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Monte Carlo Analysis Importance Sampling Monte Carlo • It should produce high-quality random numbers uniformly distributed in the interval (0, 1). • The computations should be fast. Separate threads of random numbers are allowed to be generated in parallel. • It should be portable (Unix and Windows platforms). To start this generator, its initial state needs to be specified. Knuth introduced an algorithm that uses a single integer, which can take on approximately 10 9 different values, in such a way that a given seed is guaranteed to produce at least 10 21 different starts before colliding with those produced by a different seed. Importance Sampling Monte Carlo The Importance Sampling Monte Carlo (ISMC) method is dedicated to the estimation of failure probabilities (or the computation of parametric yield in circuit design terms) and, conversely, to the estimation of the thresholds corresponding to <strong>user</strong>-defined yield. Note Estimation of low failure probabilities is often called a “high sigma” problem in the EDA literature. The terms “low probability estimation” and “rare events simulation” are used in this section to mean the same thing. Rare events can be defined as the regions of the input parameter space that have a very small volume with respect to the measure induced by the joint probability of the parameters. The associated probabilities of interest are close to zero, and may range from 10 −4 to 10 −10 . In this context, Monte Carlo analysis is used as a verification tool to check that the probability of exceeding a performance specification is acceptably small. The Monte Carlo algorithm is an iterative simulation method that may be described briefly as a random exploration of the space of input parameters. The fundamental problem with this technique is that the sample size has to be large when the probabilities to estimate are small. For example, estimating a probability of around 10 −K (where K > 2) to a target accuracy of 10% will involve more than 10 −(K + 2) simulations of the circuit performances. The ISMC method is implemented using an adaptive procedure based on importance sampling, and has the following properties: • It is as insensitive as possible to the dimension of the problem. • It requires no prior knowledge to function. Specifically, it functions if nothing is known about the output distribution and its tails. • It does not need to be manually tuned to work with a given cell or circuit. 452 Eldo® User's Manual, 15.3
Monte Carlo Analysis Importance Sampling Monte Carlo • It includes a robust and reliable accuracy estimator. Figure 11-10. The ISMC Method Eldo® User's Manual, 15.3 453
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Eldo® User's Manual Release 15.3
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Table of Contents Chapter 1 Introdu
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Table of Contents Preparing and Ins
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Table of Contents Chapter 7 Running
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Table of Contents Eldo Reduction .
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Table of Contents Chapter 12 Statis
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Table of Contents Simulating a Bloc
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Table of Contents atanh . . . . . .
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Table of Contents xmin . . . . . .
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Table of Contents COS. . . . . . .
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Table of Contents One Step Relaxati
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List of Figures Figure 1-1. Cascade
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List of Figures Figure 14-1. Mixed-
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List of Tables Table 1-1. Documenta
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Chapter 1 Introduction to Eldo The
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Introduction to Eldo Getting Starte
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Introduction to Eldo Getting Starte
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Eldo Input and Output Files Introdu
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Introduction to Eldo Eldo Documenta
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Introduction to Eldo Documentation
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Chapter 2 Running Eldo This chapter
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Running Eldo Multi-Threading Eldo S
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Running Eldo Multi-Threading Eldo S
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Running Eldo Simulation Connection
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Running Eldo Simulation Connection
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Running Eldo Eldo Initialization Fi
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Running Eldo Location Maps Location
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Running Eldo Performance Bottleneck
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Running Eldo Statistics File Statis
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Running Eldo Additional Tools and U
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Chapter 3 Eldo Premier This chapter
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Eldo Premier Overview of Eldo Premi
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Eldo Premier Automatic Activation o
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Eldo Premier Handling Matrix-Like C
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Eldo Premier Eldo Premier Output El
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Eldo Premier Forcing Elaboration Ti
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Netlist reduction is activated with
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Eldo Premier Supported Commands Tab
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Eldo Premier Supported Commands Tab
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Table 3-3. Eldo Premier—Supported
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Eldo Premier Supported Models Enabl
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o Eldo Premier Other Supported Func
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Eldo Premier Miscellaneous Limitati
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Chapter 4 Eldo Netlist Setup This c
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Eldo Netlist Setup Netlist Structur
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Subcircuit Definitions and Calls El
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Eldo Netlist Setup Simulator Comman
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Eldo Netlist Setup General Aspects
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Eldo Netlist Setup Case-Sensitivity
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Eldo Netlist Setup Numerical Values
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Eldo Netlist Setup Functions, Opera
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Function PWL_LIN(xvalue, interp, x1
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Notes Eldo Netlist Setup Arithmetic
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Eldo Netlist Setup Operators Operat
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Eldo Netlist Setup Operators Bitwis
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Eldo Netlist Setup Expressions Spec
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Eldo Netlist Setup Directives Direc
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Eldo Netlist Setup Directives Inter
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Eldo Netlist Setup Directives to Po
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Eldo Netlist Setup Working With Sub
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Eldo Netlist Setup Subcircuits Spec
