າݭѨᏘگԺטҲ఼ᕭگጡ̝నࢍ
ౘځᇃ! അॎڌ
઼ϲ๔ৈԫఙጯੰ̄̍ր
ၡ! ࢋ
ώ͛೩ʑາݭѨᏘگԺטҲ఼ᕭگጡనࢍΞϡٺԺטᏘگᄃϠ
ੈཱིĄѩҲ఼ᕭگጡѣໂᆵၟͤᐛᄃа١Ϡੈཱི۞ਕ˧Ăਕ႕֖ன
ቢ఼ੈր۞ࢋՐĄ҃ͷĂѩᕭگጡٺၟͤᐛதܢܕѣ࠹༊ੲथ۞ഴ
தĂТॡ఼۞̬ˢຫεϺߏޝ̈Ăྮ͎̇ͧТ৺۞ՎลܡԩёҲ఼ᕭگ ጡᔘࢋ̈Ąѩᕭگጡ۞నࢍ̳ёߏϤቭЪቢᄃ็Ꮾቢ۞ඈड़ྮפĄֹϡ IE3D ჃሀᑢహវࢍზঈপّĄሀᑢඕڍᄃྮ၁ᅫณീඕڍѣ࠹༊։
р۞ʑّĄ
ᙯᔣෟĈᏘگԺטăᗔੈăҲ఼ᕭگጡĄ
A NOVEL SPUR-FREE LOW PASS FILTER DESIGN
Ming-Guang Chen Jan-Dong Tseng
Department of Electronic Engineering National Chin-Yi Institute of Technology
Taichung, Taiwan 411, R. O. C.
Key Words: harmonic suppression, spurious-free, low pass filter.
ABSTRACT
In this paper, a novel spur-free low pass filter suppressing harmonics is proposed. This low pass filter has a broad stop band and a high rejection ratio which can meet the requirements for modern wireless communication systems. Furthermore, the filter shows a very sharp attenuation slope above the cutoff frequency and a low insertion loss in the pass band, and is quite small compared to stepped impedance low pass filters of the same order.
The design formula of this novel low pass filter is based on the equivalent circuit of coupled lines and transmission lines. The filter is evaluated by an IE3D electromagnetic simulator. The simulated data are in good agreement with the experimental results.
˘ă݈! ֏
Ҳ఼ᕭگጡдధк఼ੈր̚Ăགྷ૱ϡٺԺטᏘگ (harmonic) ᄃϠ (spurious) ܫཱིĄࠎ˞ᒔѣᐹ։۞
