may be used for networks which can be expressed in terms of a cross-quantity divided by a through-quantity such as, for example, an electronic network in which by Ohm's law, resistance is the quotient of voltage divided by current. Although for the sake of example the invention is described in terms of electronic resistor networks, it should be understood that the algorithms, methods, and systems described are applicable to other electrical and mechanical networks, such as a network of inductors, field effect or bipolar transistors, or fluid pumps, without departure from the concepts of the invention.
Given a particular network resistance value, there are a very large number of possible implementations using various numbers of various sizes of individual resistor elements. In the implementation of physical networks, engineering considerations narrow the possible implementations. For example it may be desirable to use a particular resistor element value for the implementation of a network, or it may be desirable to implement the network within a particular planar area of an integrated circuit. Once the network has been broken down into a number of individual elements arranged in various subnetworks of elements connected in series or parallel, an implementation is chosen.
Generally, it is preferred in the electronic arts to use matching network elements to layout a network in a given area determined by design specifications or space available on a chip. With the area given as an initial constraint, the number of rows may be selected. The selection of the number of rows is generally related to the total area available for the network, the number of elements in the network, and the values of the individual elements. The values of the individual elements is generally determinative of the length and width of each element. Other design factors known in the arts may influence how much additional space may be required between elements to avoid interference or other detrimental conditions.
FIG. 1 depicts an example of a network 10 for the purposes of explaining the layout of a given network according to the invention. The network 10 has three subnetworks Sn. Each of the subnetworks Sn has a number of elements ESn,m connected in series or in parallel, in this case resistors. A first subnetwork S1 is made up of four elements ES1,1, ES1,2, ES1,3, and ES1,4, connected in series. A second subnetwork S2 is made up of six elements ES2,1, ES2,2, ES2,3, ES2,4, ES2,5, and ES2,6, connected in parallel. A third subnetwork S3 is made up of five elements ES3,1, ES3,2, ES3,3, ES3,4, and ES3,5, connected in parallel.
In this example there are three subnetworks Sn and a total of 15 individual elements ESn,m. It should be understood that the individual elements ESn,m are interchangeable matching elements arbitrarily numbered “m” for reference for the purposes of this illustrative example. The network 10 is shown and described for the sake of example only and is not intended to limit the invention to one specific application or level of complexity. It may be expected that the actual implementation of the invention by those skilled in the arts will involve many more subnetworks and elements in complex arrangements. For instance, the network of the example could itself be a small subnetwork within a larger network. For the sake of this example a layout and schematic are devised for the network 10 shown.
FIG. 2 is a process flow diagram illustrating an example of the steps in a preferred embodiment of the invention. An area is selected for occupation by a network having a number of subnetworks and individual elements connected either in series or in parallel, as shown in step 100. The total number of rows of elements is determined, preferably based on factors such as area available and element size, step 102. The number of columns is determined, in step 104, preferably based on the total number of elements in the network and the number of rows. As shown at step 106, the number of elements per row is determined, including both a whole number value and if necessary, a remainder. The remainder values are retained for later summing and inclusion within the network area. The element sequencing is determined at step 108 by dividing a selected reference value by the number of elements needed per row. At step 110, the element locations are allocated according to the sequencing and the number of elements per row. At step 112, the elements are arranged into a network layout or a schematic is generated.
FIG. 3A provides a graphical representation of a network area 30 with a selected number of rows Ri. As shown for the sake of example, three rows, R1, R2, and R3 have been elected for the implementation of the network 10. Typically, the number of rows is selected based on factors such as the area available and the size of the desired elements. It should be understood that the number of rows need not be a whole number factor or multiple of the number of subnetworks Sn or number of elements E. The number of columns C in the network area 30 is preferably determined based on the quotient of the number of elements E and the number of rows R.

C=E/R  (1).

The number of subnetwork elements to be placed in each row ESnR is preferably determined by the quotient of the number of elements per subnetwork ESn and the number of rows R. Of course, there may often be a remainder rSn for a subnetwork.

ESnR=ESn/R  (2).

Both the whole number results and the remainders are retained for each subnetwork Sn. Preferably, once all of the quotients ESnR have been determined, all of the remainder values rSn are summed.

r=ΣrSn  (3).

The number of remainder elements Er per row R may then be determined using equation (2), dividing the remainder sum r by the number of rows R.

Er=r/R  (2).

In the present numerical example, using equation (2) the number of subnetwork elements ESnR per network row R is determined as follows:

ES1R=ES1/R  (2)

ES1R=4/3

ES1R=2

rS1=1

ES2R=ES2/R  (2)

ES2R=6/3

ES2R=2

rS2=0

ES3R=ES3/R  (2)

 ES3R=5/3

ES3R=1

rS3=2

The remainder elements are summed for inclusion in the network,

r=ΣrSn=rS1+rS2+rS3  (3),

r=1+0+2=3

and the number of remainder elements per row is determined,

Er=r/R  (2).

