:.4GHz ISM Design of.4 GHz Planar Filters for ISM Band : : 86059 :
Series IV Sonnet FR 4
Abstract By means of the Step Impedance Resonator and Two Step Impedance Filters architecture, two central frequency with.4 GHz, higher and lower than the passband which finally has two transmission zero poles Step Impedance Flat Filter could be carried out, as I describe in this dissertation. This thesis includes two points, one for circuit designation, and the other is experiments. According to the structure of filter, the input admittance matrix of the filter is obtained with the advantage of network analyses and linear algebraic techniques. The matrix enables us to establish an equivalent circuit model of a step impedance filter. Based on the filter theory, the types of the capacitor and inductor coupling are calculated to derive a prototype bandpass filter. Finally, making the equivalent circuits and filter prototypes matched, six step impedance filters could be designed, and simulated each filter with Series IV and Sonnet program for their frequency response. As concerns about the experiments, a microstrip step impedance filter with couple lines is made on an FR4 double-sided circuit board. The frequency response of the filter is measured. Regardless of the possible experimental errors, the measurement approximately has the same result as the simulation. This experiment provided the equivalent circuit model of a step impedance filter and filter design procedures are correctly in proposed. 3
4
...3 4 5...7 0......3 5.4 5 7. 7. 0.3 S domain.. 7...34 3. 34 5
3...34 3.3..38..84 4....... 84 4..84 4.3.88 4.4 Type A.90 4.5 Type D.95.99 00 6
- 4 - (a).9 (b) 9-0 -3 One port...3-4 π....4-5 S domain..5-6 Low pass to band pass transformation...8-7 S domain 9 (a) 9 (b) 9-8 open stub short stub.30-9 3 (a).3 (b) 3 3-36 3-37 3-3 Type A..43 3-4 Type A..46 7
3-5 Type A Strip line.. 48 3-6 Type A..50 3-7 (a) Type A Microstrip line...5 (b) Type A 5 3-8 Type A Sonnet..54 3-9 Sonnet Type A.55 3-0 Type B.59 3- Type B.60 3- Type C.6 3-3 Type C.64 3-4 Type C Strip line.65 3-5 Type D.7 3-6 Type D.73 3-7.74 3-8 Sonnet Type D 75 3-9 Type E II..79 3-0 Type E..79 3- Type F..8 3- Type F strip line..83 4- (a) Type A.86 (b) Type D...86 8
4- TRL 89 4-3...90 4-4 Type A...9 4-5 Type A (a) S (b) S..93 4-6 Type A (a) S (b) S..94 4-7 Type D..95 4-8 Type D (a) S (b) S..97 4-9 Type D (a) S (b) S..98 9
-...3-7 - 3 3-39 3- Type A..4 3-3 Type A even mode odd mode...47 3-4 Type A Strip line.. 47 3-5 Type A...50 3-6 Type A...5 3-7 Type B...58 3-8 Type B even mode odd mode..6 3-9 (a) Type C.. 63 3-9 (b) Type C even mode odd mode....63 3-9 (c) Type C Strip line..... 65 3-9 (d) Type C Microstrip line...66 3-0 (a) Type D..70 3-0 (b) Type D even mode odd mode...70 3-0 (c) Type D Strip line.70 3-0 (d) Type D Microstrip line..7 0
