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C S K Thut Siu Cao Tn

Nghim Xun Anh

31.3.2005


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Mc lc

1 Gii thiu 1

1.1 S bt u ca truyn dn khng dy . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Ph tn s v tuyn hin nay . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 L thuyt ng truyn 11

2.1 Phng trnh truyn sng trn ng dy . . . . . . . . . . . . . . . . . . . . . 12

2.1.1 M hnh mch in thng s tp trung ca ng truyn - Cc thng ss cp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.1.2 Phng trnh truyn sng . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.1.3 Nghim ca phng trnh sng. Sng ti v sng phn x . . . . . . . . 162.1.4 Cc thng s th cp . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2 Cc ng truyn sng v ng dn sng thc t . . . . . . . . . . . . . . . . . . 22

2.2.1 Phng trnh Helmholtz . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.2.2 Nghim tng qut cho cc sng TEM, TE v TM . . . . . . . . . . . . . 23

2.2.3 Truyn sng trong khng gian t do . . . . . . . . . . . . . . . . . . . . 29

2.2.4 Dy song hnh - twin wire line . . . . . . . . . . . . . . . . . . . . . . 29

2.2.5 Cp ng trc - Coaxial Cable . . . . . . . . . . . . . . . . . . . . . . . 31

2.2.6 ng dn sng hnh ch nht -Rectangular Waveguide . . . . . . . . . . 32

2.2.7 ng truyn di - stripline . . . . . . . . . . . . . . . . . . . . . . . . 37

2.2.8 ng truyn vi di - Microstrip line . . . . . . . . . . . . . . . . . . . 40

2.2.9 ng truyn ng phng coplanar-CPW . . . . . . . . . . . . . . . . . 44

2.2.10 Tn hao trn ng dy truyn sng . . . . . . . . . . . . . . . . . . . . 45

2.3 Hin tng phn x sng trn ng dy - H s phn x . . . . . . . . . . . . . 502.4 Cc loi suy hao, sng ng v phng trnh tr khng ng truyn . . . . . . 55

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2.4.1 Suy hao phn hi - Return Loss . . . . . . . . . . . . . . . . . . . . . . 55

2.4.2 Hin tng sng ng v h s sng ng . . . . . . . . . . . . . . . . 56

2.4.3 Tr khng vo ca ng truyn . . . . . . . . . . . . . . . . . . . . . . 59

2.5 Cc ng truyn cng hng v phn cng hng . . . . . . . . . . . . . . . . 63

2.5.1 ng truyn mt phn t bc sng . . . . . . . . . . . . . . . . . . . 64

2.5.2 ng truyn na bc sng . . . . . . . . . . . . . . . . . . . . . . . . 65

2.5.3 Tr khng ng truyn khi tn s thay i . . . . . . . . . . . . . . . . 65

3 th Smith 67

3.1 C s ca th Smith . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

3.2 Cc th vng trn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.3 th Smith . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

3.3.1 M t th Smith . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

3.3.2 c tnh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

3.4 ng dng c bn ca th Smith . . . . . . . . . . . . . . . . . . . . . . . . . 86

3.4.1 Tnh h s sng ng, h s phn x v tr khng ng dy . . . . . . 87

3.4.2 Tnh tr khng mch phc hp . . . . . . . . . . . . . . . . . . . . . . . 88

3.5 Phi hp tr khng v iu chnh phi hp tr khng . . . . . . . . . . . . . . . 90

3.5.1 Phi hp tr khng bng cc phn t tp trung (cc mng hnh L) . . . . 92

3.5.2 Mch iu chnh phi hp tr khng dng mt dy chm . . . . . . . . 97

3.5.3 iu chnh phi hp tr khng hai dy chm - Double-Stub Tunning . . 107

4 Phn tch mch cao tn 111

4.1 Tr khng v in p v dng in tng ng . . . . . . . . . . . . . . . . . . 112

4.1.1 in p v dng in tng ng . . . . . . . . . . . . . . . . . . . . 112

4.1.2 Khi nim v tr khng . . . . . . . . . . . . . . . . . . . . . . . . . . 115

4.2 Nhng c im tr khng ca cc mng mt ca . . . . . . . . . . . . . . . . . 117

4.3 Cc ma trn tr khng v dn np . . . . . . . . . . . . . . . . . . . . . . . . . 118

4.4 Ma trn tn x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

4.5 Ma trn truyn (ABCD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

4.6 Cc mng hai ca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130


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Danh sch hnh v

1.1 M Morse quc t vn cn l chun cho tn hiu cp cu - SOS (......) . . . . . 3

1.2 Dng iu ch ca m Morse, c minh ha cho ch R. Ngy nay, dng xung

nh ch ra trn s c s dng gim ph tn pht, nhng my pht sparkgap ca Marconi khng cn nghi ng g na lm rng bng tn rt nhiu . . . 4

1.3 Joel Earl Hudson ang ng cnh my pht spark gap ca Marconi vo nm 1907. 5

1.4 Ngun nng lng chnh cho my pht ca Marconi ti South Wellfleet . . . . . 6

1.5 Trm pht v tuyn u tin ca Marconi ti South Wellfleet, Cap Cod, Massachusetts.Ngi dn a phng d on rng cc anten s b git ngay cn bo utin. H ng, v Marconi dng chng li . . . . . . . . . . . . . . . . . . 7

2.1 ng truyn sng . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2 Mch in tng ng ca on ng truyn vi phn . . . . . . . . . . . . . . 14

2.3 Sng ti v sng phn x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.4 (a) ng truyn hai dy ni chung v (b) ng dn sng khp kn . . . . . . . . 23

2.5 Dy song hnh - Mt phng tit din . . . . . . . . . . . . . . . . . . . . . . . . 30

2.6 Dy song hnh - Phn b trng . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.7 Cp ng trc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.8 Phn b trng trong cp ng trc . . . . . . . . . . . . . . . . . . . . . . . . 332.9 Dng hnh hc ca ng dn sng . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.10 ng truyn di (a) Dng hnh hc. (b) Cc ng sc t trng v in trng 37

2.11 Dng hnh hc v mt ct ngang ng truyn vi di . . . . . . . . . . . . . . . 41

2.12 Cc ng sc t trng v in trng . . . . . . . . . . . . . . . . . . . . . . 41

2.13 Cu trc tng ng ca ng truyn vi di cn TEM, lp in mi nnb dy d v hng s in mi tng i r c thay th bng mi trng ngnht c hng s in mi tng i hiu dng

epsilone. . . . . . . . . . . . . . 42

2.14 ng truyn coplanar (CPW) chun . . . . . . . . . . . . . . . . . . . . . . . 44

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2.15 Mt dng in trn tit din (a) dy dn trn (b) di dn hnh ch nht . . . . 47

2.16 Quan h gia (a) R v tn s (b) Suy hao v tn s . . . . . . . . . . . . . . . . 47

2.17 Gc tn hao . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

2.18 Biu din s bin thin ca h s phn x theo v . . . . . . . . . . . . . 51

2.19 ng truyn c kt cui tr khng ti ZL . . . . . . . . . . . . . . . . . . . 53

2.20 Minh ha sng ti, sng phn x v sng tng . . . . . . . . . . . . . . . . . . . 57

2.21 Minh ha sng ng . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

2.22 Mt ng truyn kt cui bi mt ngn mch . . . . . . . . . . . . . . . . . . 59

2.23 (a) in p (b) dng in v (c) tr khng (Rin = 0 hoc ) bin i dc ngtruyn u cui ngn mch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

2.24 Mt ng truyn kt cui bi mt ngn mch . . . . . . . . . . . . . . . . . . 61

2.25 (a) in p (b) dng in v (c) tr khng (Rin = 0 hoc ) bin i dc ngtruyn c ti h mch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

2.26 Phn x v truyn i ti giao ca hai ng truyn c tr khng c tnh khc nhau 63

2.27 B chuyn i tr khng mt phn t bc sng . . . . . . . . . . . . . . . . . 64

3.1 th Smith . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

3.2 nh x gia mt phng z v mt phng . . . . . . . . . . . . . . . . . . . . . 693.3 nh x r gia mt phng z v mt phng . . . . . . . . . . . . . . . . . . . . 70

3.4 nh x x gia mt phng z v mt phng . . . . . . . . . . . . . . . . . . . . 71

3.5 Biu din vng trn trong mt phng phc . . . . . . . . . . . . . . . . . . . 71

3.6 Cc vng trn ng r trong mt phng phc . . . . . . . . . . . . . . . . . . . 73

3.7 Cc vng trn ng x trong mt phng phc . . . . . . . . . . . . . . . . . . 75

3.8 th Smith . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

3.9 th Smith hn hp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

3.10 Ly i xng qua gc ta . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

3.11 th Smith minh ha v d 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 83



3.14 Bng v nt sng trn th Smith . . . . . . . . . . . . . . . . . . . . . . . . 86

3.15 Mch in minh ha v d 3.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . 873.16 th Smith minh ha v d 3.5 . . . . . . . . . . . . . . . . . . . . . . . . . . 88


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3.17 Mch in minh ha v d 3.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

3.18 th Smith minh ha v d 3.6 . . . . . . . . . . . . . . . . . . . . . . . . . . 90

3.19 Mng khng tn hao phi hp mt ti c tr khng bt k vi mt ng truyn 91

3.20 Mng phi hp hnh L (a) Mng c dng khi zL nm trong vng trn 1 + jx(b) Mng c dng khi zL nm ngoi vng trn 1 + jx . . . . . . . . . . . . . 92

3.21 Li gii cho v d 3.7 (a) th Smith cho cc mch phi hp L . . . . . . . . . 94

3.22 Hai kh nng cho mch phi hp L . . . . . . . . . . . . . . . . . . . . . . . . 95

3.23 Quan h gia ln ca h s phn x vi tn s ca mch phi hp Hnh 3.22 . 96

3.24 Cc mch iu chnh phi hp dng dy chm n (a) Dy chm song song. (b)Dy chm ni tip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

3.25 Li gii cho V d 3.8. th Smith cho cc mch iu chnh phi hp dngdy chm song song h mch . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

3.26 Hai gii php cho mch iu chnh phi hp dy chm song song . . . . . . . . 100

3.27 ln ca h s phn x theo tn s cho cc mch iu chnh phi hp trkhng Hnh 3.26 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

3.28 Ligii cho V d 3.9- th Smith cho cc mch iu chnh phi hp dng dychm ni tip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

3.29 Hai gii php iu chnh phi hp dng dy chm ni tip . . . . . . . . . . . . 103

3.30 ln ca h s phn x theo tn s cho cc mch iu chnh phi hp trkhng trn Hnh 3.29 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

3.31 Li gii cho V d 3.10- th Smith cho b iu chnh phi hp dng dychm n ngn mch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

3.32 Mch phi hp dy chm kp (a) Mch ban u c ti khong cch bt k kt dy chm th nht (b) Mch tng ng c ti nm ti dy chm th nht . . 107

3.33 th Smith m t hot ng ca mt mch iu chnh phi hp tr khng haidy chm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

3.34 Hai gii php iu chnh phi hp dy chm kp . . . . . . . . . . . . . . . . . 109

3.35 ln ca h s phn x theo tn s cho cc mch phi hp ca Hnh 3.34 . . . 110

4.1 Dng hnh hc ca ng dn sng mt phn cha cht in mi v ng truyntng ng ca n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

4.2 Mng mt ca bt k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

4.3 Mng N cng bt k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

4.4 Dch chuyn cc mt phng tham chiu i vi mt mng N cng . . . . . . . . 1254.5 Mng N cng c tr khng c tnh khc nhau . . . . . . . . . . . . . . . . . . 126


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4.6 (a) Mch hai cng; (b) Kt ni chui mch hai cng . . . . . . . . . . . . . . . 128

4.7 Mng hai ca vi tr khng ti v ngun tng qut . . . . . . . . . . . . . . . . 133


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Chng 1

Gii thiu

Chng ny gii thiu tng quan v lch s ca thng tin v tuyn (khng dy) v mt s ngdng chnh ca cng ngh ny. Bn cnh , ni dung mn hc s c tm lc qua gip ngi c c ci nhn khi qut v mn hc.

