Abstract
Purpose
Cables are ubiquitous in electronic-based systems. Electromagnetic emission of cables and crosstalk between wires is an important issue in electromagnetic compatibility and is to be minimized in the design phase. To facilitate the design, models of different complexity and accuracy, for instance, circuit models or finite element (FE) simulations, are used. The purpose of this study is to compare transmission line parameters obtained by measurements and simulations.
Design/methodology/approach
Transmission line parameters were determined by means of measurements in the frequency and time domain and by FE simulations in the frequency domain and compared. Finally, a Spice simulation with lumped elements was performed.
Findings
The determination of the effective permittivity of insulated wires seems to be a key issue in comparing measurements and simulations.
Originality/value
A space decomposition technique for a guided wave on an infinite configuration with constant cross-section has been introduced, where an analytic representation in the direction of propagation is used, and the transversal fields are approximated by FEs.
Keywords
Citation
Hollaus, K., Bauer, S., Leumüller, M. and Türk, C. (2022), "Measurement and modeling of effective cable parameters of unshielded conductors", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 41 No. 3, pp. 1041-1051. https://doi.org/10.1108/COMPEL-03-2021-0098
Publisher
:Emerald Publishing Limited
Copyright © 2022, Karl Hollaus, Susanne Bauer, Michael Leumüller and Christian Türk.
License
Published by Emerald Publishing Limited. This article is published under the Creative Commons Attribution (CC BY 4.0) licence. Anyone may reproduce, distribute, translate and create derivative works of this article (for both commercial and non-commercial purposes), subject to full attribution to the original publication and authors. The full terms of this licence may be seen at http://creativecommons.org/licences/by/4.0/legalcode
1. Introduction
One main goal of the present work is to match measurement data, Spice (LTSpice, 2020) and finite element (FE) simulations to create models of different complexity. A configuration as simple as a single insulated wire above ground needs to be modeled, built and tested to extract the equivalent RLGC-parameters, characteristic impedance Z0, velocity factor vf, as well as delay time td. Naturally, simulation data and measurement data should match, but due to imperfections of the physical test setup, such as connectors, stray capacitances, imperfect return conductors (e.g. copper ground plane), measurement inaccuracies, imperfect terminations and models for simulation that use a 0.5 mm copper plane for current return, have no connectors and stray effects involved, this is not easy to accomplish. Theory and exemplary simulation data of micro-strips of a printed circuit board (PCB) can be found in Hollaus et al. (2008), Caniggia and Maradei (2008), Chaturvedi et al. (2016) as well as in Eisenstadt and Eo (1992). Careful consideration of parasitic effects is necessary, and concise analysis of their order is a prerequisite to obtaining reliable results. Because the setup here appears to be simple, it serves as a basis for more complex models which involve coupling effects between high impedance traces or low impedance loops on a PCB. Measured data and simulation, as well as underlying models, still need to match.
2. Measurement setups
Each test setup requires a specific configuration and termination. Apart from the Spice simulation (LTSpice, 2020), the setups use either a polyvinyl chloride (PVC) or silicone insulated single wire above a copper ground plane (1.0 m times 1.0 m and 0.5 mm thick), which can be considered infinite. The PVC insulated wires have a copper-conductor of 1.5 mm2 and red and black insulation with a diameter of 3.0 mm. The silicone insulated wires have a copper conductor of 1.0 mm2 and red and black insulation with a diameter of 2.3 mm. All four wires are 1.0 m long. The wires are fixed to the ground plane with adhesive tape to minimize the distance between insulation and copper – there should ideally be no air gap between cable and ground plane. The test equipment is connected via SMA-connectors with their ground terminals soldered to the ground plane and the inner terminal to the cable under test (CUT).
2.1 Time domain reflectometry
The time domain reflectometry (TDR)-test uses an HP8753D 6 GHz vector network analyzer (VNA) which subsequently converts the acquired response into the time domain by means of an inverse fast Fourier transform. The calibration requires a test cable that is terminated with the system impedance of 50 Ω, an open and a short standard. The test requires the far end to be open to provide a quasi-full positive reflection of the incident signal. The TDR-test set is connected to the near end of the CUT.
2.2 Frequency domain testing – S-parameters
The acquisition of the S-parameters uses a Rohde & Schwarz ZVL6 as VNA. The calibration requires a full two-port through-open-short-match procedure. The measurement requires the CUT to be connected to both ports of the VNA. It represents a fully terminated CUT.
All data from the VNA consist of input reflection coefficient S11, forward transmission gain S21, reverse transmission gain S12 and output reflection coefficient S22 with magnitude in dB and the respective phases in degrees. A conversion to a linear scale and into radians [as in Tuerk et al. (2020)] needs to be accomplished before application of the following set of equations (1) and (2).