3- Type E.78 3- Type E even mode odd mode..78 3-3 (a) Type F even mode odd mode..8 3-3 (b) Type F Strip line..8 4- (a) Type A Sonnet.....87 4- (b) Type D Sonnet.....88
- Wireless LAN Personal communication system Mobil satellite communication system Radio frequency, RF IC [ ] - (-) [3] 90 Zobel
Image parameter method [4 5] 950 Darlington Insertion loss method [6 7] passband stopband Dielectric resonator, DR [8 9] DR RF - IC DR Multi-layer ceramic, MLC [0 ] Step impedance resonator, SIR [-5] 3
: Receiver Image frequency Transmission zero (-) (Microstrip Line) Step impedance planar filter - 50Ω 50Ω 4
-3 Y-Matrix Lump element Prototype Series IV Sonnet -4 5
[6,7] 6
- (stepped impedance resonators)[] 979 M. Maktmoto S. Yamashita insertion loss spurious response -(a) Z Z l l l l +l Impedance ratio K Z K = tan βl tan β l (-) Z -(a) (-) open stub resonator β = β = β = phase constant (-) tanθ (tanθ T K = (-3) + tanθ T tanθ tanθ ) where θ i 7
θ T = θ + θ (-4) θ = θ = tan K θ T -(b) θ θ K T 8
Inner conductor Z Z l l Outer conductor l -(a) θ T =θ +θ Z Z K=Z /Z θ θ 50 0.0 6.0 0 4.0 θ T 90 0.6.0.0 60 0.4 0. 30 K=0. 0 30 60 90 θ -(b) 9
- - a a l Yup b l 50Ω 50Ω Ydown c l d l - - TEM Transverse Electromagnetic Wave 0
[] Step - [Y up ] [Y down ] a b c d l 50Ω : a b { } [ Y ] [ Y ] a b [ ] = S [ I ] + S [ Y ][ Y ] up ( ) Y + (-5) d c { } [ Y ] [ Y ] d c [ ] = S [ I ] + S [ Y ][ Y ] down ( ) Y + (-6) [ Y ] = [ Y ] + [ Y ] total up down a b { } [ Y ] [ Y ] d c d c { I + S Y Y } [ Y ] [ Y ] a b = [ I ] + S [ Y ][ Y ] ( ) S + + [ ] [ ][ ] ( ) S + (-7) S = j tan( βl) l [Y a ] [Y b ] [Y c ] [Y d ] a b c d characteristic Y-Matrix Step
(-7) [ ] [ ] [ ] down up total Y Y Y + = = ( ) ( ) [ ] ( ) ( ) [ ] O S S S S O S S S S c d c d b a b a c d c d b a b a + + + + + + + + + + + λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ (- 8) od d ed d oc c ec c ob b eb b oa a ea a Y Y Y Y Y Y Y Y = = = = = = = = λ λ λ λ λ λ λ λ (-9) [ ] = O (-0) [ ] = O (-) Step 3 (a). one port -3 ( ) ( ) ( ) ( )... t Y t Y t Y t Y 3 + + + =, t=jω -
- Y n K K = t t o i ( t) + K t +... i= t + + ωi -3 K o L o L o t Lo = H -4 Ko K t C C C = K F -5 t K t i + ω i Ki C i = F, L H i = -6 ω K i Y (t) Y (t) Y 3 (t) i Y(t) -3 One port 3
4 (b). [Y total ] -8 π -4 [Y total ] [ ] = Y Y Y Y Y total -7 Y =Y Y =Y ( ) ( ) ( ) S Y, S Y S Y + ( ) ( ) ( ) ( ) ( ) + + + + + + + + + + + = c d c d b a b a c d c d b a b a S S S S S S S S S Y λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ (-8) ( ) ( ) ( ) ( ) + + + + + = + c d c d b a b a S S S S S Y S Y λ λ λ λ λ λ λ λ -9-4 π -Y Y +Y Y +Y
