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1 | | -function [paramDebye, paramSarkar] = calcDjordjevicSarkarApprox(varargin) |
2 | | -% calcDjordjevicSarkarApprox - Approximate Djordjevic–Sarkar model with multi-term Debye model |
| 1 | +function [paramDebye, paramSarkar] = CalcDjordjevicSarkarApprox(varargin) |
| 2 | +%function [paramDebye, paramSarkar] = CalcDjordjevicSarkarApprox(varargin) |
| 3 | +% |
| 4 | +% Approximate Djordjevic–Sarkar model with multi-term Debye model |
3 | 5 | % |
4 | 6 | % Fits a wideband dielectric model using a single permittivity and loss tangent |
5 | 7 | % measurement at one frequency. The Djordjevic–Sarkar [1] model is calculated from |
6 | 8 | % these values and approximated using multiple Debye terms. The poles are placed |
7 | 9 | % logarithmically between f1 and f2. One term per decade is used by default. |
8 | 10 | % |
9 | | -% INPUT PARAMETERS (Name-Value pairs): |
10 | | -% Required: |
11 | | -% 'fMeas' - Frequency of the Measurement [Hz] |
12 | | -% 'epsRMeas' - Relative permittivity ε_r at 'fMeas' |
13 | | -% 'tandMeas' - Loss tangent tan(δ) at 'fMeas' |
14 | | -% 'f2' - Upper corner frequency of the Djordjevic–Sarkar model [Hz] |
| 11 | +% required name-value pairs: |
| 12 | +% - 'fMeas' : Frequency of the measurement [Hz] |
| 13 | +% - 'epsRMeas' : Relative permittivity ε_r at 'fMeas' |
| 14 | +% - 'tandMeas' : Loss tangent tan(δ) at 'fMeas' |
| 15 | +% - 'f2' : Upper corner frequency of the Djordjevic–Sarkar model [Hz] |
15 | 16 | % |
16 | | -% Depending on 'lowFreqEvalType': |
17 | | -% 'lowFreqEvalType' - Low-frequency behavior: |
18 | | -% 0 = use 'f1' (default), typical Djordjevic–Sarkar |
19 | | -% 1 = use 'epsRdc' |
20 | | -% 'f1' - Lower corner frequency [Hz], required if lowFreqEvalType = 0 |
21 | | -% 'epsRdc' - DC permittivity, required if lowFreqEvalType = 1 |
| 17 | +% optional name-value pairs: |
| 18 | +% - 'lowFreqEvalType': Low-frequency behavior: |
| 19 | +% 0 = use 'f1' (default), typical Djordjevic–Sarkar |
| 20 | +% 1 = use 'epsRdc' |
| 21 | +% - 'f1' : Lower corner frequency [Hz] (required if `lowFreqEvalType` = 0) |
| 22 | +% - 'epsRdc' : DC permittivity (required if `lowFreqEvalType` = 1) |
| 23 | +% - 'sigmaDC' : DC conductivity [S/m], usually neglected, default: 0 |
| 24 | +% - 'nTermsPerDec' : Debye poles per frequency decade, default: 1 |
| 25 | +% - 'plotEn' : Enable plotting (0 = off, 1 = on), default: 0 |
22 | 26 | % |
23 | | -% Optional: |
24 | | -% 'sigmaDC' - DC conductivity [S/m], usally neglected, default: 0 |
25 | | -% 'nTermsPerDec' - Debye poles per frequency decade, default: 1 |
26 | | -% 'plotEn' - Enable plotting (0 = off, 1 = on), default: 0 |
| 27 | +% output: |
| 28 | +% - paramDebye : Struct with multi-term Debye model: |
| 29 | +% .epsInf – Permittivity at infinite frequency |
| 30 | +% .deltaEpsT – Array of Δε'_i values |
| 31 | +% .wi – Array of angular pole frequencies ω_i |