1.1 S bt u ca truyn dn khng dy

WIRELESS TELEGRAPHY-Vo thi im khi mi quan h ang cng thng gia Ty BanNha v Quc gia ny, khng g c th c cho n hn mt bin php thit thc c th mang

thng tin in gia cc im cch xa nhau trn mt t, v gia cc tu chin trn bin m khngcn bt k kt ni c sp t trc no gia hai im. Vo nm ngoi Guglielmo Marconi,mt sinh vin ngi Italia, pht trin mt h thng in bo khng dy c th truyn cc tnhiu Morse thng minh ti nhng ni cch xa trn 10 dm (1 dm 1.6 km). Tuy nhin, ngithit k mt thit b ph hp cho nhng yu cu v in bo khng dy t nc ny li l nh

pht minh ngi M. Sau nhiu thng th nghim W.J.Clarke thuc cng ty Cung cp in caM thit k mt thit b in bo khng dy hon chnh c kh nng s nhanh chng ca vo s dng.

-Scientific American April, 1898

Thng bo ny xut hin vo gn thi im bt u ca cng ngh v tuyn. T inWebmaster lit k hn 150 nh ngha bt u bng t radio (v tuyn), nh ngha u tin l.

1a ... s pht v nhn cc xung in hoc tn hiu bng sng in t m khng cndy dn kt ni (bao gm wireless (khng dy), television (truyn hnh) v radar).

Cho n nay thut ng khng dy (wireless) c s dng ng ngha vi v tuyn (radio).Ngy nay cc ng dng ca thng tin v tuyn bao gm khng ch cc i pht thanh AM (iubin), FM (iu tn) v truyn hnh, m cn rt nhiu cc ng dng khc ca v tuyn nh in

thoi ko di (cordless phone), in thoi di ng t bo (cell phone), iu khin t xa TV vVCR, kha xe hi t xa, m ca gara ...vv.

1


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http://www.ebook.edu.vn2 CHNG 1. GII THIU

C mt s nghi vn c t ra l ai thc s l ngi pht minh v tuyn l mt phngthc truyn tin? Mahlon Loomis, mt nha s ngi M, th nghim in bo khng dy bngvic s dng hai dy ng c s h tr ca hai con diu, di l l ng mnh, lm anten vmt ng h o c th o c dng in rt b cm nhn nhng thay i v dng chy qua

dy th hai khi ni t ca dy dn th nht b ngt qung. ng nhn c bng sng chvo nm 1873 cho h thng ny.

James Clerk Maxwell, ngi c bn phng trnh Maxwell ni ting, tin on v slan truyn ca sng in t trong chn khng vo nm 1862.

Alexander Popov c cho l " s dng thit b ca mnh t c thng tin phc vnghin cu v in kh quyn ... Vo ngy 7 thng 5 nm 1895, trong mt bui thuyt trnh trcHi cc nh Vt l Nga ca St. Petersburg ng tuyn b rng mnh pht i v nhn c cctn hiu mt khong cch 600 yards(1 yard = 91.44 cm). Vo nm 1888 Heinrich Hertz thchin trnh din mt th nghim trong lp hc ti i hc bch khoa Karlsruhe Berlin v vic

to ra v thu nhn cc sng in t truyn lan nh Maxwell tin on.Oliver Lodge, mt gio s thuc i hc Liverpool th nghim vi in bo khng dy vo

nm 1888 v ng sng ch ra mt h thng vo nm 1897. Marconi mua bng sng chca ng vo nm 1911.

Trong tim thc ca cng chng Guglielmo Marconi l ngi danh ting nht v vic "phtminh" ra radio. ng c trao bng sng ch v iu ; v vy, C quan cp Bng sng chtin rng ng pht minh ra v tuyn. Tuy nhin, bo co ca Hi qun M tuyn b

Marconi chc chn khng th c gi l nh pht minh. ng gp ca ng y chyu l cc lnh vc nghin cu ng dng v pht trin k thut. ng y c mts nhy bn rt thc dng trong kinh doanh, v ng y khng b cn tr bi cngs khn trng thc hin cc nghin cu c bn, iu lm cho Lodge v Popovchm tr trong vic pht trin mt h thng v tuyn thng mi

iu ny c l l mt m t chnh xc v vai tr ca Marconi trong vic pht trin cngngh v tuyn, mt mi trng thng tin mi. Nikola Tesla c bng sng ch sm hn, mc dtm im cng vic ca ng dng nh nhm n truyn nng lng ch khng phi l thngtin qua sng v tuyn. Tesla c bit n vi cun dy Tesla to ra in cao p, cc tn hiu

nhn c trn thc t gm cc cm nhiu (bt ngun t vic phng in mnh trong kh quynm ng thc hin) lan truyn vng quanh tri t. Vo nm 1943 Ta n ti cao M ra phnquyt rng cc bng sng ch ca Marconi khng hp l do nhng m t trc ca Tesla,nhng vo thi im c Marconi v Tesla u qua i.

T u nhng nm 1900, radio c mt trong nhiu ng dng thng tin. Vo nm 1962,George Southworth, mt nh nghin cu ni ting trong lnh vc vi ba, vit mt cun sch v40 nm kinh nghim ca mnh trong lnh vc ny. ng bt u:

Mt trong nhng pht trin k thut ngon mc nht ca thi i ca chng ta lv tuyn. T s khi u mang tnh bc ngot ca th k bt u vi in bo gia

tu thy vi t lin, v tuyn c pht trin m rng qua nhiu nm sang inbo gia cc chu lc, truyn hnh, nghin cu v tr v sang c thng tin v tinh.


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Ngy nay, sau hn 40 nm, Southworth c th lm cho danh sch cc ng dng v tuyn camnh di ra thm na. Cc ng dng mi s bao gm thit b m ca gara, cc v tinh nh vton cu GPS, in thoi t bo (cell phone), mng my tnh khng dy (Wireless LAN), ccng dng radar nh o tc , dn ng tu thy v my bay, do thm qun s, dn ng v

kh, kim sot khng lu v cc h thng ngn nga va chm cho t. Ph tn cho cc thit bkhng dy thc t bt u t 535 kHz v iu khin tivi m rng ti di hng ngoi.

S pht trin ca cc ng dng khng dy dng nh khng bao gi l c im kt. Chcchn thp k qua cho thy s bng n trong pht trin cc ng dng v s lng h thngcng rt ln. Bng chng l s ng dng ca in thoi di ng, m ngy nay cnh tranh gaygt vi in thoi c nh v s lng ng dng.

Hnh 1.1: M Morse quc t vn cn l chun cho tn hiu cp cu - SOS (......)

Hu ht ton b mt m m Morse c cho trong Hnh 1.1. M Morse vn cn hu ch,mc d rt t ngi c th dch n ngay lp tc. Mt tn hiu bo hiu cp cu s dng m trongHnh 1.1 c th c pht i nh s dng mt my pht hoc thm ch l mt chic n chpflash. Truyn v tuyn ca Marconi ban u s dng iu ch xung m, chm v gch c thchin bng vic tt v bt my pht. Mt s phao cu h hng hi c th c nhn bit bi mMorse m n ca chng chp sng.

Ngy nay, nu Marconi cn sng chc hn ng s cn mt giy php pht sng, v nu nhng mun tip tc vi k thut truyn dn trc y ca mnh th giy php ca ng chc chns b nh ch do ph tn pht qu rng (Hnh 1.2). Ngun RF ca Marconi l b dao ng sparkgap (Hnh 1.3) chim mt bng tn truyn rt rng. c cp nng lng bi mt my pht invi sc nga, my pht khi hot ng c th nghe thy cch vi dm m khng cn my thuradio.

Marconi t thnh tu ln nht l vo thng 12 nm 1901, khi k t "s" c nhn tiSt.Johns, Newfoundland. N c pht i t Poldhu, Cornwall Anh quc, 1800 dm ngang quai Ty Dng. T trm South Wellfleet (Hnh 1.4, 1.5), chnh Marconi pht i bn tin qua

i Ty Dng u tin vo ngy 17 thng 1 nm 1903, mt thng ip t tng thng M giti vua nc Anh.


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Hnh 1.2: Dng iu ch ca m Morse, c minh ha cho ch R. Ngy nay, dng xung nhch ra trn s c s dng gim ph tn pht, nhng my pht spark gap ca Marconi

khng cn nghi ng g na lm rng bng tn rt nhiu

1.2 Ph tn s v tuyn hin nay

Ph tn s v tuyn ngy nay rt cht tri. t c mt giy php thng mi pht sngkm theo l bn phn s dng bng tn mt cch hiu qu, s dng bng tn mang thng tin cntruyn phi cng hp theo nhu cu thc t cng tt (Bng 1.1 v 1.2).

Ch mi phn b tn s cho nc M khng thi cng khng th b tr vo mt bng ckch thc tng i. Vic phn b tn s chim nhiu trang v iu lut v qui nh ca U

ban Truyn thng Lin bang, v c hng trm ch thch. Do c nhng thay i thng xuyn v

qui nh v iu lut nn n bn mi nht lun cn c tham kho.

Nh chng ta thy trn Bng 1.3, nhng ngi chi radio nghip d ngy nay c phn brt nhiu tn s. iu ny l do lch s cc n lc tin phong ca h, c bit l cc tn s caohn. Chng ta c c s pht trin nhanh chng v v tuyn sng ngn l nh phn ln vocc kt qu th nghim ca nhng ngi khai thc v tuyn nghip d. George Southworth chra rng vo khong nm 1930:

iu th v l trong khi nhng ngi lm in thoi (nhng nh nghin cu tiPhng th nghim ca Bell Telephone) ang thc hin cng trnh nghin cu chuyn

su v cc tn s thp hn ... th nhiu iu xy ra th gii bn ngoi vi cc tns cao hn ... Ngi ta ni rng u im ca sng ngn c khm ph u tin


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http://www.ebook.edu.vn1.2. PH TN S V TUYN HIN NAY 5

Hnh 1.3: Joel Earl Hudson ang ng cnh my pht spark gap ca Marconi vo nm 1907.

bi mt ngi chi v tuyn nghip d, ngi t to cho mnh mt my thu sngngn v sau khi nghe pht hin ra rng anh ta c th nghe cc sng hi ca cc

trm pht qung b xa ... vi khong cch xa hn khong cch tn s c bnc th nghe c. Cc tay chi v tuyn nghip d sau t to cho mnh cc mypht sng ngn v ngay sau xc tin truyn thng hai chiu.

Hot ng ng thi ca li phn b bc x phc tp, mt phn ca n c cho trongBng 1.3, ph thuc vo mi ngi s dng chim dng tn s chnh xc ca mnh, dng iuch, rng bng tn v cng sut bc x hiu dng v hn na, khng xm nhp vo cc bngtn khc bng vic pht cc tn hiu gi vi thit b ca mnh. y l nhim v v thch thc

Bng 1.1: n nh bng tn chungf Bng tn M t

30-300 Hz 104 103 km ELF Tn s cc thp300-3000 Hz 103 102 km VF m tn3-30 kHz 100-10 km VLF Tn s rt thp30-300 kHz 10-1 km LF Tn s thp0.3-3 MHz 1-0.1 km MF Trung tn3-30 MHz 100-10 m HF Cao tn30-300 MHz 10-1 m VHF Tn s rt cao300-3000 MHz 100-10 cm UHF Tn s cc cao

3-30 GHz 10-1 cm SHF Tn s siu cao30-300 GHz 10-1 mm EHF Tn s v cng cao (sng milimet)


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Hnh 1.4: Ngun nng lng chnh cho my pht ca Marconi ti South Wellfleet

Bng 1.2: Cc bng tn viba k hiu theo ch cif(GHz) Tn bng tn

1-2 Bng L2-4 Bng S4-8 Bng C

8-12.4 Bng X12.4-18 Bng Ku18-26.5 Bng K26.5-40 Bng Ka

i vi k thut cao tn ngy nay.

Vic n nh chung cc bng tn c cho trong Bng 1.1 v cc bng tn vi ba c t tntheo ch ci c cho trong Bng 1.2. Ngoi ra, tin t ca cc n v thng dng nh kilo-,Mega-, Giga- ... vv trong mi quan h vi cc n v chun thng qua cc h s tng ng ccho trong Bng 1.4.