Step 3 (a) (-8) (-9) : SC SC SC SC + S LC + S LC + S L3C3 + S L4C 3 4 Y ( S ) = + + + (-0) 4 SC SC + S L5C5 + S L6C 5 6 Y ( S) + Y ( S) = + (-) 6 (-9) (-8) (-9) (-0) (-) S domain -5 L C L 3 C 3 L C L 4 C 4 L 5 L 6 L 5 L 6 C5 C6 C5 C6-5 S domain 5
Y Y L + Y + Y ea eb =, C = ( Yea Y ) - ( ) eb ea eb Y Y L + ed ec =, C = ( Y ) ed Y -3 ( Y + Y ) ec ed ec Y Y L + oa ob =, C3 = ( Yoa Y ) -4 ( Y + Y ) 3 ob oa ob Y Y L + od oc =, C4 = ( Yod Y ) -5 ( Y + Y ) 4 oc od oc Y Y L + ea eb =, C5 = ( Yea Y ) -6 ( Y + Y ) 5 eb ea eb Y Y L + ed ec =, C6 = ( Yed Y ) (-7) ( Y + Y ) 6 ec ed ec (-) (-7) L,,,,, -3 L,, 4, 4, 6, 6 short stub open stub 6
-3 S domain - Chebyshev N f O.445GHz 83MHz passband f BL f BH.4GHz.483GHz passband ripple 0.dB passband VSWR.36 83 MHz - Normalized Chebyshev lowpass prototype -6 Normalized Chebyshev lowpass prototype 7
g i Li Ci g j L j C j -6 Lowpass to bandpass transformation J inverter K inverter J inverter J inverter S domain -7 a b -7 a J inverter -7 b J inverter -7 frequency domain open stub short stub -8 a b 8
J C L PC C PC L PC C PC (a) J L L PL C PL L PL C PL (b) -7 S domain 9
ZC ZLPC ZC PC ZLPC ZC PC (a) ZL ZL PL ZCPL ZL PL ZC PL (b) -8 open stub short stub 30
-8 open stub short stub - - -8 Series IV -9-9 a b -8 a b S S GHz insertion loss return loss db - : 3
S IL,RL (db) S (a) -9 3
IL,RL (db) S S (b) -9 33
3-3- 3-3 3-3- frequency domain Type A Type F Type A Type C J inverter Type D Type F J inverter 3-3- a b 3- I L 5 C 5 L 6 C 6 I UP I DN I UP -3 I DN 34
II L C L 3 C 3 L C L 4 C 4 II UP II DN II UP -3 II DN 3- a I L PC C PC II C 3- b I L PL C PL II L frequency domain passband 3-3-(a),(b) I passband II 35
L C L 3 C 3 II UP L C L4 II DN C4 L 5 L 6 II L 5 L 6 C 5 C 6 C 5 C 6 I UP I DN I I UP I DN 3-36
C I L PC C PC II L PC C PC (a) L I L PL C PL II L PL C PL (b) 3-37
3-3 Step 3-3- 3- Series IV Step Step (-) (-7) even mode odd mode Step 3 Step even mode odd mode Series IV (S,S ) Step even mode odd mode Step 4 (Z e >Z o ) Step even mode odd mode 38
Strip Line Microstrip Line (W) (S) (L) (3-) : 3- Step 5 Step 4 (W) (S) (L) Series IV Step Coupled microstrip (W) (S) (L) Quasi-TEM even mode odd mode Coupled microstrip Step 6 Step 5 (W) (S) (L) 39
Series IV (W) (S) (L) Sonnet Type A Type F Type A Type C Type D Type F : Type A Type B Type C Type D Type E Type F II f <f 3 f >f3 f >f 3 f <f 3 f >f 3 f >f 3 f >f 4 f <f4 f <f 4 f >f 4 f <f 4 f <f 4 f L C L 5 C 5 f L C L 6 C 6 f 3 L 3 C 3 f 4 L 4 C 4 40
3-3. Type A Type A 3- I ZL 5 ZC 5 ZL 6 ZC 6 II ZL ZC ZL ZC ZL 3 ZC 3 ZL 4 ZC 4 3-(a) Type A I I 3-3 a I passband C PC L PC f P =.5GHz f O =.445GHz Type A L 5 C 5 f=f P L 5 C 5 f =.09GHz f O L 6 C 6 f=f P L 6 C 6 f =3.08GHz f O L 5 C 5 L 6 C 6 f=f P Type A II II 3-3 b Type A L =-L 5 C =(-/)C 5 3-3(a) f L =-L 6 C =(-/)C 6 3-3(a) f even mode L 3 C 3 f 3 =.GHz L 4 C 4 f 4 =.85GHz odd mode f 3 >f II up passband II passband Type A L 4 C 4 f 4 f II DN passband II DN passband 4