Er=3/3=1

At this point in the numerical example, it should be appreciated that it has been systematically determined that the network 10 layout will have three rows Ri containing five columns C. Each of the rows Ri will include one element of subnetwork one Es1, two elements of subnetwork two Es2, one element of subnetwork three Es3, and one of the remainder elements Er, distributed among the rows Ri as further described.
Now referring primarily to FIG. 3B, the sequencing ZSn of the elements ESn within each of the rows Ri is preferably determined using a reference value X. The reference value may be an arbitrarily selected value. In this example, the arbitrary reference value twelve is used. It should be understood that the reference value is used to determine the sequence of the elements relative to one another, and is not a physical measurement. Preferably, the actual physical spaces between the elements are determined by operational considerations known in the arts. The sequencing ZSn between the elements ESn in each row Ri is determined by dividing the reference value X by the number of subnetwork elements per row ESnR. In performing this operation for the elements ESn of each subnetwork, for all but the first element ESn, the reference value X is preferably incremented by a small additional offset value Y, preferably less than about 10 percent of the reference value X, so that the beginning points of elements ESn on each adjacent row Ri are offset from one another in the result.

ZSn=(X+Y)/ESnR  (3).

This operation is performed for the each of the subnetwork elements ESnR determine to be included in each row, and also with the sum of the remainders r. Accordingly, continuing the numerical example yields:

Zs1=(X+Y)/ES1R  (3)

ZS1=(12+0)/1

ZS1=12

ZS2=(X+Y)/ES2R  (3)

ZS2=(12+0.1)/2

ZS2=6.05

ZS3=(X+Y)/ES3R  (3)

ZS3=(12.1+0.1)/1

ZS3=12.2

Zr=(X+Y)/Er  (3).

Zr=(12.2+0.1)/1

Zr=12.3

The example is further illustrated with reference to FIG. 3C. In order to determine the placement of each element within a row, the beginning location LESn of each element ESn is determined by multiplying it with the applicable sequencing value ZSn.

LESn=ZSn*ESn  (5)

For the first subnetwork element ES1, the sequencing value has been determined to be ZSn=12.0, thus the first element ESn of the first subnetwork, will begin 12.0 reference units from the beginning (0.0 reference units) of the first row:

LESn=ZSn*ESn  (5).

LES1=12.0*1

LES1=12.0

Since there are two elements of the second subnetwork S2 in each row, as indicated by ES2R=2, the operation of equation (5) is performed twice, once for each element:

LES2,1=Z2*ES2,1  (5)

LES2,1=6.05*1

LES2,1=6.05

LES2,2=Z2*ES2,2  (5).

LES2,2=6.05*2

LES2,2=12.1

Row three R3, and the set of remainders r, have each been allocated one element per row, therefore for row three R3:

LES3=Z3*ES3  (5),

LES3=12.2*1

 LES3=12.2

and for the remainder;

Lr=Zr*Er  (5).

Lr=12.3*1

Lr=12.3

Each of the location values LESn is identified with a particular element ESn,m and the values are sorted, preferably using common sorting techniques, to determine the element order. For the first row R1, further referring to FIG. 3B, element ES2,1, with a location of LES2,1=6.05, is allocated the first location in the first row R1. Element ES1, with a location of LES1=12.0, is placed second. Element ES2,2 is placed third since ES2,2=12.1. Next, LES3=12.2, therefore element ES3 is placed at the next location. Using Lr=12.3, a location is allocated to one of the remainder elements.
It can be seen that the first row R1 has one element E of subnetwork one S1, two elements E of subnetwork two S2, and one element E of subnetwork three S3, plus one additional remainder element Er. Thus, the five columns C in the first row R1 of the network layout 11 have been systematically determined, distributing elements E of the various subnetworks Sn throughout.
Further referring primarily to FIG. 3C, in populating subsequent rows Ri, a shifting technique is preferably used in order to ensure that the subnetwork elements ESn are distributed in order to help alleviate the effects of unfavorable factors. Various shifting techniques known in the arts may be used. In the present example, a right shift is used wherein the elements of the second row R2 are copied from the first row R1, shifting each element one location to the right. The rightmost element is then shifted to the leftmost position of the row. The third row R3 is determined in the same manner, using a copy of row two R2 shifted one element to the right.
Preferably, the remainder locations Lr are populated in sequence. This is shown in FIG. 3D. Also shown in FIG. 3D, appropriate series and parallel connections, in this case electrical connections, differentiated in the figure by dashed lines, are made among the elements of the network. The electrical connections are preferably made using methods and tools known in the arts. It will be appreciated by those skilled in the arts that the network layout 11 of FIG. 3D is electrically equivalent to the resistor network 10 of FIG. 1. The network layout 11 is more resistant to unfavorable factors due to the distribution of subnetwork elements. The layout 11 of FIG. 3D is also consistently reproducible using the invention and uses only the specified area 30.
FIG. 4 illustrates an example of a preferred embodiment of a system of the invention. Characteristics 40 of a network including a subnetwork breakdown are preferably input to a machine 42 for executing an algorithm 44 for determining the physical layout of the network with a combination of matching series and parallel elements. Instructions 46 are generated for the layout 48 of the network and additional machinery 50 implements the determined network layout 48 in the form of an integrated circuit 52.
The invention provides systems, methods, and algorithms for determining and realizing the layout of a network of matching parallel and series elements. The invention provides many advantages including but not limited to the systematization and automation of network layout, resulting in reduced design time and costs. The invention may also be advantageously used to generate layout schematics and to increase consistency in network layout. While the invention has been described with reference to illustrative embodiments, this description is not intended to be construed in a limiting sense. Various modifications and combinations of the illustrative embodiments as well as other embodiments of the invention will be apparent to persons skilled in the art upon reference to the description and claims.

