Optimization of Monopole Four-Square Array Antenna Using a Decoupling Network and a Neural Network to Model Ground Plane Effects

Transcription

1 Optimizatin f Mnple Fur-Square Array Antenna Using a ecupling Netwrk and a Neural Netwrk t Mdel Grund Plane Effects Pedram azdanbakhsh, Klaus Slbach University uisburg-essen, Hchfrequenztechnik, Bismarckstr.8, -708, uisburg, Germany pedram.yazdanbakhsh@uni-due.de Abstract - n this paper we prpse a methd t design the decupling and matching netwrk fr the mnple fur- square array antenna n a finite grund plane. t has been fund that the mutual cupling f the antenna elements placed n a finite grund plane (chassis depends strngly n the dimensins f the chassis. T mdel the chassis effects, in the secnd step, we designed an Artificial Neural Netwrk (ANN which allwed us t ptimize the chassis size that leads t an even better result fr the prpsed decupling netwrk. n this way the ptimizatin prblem fr this array antenna is intrduced using the methd f genetic algrithms.. NTROUCTON n the previus paper [], the ptimizatin prblem fr a Mnple Fur-Square Array Antenna has been defined and ptimizatin was perfrmed using the methd f Genetic Algrithm (GA []. Under the assumptin that the antennas were munted n an infinite grund plane we bserved that the mutual cupling between the antennas distrted the beam patterns and reduced the radiatin efficiency. n this paper we prpse a methd t design a decupling netwrk fr the Mnple Fur-Square Array Antenna n a finite grund plane size. As shwn in [], the grund plane can heavily influence the mutual cupling f the antenna elements placed n it, in principle due t the excitatin f current mdes n its surface which can resnate at certain length and width dimensins. ntrducing a cst-functin, an ptimizatin prblem has been defined t find the minimum cupling between the antennas. n this paper we have taken the next step. Then t imprve the decupling results, additinal lumped elements (Capacitrs/ nductrs have been cnsidered between adjacent and ppsite antennas. The ptimal value f each capacitr/inductr as well as the length and diameter f each mnple antenna, array distance and grund plane dimensins have been fund after ptimizing a cst functin, based n just the maximum decupling criterin. The next, mre sphisticated step emplys seven criteria; maximum decupling, minimum envelpe crrelatin f beams, maximum frnt-t-back rati, best fit t the ideal secant-squared elevatin pattern, suitable beam crssver levels between dbi and 6 dbi, maximum directivity and maximum efficiency f each antenna. Fr this ptimizatin prblem, we cnsider fur realistic mnple antennas f variable length, diameter and array distance n a finite grund plane with variable dimensins. Six variable capacitrs /inductrs have been als used between neighburing and ppsite antenna prts t accmplish the RF decupling netwrk. The current and vltage excitatins f the mnple antennas are related via the admittance matrix, where the surce pen-circuit vltages f the feed netwrk can be als varied ver a certain range. n this step a high accuracy hierarchical neural netwrk structure [] has been designed t mdel the grund plane effects and utilize this mdel in ur cst functin. The inputs t ur neural netwrk mdel cnsist f: Antenna length, Antenna diameter, Array distance, Chassis length, Chassis height, neighburing capacitance/ inductance and ppsite capacitance/ inductance and the utputs cnsist f the admittance matrix elements f the array with lumped elements munted n the finite chassis. Finally the ptimized values f neural netwrk inputs as well as the surce vltages have been fund using a GA in ur full degree ptimizatin.. COUPLNG EFFECTS OPTMATON The Mnple Fur-Square Array Antenna munted n an infinite grund plane is depicted in Fig.. The frequency dependent impedance matrix characterises the mutual cupling