# CODESTAR Streszczenie raportu

Project ID:
IST-2001-34058

Źródło dofinansowania:
FP5-IST

Kraj:
Romania

## Reduced-order modelling (ROM) workbench

This result consists in methodology and software dedicated to extraction of compact models for on-chip passive structures with high frequency electromagnetic field effects, such as: skin effect, current crowding, induced voltage, propagation delay, cross-talk, charge relaxation, etc. It is dedicated to analog/RF/wireless chip and electronic system designers. It can be also used to build model libraries for new (nano) technology design kits.

The methodology is based on the original "All Levels Reduced Order Modelling (ALLROM)" and "Very Fast Simulation (VFS)" strategies, described in details in [D8], [D11] and [D16]. ALLROM consists in a series of ROM techniques, which can be applied successively and/or alternatively at several stages:

- Macro modelling (CellHO = Cell Homogenisation, ELOB = Equivalent Layer of Open Boundary Condition, dFIT = dual Finite Integrals Technique),

- Apriori (PROM = Phenomenological based ROM, CROM = Coarsest ROM based on lumped circuit having equivalent energy,

- TCR = Tree/Cotree Reduction and MEEC = Magneto-Electro Equivalent Circuit), "on the fly" (FredHO = Frequency dependent Hodge Operators, ASPEEC = Algebraic Sparcefied Partial Equivalent Electric Circuit, BANESSA = Branch and Nodes Elimination by Symbolic Successive Approximation) and

- Aposteriori (KROM = Krylov based ROM, TBR = Truncated Balanced Reduction of semi-state/descriptor systems, Avectorfit = automated frequency Characteristic fitting by vectorfit).

The embedding of ROM techniques in the early electromagnetic modelling stages is extremely efficient, allowing the reduction of DOFs number up to 10 million times.

The VFS strategy has a complementary aim, to reduce the time required for simulation and compact model extraction.

It consists in a series of acceleration techniques, such as:

- AFS = Adaptive Frequency Sampling,

- TLTM = Transmission Line model based on Transversal Magnetic Field with interpolated frequency dependent p.u.l. parameters,

- FTS = Frequency vs Time domain or Semi-space state simulation

- PDS = Parallel or Distributed Simulation.

By this strategy, the simulation time was reduced up to 10,000 times, to 20s in simple cases and <1000s for complex structures. The software is written in C++ and was tested under Linux OS. It complies EDA/TCAD standards, in order to be easily integrated in several design environments.

The input files describe layout and technology in standard formats (such as .cif and. sipp).

The output files contains the compact model of the device in SPICE format, as well as other numerical or graphic results (.snp, .vtk, Smith diagram, lumped or p.u.l. parameters, quality factor, etc.) very useful in the design process.

The code has following main features: import, load, save, interactive graphic edit, solve, simulate, reduce order and Spice model synthesis.

The methodology and software were benchmarked against measured data for Codestar standard test structures: meander resistors, capacitors, spiral inductors, interconnect/transmission lines, and challenging structures: coupled inductors, LC cells.

The simulation results over 0-40GHz frequency range have an accuracy better then 5% in standard cases, and better than technological errors for challenging cases.

There is also available a software toolbox called ¿ROM Workbench¿, developed in Matlab and compiled under Linux. It can be used to decide which ROM technique is the most appropriate for the reduction of models, obtained from the electromagnetic field analysis. Its aim is to allow the user to reduce models by means of as many state of the art ROM techniques as possible, and to compare the results.

The ROM workbench consists of:

- A series of benchmark problems;

- A set of model order reduction methods;

- Criteria for results evaluation and comparison.

To start with the workbench, a system description generated by one of the field solvers is used. Such an output can be either a linear time invariant system described by means of semi-state space matrices, or the frequency characteristic described by the variation of the impedance, admittance or S-parameter matrices with respect to the frequency. The reduction can be carried out by means of various methods.

These methods include:

- Explicit moment matching,

- Krylov subspace techniques,

- Laguerre techniques,

- A two-step Lanczos strategy,

- Also a new two step reduction strategy, based on a PRIMA technique followed by a truncated balanced reduction,

- Truncated balanced realisation procedures.

