Balanced truncated models of RC interconnect circuits and their simulation

Bao-guo, Yuan; Wang, Ben; Wang, Sheng-Guo

doi:10.1007/bf02687928

Cited by 7 publications

(7 citation statements)

References 4 publications

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“…The BTM model reduction method has been a successful model reduction method for many problems, such as to the high order distributed RC interconnect line [4,16,17,19]. It has been noticed that the BTM method may not keep the DC match well, thus the DC match or frequency-weighted BTM has been developed [4,7,15,19] to compensate a match in the low frequency range, but with a cost of its high frequency performance and computation load.…”

Section: Reduced Models and Time Response Performancementioning

confidence: 99%

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An example of balanced truncation method and its surprising time domain performance

Wang

2008

2008 IEEE Conference on Cybernetics and Intelligent Systems

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This paper presents an example of using the balanced truncation method (BTM) for a distributed RLC interconnect model reduction. The example shows a surprising result and some possible hidden phenomenon in model reduction methods. We find that a high order BTM model has much worse performance than a low order BTM model, in view of the original model and their step responses in the time domain. This unexpected finding contradicts to our common expectation from the well-known approximation error upper bound results of the BTM in frequency domain. It reveals a fact that though the high order system keeps more states than the low order system, the approximation error behavior in the time domain may be totally different from its counterpart in the frequency domain. In addition, the paper also presents a closed form of the state space model for general evenly distributed RLC interconnect line circuits. The closed form has a very low computation complexity of O(1), which may be extended for use not only in circuits, but also in various complex systems with transmission lines, networks, or delay lines. Since the BTM is a popular practical model reduction method in various areas, thus this example may bring some further insight thinking for development.

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Section: Reduced Models and Time Response Performancementioning

confidence: 99%

“…There is a growing of publications of the BTM for the VLSI interconnects model reduction in the literature such as [4,8,16,17]. It may also be used for model reduction of various high order plants in other complex or intelligent systems.…”

Section: Introductionmentioning

confidence: 99%

An example of balanced truncation method and its surprising time domain performance

Wang

2008

2008 IEEE Conference on Cybernetics and Intelligent Systems

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“…Recently, some new effort is for error bounded Padé approximation via bilinear conformal transformation [2]. Other methods include popular BTM [4,6,9,17,18,20], PVL (Padé approximation via Lanczos approach), Klyrov space decomposition, Klyrov-Arnoldi-based reduced order modelling [1,3], projectionbased methods [14], and even length-division order (ELO) model reduction [12,13].…”

Section: Introductionmentioning

confidence: 99%

“…It is noticed that the BTM is useful for model reduction [4,9,17,18,20]. Its major advantage is that the reduced order model has a guaranteed performance by predicting its reduction-error upper-bound over the whole frequency range [4,20].…”

Section: Introductionmentioning

confidence: 99%

“…However, there is a lack of a BTM parameterization theory for evenly distributed RC interconnect and/or transmission lines to give a uniform vision on their characteristics and inherent mechanics of the reduction models for various RC parameters, and their general reduction model closed-forms and performance [17,18]. Thus, it will be very interesting to further develop practical parameterization theory and results of the BTM reduction models for these interconnect and transmission lines with various RC parameters.…”

Section: Introductionmentioning

confidence: 99%

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Parameterization Theory of Balanced Truncation Method for Any Evenly Distributed RC Interconnect Circuits

Wang

2008

2008 7th World Congress on Intelligent Control and Automation

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This paper presents a parameterization theory of balanced truncation method (BTM) for any evenly distributed RC interconnect (or transmission) lines and their BTM reduction models. The parameterization theory shows that any evenly distributed RC interconnect line circuits of a same order have the same balanced gramian, BTM error upper-bound, and BTM approximation error, which are independent of their RC parameters. Thus, the prototype model is proposed for research to dramatically reduce the computations for various RC parameters. Under normalized (scaled) time axis and frequency axis, the step responses and Bode plots of their BTM reduction models are also the same as ones of the prototype BTM reduction models, respectively. The simulations demonstrate and validate the theory. The reduction model order can be identified by the prototype model. The new results can be applied to not only the interconnect model reduction, but also control systems with transmission lines, internet or time delay units. Moreover, it may open a new approach for research on time delay systems by using RC interconnect block to substitute some time delay blocks for analysis.

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Parameterization theory of balanced truncation method for any evenly distributed RC interconnect circuits and transmission lines

Wang

2010

Automatica

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Balanced truncated models of RC interconnect circuits and their simulation

Cited by 7 publications

References 4 publications

An example of balanced truncation method and its surprising time domain performance

An example of balanced truncation method and its surprising time domain performance

Parameterization Theory of Balanced Truncation Method for Any Evenly Distributed RC Interconnect Circuits

Parameterization theory of balanced truncation method for any evenly distributed RC interconnect circuits and transmission lines

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