Hybridization of FDTD with Nested Shielded Multiconductor Transmission Lines and ngspice Interconnections

Hybridization of FDTD with Shielded Multiconductor Transmission Lines and ngspice junctions (EMI Analyses and Predictions - 3) Alberto Gascón Bravo ([email protected]) L. Díaz Angulo ([email protected]) Ferran Silva ([email protected]) Marcos Quílez ([email protected]) Salvador G. García ([email protected]) Enrique Pascual ([email protected]) 2025 ESA Workshop on Aerospace EMC 14/5/2025 Motivation Take-home message: we want to include in a 3D FDTD full-wave solver the capacity to treat arbitrary wiring networks with arbitrary connections Motivation Finite-Difference Time-Domain (FDTD) is a widely used method to discretize Maxwell’s equations in time and space and solve CEM problems but Courant (stability condition): Δt ≤ Δx/c·√3 and Nsteps = tf/Δt How to treat sub-cell structures? 3 ⇊ Δx ⇊ Δt ↑↑ Nsteps Take-home message: we want to include in a 3D FDTD full-wave solver the capacity to treat arbitrary wiring networks with arbitrary connections Holland thin-wire formalism ❌Connections between wires limited to RLC components: not arbitrary & scale poorly with complexity ❌TW can be extended to multiwires, but not to arbitrary bundles (nested shielded transmission lines) EI 4 Proposal: full-wave + MTL + ngspice Full-wave domain (3D): planewave incidence, E/H update, field probes, boundaries, bulk bodies (PEC or other materials) 5 Multiconductor Transmission Line (MTL) domain (2D + 1D): 2D: computation of p.u.l. parameters (dedicated solver) 1D: I/V update of single wires, shielded multiconductor transmission lines and bundles; I/V probes, shield transfer impedance, connectors (line-structure connection) Proposal: full-wave + MTL + ngspice Full-wave domain (3D): planewave incidence, E/H update, field probes, boundaries, bulk bodies (PEC or other materials) 6 full-wave - MTL integration: formulation ●{V},{I} : vectors of voltages and currents (n x 1) ●{ET}: external field (outermost conductor) (n x 1) ●[L], [C], [R], [G]: p.u.l matrices (n x n) ●[Z], [Y]: shield transfer impedance and admittance (n x n) Telegraphist equations: (V,I) update in bundle and interaction with external field Maxwell’s equations: field propagation and interaction with currents Field domain MTL domain I E 7 n = 5 1 2 3 {1} {2} {3} {5} {4} full-wave - MTL integration: formulation ●{V},{I} : vectors of voltages and currents (n x 1) ●{ET}: external field (outermost conductor) (n x 1) ●[L], [C], [R], [G]: p.u.l matrices (n x n) ●[Z], [Y]: shield transfer impedance and admittance (n x n) Telegraphist equations: (V,I) update in bundle and interaction with external field Maxwell’s equations: field propagation and interaction with currents Field domain MTL domain I E 8 0 ZT,12 ZT,13 0 0 ZT,12 0 0 0 0 ZT,13 0 0 ZT,34 ZT,35 0 0 ZT,43 0 0 0 0 ZT,53 0 0 [Z] = n = 5 1 2 3 {1} {2} {3} {5} {4} Multiconductor Transmission Line (MTL) domain (2D + 1D): 2D: computation of p.u.l. parameters (dedicated solver) 1D: I/V update of single wires, shielded multiconductor transmission lines and bundles; I/V probes, shield transfer impedance, connectors (line-structure connection) Proposal: full-wave + MTL + ngspice Full-wave domain (3D): planewave incidence, E/H update, field probes, boundaries, bulk bodies (PEC or other materials) 9 Wire panel Works as oneand two-conductor TL Used to test: ● line terminations with electronic components: ○ zener diode ○ operational amplifier TL701CP (Texas Instruments) N-type connectors 4 cm 10 cm 40 cm 16 ngpsice terminations: zener diode ● Zener diode (VB = 3.9 V) ● Excitation: 5 V, 50 kHz sinusoidal signal ● Clipping at ~ 0.7V (typical of Si diodes) and 3.9 V 17 ● Wire panel with op-amp at line end (10x inverter amplifier, Vin = ± 15V) ● Test no saturation (Vsrc = 0.2V) and saturation regime (Vsrc = 2V) ngpsice terminations: op-amp saturation no saturation 18 ● Excitation on a wire, same op-amp at the end of the other wire ● Test with sinusoidal and square pulse ● f = 1 MHz, V = 20 V: need high frequency and amplitude to have a measurable crosstalk Crosstalk in components square pulse sine pulse 19 Conclusions ● Hybridization of 3D-FDTD with MTL and ngspice: networks of shielded bundles, with arbitrary interconnections, in a full-wave solver. ● ngspice interconnections: allow for electronic components, straightforward simulation of dispersive elements in time domain ● Experimental validation of simulations covering main new features. ●All tools integrated in openSemba, a full-wave open-source FDTD solver ○ You can find it at https://github.com/OpenSEMBA ○ You are welcome to try it! More users, better software Acknowledgements Thanks to the GCEM-UPC for their collaboration with the experimental validations at the ECM laboratories. This work was funded in part by: ● Spanish National Project PID2022-137495OB-C31 (ESAMA) ● European Union under GA no 101101961 - HECATE. 20 Backup 21 Iterative solution 22 Fields Transmission line (interior) Transmission line (extremes) (needs I) Transmission line (extremes) (circuit equivalent) Bundle 23 full-wave - MTL integration: p.u.l matrices [L]1 0 0 0 [L]2 0 0 0 [L]3 [L]1 = Lin-cell [L]2 = [L]2x2 [L] = [C]1 0 0 0 [C]2 0 0 0 [C]3 [C]1 = Cin-cell [C]2 = [C]2x2 [C]3 = [C]2x2 [C] = [L], [C] pul matrices (n x n): ● full-wave domain: in-cell ● MTL domain: ii, ij, to reference conductor (2,3→1),(4,5→3) [L]3 =[L]2x2 1 2 3 24 {1} {2} {3} {4} {5} 0 ZT,12 ZT,13 0 0 ZT,12 0 0 0 0 ZT,13 0 0 ZT,34 ZT,35 0 0 ZT,43 0 0 0 0 ZT,53 0 0 [Z] = [Z] matrix (n x n): ● input, provided by manufacturer or characterized by dedicated measurements ● current on wire → voltage on shielded/shield [G] = (σ/ε) [C] [R] = [R]5x5 Complexity/Electrical size Image sourced from: https://help.altair.com/feko/