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Eldo Netlist Setup Subcircuits Rela
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Eldo Netlist Setup Device Libraries
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Eldo Netlist Setup Encrypting Libra
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Eldo Netlist Setup encrypt_eldo Too
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Eldo Netlist Setup encrypt_eldo Too
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Eldo Netlist Setup Protection of En
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Eldo was not able to find the reque
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Eldo Netlist Setup Running Multiple
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Eldo Netlist Setup Merging Instance
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Chapter 5 Simulator Compatibility E
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Simulator Compatibility Hybrid Comp
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Simulator Compatibility Devices in
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Simulator Compatibility Devices in
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Simulator Compatibility Commands in
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Simulator Compatibility Commands in
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Simulator Compatibility Options in
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Netlist in Compat Mode Some aspects
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Simulator Compatibility Arithmetic
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Simulator Compatibility Spectre Com
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Simulator Compatibility Spectre Com
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Eldo can be launched on the Spectre
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Simulator Compatibility Working wit
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Simulator Compatibility Troubleshoo
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Error Code Related Topics Spectre C
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Simulator Compatibility Spectre to
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spect2el Command Reference Simulato
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Simulator Compatibility spect2el Co
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Simulator Compatibility spect2el Co
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Chapter 6 Setting Up An Analysis Th
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DC and Operating Point Analyses The
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Setting Up An Analysis Performing a
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Setting Up An Analysis Operating Po
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Setting Up An Analysis DC Convergen
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Setting Up An Analysis DC Convergen
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Setting Up An Analysis Saving and R
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Setting Up An Analysis Transient An
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.SAVE END in Combination with .REST
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AC Analysis Results Setting Up An A
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Loop Stability Analysis Setting Up
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Setting Up An Analysis Pole Zero An
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Setting Up An Analysis Pole Zero An
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Hand Selection Setting Up An Analys
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Setting Up An Analysis Transfer Fun
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Setting Up An Analysis Noise Analys
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Setting Up An Analysis Transient No
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Transient Noise Analysis Principles
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Figure 6-10. PSD of a Flicker Noise
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o Setting Up An Analysis Transient
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Setting Up An Analysis Statistical
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Setting Up An Analysis Worst Case A
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Setting Up An Analysis DC Mismatch
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Setting Up An Analysis DC Sensitivi
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AC Sensitivity Analysis Results Set
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Design of Experiments Analysis Resu
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Setting Up An Analysis Aging and Re
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High Impedance Node Check Setting U
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Results Setting Up An Analysis View
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Setting Up An Analysis RF Analyses
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Setting Up An Analysis RF Analyses
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Chapter 7 Running Parametric Analys
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Running Parametric Analyses Tempera
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Running Parametric Analyses Assigni
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Running Parametric Analyses .STEP S
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Running Parametric Analyses Nested
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Running Parametric Analyses .DATA P
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Running Parametric Analyses Removin
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Running Parametric Analyses .ALTER
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Running Parametric Analyses Using O
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Chapter 8 Specifying Simulation Out
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Specifying Simulation Output Output
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Specifying Simulation Output Types
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Examples of Wildcard Usage in Subci
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See Also • .PLOT command in the E
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Compound Waveforms Specifying Simul
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Specifying Simulation Output Tabula
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Specifying Simulation Output Dynami
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Specifying Simulation Output Extrac
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Specifying Simulation Output Plot a
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3. Right-click on the sweep paramet
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Specifying Simulation Output Exampl
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Specifying Simulation Output Exampl
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Safe Operating Area (SOA) Checks Sp
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Specifying Simulation Output Plotti
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See Also • .CHECKSOA in the Eldo
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Specifying Simulation Output Safe O
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Specifying Simulation Output High I
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Specifying Simulation Output High I
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• .OPTION PRINT_OPTION=0 (in the
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Specifying Simulation Output Increm
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Chapter 9 Analyzing Simulation Resu
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File Extension Table 9-1. Eldo Stan
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File Extension _csdf.trX _csdf.acX
