## Modeling and Simulation of VLSI Interconnections with Moments (1989)

Citations: | 16 - 0 self |

### BibTeX

@TECHREPORT{Mccormick89modelingand,

author = {Steven Paul Mccormick and Steven Paul Mccormick},

title = {Modeling and Simulation of VLSI Interconnections with Moments},

institution = {},

year = {1989}

}

### Years of Citing Articles

### OpenURL

### Abstract

### Citations

189 | Signal delay in RC tree networks
- Rubinstein, Penfield, et al.
- 1983
(Show Context)
Citation Context ...e terms, and assumes a constant to and v(0) between input and output transitions. In a more limited sense, the problem addressed in this chapter has been the subject of much recent research. Penfield =-=[47]-=-, Wyatt [15] and Lin and Mead [16] have shown methods for computing the normalized first moment (Elmore delay) only of RC trees, RC meshes and RC networks, respectively.' Horowitz [18] has developed a... |

120 |
K.Singhal, Computer Methods for Circuit Analysis and Design
- Vlach
- 1983
(Show Context)
Citation Context ...racy and computation time of the simulator are greatly dependent on the accuracy and efficiency of this conversion method. 3.6.1 Basic principles While general inverse Laplace transform methods exist =-=[46]-=-, they are not appropriate for the moment representation. Strictly speaking, the inverse Laplace transform of the moment polynomial would yield impulses, doublet (double impulses), etc. Too much infor... |

12 |
Transient analysis of lossless transmission lines
- Branin
- 1967
(Show Context)
Citation Context ...UTIONS hNuncoupled mode signals FIGURE 5-6: Modal analysis circuit. jrm(t) = 2 htmjtm(t - I/). Zm receive interface circuit This method, known as the method of characteristics, was first presented in =-=[55]-=- for a single transmission line. The circuit that results from the above substitutions can be transformed into the circuit shown in Figure 5-6 by moving the transmission line impedances and sources ou... |

12 |
Macromodeling CMOS circuits for timing simulation
- Brocco, McCormick, et al.
- 1988
(Show Context)
Citation Context .... Simulation speed is then considerably improved. This feature is demonstrated in the next chapter. The macromodeling techniques in this thesis are based on the successful methods developed by Brocco =-=[26,56]-=-. The methods are modified to fit into the moment representation framework. Because of the more precise circuit and waveform specification ability of the moment representation, the macromodeling is im... |

11 |
Macromodeling and optimization of digital MOS VLSI circuits
- Matson, Glasser
- 1986
(Show Context)
Citation Context ... functions are used. Previous macromodeling efforts for circuit simulation have macromodeled 1. logic gate output waveform delay time and slope versus input waveform slope and output load capacitance =-=[57,26,25]-=-, 2. MOSFET id, versus d, and vg,, [9,58],s6.3. TRANSISTOR DRIVER CELL MODEL 111 (a) (b) I I FIGURE 6-2: Illegal (a) and legal (b) macromodel cells for a cross-coupled inverter circuit. 3. ECL gate dr... |

9 |
Matrices and Linear Transformations
- Cullen
- 1972
(Show Context)
Citation Context ... 2 2c 3 r 2 3 1 c 7c 2 r 2 31c 3 r 2 3 q -_ S + 31 3 1 + cr2 + 312 FIGU360RE 6 Distributed3 15120 element 45RC template945 FIGURE 4-3: Distributed RC element template in linear algebra texts (such as =-=[51]-=-), so only the interesting results are presented here. First we start with a definition. A field is a numbering system in which the operations of addition, subtraction, multiplication and division (ex... |

8 |
Circuits, Signals and Systems
- Siebert
- 1986
(Show Context)
Citation Context ...------------------- ----- -------------- ·- ._ 51 t (3.7)s52 CHAPTER 3. THE MOMENT REPRESENTATION properties. The Laplace transform properties are derived in most any circuit theory textbook, such as =-=[45]-=-. 3.3.1 Shifting in Time stant: Shifting a waveform in time results in a multiplication of the Laplace transform by a conv(t- r) + e V(s). This fact was already used in going from Equation (3.1) to (3... |

7 |
Signal propagation delay in RC models for interconnect
- Wyatt
- 1987
(Show Context)
Citation Context ...f a function, the second moment relates to the mean and variance of a function, and so forth. 1 also equals the Elmore time constant presented in Section 1.1.3 and discussed in the RC tree literature =-=[13,14,44]-=-. For any initial delay, to, we find the n th order projection of any Laplace transform, V(s), into the moment representation domain by taking the Maclaurin series expansion (Taylor's series expansion... |