Mn hc K thut siu cao tn lin quan n cc mch in hoc cc phn t in hot ngvi cc tn hiu in t vng tn s siu cao. Phm vi ca tn s ny ty thuc vo cc qucgia v cc t chc quc t khc nhau, thng nm trong phm vi t 1 GHz n 300 GHz, tngng vi bc sng t 30 cm n 1 mm (xem Bng 1.1) Mn hc s c chia ra lm hai phnv c phn b trong hai hc k lin tip. Phn th nht l "L Thuyt C s Siu cao tn" cn

phn th hai s trnh by v "Mch Siu Cao Tn".L thuyt C s Siu cao tn bao gm nhng ni dung chnh sau y:


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Hnh 1.5: Trm pht v tuyn u tin ca Marconi ti South Wellfleet, Cap Cod,Massachusetts. Ngi dn a phng d on rng cc anten s b git ngay cn bo u

tin. H ng, v Marconi dng chng li

1. C s truyn sng trn ng truyn sng. Gii thiu cc loi ng dy truyn sngdng trong mch siu cao tn bao gm: Dy song hnh, cp ng trc, ng truyn vi

di (microstrip line), ng truyn di (strip line), coplanar waveguilde CPW, ng dnsng hnh ch nht, hnh trn vv...

2. th Smith- Mt cng c hu ch trong vic gii quyt cc bi ton nh phi hp trkhng, phn tch v thit k mch siu cao tn nh cc b khuch i cao tn (LNA, cngsut) ... vv.

3. Ma trn tn x - l c s cho vic phn tch nh gi mch siu cao tn nh kh nngtruyn dn nh Suy hao xen, Suy hao phn hi vv...

Mch Siu cao tn bao gm nhng ni dung chnh sau y:

1. Gii thiu cc phn t tch cc s dng trong mch siu cao tn, nguyn l hot ng v


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Bng 1.3: Phn b tn s MTn s [kHz] Mc ch phn b490-510 Distress (telegraph)

510-535 Government535-1605 AM radio1605-1750 Land/mobile public safety1800-2000 Amateur radioTn s [MHz] Mc ch phn b26.96-27.23, 462.525-467.475 Citizen band radios30.56-32, 33-34, 35-38, 39-40, 40.02-40.98,41.015-46.6, 47-49.6, 72-73, 74.6-74.8,75.2-76, 150.05-156.2475, 157.1875-161.575,162.0125-173.4 220-222, 421-430, 451-454,456-459, 460-512 746-824, 851-869, 896-901,935-940

Private mobil radio (taxis, trucks, buses,railroads)

74.8-75.2, 108-137, 328.6-335.4, 960-1215,1427-1525, 220-2290, 2310-2320, 2345-2390

Aviation (communication and radar)

162.0125-173.2 Vehicle recovery (LoJack)50-54, 144-148, 216-220, 222-225, 420-450,902-928, 1240-1300, 2300-2305, 2390-2450

Amateur radio

72-73, 75.2-76, 218-219 Radio control (personal)54-72, 76-88, 174-216, 470-608 Television broadcasting VHF and UHF88-99, 100-108 FM radio broadcasting824-849 Cellular telephones

1850-1990 Personal communications1910-1930, 2390-2400 Personal comm. (unlicensed)1215-1240, 1350-1400, 1559-1610 Global Positioning Systems (GPS)Tn s [GHz] Mc ch phn b0.216-0.220, 0.235-0.267, 0.4061-0.45, 0.902-0.928, 0.960-1.215, 1.215-2.229, 2.320- 2.345,2.360-2.390, 2.7-3.1, 3.1-3.7, 5.0- 5.47,5.6-5.925, 8.5-10, 10.0-10.45, 10.5- 10.55,13.25-13.75, 14-14.2, 15.4-16.6, 17.2- 17.7,24.05-24.45, 33.4-36, 45-46.9, 59-64, 66-71,

76-77, 92-100

Radar, all types

2.390-2.400 LANs (unlicensed)2.40-2.4835 Microwave ovens45.5-46.9, 76-77, 95-100, 134-142 Vehicle, anticollision, navigation10.5-10.55, 24.05-24.25 Police speed radar 0.902-0.928, 2.4-2.5, 5.85-5.925 Radio frequency identi.cation (RFID)3.7-4.2, 11.7-12.2, 14.2-14.5, 17.7-18.8, 27.5-29.1, 29.25-30, 40.5-41.5, 49.2-50.2

Geostationary satellites with .xed earthreceivers

1.610-1626.5, 2.4835-2.5, 5.091-5.25, 6.7-7.075, 15.43-15.63

Nongeostationary satellites, mobile receivers(big LEO, global phones)

0.04066-0.0407, 902-928, 2450-2500, 5.725-5.875, 24-24.25, 59-59.9, 60-64, 71.5-72,103.5-104, 116.5-117, 122-123, 126.5-127,152.5-153, 244-246

Unlicensed industrial, scienti.c, and medicalcommunication devices


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Tn s [GHz] Mc ch phn b3.3-3.5, 5.65-5.925, 10-10.5, 24-24.25, 47- 47.2 Amateur radio6.425-6.525, 12.7-13.25, 19.26-19.7, 31-31.3 Cable television relay27.5-29.5 Local multipoint TV distribution

12.2-12.7, 24.75-25.05, 25.05-25.25 Direct broadcast TV (from satellites)0.928-0.929, 0.932-0.935, 0.941-0.960,1.850- 1.990, 2.11-2.20, 2.450-2.690, 3.7-4.2,5.925-6.875, 10.55-10.68, 10.7-13.25, 14.2-14.4, 17.7-19.7, 21.2-23.6, 27.55-29.5, 31-31.3, 38.6-40

Fixed microwave (public and private)

Bng 1.4: Cc tin t chunTin t Vit tt H stera T 1012

giga G 109

mega M 106

kilo k 103

hecto h 102

deka da 10deci d 101

centi c 102

milli m 103

micro m 106

nano n 109

pico p 1012femto f 1015

atto 1018

phm vi ng dng ca chng

2. Nguyn tc thit k mch khuch i siu cao tn (LNA, cng sut), mch dao ng siucao tn

3. Mch chia cng sut, ghp nh hng v ghp hn hp (hybrid), Circulator v Isolator

v cui cng l cc im gin on (discontinuities).4. Mch lc siu cao tn (thng di, cao, thp, chn di).

Ty theo khi lng thi gian dnh cho bi tp ln (hay thit k mn hc) sinh vin s cgiao nhim v thit k mt mch c th (ty chn hoc c giao).


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Chng 2

L thuyt ng truyn

Xt nhiu kha cnh l thuyt ng truyn lm cu ni cho s cch bit gia php phn tchtrng v l thuyt mch c s, v v vy n rt quan trng trong phn tch mch siu cao tn.

Nh chng ta s thy, hin tng lan truyn sng trn cc ng dy c th c tip cn t vicm rng l thuyt mch, hoc t s bin i c bit cc phng trnh Maxwell; Trong khunkh ca chng trnh chng ta s ch trnh by cch tip cn t quan im l thuyt mch cs v ch ra s truyn lan sng ny c m t bi cc phng trnh rt ging cc phng trnhsng cho truyn lan sng phng nh th no.

Khi khong cch t ngun n ti ca mt mch in c chiu di so snh c vi bcsng hoc ln hn nhiu ln so vi bc sng th tn hiu c pht i t ngun phi mt mt

khong thi gian (mt vi chu k) lan truyn n ti. Ta gi l hin tng truyn sngtrn ng dy.

Truyn sng siu cao tn trn ng dy c cc h qu sau:

C s tr pha ca tn hiu ti im thu so vi tn hiu ti im pht.

vr(t) = vt(t .l) (2.1)

Khong thi gian tr ny s t l vi chiu di ca ng truyn. Trong l khongthi gian cn thit sng di chuyn c mt n v chiu di ca ng truyn [s/m]

C s suy hao bin tn hiu khi lan truyn

vr(t) = K(l).vt(t .l) (2.2)

H s suy hao K(l) < 1 v ph thuc vo chiu di ca ng truyn.

C s phn x sng trn ti v trn ngun. iu ny dn n hin tng sng ng trnng dy.

Sng ng, hay cn gi l sng dng, l sng m lun duy tr v tr khng i.Hin tng ny c th xut hin do mi trng chuyn ng ngc vi chiu

di chuyn ca sng, hoc n c th xut hin trong mt mi trng tnh do sgiao thoa gia hai sng chuyn ng ngc chiu nhau.

11


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http://www.ebook.edu.vn12 CHNG 2. L THUYT NG TRUYN

y ta khng xt v trng hp mi trng chuyn ng m l mi trng tnh (ngtruyn). Sng ng trn ng truyn l sng m trong phn phi dng, p hay cng trng c to thnh bi s xp chng hai sng lan truyn ngc chiu nhau. Kt qul mt lot cc nt (khng dch chuyn) v cc im bng sng (dch chuyn ti a) ti

nhng im c nh dc theo ng truyn. Sng ng nh vy c th c hnh thnhkhi mt sng c truyn vo mt u ca ng truyn v b phn x ngc tr li tu kia do s bt phi hp tr khng, h mch hoc ngn mch.

Cc hin tng trn s c phn tch c th trong cc phn sau.

Mt s khi nim khc cng cn cp y l mch in thng s tp trungv mchin c thng s phn b hay phn b ri.

Thng s tp trung ca mch in l cc i lng c tnh in xut hin hoc tn ti mt

v tr no ca mch in. Thng s tp trung ca mt phn t in c th xc nhc thng qua phn tch, tnh ton hoc c th o c trc tip. Chng hn cc phn tin tr, in cm, in dung, ngun p, ngun dng, diode, transitor ... u l cc phnt thng s tp trung.

Thng s di ca mch in cng l i lng c tnh in, nhng khng tn ti duy nht mt v tr c nh, m chng ri u trn chiu di ca mch in . Thng s phn bthng c dng trong cc h thng truyn sng (ng dy truyn sng, ng dn sng,khng gian t do) biu th cc c tnh tng ng v in ca h thng. Thng s phn

b thng l cc thng s tuyn tnh c xc nh trn mt n v chiu di ca ngtruyn sng. Chng ta khng th o c trc tip gi tr ca cc thng s phn b m chc th suy ra chng t cc php o tng ng trn cc thng s khc. Vn ny sc cp chi tit hn phn sau.

2.1 Phng trnh truyn sng trn ng dy

Trong phn ny, chng ta s tm cch thit lp phng trnh nu ln mi quan h gia in pv dng in ti mt im c ta bt k trn ng truyn sng, t gii phng trnh tnhin p, dng in v rt ra cc c tnh truyn sng.

Mt cch tng qut, kho st mt h truyn sng chng ta phi xut pht t h phngtrnh Maxwell trong mi trng khng ngun, trong c cc i lng vt l c bn l cng in trng E v cng t trng H.

E = j H (2.3a)

H = j E (2.3b)

. D = 0 (2.3c)

. B = 0 (2.3d)


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http://www.ebook.edu.vn2.1. PHNG TRNH TRUYN SNG TRN NG DY 13

Trong D = E, B = H

Tuy nhin v ta ch kho st vic truyn sng trong mt khng gian nh c nh hng nn

ta c th n gin ha vic gii h phng trnh Maxwell bng vic gii h phng trnh tngng vit cho in p v dng in trong in p thay cho in trng E v dng in thaycho t trng H nh chng ta s thy trong Mc 2.1.2.

2.1.1 M hnh mch in thng s tp trung ca ng truyn - Cc thngs s cp

S khc nhau c bn gia l thuyt mch v l thuyt ng truyn l kch thc in. Trongphn tch mch in ngi ta thng gi thit rng kch thc vt l ca mt mch nh hn rt

nhiu bc sng in, trong khi di cc ng truyn c th l mt phn ng k ca bcsng hoc nhiu bc sng. V vy, mt ng truyn l mt mch thng s phn b, inp v dng in c th thay i v bin v pha theo di ca n.

Hnh 2.1: ng truyn sng

Mt ng truyn thng c biu din bng mt ng hai dy nh trn Hnh 2.1, do ccng truyn (h tr sng TEM) lun c t nht hai dy dn.

Xt mt ng truyn sng chiu di , c ta c xc nh nh trn Hnh 2.1. u vong truyn c ngun tn hiu Vs, tr khng ngun Zs, u cui ng truyn c kt cui

bi ti ZL.

Gi thit ng truyn c chiu di ln hn nhiu ln bc sng hot ng nn n ccoi l mch c thng s phn b.

