Electromagjnetic Field Plot of an Inductive Windo , w by the Moment Method

A moment method is used to plot the electromagnetic field of an inductive window in a TE 10 -mode rectangular waveguide. Green's dyadic functions are derived based on Tai's approach, which is a modified form of Hansen's vector wave functions. Based on the computed electric fields, the S matrix and the equivalent aperture reactance of the waveguide window are calculated. This calculation agrees with the previously published closed-form results of Marcuvitz. l. INTRODUCTION T HE objective of this paper is to show a plot of electromagnetic field of an inductive window obtained by the moment method. Waveguide windows are widely used in filter and impedance matching sections in rectangular waveguide systems. Although the impedance of this window has been investigated in the past, the electromagnetic fields in close proximity to the window have not been studied w~ll [1]-[4]. To the authors' kriowledge, no field plots are a,vailable. This paper proposes a method to obtain the field plots in a rectangular waveguide with a window using Green's functions [4]-[6]. Specifically, the total field near the window may be divided into two field contributions by the induction theorem [4]-[6]. These fields are the incoming field and the scattered field which is generated by an equivalent mathematical source which is used ~o represent the window. II. PLOT OF ELECTRIC FIELPS In Fig. 1, a conducting iris of d X b to form a waveguide window of (a(f) X b is illustrated. A graphical representation of the incoming, scattered, and total fields in the waveguide was obtained by plotting the instantaneous fields at a given point in time as a function of position r in the domain of the waveguide. Manuscript received February 6, 1991 ; revised April 5, 1991. J. R. Natzke was with the Department of Electrical and Computer Engineering, Marquette University, Milwaukee, WI 53233. He is now with the Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109. M. R. Wolski was with the Department of Electrical and Computer Engineering, Marquette University, Milwaukee, WI 53233. He is now with Medical Advances, Inc., Milwaukee, WI 53226. T. Koryu Ishii is with the Department of Electrical and Computer Engineering, Marquette University, Milwaukee, WI 53233. IEEE Log Number 9101007. T b X conducting diaphragm Fig. 1. Waveguide window in a section of rectangular waveguide. The instantaneous fields in general are expressed by E(r,t) = Re{E(r)eiwt} (1) H(r,t) = Re{H(r)eiw'} . (2) Only plots of the electric fields shall be shown in this paper. Consider first the case with only the TE 10 dominant mode propagating in the waveguide as the incoming field. The incoming electric field for this mode has only a y component. Since the incoming electric field E~(r, t) is independent of the position y, its magnitude is independent of y for 0 < y < b. The amplitude H 0 of the longitudinal component of the incoming magnetic field was set to 1 TT Ho=-Wf-L a (A j m) (3) such that the amplitude of E~ was normalized to 1 (V j m). The width, a, and the height, b, of the waveguide were chosen for X-band rectangular waveguide. The operating frequency, f, was chosen such that all modes were in cutoff except for TE 10 . The waveguide wavelength, Ag , was determined by common waveguide theory [1]-[4]. Calculations are performed using a VAX computer [8]. 0018-9480/91/0800-1296$01.00 ©1991 IEEE NATZKE eta/. : ELECTROMAGNETIC FIELD PLOT to ~ ~ to . 'tJ o.o ::l -~ Cll ·I.O . , ~ ·to Fig. 2. Scattered electric field: wt = 0.007T, f = lO.OOGHz, Ag = 4.87 em, a= 1.905 em, b = 0.952 em, diaphragm width= 0.762 em. 2.o ~ 2:3. I.O . 'tJ o.o 2 ·c: Cll ·l.o . , ~ ·to Fig. 3. Total electricfield:wt = 0.007T,f = lO.OOGHz,Ag = 4.87 cm,a = 1.905 cm,b = 0.952cm, diaphragm width= 0.762cm. 1.00 --. / 1-. I 1/-. ~-~ . :r. ,1J 0 . 75 d) "0 ::J . [7 . v . c 0 . 50 01 <U ~