ᏘگԺטड़ਕĂMoon Que Lee Լត˘ਠ૱֍۞ฟྮണ߱
నࢍ͞ё[1]Ą˘ਠ૱֍۞Վลܡԩ (stepped-impedance) ᄃโϣޮඈё (Kuroda-identity) Ҳ఼ᕭگጡ೩ֻ͐পա (Butterworth) ᄃ̷ͧౠ͈ (Chebyshev) পّͽֻన
ࢍ [2]Ąࠎ˞זੲथ۞ၟͤᐛதᜩᑕĂ˯۞ᕭگ ጡ࠰ᅮࢋкลݭё͞ਕ၁னĂ҃Қତลᇴк˵Тॡᆧ ΐ˞ᕭگጡ۞វ᎕ᄃ̬ˢຫεĄܕѐֽĂҲ఼ᕭگጡֹϡ photonic-bandgap structure ᄃ៩۩ତгඕၹ (defect ground structure) ԫఙĂϡͽഴ̈ྮ͎̇ᄃᆧΐၟͤᐛதᜩ ᑕ۞த [3,4]Ăפ็۞ᕭگጡĄ˵ѣˠ೩̼̈Η జજ (semi-lumped) Ҳ఼ᕭگጡనࢍĂϡͽ྿זᒺ̈ྮ
͎̇۞ϫ۞ [5]Ą҃Ăֹϡγΐ۞జજ̮Іົ೩ᄦ
Input lL
lL
Zs
Zoe , Zoo
lf
lc
lc
ls
w1
w2
g
Output
ဦ1! ѨᏘگԺט̝Ҳ఼ᕭگጡඕၹဦ
ү˯۞ᙱޘĄቢፚבᇴ (elliptic-function) Ҳ఼ᕭگ ጡ ѣ࠹ ༊ᐹ։ ۞ јڍ ĂҲј ώ ͷٽ ٺᄦү [6-10]Ą Giannini ඈˠ೩ፚבᇴҲ఼ᕭگጡֹϡૄώ۞͞ԛඕ ၹ೩ֻѣੲथᆵᐛ఼۞ၟͤᐛதᜩᑕĂҭၟͤᐛ
(stop-band) ݒߏব৫۞ [7]ĄLung-Hwa Hsieh ֹϡՎลܡ ԩҚ৺͞ёĂనࢍٺ̙Тᐛத۞ᕭگጡҚତ [8]Ă྿ז ᆵၟͤᐛᄃੲथ۞ၟͤᐛதᜩᑕĂҭ˫ົֹྮ͎̇
ត̂ĄSaavedra[9]ྻϡ slow-wave ֽᒔՀᐹ։۞ड़ਕĄ Min[10]ྻϡጱԫఙనࢍᕭگጡĂଂ҃ᒔໂࠎᐹ։
۞ᕭگጡड़ਕĄҭѩԫఙ۞̍үޘᔘߏΪਕд77 K ۞ ᒖဩ˭̍үĄ
̼̈ᄃड़ਕ۞گҲ఼ᕭگጡߏధкቢ఼ੈ
րٙ̚ࢋՐ۞Ąጀӵё(hairpin)ඕၹЯࠎѣᐹ։۞̈
̼ ͎ ̇ ᄃ ट ٽ ᄦ ౄ ۞ ᐹ ᕇ Ă ̏ གྷ ѣ ధ к ۞ ࡁ տ ј ڍ [11-15]Ąଂ˘ਠ۞ΗگܜጀӵёВॎזܕ۞Վลܡԩጀ ӵёВॎĂ͎̇۞ᖎ̼̏གྷѣ࠹༊۞јڍ [16-20]ĄՎลܡ ԩጀӵёВॎ̏གྷѣˠྻϡ؈ (odd) ઊ (even) ሀᄃშྮ
ሀ(network models)͞ڱೡ [17-19]Ą҃д Sagawa[17]
̈́Lee Tsai[19]۞ኢ͛̚ĂΪ೩ֻ ABCD ੱ۞ܕҬܑ
ϯёĂ֭ዋϡ۞ྮనࢍ͞ڱĂЯѩĂ̙टٽۡତనࢍ
ٙᅮ۞ྮĄ
ώ͛೩˘າݭቢѨᏘگԺט̝Ҳ఼ᕭگ ጡనࢍĄѩᕭگጡֹϡ็ᏮቢᄃቭЪቢநኢԱL-C ඈ ड़ྮሀ[21-24]ĂѩҲ఼ᕭگጡѣ࠹༊ᐹ։۞̼̈
͎̇Ăੲथ۞ၟͤᐛதᜩᑕᄃໂᆵ۞ၟͤᐛᐛதᜩᑕĄ
҃ͷĂ՟ѣЇңγΐ۞జજ̮ІĂ̙ົᆧΐᄦү˯۞ᙱޘĄ ᕭگጡ۞ሀᑢߏֹϡIE3D ჃሀᑢహវĄ
˟ăඈड़ྮ
ဦ1 ࠎາݭቢѨᏘگԺט̝Ҳ఼ᕭگጡඕၹĄ ѩඕၹΒӣ็Ꮾቢl ᄃs l ̈́ቭЪቢ۞ܜޘL l Ąc Z ߏ็Ꮾ s