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Interpreting the Output Log (.chi)
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Analyzing Simulation Results Simula
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Analyzing Simulation Results Simula
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Analyzing Simulation Results Error
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Analyzing Simulation Results EZwave
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Related Topics EZwave Joint Wavefor
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Analyzing Simulation Results Marchi
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Analyzing Simulation Results Diagno
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Analyzing Simulation Results Non-Co
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Nodes/Devices Impacting Time-Step A
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Analyzing Simulation Results Perfor
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Analyzing Simulation Results Using
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Analyzing Simulation Results Statis
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Chapter 10 Post-Layout Simulation T
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Post-Layout Simulation Post-Layout
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Post-Layout Simulation DSPF File St
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o ii. iii. Post-Layout Simulation E
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Connecting a Source to a DSPF Backa
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SPEF File Structure Post-Layout Sim
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Page 409 and 410: Chapter 11 Monte Carlo Analysis Mon
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Page 415 and 416: The Monte Carlo Flow Monte Carlo An
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Monte Carlo Analysis Additional Unc
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Monte Carlo Analysis Input/Output S
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Monte Carlo Analysis Input/Output S
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Monte Carlo Analysis Graphical Outp
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Stopping Test for AVG Monte Carlo A
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Monte Carlo Analysis SETTLING Techn
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Monte Carlo Analysis MCCONV Extract
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Monte Carlo Analysis Global Sensiti
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Monte Carlo Analysis Large Scale Va
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Monte Carlo Analysis Large Scale Va
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Figure 11-21. Monte Carlo Analysis
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Monte Carlo Analysis Importance Sam
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Monte Carlo Analysis Importance Sam
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Monte Carlo Analysis Model-Based Ap
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Monte Carlo Analysis Further Exampl
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Monte Carlo Analysis Parameter Nami
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Five independent random variables w
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Monte Carlo Analysis Problems in St
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Monte Carlo Analysis Problems in St
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Figure 11-22. LIMIT Distribution wi
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Figure 11-23. Four Random Samples f
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Monte Carlo Analysis Obsolete Featu
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Chapter 12 Statistical Experimental
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Statistical Experimental Design and
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Statistical Modeling for Discrete C
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Conducting a Screening Experiment G
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Chapter 13 Optimization The purpose
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Optimization Optimization in Eldo O
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Optimization Optimization Options .
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Table 13-1. Eldo Optimization Metho
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Figure 13-2. Discretization of Desi
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Optimization Specifying Tracking wi
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Optimization Scaling Design Variabl
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Optimization Scaling Design Variabl
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Optimization Design Objectives Desi
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Scalar Design Objectives Optimizati
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Optimization Specifying Design Obje
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Notes Optimization Specifying Desig
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Optimization Types of Design Object
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Optimization Design Objectives for
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Optimization Eldo Optimizer SQP Alg
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Figure 13-3. Illustration of Optima
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Optimization Eldo Optimizer/Search
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Conducting an Eldo Optimization Opt
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Smooth and Non-Smooth Problems Opti
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Optimization of Sweep Simulations O
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Optimization Optimization of Sweep
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Optimization Optimization of Sweep
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Optimization Post-Analysis of Optim
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Optimization Explicitly Declaring R
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Optimization ASCII Optimization Fil
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o o Goal Value — Goal value of th
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Optimization Monitoring Design Obje
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Code Table 13-3. Optimization Resul
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Optimization Normal and Elastic Mod
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Optimization Designing a Low Noise
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Optimization MOS Characterization R
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Optimization Robust Optimization Us
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Optimization Robust Optimization Us
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Optimization Setup Time Computation
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Chapter 14 Working with S, Y, Z Par
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Working with S, Y, Z Parameters S,
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The default mixed-mode can be set u
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Working with S, Y, Z Parameters Out
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Working with S, Y, Z Parameters Sim
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Working with S, Y, Z Parameters Tec
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Working with S, Y, Z Parameters Imp
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• Simulation of passive networks
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Working with S, Y, Z Parameters Ins
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Working with S, Y, Z Parameters Tou
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Working with S, Y, Z Parameters Tou
