ACES JOURNAL, VOL. 18, NO. 4, NOVEMBER 2003 33 Aperture-Coupled Stripline-to-Waveguide Transitions for Spatial Power Combining Chris W. Hicks∗, Alexander B. Yakovlev#,andMichaelB.Steer+ ∗Naval Air Systems Command, RF Sensors Division 4.5.5, Patuxent River, MD 20670 #Department of Electrical Engineering, The University of Mississippi, University, MS 38677-1848 +Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, NC 27695-7914 Abstract power. However, tubes are bulky, costly, require high operating voltages, and have a short lifetime. As an A full-wave electromagnetic model is developed and alternative, solid-state devices offer several advantages verified for a waveguide transition consisting of slotted such as, lightweight, smaller size, wider bandwidths, rectangular waveguides coupled to a strip line. This and lower operating voltages. These advantages lead waveguide-based structure represents a portion of the to lower cost because systems can be constructed us- planar spatial power combining amplifier array. The ing planar fabrication techniques. However, as the fre- electromagnetic simulator is developed to analyze the quency increases, the output power of solid-state de- stripline-to-slot transitions operating in a waveguide- vices decreases due to their small physical size. There- based environment in the X-band. The simulator is fore, to achieve sizable power levels that compete with based on the method of moments (MoM) discretiza- those generated by vacuum tubes, several solid-state tion of the coupled system of integral equations with devices can be combined in an array. Conventional the piecewise sinusodial testing and basis functions in power combiners are effectively limited in the num- the electric and magnetic surface current density ex- ber of devices that can be combined. To overcome pansions. Electric and magnetic dyadic Green’s func- these limitations and produce high power levels at mi- tions used in this integral equation formulation are de- crowave and millimeter-wave frequencies, in a past few veloped for an infinite rectangular waveguide in the years there has been a considerable activity in develop- form of partial expansion over the complete system ing spatial power combining systems [1], [2], [3]. The of eigenfunctions of a transverse Laplacian operator. output power of individual solid-state devices in a pla- Numerical results are obtained and compared with a nar array is combined to produce moderate-to-high commercial microwave simulator for a few represen- power levels. It is desirable to utilize a single solid- tative structures, including various configurations and state amplifier, however, as frequency increases, the /f 2 planar arrays of slotted waveguide modules coupled to output power levels become low due to the 1 fall- a strip line. off of available power [4]. By utilizing power combin- ing techniques light-weight, reliable, and low cost am- plifiers and oscillators can be potentially designed to I. Introduction meet the demand of military and civilian applications. Fundamental understanding of spatial power com- Military and civilian applications require sizable bining systems has primarily been done by experimen- power at microwave and millimeter-wave frequen- tal investigation. Several experimental free space and cies. Medium to high power levels are needed for dielectric quasi-optical power combiners and waveg- applications such as communications, active missile uide spatial power combiners have been successful at seekers, radar, and millimeter-wave imaging. To meet demonstrating the fundamental concept of generating this need, klystrons, traveling-wave tubes, and gridded usable output power levels using spatial and quasi- tubes are heavily utilized to generate medium to high optical techniques. Although great strides have been 1054-4887 © 2003 ACES 34 ACES JOURNAL, VOL. 18, NO. 4, NOVEMBER 2003 made, to date, quasi-optical/spatial power combin- between the middle and upper waveguides. The strips ing systems have not yet out performed conventional are located inside of the middle waveguide region. The power combiners. In order to capture the full potential objective of stripline-to-waveguide transition is to effi- of quasi-optical/spatial systems to generate high power ciently couple energy from the lower waveguide to the levels, numerical modeling and computer aid engineer- upper waveguide. An incident electromagnetic field is ing tools are needed to fully understand these systems illuminated at the input port of the lower waveguide. [5]. The development of computer models helps to re- This signal travels into the lower waveguide and in- duce the cost and time associated with experimental duces magnetic currents on the lower slots where the work, and