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Optimization Normal and Elastic Modes of Termination Figure 13-19. Illustration of Slack It is clear that there is no feasible solution. Running the Eldo optimizer on this example: .PARAMOPT X1=(-2, *, *) .PARAMOPT X2=(-2, *, *) .OBJECTIVE DC LABEL=CIRCLE1 ( (X1-1)**2 + X2**2 ) UBOUND=0.75 .OBJECTIVE DC LABEL=CIRCLE2 ( (X1+1)**2 + X2**2 ) UBOUND=0.75 gives the following output: ==> Starting Optimization... Iteration 0: Feas = 1.2e+01, Optim = 6.0e+00 Iter Simul LS Step Merit Function Feas Optim Slack 1 10 1.0e+00 6.3505943e-01 1.2e+00 6.0e-04 0.0e+00 2 16 3.3e-01 1.7787634e+00 3.9e-01 7.8e-01 0.0e+00 3 22 1.9e-01 4.3108310e+00 2.9e-01 9.0e-01 0.0e+00 4 28 3.4e-02 3.7393098e+01 2.5e-01 1.3e+00 0.0e+00 5 34 3.7e-04 6.5283185e+03 2.5e-01 1.9e+00 0.0e+00 6 40 1.0e-00 1.5304677e+04 2.5e-01 2.0e+00 3.5e+00 7 46 2.2e-01 1.5238534e+04 5.1e-03 7.7e+03 3.6e-01 8 53 1.3e-02 1.4929878e+04 5.1e-03 7.5e+03 3.5e-01 9 61 9.9e-01 1.5000628e+04 1.1e-02 1.9e+03 3.5e-01 Iter Simul LS Step Merit Function Feas Optim Slack 10 65 1.0e+00 1.5000626e+04 4.1e-04 2.8e+01 3.5e-01 11 69 1.0e+00 1.5000625e+04 1.2e-07 1.4e+01 3.5e-01 ==> End Of The Optimization Phase 662 Eldo® User's Manual, 15.3
Optimization Normal and Elastic Modes of Termination The column Slack is the value of the global constraint violation — the norm of the artificial variables (v 1 , v 2 ) added to the upper bound UBOUND for each constraint. The constraints become: • (x 1 + 1) 2 + x 2 2 ≥ 0.75 + v 1 . • (x 1 − 1) 2 + x 2 2 ≤ 0.75 + v 2 . The value of the slack becomes strictly positive after the 6th iteration. This phenomenon can be interpreted as follows: • After the 6th iteration the algorithm detected that the problem is locally infeasible. • Two artificial variables are then introduced such that the constraints become consistent. Graphically, this can be interpreted as increasing the radius of the two circles such that they do intersect. • The goal of the algorithm is then to find a solution point such that the constraint violation is minimized. The final solution is given in the following output: Section 2 - Status Of Variables ------------------------------- Name Status Init Value Final Value X1 FR -2.0000e+00 -5.0009e-07 X2 FR -2.0000e+00 1.6166e-05 Section 3 - Status Of Objectives -------------------------------- *** Inequality Constraints in simulator id(0) Type Name Init Value Opt Value Violation UPR CIRCLE1 *** 1.3000e+01 1.0000e+00 *** 2.5000e-01 UPR CIRCLE2 *** 5.0000e+00 1.0000e-00 *** 2.5000e-01 Constraint violations have been minimized. The actual value of the violation is v 1 = 0.25 for the first constraint and v 2 = 0.25 for the second. The solution point is approximately the origin (0, 0). The algorithm automatically increased the radius of each circle such that the feasible domain becomes a non empty set. The feasible set reduces to the singleton (0, 0). Related Topics Constraint Violations Eldo® User's Manual, 15.3 663
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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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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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SPEF File Example for Corners Post-
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Post-Layout Simulation Eldo Reducti
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Post-Layout Simulation Reduction Ou
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Post-Layout Simulation Reduction Re
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Chapter 11 Monte Carlo Analysis Mon
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Introduction to Monte Carlo Analysi
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Monte Carlo Analysis Introduction t
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The Monte Carlo Flow Monte Carlo An
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Monte Carlo Analysis Monte Carlo Ba
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Monte Carlo Analysis Monte Carlo Ba
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Monte Carlo Analysis Specifying a M
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Monte Carlo Analysis Statistical Va
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Monte Carlo Analysis Specifying Sta
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Specifying Statistical Parameters M
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Controlling Statistical Parameter V
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How to Specify a Distribution Funct
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Gaussian or Normal Distribution Mon
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User-defined Distribution Monte Car
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Monte Carlo Analysis Correlation Be
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Monte Carlo Analysis Local and Glob
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Monte Carlo Analysis Specifying Sta
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Monte Carlo Analysis Tolerance Sett
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Examples Monte Carlo Analysis Toler
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Monte Carlo Analysis Sampling Plan
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Monte Carlo Analysis Importance Sam
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Monte Carlo Analysis Latin Hypercub
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Monte Carlo Analysis Model-Based Mo
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Monte Carlo Analysis Model-Based Mo
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Monte Carlo Analysis Post-Analysis
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Monte Carlo Analysis Output of Unce
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• MCCORR(LABEL_EXT1,LABEL_EXT2) M
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Extracts the total number of Monte
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Monte Carlo Analysis Output of Unce
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Monte Carlo Analysis Primary Statis
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Approximations of the CDF Monte Car
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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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Figure 11-21. Monte Carlo Analysis
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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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Scalar Design Objectives Optimizati
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Optimization Specifying Design Obje
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Notes Optimization Specifying Desig
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Chapter 16 Electrothermal Simulatio
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Electrothermal Simulation Specifyin
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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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Figure 17-3. Output Buffer Model Bu
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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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Command _simu_set _simu_set_cond _s
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Eldo Control Language Extended Simu
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Eldo Control Language Parallel Oper
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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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