3 |
Theory and Computer-aided Analysis of Lossless Transmission Lines
- Ho
- 1973
(Show Context)
Citation Context ...coupled transmission lines are related to the eigenvalues of the matrix product, LC, where L is the inductance matrix per unit length of the conductors and C is the capacitance matrix per unit length =-=[53]-=-. If the mn h eigenvalue of LC is Am, then the propagation velocity of mode m is U, = 1/rv-n.s5.1. MODAL ANALYSIS OF COUPLED LOSSLESS TRANSMISSION LINES r-i U-B 1.0 . .8 .6 .4 .2 0.0 I Vin (t) V1 (t) ... |

2 |
Computer Design Aids for VLSI Circuits
- Sangiovanni-Vincentelli
- 1984
(Show Context)
Citation Context ...r, G nor C is invertible. More is said about this later. The procedure for constructing Y(s) from knowledge of the circuit branch elements is identical to the procedure used in SPICE and described in =-=[49]-=-. It goes as follows. Initially, empty matrices are created for i"s) = 0 and i(s) = 0. Then, one by one the contributions of each branch element are added to the matrices. Each branch element type has... |

1 |
Charge sharing models for MOS circuits
- Chu, Horowitz
- 1986
(Show Context)
Citation Context ...veloped a second order method which computes the first and second moments of RC trees. The trees in these cases could also contain switching elements, thus being able to model charge sharing circuits =-=[48]-=-. The method presented in this chapter is much more general. It is capable of finding the moment polynomial of the voltage on any node of any circuit containing linear resistors, capacitors, inductors... |

1 |
Time-domain analysis and measurement techniques for distributed RC structures. I. analysis in the reciprocal time domain
- Happ
- 1969
(Show Context)
Citation Context ... number of elements that cannot be included directly into time-domain circuit simulators like SPICE. For instance, the distributed RC element of Figure 4-3 is described by Laplace transform equation, =-=[50]-=- 2(s) ] = ' /coth((V') -V/ csch( ) - csch(v/-) £/ coth(v/rs) [li(s) v V2(s) J Taking the Maclaurin Series gives the moment representation matrix entries shown in Figure 4-3. 4.1.2 Moment Polynomial Ma... |

1 |
An algorithm for MOS logic simulation," Lambda
- Bryant
- 1980
(Show Context)
Citation Context ...nt, any unmarked node represents a floating node, and indicates an unsolvable network. The node tracing algorithm is done with a modification of the standard depth-first search algorithm described in =-=[52]-=-. It is expressed algorithmically below, where 5 represents the undirected graph of the circuit. -~~ 1___~__IC_ ---- l~·II 83 II _ ·I_·__ I_ _ _ _s84 CHAPTER 4. GENERAL LINEAR NETWORK SOLUTIONS Algori... |

1 |
Handbook of Numerical Methods and Applications, ch. 9
- Kelly
- 1967
(Show Context)
Citation Context ...e not all distinct, care should be taken to ensure that the eigenvectors are linearly independent. The eigenvalues and eigenvectors may be found with any standard algorithm such as those described in =-=[54]-=-. The voltage and current modal matrices are related by where A= MI = L - 1 My A, My = C - 1 Ml A, l/u2u 0 0 1/UN Figure 5-4 depicts the modal analysis method. First, a set of voltages applied to the ... |

1 |
A tabular approach to fast timing simulation including parasitics
- Overhauser, Hajj
- 1988
(Show Context)
Citation Context ...fforts for circuit simulation have macromodeled 1. logic gate output waveform delay time and slope versus input waveform slope and output load capacitance [57,26,25], 2. MOSFET id, versus d, and vg,, =-=[9,58]-=-,s6.3. TRANSISTOR DRIVER CELL MODEL 111 (a) (b) I I FIGURE 6-2: Illegal (a) and legal (b) macromodel cells for a cross-coupled inverter circuit. 3. ECL gate drive values versus effective load capacita... |

1 |
Fast on-chip delay estimation for cell-based emitter coupled logic
- O'Brien, Wyatt, et al.
- 1988
(Show Context)
Citation Context ... MODEL 111 (a) (b) I I FIGURE 6-2: Illegal (a) and legal (b) macromodel cells for a cross-coupled inverter circuit. 3. ECL gate drive values versus effective load capacitance and input pulse duration =-=[59]-=-. In this thesis, macromodel functions describe moment representation values or circuit element values versus the input waveform slope and output driving-point (or load) admittance. Transistor driver ... |