Model for Shielded Suspended Substrate Microstrip Line

Transcription

1 Circuit Theory Laboratory Report Series CT-38 Model for Shielded Suspended Substrate Microstrip Line Anu Lehtovuori and Luis Costa Helsinki University of Technology Department of Electrical and Communications Engineering Circuit Theory Laboratory Espoo 1998

2 Distribution: Helsinki University of Technology Circuit Theory Laboratory PO Box 3000 FIN HUT Tel Fax ISBN ISSN Pika-Jäljennös Helsinki 1998

3 A Lehtovuori and L Costa, Model for Shielded Suspended Substrate Microstrip Line, Circuit Theory Laboratory Report Series, No CT-38, Espoo 1998, 12 pp, ISBN , ISSN Abstract An improved and extended model for a shielded suspended substrate microstrip line in APLAC is presented The differences in the various suspended substrate microstrip line model equations are investigated Keywords: Circuit simulation, suspended microstrip line, APLAC, transmission line

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5 Contents 1 Introduction 1 2 Model for shielded suspended substrate microstrip line 2 21 Suspended and inverted microstrip line in Msslin 2 22 Suspendedmicrostripline 4 23 Invertedmicrostripline 5 24 Symmetricshieldedsuspendedsubstratestripline 6 3 Comparison results 9 31 Impedanceofthesuspendedsubstratemicrostripline 9 32 Impedance of the shielded suspended substrate microstrip line 10 4 Conclusions 11 i

6 List of Figures 1 Suspendedsubstratemicrostripline 2 2 Invertedsuspendedsubstratemicrostripline 3 3 Suspendedsubstratemicrostripstructurewithsidewalls 7 List of Tables 1 Impedanceofthesuspendedsubstratemicrostripline 9 2 Impedanceoftheinvertedsubstratemicrostripline 10 3 Impedance of the shielded substrate microstrip line with symmetric sidewalls 10 4 Impedance of the shielded substrate microstrip line with asymmetric sidewalls 11 ii

7 1 Introduction The purpose of this work is to improve and extend the model for a shielded suspended substrate microstrip line (Sslin) implemented in APLAC, a circuit simulator, which has been developed in the Circuit Theory Laboratory After this, Msslin, the component model for the suspended substrate microstrip line as well as for the inverted microstrip line, will be redundant as its model equations are integrated into the Sslin component At the same time a comprehensive documentation on the shielded suspended substrate microstrip line is provided The shielded suspended substrate microstrip line has already been implemented in APLAC However, better models, more accurate equations and quicker computation is always sought and therefore some changes and improvements have been made and more alternative model equations are now in use The component MultiLayerStruct, which is based on the Master s Theses of Laamanen [3] and Rekonen [5], is always used in APLAC, if a side wall has been defined in Sslin, the structure is asymmetric or level 2 is specified The equations for a symmetric structure presented by Shu, Xiao-xia and Yun-ji [6] have been added, and are used in level 1 Computation is quicker using them than using MultiLayerStruct When side walls are not specified, level 0 uses equations by Pramanick and Bhartia [4], which have earlier been used in Msslin and are now added to Sslin New equations by Tomar and Bhartia [7], which are accurate over a wider range than the equations of Msslin, have also been added and they are used in level 1 Both levels 0 and 1 can be used for the inverted microstrip line as well Level 2 uses MultiLayerStruct for a structure with or without side walls 1

8 2 Model for shielded suspended substrate microstrip line Suspended and inverted microstrip lines are among the principal transmission media used in the upper microwave and lower millimeter-wave bands Most of the microstrip components, such as power dividers, transistor amplifiers, directional couplers, receiver mixers, and frequency multipliers are manufactured using suspended substrate lines Due to the symmetrical shielding, the suspended substrate line is particularly useful for integrated circuits with waveguide components, and the wide range of impedance values achievable makes these media particular suitable for filters In comparison with the microstrip, the suspended substrate line has many advantages The most interesting aspect is that the presence of an air gap between the substrate and the ground plane reduces the effects of dispersion on the propagation constant, generally to such an extent that the quasi-static results remain useful even at very high frequencies Structural inaccuracies are smaller due to the wider conductors, so also electrical properties are more precise Because more of the field is in the air, higher characteristic impedances Z L can be realized The disadvantages are difficulties in miniaturization, critical housing technology (because the housing also acts as an electrode), and the increased complexity of utilizing hybrid elements So, although suspended and inverted microstrip lines have many good properties, they are large and difficult to produce 21 Suspended and inverted microstrip line in Msslin The equations from [4], that were used by Msslin, are now in use in level 0, if a side wall is not defined By default, the structure of the suspended microstrip line is the one shown in Fig 1 and the structure of the inverted microstrip line the one in Fig 2 6 h u?6 w - h?6 ε r h l? Figure 1: Suspended substrate microstrip line 2

