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ECEN 3410 - Electromagnetic Fields and Transmission Spring semester 2005, University of Colorado at Boulder Examples of parallel-plate waveguides 1. Parallel plate waveguide modes An air-filled parallel-plate waveguide has a plate separation of 1.25 cm. a) Find the cutoff frequencies of the TEo, TMo,TE1, TM1, TE2 and TM2 modes. b) Find the phase velocities of those modes at 15 GHz. c) Find the lowest order mode that cannot propagate in this w.g. at 25 GHz 2. Extreme low frequency propagation in the earth-ionosphere waveguide Extreme low frequencies (ELF) are ideal for communicating with deeply submerged submarines because below 1KHz EM waves penetrate into sea water. Propagation at these frequencies takes place in the "waveguide" formed between the earth and the ionosphere. Low propagation losses allow nearly worldwide communication from a single transmitter. In a simple model, the surface of the earth and the bottom of the ionosphere form the boundaries of a terrestrial parallel plate w.g. with lossy walls. The ionosphere is approximated by an isotropic layer beginning at a given altitude and extending to infinity with no horizontal variations. Energy is lost through the "walls" either into the finitely conducting ionosphere or into the ground, with the former loss being dominant. The important feature is that below 1kHz there is a single propagation mode, a so-called quasi TEM mode. All the other modes are evanescent and are undetectable at distances beyond 1000km. In the far field the wave consists of a vertical electric field and a horizontal magnetic field transverse to the direction of propagation. The leakage of energy into the ocean gives rise to a plane wave propagating downward, and it is the signal that submarine receivers detect. Consider an idealized w.g. where both the ionosphere and the earth are perfect conductors. Neglect the curvature of the w.g. The height of the w.g. can vary between 70 and 90 km, assume it is 80km and constant. Find all the propagating modes at an operating frequency of 100Hz, 1kHz and 10 KHz.