between the elements f array, and accrding t V V V V = relates the prt-vltages V n t the driving prt currents n. ij is the mutual impedance between elements i, j and jj is the self impedance f element j. Sme relatinships can be used [5] t give the self impedance as a functin f the length and diameter f each antenna and mutual impedance as a functin f the antenna length and element spacing f array. The reductin f the grund plane has tw majr detrimental effects. The first is an increase in back lbe radiatin due t diffractin and the secnd is a change in the impedance f the antenna, which will increase the return lss. (

2 B. ecupling and Matching Netwrk n the secnd part we have cnnected six lumped capacitrs/inductrs between adjacent antenna prts t accmplish the RF decupling and matching netwrk (MN as shwn in Fig.. Passive MN cmpensate fr the prblem f mutual cupling between the radiatrs. The decupling netwrk cnsists f the cmpnents jb (Capacitance C r inductance L between neighburing antennas and jb (Capacitance C r inductance L between ppsite antennas. Aviding the crssing f tw transmissin lines between ppsite antennas, a crss-cupler, als knwn as 0 db cupler, has been assumed between the antenna prts [6]. Fig. Fur-square array fr multi-beam applicatins Furthermre, in an investigatin f radiatin prperties f a small phased array antenna n a chassis it was fund that radiatin pattern, radiatin resistance f the elements and the mutual cupling f the elements depend strngly n the dimensins f the grund plane []. A. Optimize the parameters f each antenna, array and chassis size T reduce the cuplings between the antennas, in the first step we have cnsidered fur mnple antennas with element spacing (d, length f ( and diameter f ( munted n a small grund plane size with dimensins f (X (X (H, as shwn in Fig.. Using CST ptimizatin tlbx, the variables d, L,, X and H have been ptimized t find the minimum values f mutual impedances (real and imaginary parts separately: d, L,, X, H ( W ( J ( = W + ( Fig. Fur-mnple array antenna n a finite grund plane The fllwing cnditins have been cnsidered in ur ptimizatin prblem: 0.5 d λ 0.50 (Crridr in the first step [] ( 0.50 L λ 0.50 ( 0.00 λ 0.0 ( H / λ 0.05 (6 0. X / λ. (7 Fig. RF- decupling netwrk using a crss-cupler nitially ignring transmissin line effects, the fllwing admittance matrix describes the MN: jb+ jb jb jb jb jb jb + jb jb jb = + (8 jb jb jb jb jb jb jb jb jb+ jb The admittance matrix f the decupled array can be als written as: = f we cnsider the netwrk shwn in Fig. n an infinite grund plane, then the admittance matrix (9 can be written as: = = + (9 (0 Fr decupling the array, the mutual admittance f the decupled system ( and shuld be zer. Slutins fr

3 B and B can be btained by minimizing the fllwing cst functin (real and imaginary parts: ( B, B ( W ( J = W + ( n ur sphisticated case, we have cnsidered a finite chassis and the decupling admittance matrix (9. Fur mnple antennas with element spacing (d, length f ( and diameter f ( and six capacitrs (with capacitance C /C / nductrs (with inductance L /L munted n a small grund plane with dimensins f (X (X (H, have been cnsidered in ur ptimizatin prblem, as shwn in Fig.. Using CST ptimizatin tlbx, the variables d, L,, X, H, C n and L m have been ptimized t minimize the fllwing cst functin: [ Cst( C, L, Cst( C, L, Cst( C, L, Cst( C L ] J = ( min, where: Cst Cn Lm = (, Wlk ( lk l k ( l= k= lk is the real and imaginary part f the mutual admittances f decupling admittance (9. being explited []. Based n this cncept, a hierarchical neural netwrk apprach was develped, using existing micrwave infrmatin / knwledge in the frmulatin f submdules (netwrks and in defining the interactins between mdules. The applied hierarchical neural netwrk structure fr the Fur-mnple array antenna n a finite grund plane with lumped