9 6 h u?6 h?6 h l? w - ε r Figure 2: Inverted suspended substrate microstrip line where Z 0 is given by Hammerstad and Jensen [1] as Z 0 =60ln f(u) u , (1) u 2 f(u) =6+(2π 6)e (30666/u)07528 (2) For the suspended microstrip u is defined as u = w, h + h l and for the inverted microstrip u = w h l (3) (4) For the suspended microstrip the effective dielectric constant ε eff is obtained from where ε eff = h 1 = h l1 = 1 [ ( )( 1+ h h1 h l h l1 ln w 1 h l εr 1 )] 2, (5) ( ln h ) 4, (6) h l ( ln h h l ) 4, (7) and for the inverted microstrip the effective dielectric constant is obtained from ε eff = [1+ hhl ( h1 h ) l1 ln whl ( 2 ε r 1)], (8) 3

10 where h 1 = h l1 = ( ln h ) 2, h l (9) ( ln h ) 2 h l (10) The accuracy of these equations is within ±1% for 1 <w/h l 8, 02 h/h l 1, and ε r 6 For ε r 10, the error is less than ±2% 22 Suspended microstrip line In addition to the above-mentioned equations now also equations from [7] canbe used for the suspended microstrip line, by specifying level 1 Results are then accurate over a wider range The effective dielectric constant of the suspended microstrip is given by ε eff = 1 (1 f 1 f 2 ) 2, (11) where f 1 =1 1 εr (12) and f 2 = 1 3 ( ) i (13) c w i h i=0 l The functions c i in (13) are given by c i = 3 j=0 ( ) j hl d ij (14) h Expressions for d s, when f =lnε r,are d 00 = ( f f f 3) 10 2, (15) d 01 = ( f f f 3) 10 4, (16) d 02 = ( f f f 3) 10 6, (17) d 03 = ( f f f 3) 10 8, (18) d 10 = ( f f f 3) 10 4, (19) d 11 = ( f f f 3) 10 4, (20) 4

11 d 12 = ( f f f 3) 10 6, (21) d 13 = ( f f f 3) 10 8, (22) d 20 = ( f f f 3) 10 5, (23) d 21 = ( f f f 3) 10 5, (24) d 22 = ( f f f 3) 10 7, (25) d 23 = ( f f f 3) 10 8, (26) d 30 = ( f f f 3) 10 6, (27) d 31 = ( f f f 3) 10 6, (28) d 32 = ( f f f 3) 10 8, (29) d 33 = ( f f f 3) 10 9 (30) Once ε eff is known, the impedance Z can be computed using the well-known equation Z = Z 0 εeff, (31) where Z 0, the impedance of an identical air-filled line, is again defined as Z 0 =60ln f(u) u , (32) u 2 with f(u) =6+(2π 6)e (30666/u)07528 (33) and u = w h l 1+ h h l (34) Over the range 05 w/h l 10, 005 h/h l 15, and ε r 20 the accuracy of these model equations (in reproducting the exact theoretical data) is generally better than 06 percent 23 Inverted microstrip line These equations are used for inverted microstrip without side walls when the level is 1 The equations are from [7] and the structure has been shown in Fig 2 The effective dielectric constant is written as ε eff =(1+f 1 f 2 ) 2, (35) 5

12 where f 1 = ε r 1 (36) and f 2 is given by equations (13)and(14) Expressions for d s, when again f =lnε r, are d 00 = ( f 57706f f 3) 10 3, (37) d 01 = ( f f f 3) 10 5, (38) d 02 = ( f f f 3) 10 5, (39) d 03 = ( f f f 3) 10 6, (40) d 10 = ( f f f 3) 10 3, (41) d 11 = ( f f f 3) 10 3, (42) d 12 = ( f f f 3) 10 5, (43) d 13 = ( f f f 3) 10 6, (44) d 20 = ( f f f 3) 10 5, (45) d 21 = ( f f f 3) 10 5, (46) d 22 = ( f f f 3) 10 6, (47) d 23 = ( f f f 3) 10 7, (48) d 30 = ( f f f 3) 10 6, (49) d 31 = ( f f f 3) 10 6, (50) d 32 = ( f f f 3) 10 7, (51) d 33 = ( f f f 3) 10 9 (52) Once ε eff is known, Z is obtained from equations (31) -(33) in the same way as in the case of the suspended microstrip line, but using u = w/b The stated error of the fit to the exact theoretical calculations is less than 06% for 1 ε r 20, 05 w/h l 10, and 006 h/h l Symmetric shielded suspended substrate stripline The structure of the suspended substrate microstrip line with side walls is presented in Fig 3 These equations from [6] are used in level 1, when the structure is symmetric The equations are divided into two ranges For narrow strips (0 <w<a/2) Z 0 = η 0 2π V + R ln 6 w/b (w/b) 2, (53) 6