Ti mt im c ta z bt k trn ng dy xt mt on dy chiu di vi phn z.Trn on dy ny cng c hin tng lan truyn sng, tuy nhin do z

nn on dy ny

c th c m hnh ha bng mch gm cc phn t thng s tp trung nh m t trn Hnh2.2, vi R, L, G, C l cc i lng c tnh trn mt n v chiu di nh sau:


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Hnh 2.2: Mch in tng ng ca on ng truyn vi phn

R= in tr ni tip, n v /m, c trng cho in tr thun ca c hai dy kim loi trnmt n v di. in tr R lin quan n tn hao kim loi (do dy dn khng phi l dnin l tng) l thng s ph thuc vo tn s hot ng (do hiu ng da, do ghp k sinh ...).

L= in cm ni tip, n v H/m, c trng cho in cm tng ng ca c hai dy dnkim loi trn mt n v di ng truyn.

G= in dn song song, n v S/m, c trng cho in dn thun ca lp in mi phncch trn mt n v di ng truyn. N lin quan n tn hao in mi (do in mikhng cch in l tng), thng c nh gi da trn gc tn hao (loss tangent) ca vt liu

in mi.C= in dung song song, n v F/m, c trng cho in dung ca lp in mi phn cch

hai dy dn kim loi trn mt n v di ng truyn.

Nh vy ta thy trn ng truyn c hai loi tn hao l tn hao kim loi gy ra bi R vtn hao in mi do G gy ra.

Mt cch tng qut mch in tng ng ca ng truyn gm hai thnh phn l:

1. Tr khng ni tipZ = R + jL (2.4)

2. v Dn np song songY = G + jC (2.5)

Trong R, L, G, C l cc thng s s cp ca ng truyn sng.

2.1.2 Phng trnh truyn sng

T mch in trn Hnh 2.2, p dng nh lut Kirchhoff cho in p ta c

v(z, t) = v(z + z, t) + R.z.i(z, t) + L.z.i(z, t)

t(2.6)


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trong khi nh lut Kirchhoff p dng cho dng in cho

i(z, t) = i(z + z, t) + G.z.v(z + z, t) + C.z. v(z + z, t)t

(2.7)

Chia 2.6 v 2.7 cho z sau ly gii hn khi cho z 0 cho cc phng trnh vi phn sau:v(z, t)

z= R.i(z, t) L. i(z, t)

t, (2.8a)

i(z, t)

z= G.v(z, t) C. v(z, t)

t, (2.8b)

Cc phng trnh ny l cc phng trnh ng truyn trong min thi gian. i vi trng thin nh iu ha vi dng sng cosin, ta c th vit li (2.8a) v (2.8b) trong min tn s thngqua php bin i Fourier nh sau:

dV(z, )dz

= (R + jL)I(z, ) (2.9a)

dI(z, )

dz= (G + jC)V(z, ) (2.9b)

Phng trnh ny tng t nh hai phng trnh Maxwell (2.3a) v (2.3b) nh cp. N chothy mi quan h gia in p v dng in ti mt im z bt k trn ng truyn sng v titn s bt k ca tn hiu.

Gii h phng trnh trn tm nghim V(z, ) v I(z, ) v t suy ra c tnh truynsng.

Ly o hm 2 v ca 2.9a v 2.9b c

d2V(z, )

dz2= (R + jL).(G + jC).V(z, ) (2.10a)

d2I(z, )

dz2= (R + jL).(G + jC).I(z, ) (2.10b)

Ngi ta nh ngha hng s lan truyn phc (l hm ca tn s) v khng ph thuc vota z nh sau:

() = () + j() =

(R + jL).(G + jC) (2.11)

Trong v l h s suy hao [dB/m] v h s pha [rad/m].

Ta c th vit li 2.10a v 2.10b nh sau:

d2V(z, )

dz2 ()2.V(z, ) = 0 (2.12a)

d2I(z, )

dz2 ()2.I(z, ) = 0 (2.12b)

y chnh l cc phng trnh sng in p v dng in. ta thy hai phng trnh trnng dng do dng nghim ca hai phng trnh cng s ging nhau.


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2.1.3 Nghim ca phng trnh sng. Sng ti v sng phn x

Phng trnh (2.12a) v (2.12b) l cc phng trnh vi phn bc hai thun nht c dng nghim(sng chy) nh sau:

V(z, ) = V+0 e().z + V0 e().z (2.13a)

I(z, ) = I+0 e().z + I0 e

().z (2.13b)

Trong V+0 (I+0 ) v V

0 (I

0 ) l nhng hng s phc c xc nh bi iu kin bin v in

p (dng in) ti ngun (z = 0) v ti ti (z = ) ca ng truyn sng.

n gin trong k hiu ta b qua bin s v ngm hiu rng cc phng trnh trn cngnh nghim ca chng l hm ca tn s (hay ph thuc vo tn s). Ta vit li (2.13) nh sau:

V(z) = V+0 ez + V0 e

+z (2.14a)

I(z) = I+0 ez + I0 e

z (2.14b)

Trong ez i din cho sng truyn lan theo hng +z cn ez i din cho sng truyn lantheo hng -z.

Nghim trn l dng iu ha thi gian ti tn s . Trong min thi gian, kt qu ny cvit (cho dng sng in p) l

v(z, t) = |V+0 | cos(t z + +)ez + |V0 | cos(t + z + )ez (2.15)

Trong l gc pha ca in p phc V0 . Ta nhn thy s hng th nht ca (2.15)biu din mt sng chuyn ng theo hng +z v duy tr mt im c nh trn sng(t z + +) = const = hng s th sng phi di chuyn theo hng +z (sng ti) khi thigian tng ln. Tng t s hng th hai trong (2.15) biu din mt sng chuyn ng theo chium ca z (sng phn x). V vy m cc biu thc trn ta s dng k hiu V+0 v V

0 cho bin

ca cc sng ny.

Ta bit rng bc sng c nh ngha l khong cch mt im trn sng di chuyn giahai im cc i hoc cc tiu v tng ng vi vic sng di chuyn c mt chu k l 2.V vy ta c

[t

z + +0 ]

[t

(z + ) + +0 ] = 2 (2.16)

T y ta rt ra bc sng trn ng dy l

=2

(2.17)

v vn tc pha c nh ngha l tc ca mt im c nh trn sng di chuyn c chobi

p =dz

dt=

d

dt(

t const

) =

= f (2.18)

Mt khc p dng (2.9a) cho (2.14a) ta rt ra c biu thc ca dng in trn ng dy

nh sau: I(z) = R + jL

V+0 e

z V0 ez

(2.19)


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So snh (2.19) vi (2.14b) ch ra rng tr khng c tnh Z0 ca ng truyn c th c nhngha nh sau:

Z0 =

R + jL

=R + jL

G + jC(2.20)

Quan h gia in p v dng in trn ng dy nh sau

V+0I+0

= Z0 = V0

I0(2.21)

Tr khng c tnh Z0 l mt s phc, ph thuc vo cu trc vt l ca ng truyn sng.

Hnh 2.3: Sng ti v sng phn x

Nh vy chng ta thy rng, sng in p v sng dng in ti mt im z bt k trn

ng truyn u l s xp chng ca hai sng l sng ti v sng phn x. Hai sng ny cminh ha ring r trong Hnh 2.3.


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2.1.4 Cc thng s th cp

Nh trnh by trong mc 2.1.1, cc thng s R, L, G, C l cc thng s s cp ca ngtruyn sng v chng lin quan n thng s ca mch in tng ng c bn cho mt vi phn di ng truyn. Tuy nhin cc thng s trn khng th hin r cc tham s c tnh caqu trnh truyn sng v khng o c c trc tip trn ng dy.

Cc thng s th cp sau y c suy ra t cc thng s s cp trn, din t kh y ctnh truyn sng v c th o trc tip nh cc thit b o chuyn dng. Chng ta ln lt khost ngha ca tng thng s.

Hng s truyn lan

Hng s truyn lan sng nh c nh ngha mc 2.1.2 l

() = () + j() =

(R + jL).(G + jC) (2.22)

vi l h s suy hao tnh trn mt n v chiu di, n v [dB/m] hoc [Np/m], l h spha trn mt n v chiu di, n v [rad/m] hoc [/m]

Quan h gia [dB/m] v [Np/m] c xc nh nh sau:

[dB/m] = 20 log10 e[Np/m] = 8.686 [Np/m] (2.23)

Tc l 1N p = 20 log e = 8.686 dB (2.24)

Hng s pha biu din bin thin v gc pha ca sng khi lan truyn trn mt n vchiu di ng truyn.

Ta nhn thy v u bin thin theo tn s tn hiu, do rt kh o chnh xc trnng truyn sng thc t. Tuy nhin chng ta s xt cc h s ny trong nhng trng hp c

bit

ng truyn khng tn hao (R=0, G=0)T (2.22) ta suy ra

=

(jL).(jC) = j

LC (2.25)

So snh (2.25) vi (2.22) ta suy ra

= 0; =

LC (2.26)

H s suy hao =0 khng nh li khng c suy hao trn ng truyn (v R=0, G=0).

H s t l vi tn s tn hiu (ng truyn c pha tuyn tnh tng ng vi trng

hp khng c tn x tn s trn ng truyn). V lc ny vn tc pha lun l hng s vimi tn s p=1/

LC


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ng truyn c tn hao thpTrong trng hp ny, cc yu t gy tn hao n ng truyn khng th b qua tuynhin nh hng ca chng khng qu ln n cc thng s truyn sng.

Tn hao thp ngha l phi tha mn cc tiu chun sau:R L (2.27a)

G C (2.27b)Khi (2.22) c th c vit li thnh

=

(R + jL)(G + jC) = j

LC.

1 +

R

jL

.

1 +

G

jC

(2.28)

Do (2.27) nn R/L v G/C l cc v cng b so vi 1. S dng cng thc chuiTaylor sau:

(1 + )u 1 + u. (2.29)trong l mt v cng b, u l hng s bt k

Vi 2.29, 2.28 tr thnh

j

LC.

1 +

R

j2L

.

1 +

G

j2C

= j

LC1 +R

j2L+

G

j2C+

R

j2L.

G

j2C (2.30)Trong biu thc (2.30), R/j2L v G/2jC l cc v cng b so vi 1, cn thnh phn(R/j2L).(G/j2C) l v cng b bc hai so vi 1 nn s hng ny c th c b qua.Khi (2.30) tr thnh

j

LC

1 +

R

j2L+

G

j2C

=1

2

R

C

L+ G

L

C

+ j

LC (2.31)

So snh (2.31) vi (2.22) ta rt ra:H s suy hao

=1

2

R

C

L+ G

L

C

(2.32)

l mt hng s (khng ph thuc vo tn s), t l vi tn hao kim loi R v tn hao inmi G ca ng truyn.

H s pha =

LC hon ton ging trng hp ng truyn khng tn hao. Nh vyvi ng truyn tn hao t th cng c pha tuyn tnh v do khng c tn x tn s.y l trng hp gn vi thc t nht bi cc ng dn sng hin nay c tn hao thp.

Tuy nhin cn lu , kt lun trn ch c tnh tng i v chng ta b qua thnh phnv cng b bc cao.


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Tr khng c tnh

Tr khng c tnh Z0 ca ng truyn c quan h vi cc thng s s cp qua biu thc sau:

Z0() =

R + jLG + jC

n v (2.33)

Ta thy rng Z0 l mt hm ca tn s v iu ny gy kh khn cho vic kho st chi tit mtng truyn sng. Tuy nhin, ta s xt mt s trng hp c bit:

ng truyn khng tn hao (R=0, G=0)T2.126 suy ra

Z0 = L

C R0 (2.34)

l mt hng s thc, c gi l in tr c tnh ca ng dy. Trong thc t ta thnggp cc ng truyn sng c R0 = 50 (cp ng trc), R0 = 300 (ng dy inthoi) vv...

Vi ng truyn tn hao thp (R L,G C).Khi

Z0 =

L

C

1 + RjL1 + G

jC

(2.35)

Do R/L v G/C l cc v cng b so vi 1 nn p dng (2.29) ta c th vit li 2.35

nh sau:

Z0

L

C.(1 +

R

j2L)(1 G

j2C)

=

L

C

1 +

R

j2L G

j2C

R

j2L.

G

j2C

(2.36)

Ta cng b i thnh phn v cng b bc 2, khi

Z0 =

L

C1 +R

j2L G

j2C (2.37)Do

R0 =

L

C(2.38a)

X0 = 12

R

L G

C

(2.38b)

Ta thy cc tn s cng cao th in khng cng nh v do ta c th coi Z0 l mt sthc.