With Zl being the characteristic impedance of the CUT
Considering ambiguities, the ± K-term must be accounted for in the following extraction of the RLGC-parameter set
3. Simulation methods
3.1 Spice simulation
Because the CUT is a sample of 1.0 m in length and the maximum frequency is 500 MHz in the case of the S-parameter measurement, the simulation model has been split into pieces of 0.1 m for the purpose of the simulation. The PUL data acquired are divided by 10 as far as L′ and R′ are concerned, C′ and G′ are multiplied by 10. In total, the CUT in the simulation represents 1.0 m, and the condition of segments being significantly shorter than λ/10 is still satisfied.
The model in Figure 1 shows 10 sections, each of them with 4 lumped elements (R1, L1, C1, G1 to R10, L10, G10, C10), the termination of the model represented by R11 and the respective parameters which are applied to all elements. To get S-parameters from the schematic, the directive .net I(R11) V1 is used. This parameter set provides the result given in section 4 in Figure 6.
3.2 Finite element method
The benchmark with details is presented in Figure 2 and consists of a PVC or silicon insulated copper wire above a copper plate. The length of the wire has been selected to be 1.0 m, and the copper plate with a thickness of 0.5 mm is assumed to have infinite dimensions. The air gap represents an estimated average in contrast to the physical setup of the measurements.
The basic boundary value problem to be solved in the frequency domain reads
4. Results
All data shown were acquired with CUTs 1.0 m in length or referred to as 1.0 m as far as simulation data are concerned.
4.1 Frequency domain data
The measurement in the frequency domain was performed using a 2-port VNA (ZVL6). Both ends of the CUT are connected to the VNA, which represents a termination with 50 Ω at either end. The obtained set of S-parameters was subsequently converted into RLGC-data. The results with the given PVC-insulated conductor can be seen in Table 1.
Measurements of a red and black silicone-insulated conductor show a similar picture, and the obtained results are given in Table 2.
It is important to note that the conductors with different colored insulators exhibit differing RLGC parameters. This will also be addressed in Section 4.2.
The data extraction requires some arithmetic: The test point chosen is the lowest frequency minimum of the imaginary part of ZS11, the impedance of the CUT derived from S11, as can be seen in Figure 3 for the conductor with the black PVC insulator.
The impedance seen at Port 1 of the VNA equals
4.2 Time domain data
As mentioned above, the TDR test set is used to acquire the “flight time” of a pulse incident on the CUT. The effective permittivity εr,eff can directly be derived from the time delay
Tables 3 and 4 show the parameter “unit” which has not been explained so far. TDR measurements usually normalize the amplitude of the reflected wave to the system impedance. A full reflection from an open terminated cable is then represented by a unit of 2, whereas no reflection at the end of a cable, i.e. a proper termination with the impedance of the conductor, will show a unit of 1.
A fraction or a multiple of a unit is consequently a measure of the impedance of the cable, as outlined in Figure 4.
The “flight time” mentioned earlier is the time a pulse incident into the CUT takes until it returns from the open end of the CUT. The pulse “travels” two times the cable length; therefore, the delay time td is half the “flight time”. The “reflection factor” mentioned in Figure 4 can be converted into an impedance value of the CUT by means of the following equation
A representative measurement is shown in Figure 5.
4.3 Spice results
To verify the applicability of the model data and their match to measured results, the acquired cable data of “PVC black” have been used. It is clear that the idealized simulation because no parasitics are considered, shows minor deviations. Yet, a first verification with the resonant frequency shows a satisfying match, as given in Figure 6.
The trace shows ZS11 derived from S11 using equation (7) but a blank and the resonance at 66.14 MHz, which is a close match to the measurement results.
4.4 Finite element simulations
Homogenous Dirichlet boundary conditions
Simulations have been carried out with Netgen/NGSolve (Schöberl, 2021). The transversal electric field is obtained by
5. Conclusions
Measurements in the frequency domain and in the time domain show a reasonably accurate match of the results.
It needs to be said that both approaches complement and confirm each other. The FD testing requires a terminated line (with the system impedance), the TD testing needs an open line end, i.e. without termination matching the system impedance.
Future work will extend the model to extract estimated emissions from a single conductor as well as bus structures at frequencies of interest. This will be examined with and without a grounded plane with subsequent verification and matching to get reliable simulation models. Three-dimensional FE models will be used to appropriately simulate relevant emissions. The simulation models shall be optimized for fast and reliable simulations based on a sensitivity analysis showing the impact of parameter variations like d0 in Figure 2.