| 32 | +% .sigmaDC – DC conductivity [S/m] |
27 | 33 | % |
28 | | -% OUTPUT: |
29 | | -% paramDebye - Struct with multi-term Debye model: |
30 | | -% .epsInf : Permittivity at infinite frequency |
31 | | -% .deltaEpsT : Array of Δε'_i values |
32 | | -% .wi : Array of angular pole frequencies ω_i |
33 | | -% .sigmaDC : DC conductivity [S/m] |
| 34 | +% - paramSarkar : Struct with Djordjevic–Sarkar model parameters: |
| 35 | +% .epsInf – High-frequency permittivity |
| 36 | +% .deltaEpsT – Total permittivity change (ε_r,DC - ε_inf) |
| 37 | +% .m1 – log10(lower angular frequency) |
| 38 | +% .m2 – log10(upper angular frequency) |
| 39 | +% .sigmaDC – DC conductivity [S/m] |
34 | 40 | % |
35 | | -% paramSarkar - Struct with Djordjevic–Sarkar model parameters: |
36 | | -% .epsInf : High-frequency permittivity |
37 | | -% .deltaEpsT : Total permittivity change (eps_r,DC - eps_inf) |
38 | | -% .m1 : log10(lower angular freq) |
39 | | -% .m2 : log10(upper angular freq) |
40 | | -% .sigmaDC : DC conductivity [S/m] |
| 41 | +% example: |
41 | 42 | % |
42 | | -% EXAMPLE: |
43 | | -% [pDebye, pSarkar] = calcDjordjevicSarkarApprox( ... |
44 | | -% 'fMeas', 1e9, 'epsRMeas', 4.2, 'tandMeas', 0.02, ... |
45 | | -% 'f1', 1e6, 'f2', 200e9, 'plotEn', 1); |
| 43 | +% [pDebye, pSarkar] = calcDjordjevicSarkarApprox( ... |
| 44 | +% 'fMeas', 1e9, 'epsRMeas', 4.2, 'tandMeas', 0.02, ... |
| 45 | +% 'f1', 1e6, 'f2', 200e9, 'plotEn', 1); |
46 | 46 | % |
47 | | -% NOTES: |
48 | | -% - Either 'f1' or 'epsRdc' must be specified depending on 'lowFreqEvalType'. |
49 | | -% - Debye model is matched to the imaginary part of the DS model, sampled at |
50 | | -% logarithmically spaced frequencies. |
| 47 | +% notes: |
| 48 | +% - Either `'f1'` or `'epsRdc'` must be specified depending on `'lowFreqEvalType'`. |
| 49 | +% - Debye model is matched to the imaginary part of the DS model, sampled at |
| 50 | +% logarithmically spaced frequencies. |
51 | 51 | % |
52 | 52 | % See also: AddDebyeMaterial, AddLorentzMaterial |
53 | 53 | % |
54 | 54 | % [1] Djordjevic, Antonije R., et al. "Wideband frequency-domain |
55 | 55 | % characterization of FR-4 and time-domain causality." IEEE Transactions |
56 | | -% on electromagnetic compatibility 43.4 (2001): 662-667. |
| 56 | +% on Electromagnetic Compatibility 43.4 (2001): 662–667. |
57 | 57 | % |
58 | 58 | % ------------------------------------------------------------------------- |
59 | 59 | % author: Tobias Ammann (2025) |
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89 | 89 | error('%s: Missing required parameter ''%s''.', p.FunctionName, param); |
90 | 90 | end |
91 | 91 | end |
92 | | - |
| 92 | + |
93 | 93 | if ((p.Results.lowFreqEvalType == 0) && ismember('f1', p.UsingDefaults)) |
94 | 94 | error(['%s: For ''lowFreqEvalType=0'' a value for f1 (Djordjevic Sarkar ',... |
95 | 95 | 'low corner frequency)must be specified.'], p.FunctionName); |
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