( ) II UP passband ( ) Type A II II passband ( ) II UP II DN Type A II passband f 3 f LA =.0 GHz f f LB =.7 GHz f LA L 3 C 3 L C Type A passband f LA f LB Type A 3- I II 3-4(a) Series IV 3-4(b) ZL ZC ZL ZC ZL 3 ZC 3 ZL 4 ZC 4 ZL 5 ZC 5 ZL 6 ZC 6 Type A Filter -04-4 -50-30 94 5 5 5 5 5 3- Type A 4
Type A I Prototype I Im[Y] Type A f 0 =.44GHz Prototype f=.09ghz fp=.5ghz f=3.08ghz 3-3(a) Type A I 43
Type A II Prototype II Im[Y] Prototype Type A f f 3 f 0 f 4 f fla=.0ghz flb=.7ghz 3-3(b) Type A II 44
3-4 Type A S S insertion loss return loss db 3-4 Type A low side f LA =.03GHz f LB =.7GHz Type A Rx insertion loss rejection Type A 3- Type A (-) (-7) Type A a b c d even mode odd mode even mode odd mode Z ea Z oa Z eb Z ob Z ec Z oc Z ed Z od 3-3 Series IV Linecalc Strip line Type A 3-4 3-4 Series IV Type A 3-5 insertion loss return loss 3-4 stripline 45
Type A IL,RL (db) S S f LA =.0GHz f LB =.7GHz 3-4 Type A 46
3-3 Type A even mode odd mode 3-4 Type A Strip line 47
Type A Strip line IL,RL (db) S S 3-5 Type A Strip line 48
strip line FR 4 Microstrip line Type A 3-3 Type A even mode odd mode Linecalc Type A 3-5 Series IV Type A 3-6 insertion loss return loss type A f LA f LB S S -0dB Quasi-TEM even mode odd mode 3-5 passband Type A a b c d b c 3-6 Type A 3-7(a) Type A 3-7(a) even mode odd mode 3-7(a) Series IV 3-7(b) 3-7(b) 49
IL,RL (db) S S 3-6 Type A 50
3-7(a) Type A Microstrip line 5
IL,RL (db) S S Ideal 3-7(b) Type A 5
3-6 Sonnet Type A Sonnet 3-8 800mil 900mil S S 3-9 (a) insertion loss return loss Type A.445GHz 00MHz VSWR.38 -.445GHz 83MHz VSWR.36 Series IV f LA 0MHz 3-9(a) Type A S S Conductor loss Dielectric loss 3-9(b) type A S S.4GHz loss 3dB.445GHz loss 0.9dB.5GHz loss.6db 3-9 c type A S S.4GHz loss 6.dB.445GHz loss 3.8dB.5GHz loss 5dB 3-9 d type A S S.4GHz loss 8dB.445GHz loss 4.6dB.5GHz loss 5.8dB 3-9 a 3-9 d 70% 30% passband loss group delay passband loss group delay 53
800mil 900mil 3-8 54
IL,RL (db) S SeriesIV S Sonnet (a) IL,RL (db) S S (b) 3-9 Sonnet Type A 55
IL,RL (db) S S (c) IL,RL (db) S S (d) 3-9 Sonnet Type A 56
3-3. Type B Type B Type B I I 3-3. Type A I 3-0 a Type B I I Type B II II 3-0 b Type B L =-L 5 C =(-/)C 5 3-0(a) f L =-L 6 C =(-/)C 6 3-0(a) f even mode L 3 C 3 f 3 L 4 C 4 f 4 odd mode f 3 <f II UP passband II passband f o Type B L 4 C 4 f 4 f II DN passband II DN passband ( ) passband ( ) Type B II II passband ( ) II UP II DN Type B II passband f f H f 3 f L f L L C L 3 C 3 II UP 57
Type B passband f L f H Type B 3-7 I II Series IV 3- ZL ZC ZL ZC ZL 3 ZC 3 ZL 4 ZC 4 ZL 5 ZC 5 ZL 6 ZC 6 Type B Filter -04-4 -50-30 38 9 46 8 5 5 5 3-7 Type B 3- Type B S S insertion loss return loss db 3- Type B f L =.7GHz f H =.9GHz Type B image rejection 58