A very robust technique included in the ROM Workbench is the vector fitting method. The workbench is able to check the passivity and to compare the reference model and the reduced one, either on the time responses (step, impulse, etc.) or on the frequency responses (Bode, Nyquist, Smith, etc). Lumped parameters, quality factors or line parameters can also be compared.

The methodology is based on the original "All Levels Reduced Order Modelling (ALLROM)" and "Very Fast Simulation (VFS)" strategies, described in details in [D8], [D11] and [D16]. ALLROM consists in a series of ROM techniques, which can be applied successively and/or alternatively at several stages:

- Macro modelling (CellHO = Cell Homogenisation, ELOB = Equivalent Layer of Open Boundary Condition, dFIT = dual Finite Integrals Technique),

- Apriori (PROM = Phenomenological based ROM, CROM = Coarsest ROM based on lumped circuit having equivalent energy,

- TCR = Tree/Cotree Reduction and MEEC = Magneto-Electro Equivalent Circuit), "on the fly" (FredHO = Frequency dependent Hodge Operators, ASPEEC = Algebraic Sparcefied Partial Equivalent Electric Circuit, BANESSA = Branch and Nodes Elimination by Symbolic Successive Approximation) and

- Aposteriori (KROM = Krylov based ROM, TBR = Truncated Balanced Reduction of semi-state/descriptor systems, Avectorfit = automated frequency Characteristic fitting by vectorfit).

The embedding of ROM techniques in the early electromagnetic modelling stages is extremely efficient, allowing the reduction of DOFs number up to 10 million times.

The VFS strategy has a complementary aim, to reduce the time required for simulation and compact model extraction.

It consists in a series of acceleration techniques, such as:

- AFS = Adaptive Frequency Sampling,

- TLTM = Transmission Line model based on Transversal Magnetic Field with interpolated frequency dependent p.u.l. parameters,

- FTS = Frequency vs Time domain or Semi-space state simulation

- PDS = Parallel or Distributed Simulation.

By this strategy, the simulation time was reduced up to 10,000 times, to 20s in simple cases and <1000s for complex structures. The software is written in C++ and was tested under Linux OS. It complies EDA/TCAD standards, in order to be easily integrated in several design environments.

The input files describe layout and technology in standard formats (such as .cif and. sipp).

The output files contains the compact model of the device in SPICE format, as well as other numerical or graphic results (.snp, .vtk, Smith diagram, lumped or p.u.l. parameters, quality factor, etc.) very useful in the design process.

The code has following main features: import, load, save, interactive graphic edit, solve, simulate, reduce order and Spice model synthesis.

The methodology and software were benchmarked against measured data for Codestar standard test structures: meander resistors, capacitors, spiral inductors, interconnect/transmission lines, and challenging structures: coupled inductors, LC cells.

The simulation results over 0-40GHz frequency range have an accuracy better then 5% in standard cases, and better than technological errors for challenging cases.

There is also available a software toolbox called ¿ROM Workbench¿, developed in Matlab and compiled under Linux. It can be used to decide which ROM technique is the most appropriate for the reduction of models, obtained from the electromagnetic field analysis. Its aim is to allow the user to reduce models by means of as many state of the art ROM techniques as possible, and to compare the results.

The ROM workbench consists of:

- A series of benchmark problems;

- A set of model order reduction methods;

- Criteria for results evaluation and comparison.

To start with the workbench, a system description generated by one of the field solvers is used. Such an output can be either a linear time invariant system described by means of semi-state space matrices, or the frequency characteristic described by the variation of the impedance, admittance or S-parameter matrices with respect to the frequency. The reduction can be carried out by means of various methods.

These methods include:

- Explicit moment matching,

- Krylov subspace techniques,

- Laguerre techniques,

- A two-step Lanczos strategy,

- Also a new two step reduction strategy, based on a PRIMA technique followed by a truncated balanced reduction,

- Truncated balanced realisation procedures.

A very robust technique included in the ROM Workbench is the vector fitting method. The workbench is able to check the passivity and to compare the reference model and the reduced one, either on the time responses (step, impulse, etc.) or on the frequency responses (Bode, Nyquist, Smith, etc). Lumped parameters, quality factors or line parameters can also be compared.