13 s l - a s r h u?6 w -?t6 b h?6 ε r? h l? Figure 3: Suspended substrate microstrip structure with side walls ε eff = 1 [ 1+ ( E F ln w b ) ln ( 1 εr )] 2, (54) where V = h b a b, (55) R = h b a b, (56) E = h b a b, (57) F = h b a b (58) For wide strips (a/2 <w<a) Z 0 = η 0 V + R w w b b +1444) (59) and where ε eff = 1 [ 1+ ( E F ln w b ) ln ( 1 εr )] 2, (60) V = h b +0247a b, (61) R = h b 05123a b, (62) E = h b 02063a b, (63) F = h b a b (64) 7

14 The above relations are valid for 10 a/b 25, 10 ε r 4, and 01 h/b 05 The results of the wide strip equations agree with those obtained using finitedifferential techniques to ±3%, the narrow strip agreement is ±2% 8

15 3 Comparison results The differences in the various suspended substrate microstrip line model equations implemented in APLAC are investigated here APLAC s testfile is as follows: Model substrate ER=9 H=06mm RHO=07 TAND=01 LEVEL=2 Sssub Ssubl MODEL substrate HU=12mm HL=12mm Sslin S1 1 2 W=08mm L=30mm L_SIDE=15mm R_SIDE=15mm Print PUBLICS LF 31 Impedance of the suspended substrate microstrip line Table 1 shows differences in impedances of the suspended substrate microstrip line for levels 0, 1, and 2 The error has been calculated in comparison with the result of level 2, which is based on MultiLayerStruct, whose accuracy is better than 05 % The results of those simulations that produced an APLAC warning regarding inaccuracy are marked with an asterisk ( ) Physical lengths in the table are in millimeters Table 1: Impedance of the suspended substrate microstrip line LEV EL ERROR% Z ε r H HU HL W L Level 2 does not recognize the inverted microstrip line, so in Table 2 the results are only for levels 0 and 1 Lengths are again in millimeters as in all the tables here 9

16 Table 2: Impedance of the inverted substrate microstrip line LEV EL Z ε r H HU HL W L Impedance of the shielded suspended substrate microstrip line Table 3 gives the calculated impedance of the shielded substrate microstrip line with symmetric side walls Here both levels 0 and 2 use MultiLayerStruct The error has, again, been calculated with respect to level 2, whose accuracy is better than 05 % in the symmetrical case Table 3: Impedance of the shielded substrate microstrip line with symmetric side walls LEV EL ERROR% Z εr H HU HL W SIDES L In the asymmetric case MultiLayerStruct is used for all levels The calculated impedances are in Table 4 10

17 Table 4: Impedance of the shielded substrate microstrip line with asymmetric side walls LEV EL Z εr H HU HL W L SIDE R SIDE L Conclusions New model equations for shielded suspended substrate microstrip line have now been implemented in APLAC They make possible quicker computations and especially with bigger ε r added equations give more accurate results 11

18 References [1] E Hammerstad, O Jensen, Accurate Models for Microstrip Computer-Aided Design, IEEE MTT-S Symposium Digest, pp , June 1980 [2] R Hoffmann, Handbook of Microwave Integrated Circuits, Artech House, Norwood, MA 02062, 1987 [3] H Laamanen, Numerical Models of Microstrip Structures, Master s Thesis, Helsinki University of Technology, Faculty of Electrical Engineering, 1980 (in Finnish) [4] P Pramanick, P Bhartia, CAD Models for Millimeter-wave Finlines and Suspended-Substrate Microstrip Lines, IEEE Transactions on Microwave Theory and Techniques, Vol MTT-33, Dec 1985, pp [5] H Rekonen, High Frequency Simulation of Printed Circuit Boards, Master s Thesis, Helsinki University of Technology, Faculty of Electrical Engineering, 1991 [6] Shu, Yong-hui, Xiao-xia Qi and Yun-ji Wang, Analysis Equation for Shielded Suspended Substrate Microstrip Line and Broadside-Coupled Stripline, IEEE MTT-S International Microwave Symposium Digest, 1987, pp [7] Tomar, Bhartia, New Quasi-Static Models for the Computer-Aided Design of Suspended and Inverted Microstrip Lines, IEEE Transactions on Microwave Theory and Techniques, Vol MTT-35, No 4, April 1987, pp , and corrections No 11, November 1987, p