Im[Y] Type B f 0 Prototype f f p f (a) I Im[Y] Type B Prototype f L f H f 3 f f 0 f f 4 (b) II 3-0 Type B 59
IL,RL (db) S S f L f H 3- Type B Type B Type A Type B even mode odd mode 3-8 even mode odd mode 3-8 a b even mode odd mode Type C a b even mode odd mode 60
3-8 Type B even mode odd mode 3-3.3 Type C Type C Type C I I 3-3. Type A I 3- a Type C I I Type C II II Type B a b even mode odd mode ZL 3 ZC 3 Z ea Z oa Z eb Z ob 3- b Type B f L ZL 3 ZC 3 f 3 Type B f 3 f L L C L 3 C 3 f 3 f L Type B Type C passband f H 6
Im[Y] Type C f 0 Prototype f f (a) I Im[Y] Type C Prototype f 3 f 0 f H f f f 4 (b) II 3- Type C 6
Type C 3-9(a) I II Series IV 3-3 3-3 Type C S S insertion loss return loss db 3-3 Type C high side f H =.9GHz Type C Type A Type C even mode odd mode 3-9(b) 3-9(b) a b even mode odd mode Type B ZL ZC ZL ZC ZL 3 ZC 3 ZL 4 ZC 4 ZL 5 ZC 5 ZL 6 ZC 6 Type C Filter -04-4 -50-30 9 4 46 8 5 5 5 3-9(a) Type C 3-9(b) Type C even mode odd mode 63
IL,RL (db) S S f H =.9GHz 3-3 Type C Type C even mode odd mode Series IV Linecalc Strip line Type C 3-9(c) Series IV Type C 3-4 insertion loss return loss 3-3 Type C 64
3-9(c) Type C Strip line IL,RL (db) S S 3-4 Type C Strip line 65
FR 4 Microstrip line Type C 3-9(b) Type C even mode odd mode Linecalc Type C 3-9(d) 3-9(d) Type C Microstrip line 3-9(c) 3-9(d) a a even mode odd mode 66
3-3.4 Type D Type D Type I I 3-5 a I passband C PC L PC f P f O Type D L 5 C 5 f=f P L 5 C 5 f f O L 6 C 6 f=f P L 6 C 6 f f O L 5 C 5 L 6 C 6 f=f P Type D II II 3-5 b Type D f 3 >f II UP passband II passband Type D L 4 C 4 f 4 L C f II DN passband II DN passband ( ) II UP passband ( ) Type D II II passband ( ) II UP II DN Type D II passband f 4 f HA =.65 GHz f f HB =.98 GHz f HB L 4 C 4 L C 67
Type D passband f HA f HB Type D 3-0(a) I II Series IV 3-6 3-6 Type D insertion loss return loss db 3-6 Type D high side f HA =.65GHz f HB =.98GHz Type D Tx Type D Type A Type D even mode odd mode 3-0(b) Type D Strip line 3-0(c) Type D FR 4 Microstrip line 3-0(d) 3-0(d) Type D b c Sonnet Type D Sonnet 3-7 S 68
S 3-8 (a) insertion loss return loss Type D.445GHz 00MHz VSWR.38 -.445GHz 83MHz VSWR.36 f HA =.6GHz f HB =3.4GHz 3-6 Type D f HA =.65GHz f HB =.98GHz 3-8(a) f HB 3-6 f HB 40MHz b c Type D 3-8(a) Type D S S Conductor loss Dielectric loss 3-8(b) Type D S S.4GHz loss 3.dB.445GHz loss 0.8dB.5GHz loss 3.8dB 3-8 c Type D S S.4GHz loss 5.4dB.445GHz loss 4.0dB.5GHz loss 7.0dB 3-8 d Type D S S.4GHz loss 8dB.445GHz loss 5.5dB.5GHz loss 8.46dB 3-8 a 3-8 d 70% 30% 69
ZL ZC ZL ZC ZL 3 ZC 3 ZL 4 ZC 4 ZL 5 ZC 5 ZL 6 ZC 6 Type D Filter -6-4 -74-36 9 69 33 58 37 8 3-0(a) Type D 3-0(b) Type D even mode odd mode 3-0(c) Type D Strip line 70