Th (3.47a) vo (2.32) ta c

= R2R0

+ GR02

(2.39)


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Vn tc truyn sng - Vn tc pha

Vn tc truyn sng hay vn tc pha c nh ngha l qung ng sng lan truyn dc theong truyn sng trong mt n v thi gian. Vn tc ny cng chnh l vn tc ca mt imc nh trn sng di chuyn dc theo ng truyn. K hiu vn tc truyn sng l p v n vl [m/s].

Nh cp trong mc 2.1.3 ta rt ra

p =

(2.40)

vi l tn s gc ca tn hiu lan truyn, n v [rad/s].

Ta bit rng l mt hm ca tn s nn vn tc pha p cng l mt hm ca tn s. iuny c ngha l vn tc truyn sng trn mt ng dy c th ln hay nh ty theo tn s catn hiu lan truyn trn ng dy. Nu tn hiu t vo u ng dy gm nhiu tn s khcnhau (chng hn nh tn hiu xung, tn hiu logic, sng iu ch ) th mi thnh phn tn ss lan truyn vi tc khc nhau. Do cc thnh phn tn s ny s n u kia ca ngtruyn nhng thi im khc nhau dn ti dn rng xung v mo dng tn hiu. Hin tngny c gi l tn x tn s (frequency dispersion).

Thng thng, hin tng tn x tn s xy ra trn cc ng truyn c tn hao, cc ngtruyn ghp hoc cc ng truyn khng ng nht cu trc vv s gy ra mo dng ln.

Vi ng truyn khng tn hao nh phn tch cc phn trc =

LC nn theo2.18, p s tr thnh mt hng s c lp vi tn s

p =

=

1LC

(2.41)

Trong trng hp ny p khng cn ph thuc vo tn s nn khng c tn x tn s v dnti khng cn mo dng tn hiu. Mt khc bin tn hiu cng khng suy gim do khng csuy hao. Nh vy, mt tn hiu c dng sng bt k t u vo ng truyn s gi nguyndng sng v bin ti u cui ng truyn. Tuy nhin c s tr pha do qu trnh lan truynsng. y l trng hp l tng nht, m bo tnh trung thc ca tn hiu.

Ta nhn thy rng khi L, C tng th vn tc lan truyn sng gim nn cc ng truyn cvn tc truyn sng thp thng c s dng vo mc ch lm tr tn hiu (m khng lm suygim bin v mo dng tn hiu) trong mt s ng dng. Thi gian tr yu cu cng cao thL, C i hi cng ln. L ln i hi khong cch gia 2 dy tng, cn C ln i hi hng sin mi ( gia hai dy ln). Cng ngh vt liu ngy nay cho php tr s t n cc gi trt 10 n vi chc.

Hng s thi gian hay thi gian tr

Hng s thi gian hay thi gian tr ca mt ng truyn sng c nh ngha l khong thi

gian cn thit sng lan truyn c mt n v chiu di ca ng truyn, n v ca l[s/m].


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T nh ngha, ta suy ra

=1

p=

(2.42)

Nh vy, nhn chung ph thuc vo tn s

Trng hp ng truyn khng tn hao th t (2.41) v (2.42), ta c

=1

p=

LC (2.43)

Khi l hng s, c lp vi tn s.

2.2 Cc ng truyn sng v ng dn sng thc t

Cc ng truyn v ng dn sng ch yu c s dng phn pht nng lng cao tn tmt im ny ti mt im khc v v vy c th c xem l cc thnh phn mch cao tn c

bn. Trong phn ny chng ta s ln lt kho st c tnh ca mt s loi ng truyn v ngdn sng c s dng ph bin. Trong phn trc ta bit rng mt ng truyn c ctrng bi mt hng s truyn lan v mt tr khng c tnh; nu ng truyn c tn hao th suyhao cng l vn cn quan tm. Cc i lng ny c rt ra nh php phn tch l thuyttrng i vi nhiu ng truyn v ng dn sng khc nhau.

Chng ta s bt u bng vic tho lun chung v cc kiu lan truyn v cc mode lan truynkhc nhau c th tn ti trn cc ng truyn v ng dn sng. Cc ng truyn gm hai haynhiu dy dn c th h tr sng in t ngang TEM, c trng bi s thiu vng cc thnh phntrng dc theo phng lan truyn. Cc sng TEM c mt in p, dng in v tr khng ctnh xc nh duy nht. Cc ng dn sng, thng gm duy nht mt dy dn, h tr cc sngin ngang TE v/hoc sng t ngang TM, c trng bi s c mt ca cc thnh phn t trngdc hay in trng dc tng ng. Vi trng hp ny ta khng th a ra mt nh ngha duynht v tr khng c tnh cho cc sng nh vy, mc d cc nh ngha c th c chn saocho khi nim tr khng c tnh c th c s dng cho cc ng dn sng vi nhng kt quc ngha.

2.2.1 Phng trnh Helmholtz

Trong mi trng ng nht, ng hng, tuyn tnh v khng c ngun, cc phng trnhMaxwell c dng

E = jH (2.44a)

H = jE (2.44b)trong

= r.0 (2.45a)

= r.0 (2.45b)


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http://www.ebook.edu.vn2.2. CC NG TRUYN SNG V NG DN SNG THC T 23

vi 0 = 109/36 = 8.842.1012[F/m] v 0 = 4.107[H/m] l hng s in mi v hngs t thm trong mi trng chn khng, r v r l hng s in mi v h s t thm tngi ca mi trng ang xt so vi mi trng chn khng.

Hai phng trnh (2.44a) v (2.44b) l mt h phng trnh gm 2 n s l E v H. V vyta c th gii cho hoc E hoc H. Do , ly curl (2.44a) v s dng (2.44b) cho ta

E = j H = 2E, (2.46)

l mt phng trnh i vi E. S dng ng nht thc sau A = (.A) 2A cho(2.46) ta c

2E+ 2E = 0 (2.47)do .E = 0 trong mi trng khng ngun. Phng trnh (2.47) l phng trnh sng hay cngi l phng trnh Helmholtz cho E. Mt phng trnh nh vy cho H cng c th c rt ra

theo cch trn 2H+ 2H = 0 (2.48)

2.2.2 Nghim tng qut cho cc sng TEM, TE v TM

Trong phn ny chng ta s tm nghim tng qut ca cc phng trnh Maxwell 2.44 cho cctrng hp c th lan truyn sng TEM, TE v TM trong cc ng truyn hoc ng dn snghnh tr. Dng hnh hc ca mt ng truyn hay ng dn sng bt k c cho trong Hnh 2.4v c c trng bi cc iu kin bin song song vi trc z. Cc cu trc ny c gi thitl ng nht theo hng z v di v hn. Cc dy dn ban u c gi thit l c tnh dn inhon ho, nhng suy hao c th c xc nh bng phng php perturbation.

Hnh 2.4: (a) ng truyn hai dy ni chung v (b) ng dn sng khp kn

Ta gi thit trng y l cc hm tun hon theo thi gian ph thuc vo ejt v sng lantruyn dc theo trc z. Cc trng in v t c th c vit nh sau:

E(x,y,z) = [e(x, y) + zez(x, y)]ejz (2.49a)


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H(x,y,z) = [h(x, y) + zhz(x, y)]ejz (2.49b)

y e(x, y) v h(x, y) i din cho cc thnh phn in trng v t trng ngang, trong khi

ez v hz l cc thnh phn in trng v t trng dc. Trong biu thc trn sng lan truyntheo phng +z; truyn theo phng -z c th c biu din bng cch thay th bng -. Hnna, nu c tn tht kim loi hay in mi th hng s truyn lan s l mt s phc; j khi c thay bng = + j.

Gi thit trong khng gian cha ng truyn hay ng dn sng l mi trng khng ngun,cc phng trnh Maxwell c th c vit thnh

E = jH (2.50a)

H = jE (2.50b)vi s ph thuc z bi h s ejz, ba thnh phn ca cc phng trnh vect c th c rtgn thnh:

Ezy

+ j Ey = jHx, (2.51a)

j Ex Ezx

= jHy, (2.51b)

Eyx

Exy

= jHz, (2.51c)

Hzy

+ j Hy = jEx, (2.52a)

j Hx Hzx

= jEy, (2.52b)

Hyx

Hxy

= jEz, (2.52c)

Su phng trnh trn c th c gii cho bn thnh phn trng ngang theo Ez v Hz (chng

hn, Hx c th c rt ra bng cch loi trEy khi (2.51a) v (2.52b)) nh sau:

Hx =j

k2c

Ezy

Hzx

(2.53a)

Hy =jk2c

Ezx

+ Hzy

(2.53b)

Ex =jk2c

Ezx

+ Hzy

(2.53c)

Ey =j

k2c

Ez

y+ H

z

x

(2.53d)


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Trong k2c = k

2 2 (2.54)c nh ngha l s sng ct, l do cho thut ng ny s c lm sng t sau. Nh ta bit

k = = 2/ (2.55)

l s sng ca vt liu in mi s dng cho ng truyn hay nhi trong ng dn sng. Nuc tn tht in mi th c th c thay bng = 0r(1 j tan ), trong tan l gc tntht ca vt liu.

Cc phng trnh (2.53(a-d)) l cc kt qu tng qut rt hu ch c th c p dng chonhiu h thng dn sng khc nhau. By gi chng ta s p dng cc kt qu ny cho cc loisng c bit.

Sng TEM

Cc sng in t ngang (TEM) c trng bi Ez = Hz = 0. Quan st t (2.53) thy rng nuEz = Hz = 0 th tt c cc trng ngang cng bng khng, tr khi k2c = 0(k

2 = 2) trongtrng hp chng ta s c kt qu v nh. V vy chng ta quay v ( 2.51) v (2.52) v pdng iu kin Ez = Hz = 0. Khi t (2.51a) v (2.52a) chng ta c th loi tr Hz tc

2Ey = 2Ey,

hay

= = k, (2.56)nh ta lu trn. (kt qu ny cng c th t c t (2.51b) v (2.52b)). V th i visng TEM s sng ct kc =

k2 2 bng 0.

By gi phng trnh Helmholtz cho Ex l2

x2+

2

y2+

2

z2+ k2

Ex = 0 (2.57)

nhng do s ph thuc ejz nn (2/z2)Ex = 2Ex = k2Ex, v khi (2.57) tr thnh2

x2+

2

y2

Ex = 0 (2.58)

Kt qu tng t cng p dng cho Ey, v vy s dng dng biu din ca E trong (2.49a) ta cth vit

2t e(x, y) = 0 (2.59)trong 2t = 2/x2 + 2/y2 l ton t Laplace hai chiu theo phng ngang.

Kt qu 2.59 ch ra rng cc trng in ngang e(x, y) ca sng TEM tha mn phng trnhLaplace. Cng theo cch ta d dng ch ra rng cc trng t ngang cng tha mn phng

trnh Laplace: 2t e(x, y) = 0 (2.60)


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Cc trng ngang ca mt sng TEM v vy ging nh trng tnh tn ti gia cc vt dn.Trong trng hp tnh in ta bit rng in trng c th c biu th bng Gradient ca mttrng in th v hng, (x, y):

e(x, y) = t(x, y) (2.61)trong t = x(/x) + y(/y) l ton t gradient hai chiu theo phng ngang. miquan h (2.61) hp l th curl ca e phi trit tiu v iu ny ng bi v

t e = jhz z = 0 (2.62)S dng thc t rng .D = t.e = 0 cng vi (2.61) ch ra rng (x, y) cng tha mn

phng trnh Laplace,2t (x, y) = 0 (2.63)

Nh chng ta bit trong trng hp tnh in. in p gia hai dy dn c th c tm thy nh

sauV12 = 1 2 =

21

E.d (2.64)

1 v 2 tng ng l in th trn dy dn 1 v 2. Dng in chy trn mt dy dn cth c xc nh theo nh lut Ampere nh sau

I =

c

H.d (2.65)

trong C l ng cong ct ngang bao quanh dy dn.