Zs
ls
cp cp
cg
Ls
cs cs
lc
Zoe , Zoo
(b) (a)
(d) (c)
ဦ2 ็Ꮾቢ̈́ቭЪቢඈड़ྮĈ(a) ಏ˘็Ꮾቢć(b)
็Ꮾቢඈड़ྮć(c) ၆ჍቭЪቢć(d) ၆ჍቭЪ ቢඈड़ྮ
ቢl ᄃs l ۞পّܡԩ(characteristic impedance)ĄL Z ᄃoe Zoo
̶Ҿߏ၆ჍटྶπҖቭЪቢ۞ઊሀᄃ؈ሀԩĄ ಏ˘็Ꮾቢl тဦ 2(a)Ξͽඈड़јs L− C π -შྮĂဦ 2 (b)Ą၆ܜޘࠎl ຫਈ็ᏮቢĂ ABCD ੱࠎ s
=
s s s
s s
s s s s s
l l
jY
l jZ l D
C B A
β β
β β
cos sin
sin cos
(1)
βsᄃYs=1/Zs̶Ҿߏಏ˘็Ꮾቢ۞࠹Ҝ૱ᇴᄃপّጱ ৼĂඈड़L− C π -შྮ۞ ABCD ੱࠎ
+ +
= +
c L c L c
L c
L
Y Z Y Z Y
Z Y
Z D
C B A
1 ) 2 ( 1
(2)
̚ZL = jωLsĂYc= jωCsĂωࠎ֎ᐛதĂL ᄃs C ߏಏs
˘็Ꮾቢ۞ඈड़ຏᄃटĄͧྵ(1)ᄃ(2)ёĂӈΞͽᒔ
ඈड़ຏL ᄃඈड़टs C ᄃ็Ꮾቢܜޘ(s l )Ă࠹Ҝ૱ᇴs (βs)ᄃপّܡԩ(Z )۞ᙯܼё s
ω β ) sin( ss
s s
l
L = Z (3)
) sin(
) cos(
1
s s s
s s s
l Z C l
β ω
− β
= (4)
ТநĂಏ˘็Ꮾቢl ϺΞͽඈड़јL L− C π -შྮĂඈ ड़ຏL ᄃඈड़टL C ࠎ L
ω β ) sin( L L
L s
l
L =Z (5)
) sin(
) cos(
1
L L s
L L L
l Z C l
β ω
β
= − (6)
Cp Cp
Cp Cp
Cg
Cg
LL LL
LL LL
Ls
ဦ3! ѨᏘگԺטᕭگጡඈड़ L-C ဦ
ѩγ၆ჍπҖቭЪቢĂдဦ 2(c)̚ĂΞͽඈड़јटπ - შྮĄຫਈπҖቭЪቢ۞ABCD ੱΞͽܑϯࠎ
− +
−
−
−
− +
=
oo oe
oo oe c
c oo oe
oo oe
c c oo oe oo
oe oo oe
Z Z
Z Z l
Z Z
j
Z Z
l Z
Z j Z
Z Z Z
D C
B A
) cot(
) (
2
) cot(
2
β
β
(7)
βcߏቭЪቢ۞࠹Ҝ૱ᇴĂl ࠎቭЪቢܜޘĂc Z ăoe Z ̶oo Ҿࠎ၆ჍቭЪቢ۞ઊሀᄃ؈ሀপّܡԩĄඈड़टπ -შྮ
۞ABCD ੱࠎ
+ +
= +
p g p g p
g p
g
Y Z Y Z Y
Z Y
Z D
C B A
1 ) 2 ( 1
(8)
̚Zg =1/jωCgĂYp = jωCpĄͧྵ(7)ᄃ(8)ёĂΞͽ
זඈड़टπ -შྮࠎ ) cot(
2 oe oo cc
oo g oe
l Z
Z Z C Z
β ω
