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

BHATTI et al. : DESIGN OF A PLANAR SLOTTED WAVEGUIDE ARRAY ANTENNA FOR X-BAND RADAR APPLICATIONSéùê 22 fmn ( xmn,lmn) úIm ê ú = - Imê Y( xmn,lmn ) úêëG ú0 û[ MC ]where Y/G 0 is calculated from the design curves, as( , l )Y xmnG0mnmn( h1 ( ymn ) h2( ymn )) g ( xmn)= + .Once this is satisfied, then active admittance of theslot become spure real. During this search process, acontinuum of couplets that satisfy this relation is found.Similarly, for the pq th slot, the same search is conductedand the continuum of couplets that make the active admittancepure real is found. But for a given acceptablecouplet for the mn th slot, there will only be one coupletfor the pq th slot that will satisfy the following equation,Yapq2sf ( , )0 pqxpq lpq VpqVma 2smn mn ( mn,mn ) mn pG= .Y f x l V VG0This procedure provides a set of acceptable coupletsfor each slot. However, which couplet to choose will dependon the required admittance level in each branchline.The final acceptable couplets in a branch-line shouldsatisfy the relationship,YN ( m)amnå = Cm,n=1 G0where C m is the required admittance level in the m thbranch waveguide.The entire procedure needs to be iterated as the newslot data will give an improved mutual coupling calculationand the solution will converge after 3 or 4 iterations.After calculating the radiating shunt slot data, the seriesfeed slot data is then calculated according to the procedurereported in [9].The sum of the series of slot resistances is given by,Må r = W ,mm=1m= and m=1, 2…M,r m is the normalized resonant resistance of the m th slot,B is the slot excitation function, K is the excitation normalizationconstant, and W=1 for the end-feed or W=2for the center feed. B m is given in terms of the aperturedistribution.where r KB 2( m),(5)(6)(7)(8)N m2 2( ) ( , )B m = å A m n ,n=1where N m is the number of shunt slots fed by the m thseries slot.Using these resistance values, the corresponding slotangles are calculated using the design curves or the followingrelationship,(9)2R b10 l é l0g ù= 0.131 êIqsinq+ JqcosqúR0k ab ë 2aû , (10)where theta is the tilt angle of the series slot, andæ p ö æ p öcos K1 cos K2I ç ÷ ç ÷q 2 2=è ø±è øJ 1- K 1-Kq22 21 2K1 b10 l0= cosq± sinq.K k 2aOnce slot resistance as a function of the slot tilt angleis known, we can calculate the slot length for differentslot angles from the design curve shown in Fig. 4. Theapplied slot length (l) is 16.5 mm and the offset lengths(x) are 2.1, 1.85, 1.6, 1.0, 0.8, and 0.7 mm after the calculationand CST-simulation.The feed waveguide is fed at the center through astandard X-band waveguide. The width of the feed slot isoptimized in CST to get the desired match at 9.375 GHz.A 3-D exploded model of the antenna assembly isshown in Fig. 9.Fig. 9. Exploded view of antenna assembly.101