elements (Fig. is shwn in Fig.5. We have chsen 0 lw-level neural mdules L, 0 knwledge hubs Ui and Multilayer Perceptrn (MLP fr high-level neural mdule H. Seven variables: Antenna length L, Antenna diameter, Array distance d, Chassis length X, Chassis height H, neighburing capacitance/ inductance C /L and ppsite capacitance/ inductance C /L have been cnsidered as the input vectr X t ur mdel and the utput vectr cnsists f 0 variables: Self admittances (,, and and mutual admittances (,,,, and f the cmplete array (real and imaginary: = f ( L,, d, X, H, C / L, C / L = (6 Based n results calculated using the CST simulatr, we have recrded 50 samples, 5 data fr training the mdel and 5 data fr testing the accuracy f mdel. i Fig. Fur-mnple array antenna n a finite grund plane with lumped elements between them The fllwing cnditins have been cnsidered in ur ptimizatin prcedure: pf Cn 0 pf ( nh Lij 0nH (5. FULL EGREE OPTMATON n this step we have designed a neural netwrk t mdel the system shwn in Fig. and utilized it in ur Full degree ptimizatin prblem. A. Hierarchical Neural Netwrk mdel n the neural netwrk research cmmunity, an advanced cncept called Cmbining Neural Netwrks that addresses issues f neural netwrk accuracy and training efficiency is Fig.5 The hierarchical neural netwrk structure B. Optimizatin Prblem Finally we have implemented this neural netwrk mdel in ur ultimate ptimizatin prblem. n this step we cnsider the system shwn in Fig. f variable Antenna length L, Antenna diameter, Array distance d, Chassis length X, Chassis height H, neighburing capacitance/ inductance C /L and ppsite capacitance/ inductance C /L. n this step we assumed that the surce impedance f the feed netwrk 0 is fixed t 50 Ω but the surce vltages V i (i=,, can be varied ver the certain range (8 and (9 []: = 50Ω (7

4 0.5 V 0.5 V 0.5 V 0.5 V 0 V 70 V 60 V 70 V (8 (9 The excitatins i (i=,, at the input terminals f each antenna can be expressed as a functin f 0, V i (i=,, and admittance matrix (6. The fllwing cst functin has been cnsidered in ur final ptimizatin prblem: ( W F + WF + WF + WF J = (0 ε + ( W5F5 + W6F6 + W7F7 (Nte that return lsses have nt been cnsidered in ur cst functin TABLE OPTMATON RESULTS FOR THE ARRA WTHOUT ECOUPLNG NETWORK OBTANE B GA p p p p p d L H X 0.8λ 0.0λ 0.006λ 0.0λ 0.5λ TABLE OPTMATON RESULTS FOR THE ARRA WTH ECOUPLNG NETWORK OBTANE B CST OPTMER p p p p p d L H X 0.λ 0.λ 0.009λ 0.0λ 0.6λ p p C L. pf.0nh where F i are the seven criteria expressed as belw: F ( i, d, : Minimum envelpe crrelatin f beams [] L F ( i, d, : Best fit t the ideal secant- squared elevatin pattern [] F ( i, d, : Suitable beam crssver level (between dbi and 6dBi [] F ( i, d, : Minimum mutual cupling, expressed in (6 F5 ( Vi,, : Maximum efficiency f each antenna [] F6 ( i, d, : Maximum directivity [] F7 ( i, d, : Maximum Frnt-t-Back rati [] Equatins (, (5, (6, (7, (, (5, (7, (8 and (9 are cnsidered fr ur ptimizatin cnditins. (a (c (b (d V. OPTMATON RESULTS A. Cupling effects ptimizatin The Cst functin ( with cnditins (, (, (5, (6 and (7 has been minimized using a GA with generatin f 5 individuals each, PCrssver = and P Mutain = Table shws the ptimizatin results fr the array withut cnsidering the decupling-matching netwrk. Using the CST ptimizatin tlbx, the Cst functin ( with cnditins (, (, (5, (6, (7, ( and (5 has been als minimized. Table shws the ptimizatin results fr the array with decupling-matching netwrk. The simulatin results f the scattering parameters f the array n a finite grund plane with and withut the decupling-matching netwrk are shwn in Fig. 6. The chsen frequency f peratin f the array is at GHz. The magnitude f S f each antenna withut the decupling netwrk is apprximately - db at the perating frequency. With the decupling netwrk, return lsses are reduced t -7 db fr S and -8 db fr S, S and S. (e (g (h Fig.6 Simulatin results f (a S, (b S and (c S withut the decupling-matching netwrk and (d S, (e S = S = S, (f S = S, (g S = S and (h S = S with decupling netwrk The magnitude f S and S f the array withut decupling netwrk are apprximately - db and -8 db respectively. With decupling netwrk the magnitudes f S, S, S, S, S and S are less than -0 db. These results shw that t remve the effect f mutual cupling cmpletely, we have t use an ptimized MN. B. Full degree ptimizatin The variatin f Average Testing Errr fr 5 testing data during the training prcess (with 5 samples f the (f

5 designed hierarchical neural netwrk mdel is shwn in Fig. 7. As training data becme mre than 06, the errr remains apprximately at 0.5%. This lw average errr n test data shws the accuracy f this mdel. 7 As an experimental example, the radiatin pattern f a squared array f fur mnple antennas which are munted n a large grund plane size is shwn in Fig. 9. [] We can see an imprvement in the side lbe level and frntt-back rati in ptimized radiatin pattern. 6 Average Testing Errr (% Number f training samples Fig.7 Hierarchical neural netwrk mdel accuracy Fr the purpse f ptimizing the cst functin described in (0 with cnditins (, (5, (6, (7, (, (5, (7, (8 and (9 a genetic Algrithm with generatins f 5 individuals each, PCrssver = and P Mutain = 0. 0 was used. Table shws the full degree ptimizatin results. TABLE FULL EGREE OPTMATON RESULTS p p p p p d L H X 0.8λ 0.0λ 0.006λ 0.08λ 0.5λ p p C L V V V.8 pf.7nh... 0 V V V V V The radiatin pattern (x-y planeθ = 90 f the mnple fur-square array antenna, crrespnding t the value f ptimized parameters in Table, is shwn in Fig. 8. The Radiatin efficiency f 0.98 has been fund fr each antenna. The return lsses f antennas are between -5 db and -5 db and the ther S- s which are less than - db shw the decupling f the array. Fig.8 Radiatin pattern f the array Fig.9 Experimental nn ptimized radiatin pattern n a large grund plane C. Cnclusins This paper has shwn that the mutual cupling f fursquare mnple antenna n a finite grund plane can be remved by the use f an ptimum decupling netwrk. The simulatin results cnfirmed that the array was matched and decupled. n a next step an artificial neural netwrk (ANN has been develped and tested fr Mnple Fur-Square Array Antenna design. t transfrms the data cntaining the Antenna length, Antenna diameter, Array distance, Chassis length, Chassis height, neighburing decupling capacitance/ inductance and ppsite decupling capacitance/ t the admittance matrix f the array munted n a finite grund plane cnsidering the decupling netwrk. The neural mdel presented in this wrk gives accurate results and requires n tremendus cmputatinal effrts. Finally this mdel has been utilized in full degree ptimizatin prblem fr a Mnple Fur square array antenna n a finite grund plane with decupling netwrk and applying additinal perfrmance requirements. The technique uses the genetic algrithm t determine the ptimal parameters. This apprach has als the advantage f escaping the lcal slutins; it tends t prduce glbal ptimal results withut requiring a great deal f infrmatin abut the slutin dmain. REFERENCES [] P. azdanbakhsh, K. Slbach, Perfrmance Optimizatin f Mnple Fur- Square Array Antenna using the methd f Genetic Algrithm, EUCAP 007, Edinburgh. [].E. Gldberg, Genetic Algrithms in Search, Optimizatin, and Machine Learning, Addisn-Wesley, Publishing Cmpany, nc. 989 [] K. Slbach, C.T. Famide, Mutual Cupling and Chassis-Mde Cupling in Small Phased Array n Small Grund Plane. EUCAP 007, Edinburgh. [] Q.J. hang, K.C. Gupta Neural Netwrks fr RF and Micrwave esign, Artech Huse, nc, 000 [5] C.A. Balanis, Antenna Thery: Analysis and esign, Third Editin, Jhn Wiley and Sns, 005. [6] J.S Nern, G. elisle, Micrstrip EHF Butler Matrix esign and Realizatin ETR Jurnal, Vl: 7, Nr: 6, ecember