Cc sng TEM c th tn ti khi c mt hai hay nhiu dy dn. Cc sng phng cng lnhng v d v sng TEM, do khng c thnh phn trng nm trong hng lan truyn; trongtrng hp ny cc dy dn ca ng truyn c th c xem l hai tm kim loi phng rngv hn. Cc kt qu trn cho thy rng mt dy dn khp kn (chng hn nh ng dn sng hnhch nht) khng th h tr sng TEM do in th tnh ni ti s bng 0 (hay c th l 1 hngs), dn ti e = 0.

Tr khng sng ca mt mode TEM c th c xc nh bng t s ca in trng v ttrng. S dng (2.52a) ta rt ra

ZTEM =Ex

Hy=

=

= (2.66)

S dng mt cp thnh phn trng ngang t (2.51a) cho ta

ZTEM =EyHx

=

=

= (2.67)

Kt hp cc kt qu ca (2.66) v (2.67) cho ta biu thc tng qut cho cc trng ngang

h(x, y) =1

ZTEMz e(x, y) (2.68)

Ta cn lu rng tr khng sng ging nh tr khng ca mt sng phng trong mi trngkhng tn hao. Ta khng nn nhm ln tr khng ny vi tr khng c tnh Z0 ca ng


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truyn. Tr khng c tnh ca ng truyn thit lp quan gia h in p ti vi dng in tiv l mt hm ca dng hnh hc ca ng dy cng nh vt liu bao ph ng dy, trongkhi tr khng sng thit lp quan h gia cc thnh phn trng v ch ph thuc vo cc hngs vt liu.

Trnh t phn tch ng truyn TEM c th c tm tt nh sau:

1. Gii phng trnh Laplace 2.63 cho (x, y). Nghim s bao gm mt s hng s cha bit

2. Tm cc hng s ny bng cch p dng cc iu kin bin cho cc in p trn cc dydn.

3. Tnh e v E t2.61, 2.49a. Tnh h, H t2.68, 2.49b.

4. Tnh V t2.64 v I t2.65

5. Hng s truyn lan cho bi 2.56, v tr khng c tnh c cho bi Z0 = V /I.

Sng TE - Transverse Electric Waves

Cc sng in ngang (cn gi l sng H) c c trng bi Ez = 0 v Hz = 0. Cc phngtrnh (2.53) khi tr thnh

Hx =j

k2c

Hzx

(2.69a)

Hy =j

k2c

Hzy

(2.69b)

Ex =j

k2c

Hzy

(2.69c)

Ey =j

k2c

Hzx

(2.69d)

Trong trng hp ny kc

= 0 v hng s truyn lan = k2

k2c nhn chung l mt hm ca

tn s v dng hnh hc ca ng truyn hay ng dn sng. p dng cc biu thc (2.69)trc ht ta phi tm Hz t phng trnh sng Helmholtz,

2

x2+

2

y2+

2

z2+ k2

Hz = 0 (2.70)

do Hz(x,y,z) = hz(x, y)ejz nn phng trnh ny c th rt gn thnh phng trnh sng haichiu cho hz:

2

x2+

2

y2+ k2c

hz = 0 (2.71)

do k2c = k2 2. Phng trnh ny phi c gii theo cc iu kin bin ca dng dn sng cth.


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Tr khng sng TE c th c xc nh theo

ZTE =ExHy

=EyHx

=

=

k

(2.72)

c xem l ph thuc vo tn s. Cc sng TE c th c h tr bn trong cc ng dn kncng nh gia hai hay nhiu dy dn.

Sng t ngang TM - Transverse Magnetic Waves

Cc sng t ngang TM (cn gi l sng E) c c trng bi Ez = 0 v Hz = 0. Cc phngtrnh (2.53) khi tr thnh

Hx =j

k2c

Ezy

(2.73a)

Hy =j

k2c

Ezx

(2.73b)

Ex =j

k2c

Ezx

(2.73c)

Ey =j

k2c

Ezy

(2.73d)

Cng nh trong trng hp TE, kc = 0 v hng s truyn lan = k2 k2c l mt hm ca tn

s v hnh dng ca ng dy hay ng dn. Ez c tm thy t phng trnh sng Helmholtz,2

x2+

2

y2+

2

z2+ k2

Ez = 0 (2.74)

do Ez(x,y,z) = ez(x, y)ejz nn phng trnh ny c th c rt gn thnh phng trnhsng hai chiu cho ez:

2

x2+

2

y2+ k2c

ez = 0 (2.75)

do k2c = k2 2. Phng trnh ny phi c gii theo cc iu kin bin ca dng hnh hc

dn sng c th.

Tr khng sng TM c th c xc nh theo

ZTM =ExHy

=EyHx

=

=

k(2.76)

n ph thuc vo tn s. Cng nh cc sng TE, cc sng TM c th c h tr bn trong ccng dn kn cng nh gia hai hay nhiu dy dn.

Trnh t phn tch cc ng dn sng TE v TM c th c tm tt nh sau:

1. Gii phng trnh Helmholtz dng rt gn (2.71) hoc (2.75) cho hz hoc ez. Nghim sgm mt vi hng s cha bit v s sng ct cha bit kc.


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2. S dng (2.69) hoc (2.73) tm cc trng ngang thz hoc ez.

3. p dng cc iu kin bin cho cc thnh phn trng thch hp tm cc hng s chabit v kc.

4. Hng s truyn lan c cho bi (2.54), v tr khng sng c cho bi (2.72) hoc (2.76).

2.2.3 Truyn sng trong khng gian t do

Trong khng gian t do khng tn hao, khng nhim in v khng nhim t, cc thng s trongmi trng chn khng c s dng gm

0 =109

36

= 8.842.1012 [F/m] (2.77)

v0 = 4.10

7 [H/m] (2.78)

Trong khng gian t do ta c th xc nh c vn tc lan truyn ca sng in t phng(sng nh sng chng hn) l

p = c =1

00 3 108m/s (2.79)

v tr khng sng l0 = 00 = 377 (2.80)

Vi mi trng khng gian t do c nhim in hoc nhim t, cc thng s tr thnh

= r.0 (2.81a)

= r.0 (2.81b)

trong : r v r l hng s in mi v h s t thm tng i ca mi trng ang xt sovi mi trng chn khng. Khi cc cng thc (2.79) v (2.80) v vn tc truyn lan v tr

khng sng vn c p dng vi iu kin l 0 v 0 c thay th bi v cho trong (2.81).

2.2.4 Dy song hnh - twin wire line

Dy song hnh l mt i dy dn kim loi chy song song nhau, cch u nhau v phn cchnhau bi mt mi trng in mi nh trn Hnh (2.5).

Nu ta gi thit rng mi trng bao quanh dy dn l ng nht th sng in t lan truyndc theo chiu di ca dy l sng TEM. S phn b in trng E v t trng H trong mt

phng tit din ca dy c v trong Hnh 2.6.Trong trng hp ny, cc thng s s cp ca dy song hnh s l:


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Hnh 2.5: Dy song hnh - Mt phng tit din

Hnh 2.6: Dy song hnh - Phn b trng

in tr :

R = Rsd (2.82)

trong Rs =

2l in tr b mt ca dy dn.

in cm :

L =

cosh1

D

2d

ln

D

d

(2.83)

in dung:

C =

cosh1

(D/2d)

lnDd (2.84)

vi


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, l h s t thm v in thm tuyt i ca mi trng chung quanh dy dn, c chobi (2.81a) v (2.81b).

D: Khong cch gia tm hai dy dn.

d: ng knh ca tit din mi dy dn v D dTr khng c tnh ca dy song hnh l

Z0 =1

cosh1

D

2d

1

ln

D

d

(2.85)

u im ca dy song hnh l d ch to, r tin v d hn ni. Nhc im chnh l suyhao ln do bc x sng ra khng gian xung quanh, c bit l cc tn s cao. V vy, dy songhnh khng c s dng cc tn s cao m c s dng nhiu trong truyn hnh t di VHF

tr xung.

2.2.5 Cp ng trc - Coaxial Cable

Cp ng trc l mt mi trng truyn sng c s dng rng ri trong thc t nh truynhnh, s liu, cc thit b o vv... nh u im nh gn, kh nng chng nhiu tt. Cp ngtrc gm mt dy dn trung tm v mt dy dn bao quanh, gia chng c nhi cht in minh c m t trn Hnh 2.7. Tt c cn c bao bc bn ngoi bi mt hoc nhiu lp vnha c tc dng chng va chm, chng m cho cp. Khi s dng, ng tn hiu thng cni vo dy trung tm cn lp dy dn bao quanh c ni ti im t (ground) ca mch in.

Nh cu trc nh vy m lp dy dn bn ngoi c kh nng chng nhiu t mi trng chungquanh tc ng ln ng dy tn hiu.

Nu gi s ng dy khng tn hao, mi trng in mi ng nht th sng in t lantruyn dc theo chiu di ca cp l sng TEM. S phn b ca in trng E v t trng Htrong mt phng tit din ca cp c cho trong Hnh 2.8.

Qua tnh ton vi vic gii cc phng trnh Maxwell ta c th xc nh c cc tham sng truyn nh sau:

in cm :L =

2ln

D

d

in dung:

C =2

lnDd

Tr khng c tnh:

Z0 =

60

ln D

d


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Hnh 2.7: Cp ng trc

2.2.6 ng dn sng hnh ch nht -Rectangular Waveguide

ng dn sng hnh ch nht l mt trong cc loi ng truyn ra i sm nht c s dng truyn cc tn hiu viba (cao tn), v ngy nay chng vn cn c s dng trong nhiu ngdng. Rt nhiu loi phn t chng hn nh cc b ghp (couplers), tch sng (detectors), bcch ly (isolators), b suy hao (attenuators) v cc ng slotted lines hin c sn trn th trng

ph hp vi nhiu loi ng dn sng tiu chun thuc cc bng tn t 1GHz n trn 220 GHz.Do xu hng hin nay l thu nh kch thc v d dng tch hp nn nhiu loi mch cao tnngy nay c ch to s dng cc ng truyn phng, chng hn nh ng truyn vi di vng truyn di ch khng s dng ng dn sng. Tuy nhin, vn c nhu cu v cc ng dnsng trong nhiu ng dng chng hn cc h thng cng sut ln, cc h thng sng milimet vtrong mt s ng dng kim tra chnh xc (chng hn b cn chnh radar - Doppler RadarCalibration).

ng dn sng hnh ch nht rng c th truyn cc mode TM v TE nhng khng truyn

c cc sng TEM bi v ng dn sng ch c mt dy dn. Chng ta s thy rng cc modeTM v TE ca mt ng dn sng hnh ch nht c cc tn s ct m di tn s sng khngth truyn lan.

Cc mode in ngang TE

Dng hnh hc ca ng dn sng ch nht c v trong Hnh 2.9, trong gi thit rng ngdn cha vt liu c hng s in mi v h s t thm . Theo ng qui c cnh di nht

ca ng dn s nm dc theo trc x, v vy a>b.Cc mode in ngang TE c c trng bi trng Ez = 0 trong khi Hz phi tha mn


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Hnh 2.8: Phn b trng trong cp ng trc

phng trnh sng dng rt gn (2.71):

2

x2

+2

y2

+ k2chz = 0 (2.86)vi Hz(x,y,z) = hz(x, y)ejz v k2c = k

2 2 l s sng ct. Phng trnh vi phn (2.86) cth c gii bng phng php phn ly bin s bng cch cho

hz(x, y) = X(x)Y(y) (2.87)

ri th vo 2.86 ta c1

X

d2X

dx2+

1

Y

d2Y

dy2+ k2c = 0 (2.88)

Tip theo, bng php phn ly bin s thng thng, mi s hng ca (2.88) phi l hng s, v

vy ta nh ngha cc hng s phn ly kx v ky sao cho

d2X

dx2+ k2xX = 0 (2.89a)

d2Y

dy2+ k2yY = 0 (2.89b)

vk2x + k

2y = k

2c (2.90)

Nghim tng qut cho hz c th c vit l

hz(x, y) = (A cos kxx + B sin kxx)(Ccos kyy + D sin kyy). (2.91)


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Hnh 2.9: Dng hnh hc ca ng dn sng

nh gi cc hng s trong (2.91) chng ta phi p dng cc iu kin bin ln cc thnhphn in trng tip tuyn vi cc thnh ng dn sng. Tc l,

ex(x, y) = 0, at y = 0, b (2.92a)

ey(x, y) = 0 at x = 0, a (2.92b)

V vy chng ta khng th s dng hz ca phng trnh (2.91) trc tip m trc tin chng ta

phi s dng (2.69c) v (2.69d) xc nh ex v ey thz:

ex =j

k2cky(A cos kxx + B sin kxx)(Csin kyy + D cos kyy), (2.93a)

ey =j

k2ckx(A sin kxx + B cos kxx)(Ccos kyy + D sin kyy) (2.93b)

Khi t (2.92a) v (2.93b) ta thy rng D=0 v ky = n/b vi n = 0, 1, 2... T (2.92b) v(2.93b) ta thy rng B=0 v kx = m/a vi m = 0, 1, 2... Nghim cui cng cho Hz khi l

Hz(x,y,z) = Amn cos

mx

a cos

ny

b ejz

(2.94)

trong Amn =AC l mt hng s bin bt k.

