Radiation Model of Finite-Length Transmission Lines

Abstract

II. Experiment Radiation from transmission lines of finite length is developed using a circuit-concept. Estimation of radi­ ation power received in an antenna load is derived un­ der the hypothetical theorem of reciprocity between " the coupling of external waves to transmission lines" and "the radiation from transmission lines”. The fit of experimental results to the estimation confirmes the reciprocity theorem, so that the prediction of radia­ tion field can be carried out. I. Introcuction Electromagnetic radiation from electric and electron­ ics instruments is one of the important topics in elec­ tromagnetic compatibility (EMC). As a most fundamental model, it is important to investigate theoretically the radiation from transmission lines. The principal propa­ gation mode in the transmission lines considered here is essentially TEM. Although, if there were a disconti­ nuity such as a bend at a point of the transmission lines, we have practically noticed that it causes the radiation fields. Discontinuities of transmission lines are often estimated as equivalent reactances at the point [1]. Since the radiation fields are very weak, it has been ignored in the past. However, it is now becom­ ing an important topic in fields of wiring, interfer­ ence in distributed-constant circuits, etc. Very few investigations on radiation from the line have been carried out [2]. In this paper we consider radiation fields from finite-length transmission lines by the use of a cir­ cuit analysis concept. The experimental results of ra­ diation power pattern form the lines suggest the recip­ rocal relation between the radiation from the line and the coupling of externally excited lines. Under the hy­ pothesis of the reciprocity theorem, the prediction of radiation power from the line model used here is deriv­ ed by the use of the equation for externally excited transmission lines. The fit of experimental results to the theoretical prediction confirms the reciprocity, so that the equation of radiation field from finite-length transmission lines is derived). We consider the radiation field from a transmission line consisting of a lossless wire of length 1 and di­ ameter d suspended at height h above a perfectly con­ ducting ground plane as shown in Fig. 1. As shown in the figure, there are transitions or vertical bends at the line terminals. One of the terminals is connected to a generator, of which output impedance 50-ohm, wave length A = 200 mm, and the other to a 50-ohm load. We measured the radiation power pattern by the use of a pyramidal horn at point P(r 3 m, 0 = 45°, ), which is connected to a spectrum analyzer of output imped­ ance 50-ohm. The conducting ground plane used here is made of aluminum of 2.8 m in diameter. The transmis­ sion line revolves together with the ground plane in a direction of . For I = 200 mm, h = 3 mm, and d = 0.8 mm, the results of radiation power pattern are shown in Fig. 2: (a) for Eg and (b) for E^. Left-side scale denotes a power level received in the antenna terminal for the gener­ ator of available out-put power -6 dBm. The right-side, which denotes electric field intensity, will be con­ sidered in the later. We consider the coupling model, i.e., the induced power at the load terminal of the transmission line when the generator and the spectrum analyzer are changed vice versa in Fig. 1. Figure 3 (a) shows the result when an external wave is a plane wave of paral­ lel polarization or Eg, and (b) perpendicular or E^. The power level is normalized by the incident electric field intensity E= 1 V/m at the origin. Figures 2 and