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VAR_LIST_BEGIN / VAR_LIST_END SEG_L
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Chapter 15 Aging and Reliability Si
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Chapter 16 Electrothermal Simulatio
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Electrothermal Simulation Specifyin
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Electrothermal Simulation Specifyin
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The .TEMPNODE statement can also be
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Electrothermal Simulation Reporting
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Chapter 17 IBIS Models Support in E
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IBIS Models Support in Eldo IBIS Re
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IBIS Models Support in Eldo Checkin
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IBIS Models Support in Eldo Buffers
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Figure 17-3. Output Buffer Model Bu
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Figure 17-5. 3_state Buffer Model B
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IBIS Models Support in Eldo Compone
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IBIS Models Support in Eldo Compone
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IBIS Models Support in Eldo IBIS Su
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IBIS Models Support in Eldo IBIS Mo
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IBIS Component Instantiates an IBIS
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IBIS Electrical Board Description I
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IBIS Models Support in Eldo IBIS El
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IBIS Models Support in Eldo Support
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D_overshoot_ampl_l 5.0 [Rgnd] 2.1 [
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Chapter 18 Eldo Control Language Th
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Eldo Control Language Examples Eldo
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Example Dir 22-plot_mos_ operating_
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Eldo Control Language Eldo Control
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Eldo Control Language Testbenches T
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Eldo Control Language Testbench Ins
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Defining and Running Simulations El
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Examples Eldo Control Language Libr
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Eldo Control Language Simulation Dy
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Command _simu_set _simu_set_cond _s
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Eldo Control Language Extended Simu
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Concurrency Issues Eldo Control Lan
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Launching ECL Simulations on Differ
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Eldo Control Language Statistical P
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Command _simu_get_stat_param_de v _
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Temporary Files Eldo Control Langua
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Debug Mode Eldo Control Language Ad
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Eldo Control Language Advanced Simu
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Eldo Control Language Advanced Simu
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Eldo Control Language Examples Usin
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Eldo Control Language .EXTRACT Alte
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Eldo Control Language .PRINTFILE Al
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Eldo Control Language .PRINTFILE Al
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Eldo Control Language .OPTIMIZE Alt
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Eldo Control Language .MPRUN with M
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Chapter 19 Post-Processing Library
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Post-Processing Library Post-Proces
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Post-Processing Library General Usa
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Post-Processing Library Macro-Like
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Post-Processing Library Working wit
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Post-Processing Library evalExpr Re
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Post-Processing Library defineVec N
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Post-Processing Library EZwave Wave
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Post-Processing Library ABS ABS Eld
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Post-Processing Library ACOSH ACOSH
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Post-Processing Library ACOTH ACOTH
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Post-Processing Library ASINH ASINH
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Post-Processing Library ATANH ATANH
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Post-Processing Library COMPRESS CO
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Post-Processing Library COSH COSH E
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Post-Processing Library COTH COTH E
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Post-Processing Library DEG DEG Eld
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Post-Processing Library DERIVE DERI
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Post-Processing Library EXP EXP Eld
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Post-Processing Library GMARGIN GMA
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Post-Processing Library IMAG IMAG E
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Post-Processing Library INTEGRAL IN
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Post-Processing Library INVDB INVDB
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Post-Processing Library LOG10 LOG10
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Post-Processing Library MAX MAX Eld
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Post-Processing Library PHASE PHASE
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Post-Processing Library RAD RAD Eld
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Post-Processing Library RELATION RE
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Post-Processing Library RMS RMS Eld
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Post-Processing Library SETTLINGTIM
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Post-Processing Library SINH SINH E
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Post-Processing Library SQRT SQRT E
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Post-Processing Library TAN TAN Eld
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Post-Processing Library TPD TPD Eld
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Post-Processing Library TPDDU TPDDU
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Post-Processing Library TPDUU TPDUU
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Post-Processing Library VMIN VMIN E
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Post-Processing Library XCOMPRESS X
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Post-Processing Library XWAVE XWAVE
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Post-Processing Library IIPX IIPX E
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Post-Processing Library Built-In DS
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Post-Processing Library CONV CONV E
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Post-Processing Library CORRELO •
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Post-Processing Library CT • fmin
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Post-Processing Library FFT • nor