Cc thnh phn trng ngang ca cc mode T Emn khi c th tm c s dng (2.69) v(2.94):

Ex =jn

k2cbAmn cos

mx

asin

ny

bejz (2.95a)

Ey =jm

k2caAmn sin

mx

acos

ny

bejz, (2.95b)

Hx =jm

k2caAmn sin

mxa

cos nyb

ejz (2.95c)


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Hy =jn

k2cbAmn cos

mx

asin

ny

bejz, (2.95d)

Hng s truyn lan c xc nh l

=

k2 k2c =

k2 m

a

2n

b

2(2.96)

n s l thc (tng ng vi mode truyn lan) khi

k > kc =

ma

2+n

b

2(2.97)

Mi mode l s kt hp ca m v n, v vy tn s ct fcmn c cho nh sau

fcmn = kc

2

= 1

2

m

a

2 n

b

2 (2.98)

Mode c tn s ct thp nht c gi l mode ch o; do ta gi thit a>b nn tn s fc thpnht xy ra vi mode T E10 (m=1, n=0);

fc10 =1

2a

(2.99)

Ti tn s hot ng f, ch nhng mode c tn s f > fc mi truyn lan c; cc mode cf > fc s dn ti mt gi tr o (hay thc), ngha l mi thnh phn trng s suy gim

theo hm m khi n i xa khi ngun kch thch. Nhng mode nh vy c gi l cc modesuy thoi hay b ct. Nu c nhiu hn 1 mode lan truyn th ng dn sng c cho l qu mcovermoded.

Tr khng sng ca ng dn sng trong trng hp truyn TE mode l

ZTE =ExHy

=EyHx

=k

(2.100)

y =

/ l tr khng thun ca vt liu in mi lp y ng dn sng. Lu rngZTE l thc khi l thc (mode truyn lan), nhng l o khi l o (mode suy thoi).

Bc sng dn sng c nh ngha l khong cch gia hai mt phng ng pha dc theong dn sng, v bng

g =2

>

2

k= , (2.101)

bc sng ny di hn (bc sng ca sng phng trong mi trng in mi dng lp yng dn sng). Vn tc pha l

p =

>

k=

1

(2.102)

ln hn 1/

-tc nh snh (sng phng) trong vt liu in mi.

Trong phn ln cc ng dng, tn s hot ng v kch thc ng dn c chn sao choch duy nht mt mode ch o T E10 s lan truyn.


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Cc mode t ngang TM

Cc mode TM c c trng bi trng HZ = 0 trong khi Ez phi tha mn phng trnh sngrt gn (2.75):

2

x2+

2

y2+ k2c

ez(x, y) = 0 (2.103)

vi Ez(x,y,z) = ez(x, y)ejz v k2c = k2 2. Phng trnh (2.103) c th c gii bng

php phn ly bin s nh s dng cho cc mode TE. Nghim tng qut khi l

ez(x, y) = (A cos kxx + B sin kxx)(Ccos kyy + D sin kyy) (2.104)

Cc iu kin bin c th p dng trc tip cho ez:

ez(x, y) = 0, at x = 0, a (2.105a)

ez(x, y) = 0 at y = 0, b (2.105b)

Ta s thy rng tha mn cc iu kin trn i vi ez s dn ti tha mn cc iu kin binbi ex v ey.

S dng (2.105a) cho (2.104) cho A=0 v kx = m/a vi m = 1, 2, 3.... Tng t, p dng(2.105b) cho (2.104) cho C=0 v ky = n/b vi n = 1, 2, 3.... Nghim cho Ez khi tr thnh

Ez(x, y) = Bmn sinmx

asin

ny

bejz (2.106)

trong Bmn l mt hng s bin bt k.

Cc thnh phn trng ngang cho mode T Mmn c th c tnh ton t (2.73) v (2.104)nh sau:

Ex =jm

ak2cBmn cos

mx

asin

ny

bejz (2.107a)

Ey =j n

bk2cBmn sin

mx

acos

ny

bejz (2.107b)

Hx =jn

bk2cBmn sin

mx

a cosny

b ejz (2.107c)

Hy =jm

ak2cBmn cos

mx

asin

ny

bejz (2.107d)

Cng ging nh cc mode TE, hng s truyn lan l

=

k2 k2c =

k2 m

a

2n

b

2(2.108)

l thc i vi cc mode truyn lan v o i vi cc mode suy thoi. Tn s ct i vi cc

mode T Mmn cng ging nh tn s ct ca cc mode T Emn cho bi (2.98). Bc sng dn sngv vn tc pha ca cc mode TM cng ging nh i vi cc mode TE.


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rng cc biu thc trng cho E v H trong (2.107) l 0 nu hoc m=0 hoc n=0. Vvy khng c cc mode T M00, T M01 hay T M10 v mode TM bc thp nht c th truyn lan(fc thp nht) l mode T M11 c tn s ct l

fc11 =1

2

a

2+

b

2(2.109)

tn s ny ln hn tn s ct fc10 ca mode T E10.

Tr khng sng lin h cc thnh phn in trng v t trng l

ZTM =ExHy

=EyHx

=

k(2.110)

2.2.7 ng truyn di - stripline

By gi chng ta xem xt ng truyn di (stripline), mt loi ng phng rt thch hp chomch tch hp cao tn v ch to bng phng php quang khc. Dng hnh hc ca mt ngtruyn di c ch ra trn Hnh 2.10(a). Mt di dn mnh rng W t ti trung tm giahai mt dn tip t rng cch nhau mt khong b, cn ton b vng gia cc mt dn tip tc nhi bi cht in mi. Trong thc t, ng truyn di thng c to nn bng cchkhc di dn gia trn mt lp nn (substrate) tip t c b dy b/2 v sau ph ln trn

bng mt lp nn c tip t khc c cng b dy.

Hnh 2.10: ng truyn di (a) Dng hnh hc. (b) Cc ng sc t trng v in trng


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Do ng truyn di c hai dy dn v cht in mi ng nht nn n c th h tr sngTEM, v y l mode hot ng thng thng. Tuy nhin, ging cp ng trc ng truynvi di cng c th h tr cc mode TM v TE bc cao hn nhng cc mode ny trong thc tthng trnh s dng (cc mode nh th c th c tr kh bng vic s dng cc c vt ni

gia cc mt dn ni t v bng vic gi cho khong cch gia cc mt phng t nh hn/4). Bng trc gic ta c th coi ng truyn di l mt loi cp ng trc c "lm dt" -c hai loi u c dy dn gia hon ton c bao quanh bi mt dy dn bn ngoi v cnhi ng u bi mt cht in mi. Cc ng sc trng cho ng truyn di c v trnHnh 2.10(b).

i vi ng truyn di vic phn tch rt kh khn. Do chng ta ch yu quan tm modeTEM nn ch cn vic phn tch trng in tnh l cho ta hng s lan truyn v tr khngc tnh. y khng gii thiu phng php gii chnh xc do qu trnh tnh ton v kt qurt cng knh. V th, chng ta s cp ti cc biu thc thc nghim vi kt qu gn ng.

Cc cng thc tnh Hng s truyn lan, Tr khng c tnh v Suy hao

Vn tc pha

p =1

00r=

c

r(2.111)

v vy hng s truyn lan ca ng truyn di l

=

p = 00r = k0r(2.112)

Tr khng c tnh ca mt ng truyn c cho bi

Z0 =

L

C=

LC

C=

1

pC(2.113)

Nh vy tm Z0 ta ch cn tm C. Nhng cp trn vic gii chnh xc rt phc tp.Trong phn ny, nhm phc v cc tnh ton trong thc t, chng ta cp ti cc cng thcn gin c xc nh bng phng php curve-fitting. Cng thc tm c cho tr khng ctnh l

Z0 = 30r

bWe + 0.441b

(2.114)

y We l b rng hiu dng ca di dn trung tm v c cho bi

Web

=W

b

0 khiW

b> 0.35,

(0.35 W/b)2 khi Wb

< 0.35.

(2.115)

Cc cng thc ny c gi thit vi b dy di dn bng 0 v c cho rng c kt qu chnh

xc 1%. Nh c th thy t (2.114) rng tr khng c tnh gim khi b rng W ca di dntng.


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Khi thit k cc mch ng truyn di ta thng cn phi xc nh b rng ca di khi chotrc tr khng c tnh (c chiu cao b v hng s in mi r), vic ny i hi php tnhngc trong cng thc trn. Cc cng thc nh vy tm c l

W

b=

x forrZ0 < 120 ,0.85 0.6 x forrZ0 > 120.

(2.116)

trong

x =30rZ0

0.441 (2.117)

Do ng truyn di l mt loi ng truyn TEM, suy hao do tn tht in mi cng cngdng vi suy hao ca cc ng truyn TEM khc v c cho bi

d = k tan 2

(2.118)

v suy hao do tn tht cht dn in c th c xc nh gn ng nh sau

c =

2.7 103RsrZ030(b t) A for

rZ0 < 120 ,

0.16RsZ0b

B for

rZ0 > 120.

(2.119)

viA = 1 +

2W

b t +1

b + t

b t ln

2b tt

, (2.120)

B = 1 +b

(0.5W + 0.7t)

0.5 +

0.414t

W+

1

2ln

4W

t

(2.121)

trong tl b dy ca di dn.

V d 2.1. Xc nh b rng ca di dn bng ng ca mt ng truyn di 50 , vi b=0.32cm v r=2.20. Nu gc tn hao in mi (loss tangent) l 0.001 v tn s hot ng l 10 GHz,

tnh suy hao theo dB/. Gi thit b dy ca di dn t=0.01mm.

Gii

Do

rZ0 =

2.2(50) = 74.2 < 120 v x=30/(

rZ0) 0.441 = 0.830, cng thc(2.117) cho b rng ca di dn l W=bx=(0.32)(0.830)=0.266 cm. Ti 10 GHz, s sng kcxc nh l

k =2f

r

c= 310.6 m1

T (2.118) suy hao in mi l

d =k tan

2=

(310.6)(0.001)

2= 0.155 Np/m.


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in tr b mt ca ng ti 10 GHz l Rs =

2=

210 109 4 107

2 5.813 107 = 0.026.Khi t (2.119) suy hao vt dn l

c = 2.7 103RsrZ0A30(b t) = 0.122 Np/m

do A=4.74 c xc nh theo 2.120. Tng suy hao s l

= d + c = 0.277 Np/m

Tnh theo dB,(dB) = 20 log e = 2.41 dB/m.

Ti 10 GHz, bc sng trn ng truyn di l

= crf

= 2.02 cm,

Do tnh theo bc sng th suy hao s l

(dB) = (2.41)(0.0202) = 0.049 dB/

2.2.8 ng truyn vi di - Microstrip line

ng truyn vi di l mt trong nhng loi ng truyn phng ph bin nht, l do chnh l

v n c th c ch to nh cc qu trnh photolithography (quang khc) v d dng c tchhp vi cc linh kin cao tn tch cc v th ng khc. Dng hnh hc ca ng truyn vi dic minh ha trn Hnh 2.11. Mt di dn rng W c in trn mt tm in mi c nit c b dy h v hng s in mi tng i r; ng sc t trng v in trng c vtrn Hnh 2.12 .

Nu lp in mi khng c mt (r = 1), chng ta c th coi ng truyn gm hai di dnphng rng W, cch nhau mt khong 2h (mt phng t c th c b i theo l thuyt nh).Trong trng hp ny ta c mt ng truyn TEM n gin vi p = c v = k0 =

00.

