Methods and systems for compact modeling of large linear circuits with a large number of terminals

A signal-bearing medium tangibly embodying a program of machine-readable instructions executable by a digital processing apparatus of a computer system to perform operations comprising model order reduction of a complex electric circuit, the operations comprising:

• formulating a set of expressions that describe the input and output characteristics of the complex electric circuit, wherein the set of expressions comprises a first model of the complex electric circuit;
• selecting a first sub-block of the first model of the complex electric circuit where the first sub-block corresponds to a first subset of input terminals to and output terminals from the complex electric circuit, wherein at least one correlation in response behavior is likely to exist between at least two output terminals comprising the first subset of input and output terminals;
• formulating a set of expressions that relate the input terminals and output terminals comprising the first subset, wherein the set of expressions comprises a first model of the first sub-block;
• performing mathematical operations on the first model of the first sub-block to identify at least one correlation between at least two output terminals of the first subset of input terminals to and output terminals from the complex electric circuit;
• generating a reduced-order second model of the first sub-block by removing from the first model aspects associated with correlated output terminals;
• and
• inserting the reduced-order second model of the first sub-block in the first model of the complex electric circuit at a position reserved for the first sub-block.

A signal-bearing medium tangibly embodying a program of machine-readable instructions executable by a digital processing apparatus of a computer system to perform operations comprising model order reduction of a complex electric circuit, the operations comprising:

• formulating a set of expressions that describe the input and output characteristics of the complex electric circuit, wherein the set of expressions comprises a first model of the complex electric circuit;
• selecting a first sub-block of the first model of the complex electric circuit where the first sub-block corresponds to a first subset of input terminals to and output terminals from the complex electric circuit, wherein at least one correlation in response behavior is likely to exist between at least two input terminals or between at least two output terminals comprising the first subset of input and output terminals;
• formulating a set of expressions that relate the input terminals and output terminals comprising the first subset, wherein the set of expressions comprises a first model of the first sub-block;
• performing mathematical operations on the first model of the first sub-block to identify at least one correlation between at least two input terminals or between at least two output terminals of the first subset of input terminals to and output terminals from the complex electric circuit;
• generating a reduced-order second model of the first sub-block by removing from the first model aspects associated with correlated input terminals or correlated output terminals;
• and
• inserting the reduced-order second model of the first sub-block in the first model of the complex electric circuit at a position reserved for the first sub-block.

A signal-bearing medium tangibly embodying a program of machine-readable instructions executable by a digital processing apparatus of a computer system to perform operations comprising model order reduction of a complex electric circuit, the operations comprising:

• selecting which response characteristic of the complex electric circuit to model;
• formulating a set of expressions of sufficient accuracy to simulate the selected response characteristic at the input and output terminals of the complex electric circuit, wherein the set of expressions comprises a first model of the complex electric circuit;
• selecting a first sub-block of the first model of the complex electric circuit where the first sub-block corresponds to a first subset of input terminals to and output terminals from the complex electric circuit, wherein at least one correlation in response behavior is likely to exist between at least two input terminals or between at least two output terminals comprising the first subset of input and output terminals;
• formulating a set of expressions that relate the input terminals and output terminals comprising the first subset, wherein the set of expressions comprises a first model of the first sub-block;
• performing mathematical operations on the first model of the sub-block to identify at least one correlation between at least two input terminals or between at least two output terminals of the first subset of input terminals to and output terminals from the complex electric circuit;
• generating a reduced-order second model of the first sub-block by removing from the first model aspects associated with correlated input terminals or correlated output terminals;
• and
• inserting the reduced-order second model of the first sub-block in the first model of the complex electric circuit at a position reserved for the first sub-block.

A computer system for performing model order reduction on a model of a complex electric circuit, the computer system comprising:

• at least one memory to store at least (1) a description of the complex electric circuit and (2) at least one program of machine-readable instructions comprising operations which perform model order reduction on models of complex electric circuits when the at least one program is executed;
• at least one processor coupled to the at least one memory, wherein the at least one processor performs at least the following operations when the at least one program is executed:
• formulating a set of expressions from the description of the complex electric circuit that describe the input and output characteristics of the complex electric circuit, wherein the set of expressions comprises a first model of the complex electric circuit;
• selecting a first sub-block of the first model of the complex electric circuit where the first sub-block corresponds to a first subset of input terminals to and output terminals from the complex electric circuit, wherein at least one correlation in response behavior is likely to exist between at least two input terminals or between at least two output terminals comprising the first subset of input and output terminals;
• formulating a set of expressions that relate the input terminals and output terminals comprising the first subset, wherein the set of expressions comprises a first model of the first sub-block;
• performing mathematical operations on the first model of the sub-block to identify at least one correlation between at least two input terminals or between at least two output terminals of the first subset of input terminals to and output terminals from the complex electric circuit;
• generating a reduced-order second model of the first sub-block by removing from the first model aspects associated with correlated input terminals or correlated output terminals;
• and
• inserting the reduced-order second model of the first sub-block in the first model of the complex electric circuit at a position reserved for the first sub-block.