= − (9)
) cot(
1
c c oe
p Z l
C =ω β (10)
៍၅(3)ᄃ(4)ёΞͽ൴னĂ༊βslsؠॡĂࡶপّܡԩZ s
Ăඈड़टC ۞ࣃົ̈ĄೱήྖᄲĂ༊నࢍॡĂs
ࡶᏴፄপّԩZ Ăಏ˘็Ꮾቢ۞ඈड़ྮΞۡତඈड़s ࠎ˘ຏĂ֭ͷඈड़टC نரĄЯѩĂనࢍώྮॡĂs ၆ٺপّܡԩZ ۞ᏴፄߏрĂΞͽഴ֭̈ᓑटs (C )۞ࣃĄඕЪဦ 2 (b)ᄃ 2(c)۞็ᏮቢᄃቭЪቢඈड़ྮs ޢΞͽזѨᏘگԺטᕭگጡͽజજ̮ІL ᄃ C ܑϯඈ ड़̝ྮĂтဦ3Ą
ᕭگጡ၁វ͎̇ΞͽϤ(3)ă(5)ă(9)ᄃ(10)αёᒔĄ
็ᏮቢᄃቭЪቢ۞ᆵޘפĂдഴ֭̈ᓑट۞ᇆᜩ۞݈
೩˭ᏴፄZs> ZoeZoo ͷZ ̂р۞୧ІĄ็Ꮾቢᄃs ቭЪቢ۞ܜޘଂ(3)ă(5)̈́(10)ˬёפĂ֎ᐛதωనؠࠎ 3-dB ၟͤ֎ᐛதĄ
Cp Cp
Cp Cp
Cg
Cg
LL LL
LL LL
Ls
F F
F F
x z x
x z x
w
ဦ4! ᕭگጡඈड़ྮͽតᇴ͞ဦܑϯ
F
PORT 1 PORT 2
F
x z x
w
A1 B1
C1 D1
[ ]
AC22 B D22[ ] [ ]
ဦ5! តᇴ͞ဦͽ ABCD ੱܑϯ̝ϯຍဦ
ˬăྮ̶ژ
˯༼ೡ˞ѨᏘگԺטҲ఼ᕭگጡ̚Ч̶Ш̮І
۞ඈड़ྮĂώ༼ྻϡ˯༼ٙඈड़ྮĂͽநኢរᙋ
ٙ೩۞ඈड़̝ϒቁّ֭೩నࢍࣧᄃ͞ڱĄဦ4 ࠎ ᕭگጡඈड़ྮ۞ྮ͞ဦĂѩ͞ဦͧဦ3 ̝̚Ч జજ̮ІĂw⇒Lsăx⇒LLăz⇒CgᄃF⇒Cpߏͽត ᇴ၆ᑕҌ圖3 ̝̚జજ̮ІĄϤٺώྮ˯˭ొ̶၆ჍĂ ߇Ξፄʑ̶ֽژĂ̶ژԆΗొЊྮޢĂΪᅮొ̶
ྮ֭ᓑĂӈΞԆјፋ࣎ྮ̶̝ژĄ
ဦ5 ࠎតᇴ͞ဦͽ ABCD ੱܑϯĂ ABCD
ੱΞ̶Ҿܑϯࠎ
=
1 0 1
1 1
1
1 w
D C
B A
(11)
2 2
2 2
D C
B A
+ + + + +
+ + + + + + + + + +
= +
xF zxF Fz xF z
F F
x zxF z F x F zx xFz F x x xF zxF Fz xF
2 2
2 2 2 2
2
1 2
1
(12) (11)ᄃ(12)ё̶Ҿܑϯࠎ֭ᓑྮ̝ ABCD ੱĄ
ABCD ֭ତ̳ёт˭ٙϯ
2 1
1 2 2 1
B B
B A B A A
+
= + (13a)
2 1
2 1
B B
B B B
= + (13b)
2 1
2 1 2 1 2 1 1
2 )( ) ( )( )
(
B B
C C B B D D A C A
+
+ +
+
−
= − (13c)
2 1
2 1 2 1
B B
D B B D D
+
= + (13d)
ͷ̏ۢS ણᇴᄃ ABCD ણᇴᖼೱт˭
D CZ Z B A
D CZ Z B S A
+ + +
−
−
= +
0 0
0 11 0
/
/ (14a)
D CZ Z B S A
+ +
= +
0 0
21 /
2 (14b)