7
Im[Y] Type D Prototype f f p f 0 f (a) I Im[Y] Type D f f 3 f 0 f L f H f4 f Prototype (b) II 3-5 Type D 7
IL,RL (db) S S f HA f HB 3-6 Type D 73
3-7 74
IL,RL (db) S S f HA f HB IL,RL (db) (a) S S (b) 3-8 Sonnet Type D 75
IL,RL (db) S S (c) IL,RL (db) S S (d) 3-8 Sonnet Type D 76
3-3.5 Type E Type E Type D I I 3-3.4 Type D I Type E II II 3-9 L 3 C 3 f 3 L C f II UP passband II passband Type D C 4 f 4 L C f II DN passband II DN passband ( ) II UP passband ( ) Type E II II passband ( ) II UP II DN Type E f 0 f f L f 4 f H f H f H f H L C L 4 C 4 Type E passband f H f H passband f L L 4 Type E 3- I II Series IV 77
3-0 3-0 Type E S S insertion loss return loss db 3-0 Type E f L =.GHz f H =.85 GHz f H =3.45GHz Type E Type A Type E even mode odd mode 3- even mode odd mode 3- c d even mode odd mode Type F c d even mode odd mode ZL ZC ZL ZC ZL 3 ZC 3 ZL 4 ZC 4 ZL 5 ZC 5 ZL 6 ZC 6 Type A Filter -6-4 -74-36 80 6 88 43 58 37 8 3- Type E 78 3- Type E even mode odd mode
Im[Y] Type E f L f 0 f f 4 f 3 f f H f H Prototyp 3-9 Type E II IL,RL (db) S S fl f H f H 3-0 Type E 79
3-3.6 Type F Type F Type C Type E c d even mode odd mode even mode odd mode Type E passband 3- Type F insertion loss return loss f L Type F Type A Type F even mode odd mode 3-3(a) 3-3(a) c d even mode odd mode Type F Strip line 3-3(b) 3-3(b) Series IV Type F 3- insertion loss return loss 3- Type F Type A Type D 80
3-3(a) Type F even mode odd mode 3-3(b) Type F Strip line 8
IL,RL (db) S S f L 3- Type F 8
IL,RL (db) S S 3- Type F 83
4- Type A Type D Type D.. Protel Type A Type D 84
3. 4. 5. FR 4 90 0 8~0 6. 7. Type A Type D Type D 85
4-(a) Type A 4-(b) Type D 86
Type A Type A Sonnet 4-(a) Type A Sonnet Type A a mil b c mil 0.5mil d 0.3mil mil 87
Type D Type D Sonnet 4-(b) Type D Sonnet Type D a.4mil b c mil.4mil d mil.3mil 4-3 88
HP879D Calibration TRL Through Reflection Line TRL 4-.4GHz 50 55 mil Through l 55mil 50 Reflection l /4.4GHz /4 655 mil Line l/4 /4.4GHz Line S 90 Through l l Reflection λ/4 l Line l+λ/4 4- TRL 4-3 TRL Through 89
Cable Wiltron 3680-0 Type A Cable 4-3 4-4 Type A 4-4 HP879D Type A S S insertion loss return loss Type A passband.395ghz.49ghz.44ghz f O =.445GHz BW=83MHz 90
MHz BW 4% Type A insertion loss passband 6.8dB 5.3dB 4.9dB low side.05ghz.48ghz passband VSWR.68 IL,RL (db) S S.48GHz.05GHz f LA f LB 4-4 Type A 4-5 a b Type A S 9
S Type A loss Sonnet 4-5 a Type A S 3dB 4-5 b Type A f LA =.05GHz f LB =.48GHz f LA =.03GHz f LB =.65GHz MHz 7MHz 4- Type A 4-(a) Sonnet 4-6 4-6 a b 4-6 a S 4-6 b Type A 9
db (a) S db MHz 7MHz (b) S 4-5 Type A (a) S (b) S 93
db (a) S db (b) S 4-6 Type A (a) S (b) S 94
