The recent development of the automated version of PWLFIT[1,2,4] opens the door also to hybrid PWL/VF[5,8,9] methods. This further possibility expands up to six the number of possible alternatives to modeling and simulation methods

1. Piero Belforte MODELING AND SIMULATION METHODS MATRIX May 5 2021
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MODELING AND SIMULATION METHODS MATRIX
The most commonly used methods used for modeling and simulation of circuits and
systems are Vector Fitting (VF) and Spice respectively. The popularity of VF is mainly
due to its compatibility with a well known commercial tool like Spice. This one-way
solution shows several limitations, mainly due to the origin the tool, conceived initially
for the design of Integrated Circuit where the effect of signal propagation can be
neglected in most applications and the circuit can be described by Ordinary Differential
Equations (ODE). This limitation is the main reason why more than thirty years ago both
DWS and PWLFIT were developed as industrial products having wideband circuits and
systems as targets [3]. The recent development of the automated version of
PWLFIT[1,2,4] opens the door also to hybrid PWL/VF[5,8,9] methods. This further
possibility expands up to six the number of possible alternatives to modeling and
simulation methods. These alternatives can be represented as elements of a 2X3 matrix
(Fig. 1) where for each cell the main features of the related method are summarized.
Figure 1

2. Piero Belforte MODELING AND SIMULATION METHODS MATRIX May 5 2021
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The feasibility of such alterative methods has been already demonstrated in some pilot
applications [5,8,9,10].
In particular the Hybrid method, where PWLFIT and VF are applied to separated time-
domain windows of the same response under analysis, can be applied to both
simulators to overcome the limitations of a method alone.
Experimental comparative analysis of the two main alternatives Spice/VF and
DWS/PWLFIT are shown in [6,7].
References
[1] Piero Belforte et aliii : Automated Framework for Time-Domain Piecewise- Linear Fitting Method
Based on Digital Wave Processing of S-Parameters IEEE Transactions on Circuits and Systems Jan. 2020
https://www.researchgate.net/publication/336912388_Automated_Framework_for_Time-
Domain_Piecewise-_Linear_Fitting_Method_Based_on_Digital_Wave_Processing_of_S-Parameters
[2] Piero Belforte et alii: Frequency Domain Behavior of S-Parameters Piecewise-Linear Fitting
in a Digital-Wave Framework, to be published
[3] Piero Belforte, Giancarlo Guaschino: DWS 9.0 Digital Wave Simulator 1989-2020,
https://www.researchgate.net/publication/338337640_DWS_90_Digital_Wave_Simulator
[4] Piero Belforte, Giulio Antonini, Domenico Spina, 2018-2020 DWS/PWLFIT PROJECT
https://www.researchgate.net/project/DWS-PWLFIT
[5] Piero Belforte, Giulio Antonini, 2019-2021: HYBRID PWLFIT/VF MODELING PROJECT
https://www.researchgate.net/project/HYBRID-PWL-VF-MODELING
[6] Piero Belforte, May 2021: COAXIAL STRUCTURES WITH LIQUID DIELECTRIC, VECTOR FITTING VS PWL
MODELING COMPARISON
https://www.researchgate.net/publication/351112150_COAXIAL_STRUCTURES_WITH_LIQUID_DIELECT
RIC_VECTOR-FITTING_VS_PWL_MODELING_COMPARISON
[7] Piero Belforte, March 2021: EXPERIMENTAL WIDEBAND CHARACTERIZATION OF A PARALLEL PLATE
CAPACITOR
https://www.researchgate.net/publication/348884239_EXPERIMENTAL_WIDEBAND_CHARACTERIZATIO
N_OF_A_PARALLEL-PLATE_CAPACITOR_VNA_VS_TDR_COMPARISON/stats
[8] Piero Belforte, June 2020: HYBRID PWLF/VF MODEL OF A COAXIAL CABLE, WAVE PROPAGATION
https://www.researchgate.net/publication/343602462_HYBRID_PWLVF_MODEL_OF_A_COAXIAL_CABL
E_WAVE_PROPAGATION

3. Piero Belforte MODELING AND SIMULATION METHODS MATRIX May 5 2021
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[9] Piero Belforte, July 2020: GENERAL HYBRID MODEL STRUCTURE FOR S-PARAMETERS
https://www.researchgate.net/publication/342701129_GENERAL_HYBRID_MODEL_STRUCTURE_FOR_S-
PARAMETERS
[10] Piero Belforte, June 2020: DIRECT MODEL SYNTHESIS (DMS), TEST OF A SPICE/PWL MODEL OF A
RG58 COAXIAL CABLE
https://www.researchgate.net/publication/342479802_DIRECT_MODEL_SYNTHESIS_DMS_TEST_OF_A_
SPICE_PWL_MODEL_OF_A_RG58_COAXIAL_CABLE
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