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Post-Processing Library HDIST HDIST
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Post-Processing Library PERIODO PER
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Post-Processing Library PSD PSD Eld
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Post-Processing Library SAMPLER 10
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Post-Processing Library Accessing W
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Post-Processing Library DISP_FILE D
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Post-Processing Library Additional
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Post-Processing Library GETSIZE GET
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Post-Processing Library SETPOINT SE
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Chapter 20 Speed and Accuracy Eldo
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Speed and Accuracy Speed and Accura
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Speed and Accuracy Integration Meth
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Speed and Accuracy Time Step Contro
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Speed and Accuracy Time Step Contro
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Speed and Accuracy Global Tuning of
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Speed and Accuracy Global Tuning of
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Speed and Accuracy Simulation of La
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Speed and Accuracy Tips for Improvi
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Speed and Accuracy IEM Overview Whe
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Speed and Accuracy IEM Tolerance Pa
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IEM Alone (.OPTION IEM) Speed and A
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Integration Method Speed and Accura
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Chapter 21 Examples The most produc
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Examples Table 21-1. Eldo Examples
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Netlist Explanation Examples Exampl
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Examples Example 2—Transient and
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Examples Example 3—AC and Noise A
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Examples Example 3—AC and Noise A
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Figure 21-8. Low Pass Filter Exampl
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Examples Example 5—Transient Anal
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Simulation Results Examples Example
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Figure 21-15. Non-inverting Amplifi
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Examples Example 8—DC Sensitivity
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Examples Example 9—Transient and
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Examples Example 11—Loop Stabilit
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Examples Example 12—Overshoot Ext
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Summary of Eldo commands used in th
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Examples Example 16—Transient Ana
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Examples Example 17—Monte Carlo S
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Examples Example 17—Monte Carlo S
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Examples Example 18—Numerical Int
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Examples Example 19—DC Mismatch C
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Examples Example 21—Post-Layout S
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Examples Example 22—Extract Gain
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Examples Example 22—Extract Gain
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Examples Example 23—Parametric Se
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Examples Example 23—Parametric Se
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Examples Example 24—Cell Characte
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Examples Example 25—Setting up an
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Examples Example 26—Spectre Compa
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Examples Example 27—Monte Carlo A
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Examples Tutorial—Using Power Ana
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Examples Tutorial—High Impedance
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Examples Transient Noise Analysis E
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Appendix A Error and Warning Messag
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Error Number Description Table A-1.
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Error and Warning Messages Global E
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Error and Warning Messages Errors R
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Error Number Table A-4. Errors Rela
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Error and Warning Messages Miscella
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Error and Warning Messages Warning
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Error and Warning Messages Global W
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Error and Warning Messages Warnings
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Warning Number Table A-11. Warnings
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Warning Number Table A-14. Warnings
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Warnings Related to Subcircuits The
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Warning Number Table A-16. Miscella
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Warning Number Warning 1021092 Warn
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Appendix B Troubleshooting Most use
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Troubleshooting File Troubleshootin
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Appendix C Eldo Interactive Mode El
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Eldo Interactive Mode Reading Infor
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Command [.]LSMODEV LSMODPAR [.]LS
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Eldo Interactive Mode Change Featur
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Eldo Interactive Mode Change Featur
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STOP IF Eldo Interactive Mode Cont
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Appendix D Eldo Conversion Utilitie
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Eldo Conversion Utilities Utility t
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Appendix E STMicroelectronics Model
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STMicroelectronics Models What Does
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Css Css Csb Csb Csb+CJSB Cbd Cdbd C
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Index — Symbols — ! comment del
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PWL_LIN(), 111 PWR(VAL1, VAL2), 110
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32-bit and 64-bit modes, 42 An Intr
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LIMIT function, 110 Limiting Output
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DSPF backannotation, 392 Examples,
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Noise Model, 1373 Syntax Errors, 36
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Third-Party Information This sectio
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3. The name of the author may not b
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USE, DATA, OR PROFITS; OR BUSINESS
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End-User License Agreement The late
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7.1. Mentor Graphics warrants that
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