4-5 Type D 4-7 HP879D Type D S S insertion loss return loss Type D passband.4ghz.49ghz.445ghz f 0 =.445GHz BW=83MHz 3MHz BW 0.8% Type D insertion loss passband 6.4dB 7.5dB 5.dB high side.68ghz 3.8GHz passband VSWR. IL,RL (db) S S 4-7 Type D 95
4-8 a b Type D S S Type D loss Sonnet 4-8 a Type D S 3dB 4-8 b Type D f HA =.68GHz f HB =3.8GHz f HA =.6GHz f HB =3.4GHz 60MHz 58MHz Type A 4- Type D 4-(b) Sonnet 4-9 4-9 a b 4-9 a S 4-9 b 35MHz 8MHz Type D 96
db (a) S db f HA f HA 58MHz 60MHz f HB f HB (b) S 4-8 Type D (a) S (b) S 97
db (a) S db 35MHz 8MHz (b) S 4-9 Type D (a) S (b) S 98
Type A Type D FR 4 Type A Type D Type A insertion loss 4.9dB Type D insertion loss 5.dB cm 3cm () () (3) LTCC 99
[], Basic Theory and Design of Microwave Filter,, [],,,,pp.-08,. [3],, [4] D. M. Pozar, Microwave Engineering Addision-Wesley Publishing Company Inc., U.S.A., 990. [5] R. E. Collin, Foundations for Microwave Engineering ed McGRAW-HILL Inc., New York, 99. [6] A. S. Sedra, and P. O. Brackett, Filter Theory and Design Active and Passive Matrix Publishers Inc., 978. [7] J. Helszajn, Microwave Planar Passive Circuit and Filters Wiley Inc., 994. [8] T. Nishikawa, RF Front End Circuit Components Miniaturized Using Dielectric Resonators for Cellular Portable Telephone, IEICE Trans., Vol. E74, No.6, pp.556-56, Jun. 99. [9] S. B. Cohn, Microwave Bandpass Filters Containing High-Q Dielectric Resonators, IEEE Trans. Microwave Theory Tech., Vol. MTT-6, No.4, pp.8-7, Apr. 968. [0] T. Ishizaki, M. Fujita, H. Kagata, T. Uwano, and H. Miyake, A Very Small Dielectric Planar Filter for Protable Telephones, 993 IEEE MTT-S Digist., H-, pp.77-80, 993. [] H. Miyke, S. Kitazawa, T. Ishizaki, T. Yamada, and Y. Nagatomi, A Miniaturized Monolithic Dual Band Filter Using Ceramic Lamination 00
Technique for Dual Mode Portable Telephones, 997 IEEE MTT-S Digist., pp.789-79, 997. [] M. Makimoto, and S. Yamashita, Compact Bandpass Filter Using Stepped Impedance Resonators, Proc. IEEE., Vol.67, No. pp.6-9, Jan.979. [3] G. Dacheng, A Compact Step Impedance Stripline Bandpass Filter, 99 IEEE International Conference on Circuits and Systems., pp.960-963, Jun. 99. [4] T. Ishizaki, and T. Tomoki, A Stepped Impedance Comb-Line Filter Fabricated by Using Ceramic Lamination Technique, 994 IEEE MTT-S Digist., WEC-4, pp.67-60, 994. [5] H. C. Chang, C. C. Yeh, W. C. Ku, and K. C. Tao, A Multilayer Bandpass Filer Integrated into RF Module Board, 996 IEEE MTT-S Digist., WEC-4, pp.69-6, 996. [6] G. F. Engen, and C. A. Hoer, Thru-Reflect-Line An Improved Technique for Calibrating the Dual Six-Port Automatic Network Anajyzer, IEEE Trans. Microwave Theory Tech., Vol. MTT-7, NO., pp.987-993, Dec. 979. [7] Hewlett-Packard Product Note 850-8A, Applying the HP 850 TRL Calibration for Non-Coaxial Measurements, 0