A computer system for performing model order reduction on a model of a complex electric circuit, the computer system comprising:

• at least one memory to store at least (1) a description of the complex electric circuit and (2) at least one program of machine-readable instructions comprising operations which perform model order reduction on models of complex electric circuits when the at least one program is executed;
• at least one processor coupled to the at least one memory, wherein the at least one processor performs at least the following operations when the at least one program is executed:
• recalling a user-specified selection corresponding to a desired response characteristic of the complex electric circuit;
• wherein that desired response characteristic of the complex electric circuit will be modeled by the computer system;
• formulating a set of expressions of sufficient accuracy to simulate the selected response characteristic at the input and output terminals of the complex electric circuit, wherein the set of expressions comprises a first model of the electric circuit;
• selecting a first sub-block of the first model of the complex electric circuit where the first sub-block corresponds to a first subset of input terminals to and output terminals from the complex electric circuit, wherein at least one correlation in response behavior is likely to exist between at least two input terminals or between at least two output terminals comprising the first subset of input and output terminals;
• formulating a set of expressions that relate the input terminals and output terminals comprising the first subset, wherein the set of expressions comprises a first model of the first sub-block;
• performing mathematical operations on the first model of the sub-block to identify at least one correlation between at least two output terminals or between at least two output terminals of the first subset of input terminals to and output terminals from the complex electric circuit;
• generating a reduced-order second model of the first sub-block by removing from the first model aspects associated with correlated input terminals or correlated output terminals;
• and
• inserting the reduced-order second model of the first sub-block in the first model of the complex electric circuit at a position reserved for the first sub-block.

A signal bearing medium tangibly embodying a program of machine-readable instructions executable by a digital processing apparatus of a computer system to perform operations comprising model order reduction of a linear system, the operations comprising:

• formulating a set of expressions that describe the input and output characteristics of the linear system, wherein the set of expressions comprises a first model of the linear system;
• selecting a first sub-block of the first model of the linear system where the first sub-block corresponds to a first subset of inputs to and outputs from the linear system, wherein at least one correlation in response behavior is likely to exist between at least two inputs or between at least two outputs comprising the first subset of inputs and outputs;
• formulating a set of expressions that describe the input and output characteristics of the first sub-block, wherein the set of expressions comprises a first model of the first sub-block;
• performing mathematical operations on the first model of the first sub-block to identify at least one correlation between at least two inputs or between at least two outputs of the sub-block;
• generating a reduced-order second model of the sub-block by removing from the first model of the first sub-block aspects associated with correlated inputs or correlated outputs;
• and
• inserting the reduced-order second model of the first sub-block in the first model of the linear system at a position reserved for the first sub-block.

A method for performing model order reduction on a model of a complex electric circuit, the method comprising:

• formulating a set of expressions that describe the input and output characteristics of the complex electric circuit, wherein the set of expressions comprises a first model of the electric circuit;
• recursively selecting sub-blocks of the model of the complex electric circuit, wherein each of the sub-blocks corresponds to a subset of input terminals to and output terminals from the complex electric circuit, wherein with respect to each of the subsets at least one correlation is likely to exist between at least two input terminals or between at least two output terminals comprising each of the subsets;
• formulating a set of expressions for each of the sub-blocks, wherein each set of expressions relates the input and output terminals of the subset corresponding to that sub-block, and where the sets of expressions for each of the sub-blocks comprise first models of each of the sub-blocks;
• performing mathematical operations on the first models of the sub-blocks to identify at least one correlation between at least two input terminals or between at least two output terminals of the sub-blocks;
• generating reduced-order second models for each of the sub-blocks by removing from the first models aspects associated with correlated input terminals or correlated output terminals;
• and
• successively inserting the reduced-order second models of the sub-blocks in the model of the complex electric circuit at respective positions reserved for each of the sub-blocks, wherein each successive insertion creates a new overall model of the complex electric circuit.

A method for performing model order reduction on a model of a complex electric circuit, the method comprising:

• selecting which response characteristic of the complex electric circuit to model;
• formulating a set of expressions of sufficient accuracy to simulate the selected response characteristics at the input and output terminals of the complex electric circuit, wherein the set of expressions comprises a first model of the complex electric circuit;
• recursively selecting sub-blocks of the model of the complex electric circuit, wherein each of the sub-blocks corresponds to a subset of input terminals to and output terminals from the complex electric circuit, wherein with respect to each of the subsets at least one correlation is likely to exist between at least two input terminals or between at least two output terminals comprising each of the subsets;
• formulating a set of expressions for each of the sub-blocks, wherein each set of expressions relates the input and output terminals of the subset corresponding to that sub-block, and where the sets of expressions for each of the sub-blocks comprise first models of each of the sub-blocks;
• performing mathematical operations on the first models of the sub-blocks to identify at least one correlation between at least two input terminals or between at least two output terminals of the sub-blocks;
• generating reduced-order second models for each of the sub-blocks by removing from the first models aspects associated with correlated input terminals or correlated output terminals;
• and
• successively inserting the reduced-order second models of the sub-blocks in the model of the complex electric circuit at respective positions reserved for each of the sub-blocks, wherein each successive insertion creates a new overall model of the complex electric circuit.