17-03-2014, 10:42 AM
Abstract- In this paper, we propose one efficient
algorithm for the transient analysis of RLC trees.
Based on MNA equations, we derive the recursive
formulas for the coefficients of Laguerre polynomials.
Via Arnoldi algorithm, we can reduce the order of
matrix directly in the time-domain instead of
frequency-domain, which is often more
time-consuming because inverse Laplace
transformation or inverse fast Fourier transformation
is needed. Furthermore, the passivity of the network
reduced by our method is guaranteed because of the
congruence transformations. It is shown through one
example on the transient analysis of one RLC tree that
the average error by our method is within 10% in
comparison with results by HSPICE and our method
can run faster than HSPICE.
Keywords-Circuit Simulation, Interconnect Tree,
Krylov Subspace, Laguerre Polynomials, Model
Reduction, RLC
I. INTRODUCTION
With the rapid development of VLSI
technology and the complexity of VLSI circuits,
interconnects are becoming one important factor
for the performance of the chips and
interconnect analysis is challenging CAD [1].
Conventional methods for interconnect analysis
are impractical. Now, one efficient way to solve
the above difficulties is model reduction. By
transforming the large matrix into one smaller
matrix, the response of the large network can be
approximated by the response of the small
network which can be calculated easily. Many
algorithms have been proposed for model
reduction [1]. Generally, they can be grouped
into two kinds. The first is direct MMT (Moment
Matching Technique) based on AWE
(Asymptotic Waveform Evaluation) technique [2]
and the second is implicit MMT based on
Krylov subspace [3][4][5]. However, for the
former, the passivity of the reduced network can
not be guaranteed. For the latter, model
reduction is completed in the frequency domain
and inverse Laplace transformation or inverse
fast Fourier transformation is needed to get the
response in the time domain. Recently, new
methods are proposed for model reduction, such
as [6] and [7].
In the field of electromagnetic, Laguerre
polynomials is one efficient tool for calculation,
such as [8]. Because the Laguerre polynomials
are orthogonal, we can use them to approximate
the signals and the result is usually quite
satisfactory. Furthermore, the methods
developed by Laguerre polynomials are stable
for most cases [9].
In this paper, we discuss the problem about
how to apply Laguerre polynomials for model
reduction and calculate the transient response of
the RLC trees. We derive the coefficients of
Laguerre polynomials and model reduction is
completed in time domain instead of frequency
domain based on the Arnoldi algorithm.
Consequently, inverse Laplace transformation or
IFFT is not needed in our method. Examples
show that our method is efficient compared to
HSPICE while keeping higher accuracy.
algorithm for the transient analysis of RLC trees.
Based on MNA equations, we derive the recursive
formulas for the coefficients of Laguerre polynomials.
Via Arnoldi algorithm, we can reduce the order of
matrix directly in the time-domain instead of
frequency-domain, which is often more
time-consuming because inverse Laplace
transformation or inverse fast Fourier transformation
is needed. Furthermore, the passivity of the network
reduced by our method is guaranteed because of the
congruence transformations. It is shown through one
example on the transient analysis of one RLC tree that
the average error by our method is within 10% in
comparison with results by HSPICE and our method
can run faster than HSPICE.
Keywords-Circuit Simulation, Interconnect Tree,
Krylov Subspace, Laguerre Polynomials, Model
Reduction, RLC
I. INTRODUCTION
With the rapid development of VLSI
technology and the complexity of VLSI circuits,
interconnects are becoming one important factor
for the performance of the chips and
interconnect analysis is challenging CAD [1].
Conventional methods for interconnect analysis
are impractical. Now, one efficient way to solve
the above difficulties is model reduction. By
transforming the large matrix into one smaller
matrix, the response of the large network can be
approximated by the response of the small
network which can be calculated easily. Many
algorithms have been proposed for model
reduction [1]. Generally, they can be grouped
into two kinds. The first is direct MMT (Moment
Matching Technique) based on AWE
(Asymptotic Waveform Evaluation) technique [2]
and the second is implicit MMT based on
Krylov subspace [3][4][5]. However, for the
former, the passivity of the reduced network can
not be guaranteed. For the latter, model
reduction is completed in the frequency domain
and inverse Laplace transformation or inverse
fast Fourier transformation is needed to get the
response in the time domain. Recently, new
methods are proposed for model reduction, such
as [6] and [7].
In the field of electromagnetic, Laguerre
polynomials is one efficient tool for calculation,
such as [8]. Because the Laguerre polynomials
are orthogonal, we can use them to approximate
the signals and the result is usually quite
satisfactory. Furthermore, the methods
developed by Laguerre polynomials are stable
for most cases [9].
In this paper, we discuss the problem about
how to apply Laguerre polynomials for model
reduction and calculate the transient response of
the RLC trees. We derive the coefficients of
Laguerre polynomials and model reduction is
completed in time domain instead of frequency
domain based on the Arnoldi algorithm.
Consequently, inverse Laplace transformation or
IFFT is not needed in our method. Examples
show that our method is efficient compared to
HSPICE while keeping higher accuracy.