## Claims

1. A method of laying out a network having subnetworks of series and parallel elements, comprising the steps of:
selecting an area to be occupied by the network; 
responsive to the selected area to be occupied by the network; 
selecting the number of rows of elements; 
determining the number of columns of elements; 
determining the number of elements to be placed in each row; 
determining the sequencing of the elements; 
allocating element locations; and 
arranging the elements into a network layout.

2. The method of claim 1 wherein the step of determining the number of columns further comprises the step of taking the quotient of the total number of elements divided by the number of rows.

3. The method of claim 1 wherein the step of determining the number of elements to be placed in each row further comprises the step of taking the quotient of the number of elements per subnetwork divided by the number of rows.

4. The method of claim 1 wherein the step of determining the sequencing of the elements further comprises the step of taking the quotient of a reference value divided by the number of elements per subnetwork in each row.

5. The method of claim 1 wherein the step of allocating element locations further comprises the step of taking the product of a sequencing value and the number of elements per row.

6. The method of claim 1 wherein the step of arranging the elements into a network layout further comprises the step of dispersing subnetwork elements within the layout.

7. The method of claim 1 wherein the network layout comprises a resistor network layout.

8. The method of claim 1 wherein the network layout comprises an inductor network layout.

9. The method of claim 1 wherein the network layout comprises a transistor network layout.

10. An algorithm for determining a layout for a network having subnetworks of series and parallel elements comprising the steps of:
accepting the input of an area to be occupied by the network; 
responsive to the input of an area to be occupied by the network; 
accepting the input of the number of rows of elements; 
determining the number of columns of elements; 
determining the number of elements to be placed in each row; 
determining the sequencing of the elements; 
allocating element locations; and 
outputting a description of a layout for arranging the elements into a network.

11. The algorithm of claim 10 wherein the step of determining the number of columns further comprises the step of taking the quotient of the total number of elements divided by the selected number of rows.

12. The algorithm of claim 10 wherein the step of determining the number of elements to be placed in each row further comprises the step of taking the quotient of the number of elements per subnetwork divided by the number of rows.

13. The algorithm of claim 10 wherein the step of determining the sequencing of the elements further comprises the step of taking the sum of an offset and the quotient of a reference value divided by the number of elements in each row.

14. The algorithm of claim 10 wherein the step of allocating elements locations further comprises the step of taking the product of a sequencing value and the number of elements per row.

15. The algorithm of claim 10 wherein the step of allocating element locations further comprises the step of dispersing subnetwork elements within the layout.

16. The algorithm of claim 10 wherein the step of outputting a description of a layout further comprises the step of generating instructions for assembling the network.

17. The algorithm of claim 10 wherein the step of outputting a description of a layout further comprises the step of generating a schematic diagram.

18. A method of laying out a network having subnetworks of series and parallel elements, comprising the steps of:
selecting an area to be occupied by the network; 
selecting the number of rows of elements; 
determining the number of columns of elements; 
determining the number of elements to be placed in each row; 
determining the sequencing of the elements; 
allocating element locations; and 
arranging the elements into a network layout; 
wherein the step of determining the number of columns further comprises the step of taking the quotient of the total number of elements divided by the number of rows.

19. An algorithm for determining a layout for a network having subnetworks of series and parallel elements comprising the steps of:
accepting the input of an area to be occupied by the network; 
accepting the input of the number of rows of elements; 
determining the number of columns of elements; 
determining the number of elements to be placed in each row; 
determining the sequencing of the elements; 
allocating element locations; and 
outputting a description of a layout for arranging the elements into a network; 
wherein the step of determining the number of columns further comprises the step of taking the quotient of the total number of elements divided by the selected number of rows.