Figures
Frequency domain, PVC
Parameter | PVC black | PVC red | Unit |
---|---|---|---|
f | 59.46036 | 57.46873 | MHz |
Zl | 65.21131 | 63.88990 | Ω |
R | 1.325222 | 4.935247 | Ω |
L | 293.0912 | 285.8608 | nH |
C | 68.92185 | 70.03098 | pF |
G | 1068.469 | 704.8839 | μS |
vp | 2.224949 · 108 | 2.235000 · 108 | m/s |
vf | 0.7416498 | 0.7450001 | 1 |
td | 4.494484 | 4.474273 | ns |
εr,eff | 1.818035 | 1.801720 | 1 |
Frequency domain, silicone
Parameter | Silicone black | Silicone red | Unit |
---|---|---|---|
f | 59.33388 | 55.78086 | MHz |
Zl | 70.32518 | 69.65358 | Ω |
R | 2.415429 | 1.786379 | Ω |
L | 307.7858 | 305.5429 | nH |
C | 62.23388 | 62.97747 | pF |
G | 639.8732 | 284.2796 | μS |
vp | 2.284874 · 108 | 2.279667 · 108 | m/s |
vf | 0.7616247 | 0.7598888 | 1 |
td | 4.376609 | 4.386607 | ns |
εr,eff | 1.723923 | 1.731809 | 1 |
Time domain, PVC
Parameter | PVC black | PVC red | Unit |
---|---|---|---|
Flight time | 9.732 | 9.568 | ns |
td | 4.866 | 4.784 | ns |
vf | 0.6855 | 0.6973 | 1 |
εr,eff | 2.128 | 2.057 | 1 |
rf | 0.145 | 0.136 | 1 |
Zl | 66.95 | 65.74 | Ω |
Time domain, silicone
Parameter | Silicone black | Silicone red | Unit |
---|---|---|---|
Flight time | 9.78 | 9.624 | ns |
td | 4.89 | 4.812 | ns |
vf | 0.6821 | 0.6927 | 1 |
εr,eff | 2.149 | 2.0839 | 1 |
rf | 0.189 | 0.187 | 1 |
Zl | 73.30 | 73.00 | Ω |
Measurement and simulation results
Measurement | Simulation | ||||
---|---|---|---|---|---|
Parameter | Unit | PVC | Silicone | PVC | Silicone |
f | MHz | 59.3 | 59.5 | 59.3 | 59.5 |
R′ | Ω/m | 1.33 | 2.42 | 1.19 | 1.45 |
L′ | nH/m | 293 | 308 | 306 | 293 |
C′ | pF/m | 68.9 | 62.2 | 81.8 | 72.9 |
G′ | mS/m | 1.07 | 0.64 | 0.12 | 0.14 |
Zl | Ω | 65.2 | 70.3 | 61.1 | 63.4 |
Relative permittivity of the insulator
εr | R′ | L′ | C′ | G′ | Zl |
---|---|---|---|---|---|
1 | Ω | nH/m | pF/m | mS/m | Ω |
3 | 1.15 | 302 | 71.0 | 0.11 | 65.2 |
4 | 1.19 | 306 | 81.8 | 0.12 | 61.1 |
5 | 1.22 | 309 | 90.5 | 0.12 | 58.4 |
Air gap width
d0 | R′ | L′ | C′ | G′ | Zl |
---|---|---|---|---|---|
mm | Ω | nH/m | pF/m | mS/m | Ω |
0.08 | 1.21 | 304 | 84.4 | 0.13 | 60.1 |
0.1 | 1.19 | 306 | 81.8 | 0.12 | 61.1 |
0.12 | 1.17 | 307 | 79.5 | 0.11 | 62.2 |
Diameter of the insulator
dins | R′ | L′ | C′ | G′ | Zl |
---|---|---|---|---|---|
mm | Ω | nH/m | pF/m | mS/m | Ω |
2.9 | 1.21 | 298 | 82.7 | 0.12 | 60.1 |
3.0 | 1.19 | 306 | 81.8 | 0.12 | 61.1 |
3.1 | 1.17 | 313 | 81.0 | 0.11 | 62.2 |
References
Caniggia, S. and Maradei, F. (2008), Signal Integrity and Radiated Emission, Wiley, ISBN 978-0-470-51166-4.
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Eisenstadt, W.R. and Eo, Y. (1992), “S-parameter-based IC interconnect transmission line characterization”, IEEE Transactions on Components, Hybrids, and Manufacturing Technology, Vol. 15 No. 4, pp. 483-490.
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