Design of a Planar Slotted Waveguide Array Antenna for X-band ...

JOURNAL OF THE KOREAN INSTITUTE OF ELECTROMAGNETIC ENGINEERING AND SCIENCE, VOL. 11, NO. 2, JUN. 2011portant to generate isolated slot admittance as a functionof slot length and the resonant length of the slot as afunction of its offset. For feed slots, the resonant lengthof the slot as a function of its tilt angle is also requiredforthe design of the array. A commercially available EMsimulation tool, HFSS, has been used to generate the basicslot data subsequently used in the array design. Inthe HFSS simulations for the shunt slot, the roundended 2.5 mm wide slot was created in a 1 mm thickbroadwall and admittance was recorded at a distance ofone-half the guide wavelength from the center of theslot; the waveguide was terminated in a short circuitplaced at a quarter-wave distance from the center of theslot. Slot length was varied and at each step of normalizedcomplex admittance, conductance (G/G r ) and susceptance(B/G r), was recorded and was normalized withresonant conductanceof the slot. The design curve thusgenerated is shown in Fig. 1. The real and imaginaryparts of the admittance are denoted as a h 1(y) and h 2(y),respectively, where y is the slot length normalized bythe resonant length, l/l r , which can be written as( , )Y x lG0( )= h ( y) + jh ( y) g( x)1 2The waveguide width and height are 21.5 mm and 5mm, respectively. Next, the slot offset is changed and ateach step, the slot resonant length is calculated wherethe imaginary component of the admittance was zero.The resulting resonant length of the slot as a functionof offset is shown in Fig. 2.We will denote the curve shown in Fig. 2 as v(x),where x is the offset of the slot from the center-line ofthe waveguide.Normalized resonant conductance, g ( x) = GrG0, ofthe isolated shunt slot as a function of offset is plottedFig. 2. Resonant length of the broadwall slot versus offset.in Fig. 3. The curve g(x) can be approximated as follows[7],2 æ p x ög ( x) = K sin ç ÷è a øa b 2 æ pb10 k0öK = 2.09 cos ç ÷b10 k0è 2 ø , (1)where a and b are the waveguide width and height respectively,and b10 is the propagation constant of TE 10mode and k0 = 2p l0.The coupling slot was also characterized in HFSS forits resonant resistance as a function of the tilt angle. Inthe simulation model, waveguide was terminated at thedistanceof the half-guided wavelength from the centerof the slot and resistance was recorded at the port locatedat thedistance of the half-guided wavelength fromFig. 1. Normalized admittance of isolated shunt slot versusslot length.Fig. 3. Normalized conductance of isolated shunt slot asa function of offset.98