ྻϡ(11)-(14)αёĂΞͽזѨᏘگԺטҲ఼ᕭگඕၹ
۞S ᄃ11 S ܑϯё 21
( )
[ ]
[ ]
( )
+ + +
+
− +
− +
− + + + +
+ + +
+
−
−
= −
' ) ' ' 2 ( ) ' ' ' ' ' ' ' 2 (
' 1 ' ' ) ' ' 1 )(
' ' 1 ( ' 2
' ) ' ' 2 ( ) ' ' ' ' ' ' ' 2 ( '
2 0 2 0
0 2 0 2
2 0 2 0
0 2 2 11
G Z z F F Z z F x z F x F Z
w wG F
x F x F z w G Z
G Z z F F Z z F x z F x F Z w S wG
(15a)
[ ]
[ ]
( )
[ ]
[ ]
− + + +
+ +
+ + +
+
− +
− +
− + + +
= +
1 ' ' ) ' ' 1 )(
' ' 1 ( '
' ) ' ' 2 ( ) ' ' ' ' ' ' ' 2 (
' 1 ' ' ) ' ' 1 )(
' ' 1 ( '
' 2
0
2 0 2 0
0 2 0 2 21 0
F x F x F z w G Z
G Z z F F Z z F x z F x F Z
w wG F
x F x F z w G Z
G S Z
(15b)
̚តᇴࠎ
C F j C F j z z
L x j L x j
w F
g
s L ω
ω
ω ω 2
2 2 1 2 2 2
' '
'= = = = = =
= Ă Ă Ă
0
-20
-40
-60
-800 3 6 9 12 15
Frequency (GHz) Magnitude |S11| and |S21| (db)
Retum loss
Insertion loss
7.7GHz 3.3GHz
ဦ6 ֹϡజજ̮Іሀᑢ̝ᐛதᜩᑕĂၟͤᐛதనࢍд 2.4GHz
ྻϡፚבᇴజજ̮Іܑ[25]Ăଂܑ̚ΞͽۢL ăs C ăg C ۞̮ІࣃĂ̏ۢ۞ˬ࣎జજ̮Іࣃˢ (15a) p ᄃ (15b) ё Ă ΄|S11|=3dB ᄃ|S21|=3dB(ω = 2πfc ॡ)ĂΞͽଂ(15a)ᄃ(15b)ё̚ՐຏL ĄϤٺٙ೩L
̝ѨᏘگԺטҲ఼ᕭگጡඕၹΪߏᙷҬፚבᇴᕭگጡ ඕၹĂඕၹ̙ТдٺѨᏘگԺטҲ఼ᕭگጡඕၹк
˞˘̈߱ଂᏮˢბזቭЪቢม۞ൺ็Ꮾቢl Ăѩൺ็ᏮቢL ඈड़ࠎຏL ĄЯࠎຏL L ĂٙͽϤፚבᇴజજ̮ІL
ܑז۞జજ̮ІࣃֽనࢍᕭگጡྮĂົѣ͌ధ۞ᄱ मĄҭѩᄱमགྷ࿅кѨ۞၁រሀᑢរᙋĂ၆ፋវ۞ঈপ
ّᇆᜩ̙̂Ąٙͽα࣎జજ̮ІࣃΞͽӀϡፚבᇴజજ
̮Іܑᄃ(15a)ă(15b)ёՐĄ
னдͽనࢍၟͤᐛதٺ 2.4GHz ̝ѨᏘگԺטҲ఼
ᕭگጡࠎּĂϤፚבᇴజજ̮ІܑĂགྷܡԩҜ̈́ᐛத
۞ᔘࣧྻზΞLs = 3.225nHĂLL = 1.32nHĂCg = 0.12pFĂ Cp = 0.653pFĄֱ̮ІࣃĂֹϡ Microwave Office 2.0
