Successfully reported this slideshow.
IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 17, NO. 11, NOVEMBER 2007 1
Overlapping T-Block Analysis and Genetic
...
IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 17, NO. 11, NOVEMBER 2007 2
d
b 22 ,µε
x
y
z
11,µεa2
Fig. 3. Geometry...
IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 17, NO. 11, NOVEMBER 2007 3
9.4 9.7 10 10.3 10.6 10.9 11.2
0
5
10
15
...
Upcoming SlideShare
Loading in …5
×

Overlapping T-block analysis and genetic optimization of rectangular grooves in a parallel-plate waveguide

776 views

Published on

Published in: Technology, Business
  • Be the first to comment

  • Be the first to like this

Overlapping T-block analysis and genetic optimization of rectangular grooves in a parallel-plate waveguide

  1. 1. IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 17, NO. 11, NOVEMBER 2007 1 Overlapping T-Block Analysis and Genetic Optimization of Rectangular Grooves in a Parallel-Plate Waveguide Yong H. Cho, Member, IEEE Abstract—Scattering characteristics of rectangular grooves in a parallel-plate waveguide are analyzed and optimized using an overlapping T-block method and a genetic algorithm. The total Ez and Hz fields for a waveguide are represented with summation of those of four overlapping T-blocks by means of superposition. Insertion loss behaviors versus frequency are computed and compared with measurement results. Index Terms—Green’s function, mode-matching, genetic algo- rithm, parallel-plate waveguide filter. I. INTRODUCTION SCATTERING characteristics of rectangular grooves in a waveguide are extensively studied [1]-[4]. In [1], [2], Bragg diffraction is utilized to obtain a band-stop filtering for finite numbers of rectangular grooves. In order to determine various coupling dimensions of irises and stubs, full-wave analysis and optimization method [4] are applied to canonical waveguide filters. In this Letter, rectangular grooves in a parallel-plate waveg- uide are analyzed with an overlapping T-block method and a genetic algorithm [5]. Using superposition scheme, a parallel- plate waveguide with finite rectangular grooves is divided into several T-blocks. A total field representation is obtained with summation of a T-block field, which has a fast convergent an- alytic series. Numerically computing the total field, behaviors of insertion loss versus frequency are automatically optimized by means of a genetic algorithm. II. FIELD ANALYSIS OF RECTANGULAR GROOVES Consider a TE-wave to the x-axis in a parallel-plate waveg- uide propagating to the x-direction shown in Fig. 1. The scattering characteristics of rectangular grooves in a parallel- plate waveguide are analyzed with an overlapping T-block method [5]. The geometry in Fig. 1 is divided into several T-blocks in Fig. 2 based on the superposition scheme in [5], [6]. Utilizing the same method in [5], the Ez fields within a Y. H. Cho is with the School of Information and Communication Engi- neering, Mokwon University, Mokwon Street 21, Seo-gu, Daejeon, 302-318, Korea e-mail: yongheuicho@gmail.com. Manuscript received March 27, 2007; revised ???. b x y z )1( d )1( 2a )2( 2a )2( d incidence T Fig. 1. Geometry of rectangular grooves in a parallel-plate waveguide with 0 and 0 ),()1( yxT ′′ ),()2( yxT ′′ ),()3( yxT ′′ ),()4( yxT ′′ ),( yxS ′′ Fig. 2. Superposition of four T-blocks and a source block T-block in Fig. 3 are given by EI z(x;y) = 1X m=1 pm sin am(x + a) sin m(y + d)ux(a) (1) EII z (x;y) = 1X m=1 pm sin( md) h Em(x;y) + RE m(x;y) i ; (2) where am = m =2a, m = p k2 1 a2 m, ux(a) = u(x+ a) u(x a)], u( ) is a unit step function, Em(x;y) = sin m(b y) sin( mb) sin am(x + a)ux(a) (3) RE m(x;y) = ami b 1X v=1 v sin( vy) v( 2 v a2 m)