computer models assist with designing ef- slots scatter energy into the lower, middle, and upper ficient quasi-optical/spatial power combining systems. waveguides. In the middle waveguide region the scat- Modeling a quasi-optical/spatial power combining sys- tered fields induce electric currents and standing waves tem is complex and challenging. There are several along the strips. The scattered energy from the strips major system components that must be modeled such along with the scattered energy from the lower slots as, the input and output sources, which are typically induce magnetic currents in the upper slots. The mag- waveguide horns with optical lenses inside, the input netic currents in the upper slots cause scattered fields and output antennas with associated transmission lines back into the middle waveguide and into the upper and control components, and the active integrated am- waveguide region. Optimum performance is achieved plifier circuitry. by varying the distance between the slots, adjusting the slot dimensions, rotating the slots, or varying the stripline dimensions. Upper Waveguide PLANAR WAVEGUIDE SPATIAL POWER COMBINING AMPLIFIER PLANE INPUT COUPLING AMPLIFIER ARRAYS OUTPUT COUPLING NETWORK NETWORK Port 3 Port 4 Output Slots Output ε r Stripline MMIC Input Slots Port 1 Input Port 2 GROUND PLANE OUTPUT PLANE a Pout AMPLIFIER PLANE b Dielectric Between Waveguides Bottom Waveguide INPUT PLANE Pin c MICROWAVE ABSORBER PHOTONIC MATERIAL Fig. 1. Aperture-coupled stripline-to-waveguide transition. Fig. 2. Aperture-coupled planar waveguide amplifier array. In this paper, an electromagnetic modeling environ- ment is developed for an aperture-coupled stripline- to-waveguide transition (with geometry shown in Fig. A full-wave electromagnetic model is developed for 1). This transition is the fundamental building block a structure that couples a waveguide to a stripline for two-dimensional spatial power combining amplifier through a set of slots and from the stripline through arrays shown in Fig. 2 and, in turn, for the planar another set of slots into a second waveguide. The sys- quasi-optical power combining systems. The transition tem modeling is based on an integral equation formu- consists of three infinite aperture-coupled rectangular lation for the induced electric and magnetic surface waveguides. The lower slots (apertures) are located current densities resulting in a coupled set of inte- on the surface between the lower and middle waveg- gral equations discretized via the method of moments uides, and the upper slots are located on the surface (MoM). The scattered electric and magnetic fields are Hicks, et al.: Aperture-Coupled Stripline-to-Waveguide Transitions for Power Combining 35 expressed in terms of dyadic Green’s functions and the S electric and magnetic surface currents. Electric and S m nˆ magnetic dyadic Green’s functions are developed for an infinite rectangular waveguide in the form of par- E , H tial expansion over the complete system of eigenfunc- i i tions of a transverse Laplacian operator. The surface Es , Hs S currents are discretized by overlapping piecewise sinu- Jimp e sodial subdomain basis functions in order to accurately model narrow longitudinal strips and transverse slots. Jind Vimp V In this formulation, a MoM matrix includes all possible self and mutual coupling effects between the slots and strips. The transition is excited with the TE10 dom- inant waveguide mode, and the scattering parameters are calculated from the forward and backward coupling Fig. 3. Geometry of a closed-boundary waveguiding structure coefficients in the waveguide regions. containing apertures and conducting strips in the presence Numerical results of the scattering characteristics of an impressed electric current source. are obtained and compared with a commercial mi- crowave simulator for a few representative structures, = ¯ including a single slot-strip-slot waveguide transition, −jωµ GEJ (r, r ) · Jind(r )dS Se multiple slot-strip-slot waveguide transitions, and pla- = nar arrays of slotted waveguide modules coupled to − GEM (r, r ) · M¯ (r )dS (1) strip lines. Sm = II. Theory H¯ (r )= GHJ (r, r ) · J¯imp(r )dV Vimp = A general electromagnetic formulation for a closed- + GHJ (r, r ) · J¯ind(r )dS boundary waveguiding structure containing arbitrarily Se shaped apertures and conducting strips (see Fig. 3) = is presented in this section. This structure is a gen- −jω GHM (r, r ) · M¯ (r )dS (2) S eral building block of the aperture-coupled stripline- m to-waveguide transition shown in Fig. 1. The formula- where tion is based on the integral representation of incident = = and scattered electric and magnetic fields in terms of GHJ (r, r )=∇× GEJ (r, r ), (3) dyadic Green’s functions