ჃహវሀᑢྮপّĄဦ6 ࠎֹϡ˯జજ̮Іࣃז
̝ᐛதᜩᑕĄ៍၅ဦ 6Ăֹϡజજ̮Іሀᑢ̝ᐛதᜩᑕĂ д ၟ ͤ ᐛ (stopband) ѣ ࣎ ็ Ꮾ ᕇ Ă ̶ Ҿ ӱ ར ٺ 3.3GHz ᄃ 7.7GHzĄӀϡё(15b)ߤរ็ᏮᕇĄ
༊S21=0ॡĂଂ(15b)ёΞͽז
[
'(1 ' ') ']
' ' ' 0) ' ' 1 (
'= +xF x +zF +z +x+x2F+w= G
⇒ (1+x'F')
[
x'(2+z'F')+z']
+w=0 (16)
C F j C F j z z
L x j L x j
w p
g
L ω
ω
ω ω 2
2 2
1 2 2 2
' '
'= = = = = =
= Ă Ă Ă
ᄃLs=3.225nHĂLL=1.32nHĂCg=0.12pFĂCp=0.653pF ˢ (16)ё̚ĂΞͽྋα࣎ྋĂ̶Ҿࠎ f = ±3.26GHzĂ
±7.718GHzĄᇴΝଫĂӈΞז f1 = 3.26GHzĂf2 =
ܑ˘! ѨᏘگԺטҲ఼ᕭگ۞L-C ̮Іࣃ fc Ls LL Cg Cp
2.4GHz 3.225nH 1.32nH 0.12pF 0.653pF Optimized L-C
values 5.2GHz 1.225nH 0.96nH 0.05pF 0.353pF
Cp Cp
Cp Cp
Cg
Cg
LL LL
LL LL
Ls
lL
lf
lc
ls
w1
w2
g
(a) (b)
ဦ7 ѨᏘگԺטҲ఼ᕭگጡĈ(a)ඕၹဦć(b)ඈड़ྮဦ
7.718GHzĄޝځቁ۞࠻Ăֹϡሀᑢహវٙז۞ඕڍᄃ
ֹϡଯጱё̄ٙז̝ඕڍߏܧ૱˘۞Ą
Ϥဦ 6 Ξͽ࠻ѩྮٺၟͤᐛ(stopband)ົѣ
࣎็ᏮᕇĂ˵Яࠎௐ˟࣎็Ꮾᕇ۞ቡ߇ĂΞͽֹѩ
ྮጾѣՀᆵ۞ၟͤᐛĄ
αăᄦүᄃณീඕڍ
ॲፂ̝݈̝ٙඈड़ྮሀᄃྮ͎̇۞Ч࠹ᙯ ё̄(3)ă(5)ă(9)ᄃ(10)Ąѩα࣎ё̄ᄃܑ˘۞ඈड़ຏ̈́
ඈड़टĂӈΞೱზྮ۞͎̇Ąဦ7(a)ăဦ 7(b)ࠎ
ѨԺטᏘگᕭگጡ۞ඕၹဦᄃඈड़ྮဦĂဦ7(b)۞ඈड़
ྮ̙֭҂ᇋຫεᄃ̙ాᜈତࢬ۞ᇆᜩĄдဦ7(b)۞ඈड़
ྮ̚ĂL ᄃs L ߏಏ˘็Ꮾቢ۞ඈड़ຏĂL C ᄃg C ߏp ቭЪቢ۞ඈड़टĄֹϡܑ˘۞̮ІࣃĂˢ(3)ă(5)ă(9)
̈́(10)αёĂӈΞԱᕭگጡ۞͎̇l ăs l ᄃL l Ą c
ྻϡ˯۞నࢍ͞ڱ̈́߹ซҖีᕭگጡྮ۞
న ࢍ Ă ̶ Ҿ ࠎ 3-dB ᕇ ۞ၟ ͤ ᐛ த ̶Ҿࠎ 2.4GHz ᄃ 5.2GHzĄֹϡ RO4003 ۞ૄڕĂૄڕݓޘࠎ 0.8128mmĂ
࠹၆̬૱ᇴεr=3.38ᄦౄĄܑ˘ߏีᕭگጡ۞ඈड़ L-C ྮ۞ࣃĂ3dB ၟͤᐛத̶Ҿࠎ 2.4GHz ᄃ 5.2GHzĄ གྷ࿅ྎࢍზޢĂనࢍٺ2.4GHz ᕭگጡ۞̶͎̇Ҿ ࠎlf =5mmĂls=7.57mmĂlL =1.69mmĂlc =3.66mmĂ
mm 6 .
