The basic TLM formulation requires that the constitutive parameters of the medium be specified as constants. Therefore, an appropriate wide-band modelling of general (dispersive, nonlinear, etc...) media cannot be performed without major modification of the algorithm. The TLM algorithm can be modified to represent general constitutive relationships. This can be done by using previously decoupled 2-D scattering matrices. The constitutive relationships are solved with equivalent node sources and state-variables.
The technique was validated by comparing SCN TLM results with calculations of the cutoff frequency of a waveguide filled with anisotropic material. The example simulated a WR-28 (7.112 mm by 3.556 mm) waveguide using regular mesh with a discretization of 24 x 12 x 4. A sapphire substrate was used as a dielectric (epsilon_u=9.34 and epsilon_v=11.49). The optical axis lies on the xy plane, rotated by an angle psi with respect to the x axis. The problem was calculated for psi of 0 deg., 45 deg. and 90 deg. using backwards Euler discretization
| Analytical Cutoff Frequency (GHz) | Axis Angle (deg.) | SCN - TLM (GHz) | Error (%) |
|---|---|---|---|
| 6.2221 | 0 | 6.21 | 0.19 |
| 6.5354 | 45 | 6.57 | -0.53 |
| 6.9012 | 90 | 6.90 | 0.02 |
Further details can be found in:
W.J.R. Hoefer, `The transmission line matrix method - theory and applications', IEEE Trans. Microwave Theory and Tech., vol. 33, Oct. 1985.
L. de Menezes, W.J.R. Hoefer, `Modelling frequency dependent dielectrics in TLM', IEEE AP-S Symposium Digest, pp. 1140-1143, Jun. 1994.
L. de Menezes, W.J.R. Hoefer, `Modelling nonlinear dispersive media in 2D-TLM', 24th European Microwave Conference Proceedings, pp.1739-1744, Sept. 1994.
P. Naylor and R. Ait-Sadi, `Simple method for determining 3-D TLM nodal scattering in nonscalar problems,' Electronic Letters, vol. 28, pp. 2353-2354, Dec. 3, 1992.