  2. 2. IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 17, NO. 11, NOVEMBER 2007 2 d b 22 ,µε x y z 11,µεa2 Fig. 3. Geometry of a T-block h ei vjx+aj ( 1)mei vjx aj i ; (4) m = p k2 2 a2 m, k1;2 = !p 1;2 1;2, v = v =b, and v =p k2 2 2 v. When x ! 1, (2) reduces to EII z ( 1;y) i b VX v=1 v v 1X m=1 pm am sin( md) 2 v a2 m h e i va ( 1)me i va i sin( vy)e i vx ; (5) where V = bk2= ] and x] denotes a maximum integer less than x. Then, the total Ez field for Fig. 1 is represented as Etot z (x;y) = T(1) E (x;y) + T(2) E (x;b y) + T(3) E (x a(1) a(2) T;y) + T(4) E (x a(1) a(2) T;b y) ; (6) where TE(x;y) = EI z(x;y)+EII z (x;y). An incident Ez field within a source block SE(x;y) in Fig. 2 is also given by SE(x;y) = sin( sy)ei sx ; (7) where s is the mode number of incidence, s = s =b, and s = p k2 2 2 s. By enforcing the Hx fields continuities at boundaries, it is possible to represent the scattering relations for a TE-wave as 1 Z x0+a(i) x0 a(i) @ @y h Etot z (x;y) + SE(x + a(1) ;y) i sin a(i) l (x x0 + a(i) ) dx y=0; b x0=0; a(1)+a(2)+T = 0 ; (8) where a(i) l = l =2a(i) . It is noted that a(i) = a(1) and a(2) for x0 = 0 and a(1) + a(2) + T, respectively. Similar to the TE analysis, we obtain the Hz fields within the geometry in Fig. 3 as HI z(x;y) = 1X m=0 qm cosam(x + a) cos m(y + d)ux(a) (9) HII z (x;y) = 2 1 1X m=0 qm m sin( md) h Hm(x;y) + RH m(x;y) i ; (10) where Hm(x;y) = cos m(y b) m sin( mb) cosam(x + a)ux(a) (11) RH m(x;y) = 1 b 1X v=0 cos( vy) v( 2 v a2 m) h sgn(x + a)ei vjx+aj ( 1)msgn(x a)ei vjx aj i ; (12) and sgn( ) = 2u( ) 1. When x ! 1, (10) becomes HII z ( 1;y) 2 1 1 b VX v=0 1 v 1X m=0 qm m sin( md) 2 v a2 m h e i va ( 1)me i va i cos( vy)e i vx : (13) The total and incident Hz fields for Fig. 1 are represented as Htot z (x;y) = T(1) H (x;y) + T(2) H (x;b y) + T(3) H (x a(1) a(2) T;y) + T(4) H (x a(1) a(2) T;b y) (14) SH(x;y) = cos( sy)ei sx ; (15) where TH(x;y) = HI z(x;y) + HII z (x;y). Note that the Hz fields, HI z(x;y) and HII z (x;y), are already given in [5]. Then, we get the scattering relations for a TM-wave as Z x0+a(i) x0 a(i) h Htot z (x;y) + SH(x + a(1) ;y) i cosa(i) l (x x0 + a(i) ) dx y=0; b x0=0; a(1)+a(2)+T = 0 : (16) III. NUMERICAL COMPUTATIONS Utilizing a binary genetic algorithm (GA) [5], [7]-[10] al- lows us to optimize the scattering characteristics of rectangular grooves in a parallel-plate waveguide in Fig. 1. We use the fitness function defined in [7] and propose an error factor as tness = 1 1 + error (17) error = (1 w) perrorpass + wperrorstop ; (18) where w is a weighting factor, errorpass = 1 Np Np 1 X i=0 ep(f0 BWp=2 + fp i )]2 (19) errorstop = 1 2Ns Ns 1X i=0 n es(fu + fs i )]2 + es(fl fs i )]2 o (20) ep(f) = IL(f) ILp when IL(f) > ILp 0 when IL(f) ILp (21) es(f) = ILs IL(f) when IL(f) < ILs 0 when IL(f) ILs ; (22)
  3. 3. IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 17, NO. 11, NOVEMBER 2007 3 9.4 9.7 10 10.3 10.6 10.9 11.2 0 5 10 15 20 25 30 Frequency [GHz] Insertionloss[dB] m = 1 m = 2 m = 3 m = 4 Measurement Fig. 4. Insertion loss characteristics for a TE-wave versus frequency with a(1) = 14:325 mm], a(2) = 11:95 mm], d(1) = 27:85 mm], d(2) = 17:07 mm], T = 16:54 mm], b = 22:86 mm], and s = 1 f0 and BWp denote center frequency and bandwidth of the pass band, respectively, fu;l = f0 (BWp=2 + fs), fp i = i BWp=(Np 1), fs i = i BWs=(Ns 1), IL(f) is an insertion loss (dB) at frequency f, ILp;s denote the goals of insertion loss (dB) for the pass and stop bands, respectively. In order to perform the numerical optimizations based on GA, we set up the parameters such as f0 = 10.3 [GHz], BWp = 0.4 [GHz], BWs = 0.2 [GHz], fs = 0.3 [GHz], ILp = 1 [dB], ILs = 30 [dB], Np = Ns = 6, w = 0.2, the numbers of bits = 16, population = 100, generation = 150, the probabilities of crossover and mutation = 0.6 and 0.1, respectively. We also adopt roulette wheel selection and elitism [7] and the initial estimates for 2a(1) , 2a(2) , d(1) , d(2) , and T shown in Fig. 1 are randomly chosen from 1 [mm] to 30 [mm]. Final results for a(1);(2) , d(1);(2) , and T in GA optimizations are shown in caption of Fig. 4. To verify our theory and optimization, we fabricate a waveguide filter shown in Fig. 1 in terms of WR-90 size (22.86 [mm] 10.16 [mm]) and measure the insertion loss. Measured and simulated results are compared in Fig. 4. When the number of modes m 4, our series solution agrees well with measurement, thus confirming that our solution converges very fast. Fig. 5 illustrates the insertion loss characteristics of the TM wave for an E-plane waveguide filter. Near to f0, the E-plane waveguide filter has band-stop behavior, whereas the H-plane waveguide filter in Fig. 4 does band-pass filtering. IV. CONCLUSION Analytic yet numerically efficient scattering equations for rectangular grooves in a parallel-plate waveguide are proposed and verified by measurement. Numerical optimizations based on a genetic algorithm are performed to obtained the band-pass filtering characteristics and compared with measurement. Our computational experiences indicate that the TE and TM series solutions shown in this Letter are very useful and accurate for genetic optimizations when the number of modes 4. 9.1 9.4 9.7 10 10.3 10.6 10.9 11.2 0 5 10 15 20 25 30 35 40 Frequency [GHz] Insertionloss[dB] m = 0 m = 2 m = 4 m = 6 Fig. 5. Simulated insertion loss characteristics for a TM-wave versus frequency with the same dimensions as Fig. 4 except for b = 10:16 mm] and s = 0 ACKNOWLEDGMENT This work was supported by the Korea Research Foundation Grant KRF-2004-003-D00255. REFERENCES [1] J. H. Lee, H. J. Eom, J. W. Lee, and K. Yoshitomi, “Transverse electric scattering from rectangular grooves in parallel-plate,” Radio Sci., vol. 29, no. 5, pp. 1225-1228, Sept.-Oct. 1994. [2] K. H. Park, H. J. Eom, and K. Uchida, “TM-scattering from notches in a parallel-plate waveguide,” IEICE Trans. Commun., vol. E79-B, no. 2, pp. 202-204, Feb. 1996. [3] C. A. W. Vale, P. Meyer, and K. D. Palmer, “A design procedure for bandstop filters in waveguides supporting multiple propagating modes,” IEEE Trans. Microwave Theory Tech., vol. 48, no. 12, pp. 2496-2503, Dec. 2000. [4] T. Shen, H.-T. Hsu, K. A. Zaki, A. E. Atia, and T. G. Dolan, “Full- wave design of canonical waveguide filters by optimization,” IEEE Trans. Microwave Theory Tech., vol. 51, no. 2, pp. 504-511, Feb. 2003. [5] Y. H. Cho, “Analysis of an E-plane waveguide T-junction with a quarter- wave transformer using overlapping T-block method and genetic algo- rithm,” IEE Proc. - Microw. Antennas Propag., vol. 151, no. 6, pp. 503- 506, Dec. 2004. [6] Y. H. Cho and H. J. Eom, “Analysis of a ridge waveguide using overlapping T-blocks,” IEEE Trans. Microwave Theory Tech., vol. 50, no. 10, pp. 2368-2373, Oct. 2002. [7] Y. Rahmat-Samii and E. Michielssen, Electromagnetic Optimization by Genetic Algorithms, New York: John Wiley & Sons, 1999. [8] M.-I. Lai and S.-K. Jeng, “Compact microstrip dual-band bandpass filters design using genetic-algorithm techniques,” IEEE Trans. Microwave Theory Tech., vol. 54, no. 1, pp. 160-168, Jan. 2006. [9] J. A. Bossard, D. H. Werner, T. S. Mayer, J. A. Smith, Y. U. Tang, R. P. Drupp, and L. Li, “The design and fabrication of planar multiband metallodielectric frequency selective surfaces for infrared applications,” IEEE Trans. Antennas Propagat., vol. 54, no. 4, pp. 1265-1276, April 2006. [10] S. Kahng, “GA-optimized decoupling capacitors damping the rectangu- lar power-bus’ cavity-mode resonances, IEEE Microw. Wireless Compon. Lett., vol. 16, no. 6, pp. 375-377, June 2006.

×