1=3
w Ăw2=0.28mmĂg=0.37mmĄဦ8 ࠎనࢍ
ٺ2.4GHz ᕭگጡ۞ሀᑢᄃ DC ז 2.5GHzĄ̬ˢຫε̈ٺ 0.3dBĂ|S11|ͽ20dB ࠎણ҂Ăͧѩࣃ̈۞ᐛଂ 3.2GHz ז9.5GHzĄ҃၁វྮ۞่͎̇ࠎ1.7cm×1.1cmĄ
Ω γ Ă న ࢍ ٺ 5 . 2 G H z ᕭ گ ጡ ۞ ͎ ̇ ̶ Ҿ ࠎ mm
=5
lf Ăls=3.52mmĂlL =1.62mmĂlc=2.84mmĂ
0
-10
-20
-30
-40
-50
-600 2 4 6 8 10 12
Frequency (GHz) (a)
(b) Magnitude |S11| and |S21| (dB)
Simulation Measurement Retum loss
Insertion loss
ဦ8 ѨᏘگԺטҲ఼ᕭگጡĈ(a) ሀᑢᄃณീć(b)
ྮ၁វဦ mm 5 .
1=1
w Ăw2=0.28mmĂg=0.52mmĄဦ9 ࠎనࢍ
ٺ5.2GHz ᕭگጡ۞ሀᑢᄃ၁វณീဦĄ៍၅ณീඕڍĂ ᕭگጡ۞఼(passband)ଂ DC ז 5.2GHzĄ̬ˢຫε̈ٺ 0.5dBĂ|S11|ͽ20dB ࠎણ҂Ăͽѩࣃ̈۞ᐛଂ 6.2GHz ז13.5GHzĄଂဦ 9(b)۞၁វྮĂΞͽ࠻నࢍٺ 5.2GHz
۞ྮ่͎̇ѣ1.3cm×0.92cmĄ
̣ăඕ! ኢ
ώ͛ᄲځາݭѨᏘگԺט̝Ҳ఼ᕭگጡֹϡ
ቢనࢍ۞߹̈́͞ڱĄѩҲ఼ᕭگጡѣ࠹༊ᐹ։۞̈
̼͎̇ĂҲ̬ˢຫεĂੲथ۞ၟͤᐛதᜩᑕᄃໂᆵ۞ၟͤ
ᐛᐛதᜩᑕĄ҃ͷĂྮ̚՟ѣЇң۞జજ̮ІĂ̙ົ
ᆧΐᄦү˯۞ᙱޘĄ֭͛̚ͽٙ൴ण۞నࢍ͞ڱ၆ၟͤᐛ
0
-10
-20
-30
-40
-50
-600 2 4 6 8 10 12 14
Frequency (GHz) (a)
(b) Magnitude |S11| and |S21| (dB)
Simulation Measurement Retum loss
Insertion loss
ဦ9 ѨᏘگԺטҲ఼ᕭگጡĈ(a) ሀᑢᄃณീć(b)
ྮ၁វဦ
த̶Ҿࠎ2.4GHz ̈́ 5.2GHz ซҖ၁ᅫྮనࢍĂ֭ณീ
ᐛதᜩᑕĄሀᑢᄃณീඕڍĂѣ࠹༊۞˘ّĄώ͛၆ ٺѨᏘگԺטҲ఼ᕭگጡ೩ֻ˘࣎ᖎಏ۞͞ڱᄃѣϡ۞
ඈड़ྮሀĂඕڍ྿זഇ۞পّࢋՐĄ
ણ҂͛ᚥ
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