S c mt ca cht in mi v c bit l cht in mi khng ph kn vng khng kh

pha trn di dn (y>h), lm phc tp vic phn tch ng truyn vi di. Khng ging ngtruyn di, ton b trng u b giam trong vng in mi ng nht, ng truyn vi dic phn ln ng sc trng nm trong vng in mi, tp trung gia di dn v mt phngt, cn mt phn nm trong vng khng kh pha trn lp nn (substrate). V l do ny ngtruyn vi di khng th h tr mt sng TEM thun ty, do vn tc pha ca cc trng TEMtrong vng cht in mi l c/

r, cn vn tc pha ca cc trng TEM trong vng khng kh

l c. V vy, s bt phi hp v pha ti min tip gip in mi-khng kh s khng th t cmt sng TEM.

Trong thc t, cc trng chnh xc ca ng truyn vi di hnh thnh mt sng TM-TEhn hp, v i hi cc k thut phn tch cao hn m chng ta khng trnh by y. Tuy

nhin, trong hu ht cc ng dng thc t, lp in mi rt mnh v mt in (tc h ), vv vy trng l cn TEM (quasi-TEM). Ni cch khc, cc thnh phn trng v c bn ging


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Hnh 2.11: Dng hnh hc v mt ct ngang ng truyn vi di

Hnh 2.12: Cc ng sc t trng v in trng

nh trng trong trng hp tnh in. V vy, cc gi tr gn ng cho tc pha, hng struyn lan v tr khng c tnh c th t c t cc nghim tnh hoc cn tnh in. Khi vn tc pha v hng s truyn lan c th c biu din bi

p =ce

, (2.122)

= k0e (2.123)

trong e l hng s in mi hiu dng ca ng truyn vi di. Do mt s ng sc trngnm trong vng in mi v mt s trong khng kh nn hng s in mi tha mn quan h,

1 < e < r (2.124)

v ph thuc vo b dy ca lp in mi h, b rng ca di dn W.

Trong phn ny s trnh by cc cng thc xc nh hng s in mi hiu dng v tr khng

c tnh ca ng truyn vi di; cc kt qu ny l nhng cng thc xp x bng phng phpcurve-fitting.


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Cc cng thc tnh Hng s in mi hiu dng, Tr khng c tnh v Suy hao

Hng s in mi hiu dng ca mt ng truyn vi di c cho xp x bi

e = r + 1

2+

r 12

11 + 12h/W

(2.125)

Hng s in mi hiu dng c th c hiu l hng s in mi ca mt mi trng ng nhtthay th vng in mi v khng kh ca ng truyn vi di nh ch ra trn Hnh 2.13. Vn tc

pha v hng s truyn lan khi c cho bi (2.122) v (2.123).

Hnh 2.13: Cu trc tng ng ca ng truyn vi di cn TEM, lp in mi nn bdy d v hng s in mi tng i r c thay th bng mi trng ng nht c hng s

in mi tng i hiu dng epsilone

Khi cho trc cc kch thc ca ng truyn vi di, tr khng c tnh c th c tnhnh sau

Z0 =

60e

ln

8h

W+

W

4h

khi W/h 1 ,

120e [W/h + 1.393 + 0.667ln(W/h + 1.444)]

khi W/h 1.(2.126)

Vi mt tr khng c tnh Z0 v hng s in mi r cho trc, t s W/dc th c xcnh l

W

h=

8eA

e2A 2 khi W/h < 2 ,

2

B 1 ln(2B 1) + r 1

2r

ln (B 1) + 0.39 0.61

r

khi W/h > 2.

Trong

A =Z060

r + 1

2+

r 1r + 1

0.23 +

0.11

r

(2.127)

B = 3772Z0

r

(2.128)


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2.2.9 ng truyn ng phng coplanar-CPW

ng truyn coplanar c s dng nhiu trong cc mch tch hp cao tn do c cu trc ngin v d ch to. ng truyn coplanar c v trong Hnh 2.14(a), gm mt di dn kimloi (gi l ng tn hiu) nm xen gia hai mt dn tip t 1 v 2. Tt c cc lp kim loiu nm v mt pha ca tm in mi r nn rt d ch to bng phng php quang khc(photolithography) hay ph kim loi (metalization). Cu trc ny h tr mode cn TEM. CPWem li mt s u im so vi ng truyn vi di ch: Th nht l d dng ch to, th hai lthun li hn trong vic hn cc linh kin th ng v tch cc trn mch in, th ba l khngcn cc tr (via) ni t xuyn qua lp in mi hay ni t qua ra bn mch, th bn l gimtn tht do bc x. Hn th na tr khng c tnh c quyt nh bi t s (a/b) nn c thkch thc khng gii hn, tuy nhin gi phi tr l tn tht cao hn. Do c mt phng t nmxen gia bt k hai dy no ln cn nn hiu ng xuyn m gia hai dy bt k l rt yu. Ktqu l cc mch s dng CPW c mt dy hn cc mch s dng ng truyn vi di.

Hnh 2.14: ng truyn coplanar (CPW) chun

S phn b ca in trng E v t trng H trong mt phng tit din ca ng truynCPW c v trn Hnh 2.14(b).


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Hng s in mi hiu dng c tnh bi

e =r + 1

2 tanh 0.775lnh

W + 1.75 +kW

h[0.04 0.7k + 0.01(1 0.1r).(0.25 + k)]

(2.131)Vi :

k =S

S+ 2W(2.132)

vi cc thng s h, S, W l chiu cao ca lp in mi, b rng ca di dn v khong cch giadi dn v t.

Tr khng c tnh ca ng truyn ng phng c xc nh l

Z0 =30

e.K(k)K(k)

(2.133)

vi:

k = tanh

S

2h

(2.134)

v t sK(k)

K(k)c nh ngha nh sau

K(k)

K(k)

=

1

ln

2

1 +

k

1 k

1khi 0 k 1

2,

1

ln

2. 1 + k1 k

khi 1

2 k 1.

Vik =

1 k2 (2.135)

2.2.10 Tn hao trn ng dy truyn sng

Vi tn hiu tn s siu cao lan truyn trn ng truyn sng mt khong cch ln th tn

hao trn ng dy tr nn rt ng k. Ngoi ra suy hao tn hiu ph thuc vo tn s nn gyra suy gim bin v mo dng tn hiu. Vic tnh ton chnh xc tn hao trn ng dy l rt

phc tp do c qu nhiu yu t nh hng n iu kin truyn sng. Do vy tn hao thngc c lng vi mt s gi thit nht nh.

Tn hao trn ng truyn c phn lm hai loi l: tn hao kim loi v tn hao in mi.

Tn hao kim loi - metal loss

Tn hao kim loi l tn hao sinh ra do in tr ca phn dn bng kim loi trn ng dy. Tn

hao ny c nh gi thng qua in tr tuyn tnh R ca ng dy, c coi gm hai thnhphn chnh: in tr ti tn s thp v in tr ti tn s cao.


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Tn s thp: Ti vng tn s thp (chiu di ca ng truyn sng l rt ngn so vi bcsng), tn hao kim loi ch yu l do in tr ca dy dn. Nu dy dn c in tr sutl (hoc in dn sut = 1/), c tit din mt ct l s th in tr ca dy dn trnmt n v chiu di l

RDC = s

= 1s

/m (2.136)

Bng 2.1: in dn sut ca mt s kim loiKim loi in dn sut [S/m] Kim loi in dn sut [S/m]Nhm 3.816 107 Bc 6.173 107ng 5.813 107 Thic 7.000 106Ch 4.560 106 Vng 4.089 107

in trRDC trong trng hp ny l hng s, khng ph thuc tn s tn hiu.

Tn s cao: Khi tn s ca tn hiu lan truyn cao (chiu di ng truyn ln hn hoc xp xbc sng), ngoi tn hao c nh nh tn s thp, ng truyn cn c thm tn haodo hiu ng da (skin effect).

Hiu ng da xy ra khi tn s tn hiu tng, dng in tn hiu chy qua tit din ca dydn khng cn phn b u trn mt phng tit din (mt dng in khng cn l mthng s trn b mt tit din) m c khuynh hng tp trung ti vng b mt chu vi catit din dy dn v gim dn v tm ca dy theo dng hm m m). Tn s tn hiucng cao th hiu ng da cng mnh, c ngha l phn b mt ca dy dn c mt dng

in rt ln trong khi bn trong dy c mt khng ng k. Ta ni rng dng dinch chy qua dy dn trn b mt m thi. iu ny lm gim tit din hiu dng ca dydn c kh nng ti tn hiu, lm tng in tr ng dy v kt qu l gy tn hao kimloi vng tn s cao.

Hnh 2.15 biu din s phn b dng in trn tit din ca dy dn trn hoc di dn hnhch nht trong cc ng truyn di, vi di, CPW biu din mt cch nh lng hiung da, ngi ta ly mc trung bnh ca mt dng in trn tit din v xc nh khong cchdtnh t b mt dy dn sao cho c th coi l mt dng in ch phn b u trong vng ,cn vng gia c mt dng in bng 0. Khong cch dny c gi l b dy ca da (skindepth).

B dy da dc tnh bi cng thc

d =

2

(2.137)

trong l h s t thm tuyt i, thng thng = 0 = 4 107 [H/m]. - in dnsut ca dy dn, n v [S.m].

Ta nhn thy tn s cng cao hoc in dn sut cng ln th b dy da dcng nh.

in tr tuyn tnh R ca ng dy c gi tr t l nghch vi tit din hiu dng ca phndn in do hiu ng da tn s cao. Mt khc, tit din hiu dng ny t l vi b dy da d


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Hnh 2.15: Mt dng in trn tit din (a) dy dn trn (b) di dn hnh ch nht

m dli t l nghch vi

nn in tr tuyn tnh do hiu ng do s t l thun vi

.

RAC

(2.138)

Nh vy tn s cao, in trR s l tng ca in tr tn s thp RDC theo (2.136) v intr tn s cao RAC

R = RDC + RAC (2.139)

th biu din s bin thin ca R theo tn s c v trn Hnh 2.16(a). Lu rng cctrc tn s v trc R c chia theo thang logarit nn dc ca ng cong l 1/2.

Hnh 2.16: Quan h gia (a) R v tn s (b) Suy hao v tn s

S bin thin ca h s suy hao theo tn s cng c biu din trn Hnh 2.16(b). Tanhn thy cng tng theo tn s nht l vng tn s cao. ng cong cng c dc 1/2 v


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t l vi R v t l vi

.

Ngoi cc tn hao do hiu ng da k trn, khi tn s tn hiu ln cn xut hin thm dngtn hao kim loi khc l tn hao do ghp k sinh gia cc ng dy t gn nhau. Gi s trn

cc ng dy u c cc dng tn hiu cao tn (cng chiu hoc ngc chiu), do t gnnhau nn chng s nh hng n nhau. Kt qu l mt dng in phn b trn tit din ming dy cng tr nn khng ng nht, do lm gim tit din hiu dng ca dy dn vlm tng tn hao chung cho h thng. Dng tn hao ny cng ang c nghin cu nhm rtra mt qui lut chung nh gi v gim thiu tn hao, nht l cc linh kin vi mch cao tn khong cch gia cc ng dy l rt nh.

V d 2.3. Tnh b dy da ca nhm, ng, vng v bc ti tn s 10 GHz.

Gii:

in dn sut (conductivity) ca cc kim loi ny c cho trong Bng 2.1. B dy da ccho bi biu thc (2.137) nh sau

d =

2

=

1

f 0=

1

(1010)(4 107)

1

= 5.03 103

1

i vi Nhm:

d = 5.03 1031

3.816

107= 8.14 107 m

i vi ng:

d = 5.03 103

1

5.813 107 = 6.60 107 m

i vi Vng:

d = 5.03 103

1

4.089 107 = 7.86 107 m

i vi Bc:

d = 5.03 103

1

6.173 107 = 6.40 107 m

Kt qu ny ch ra rng phn ln dng in chy trong mt cht dn in tt ch din ratrong vng cc mng gn b mt ca vt dn

Tn hao in mi - Dielectric loss

Trong iu kin l tng, lp in mi phn cch gia hai lp dy dn ca ng truyn sng

phi l cch in hon ton (khng c dng in qua lp in mi, tc in dn ca lp inmi G=0).


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Tuy nhin, trong thc t cc cht in mi c s dng nhn chung c in dn khc khng.iu ny gy thm mt dng tn hao na m ta c cp trong cc phn trc gi l tn haoin mi. Tn hao ny c nh gi thng qua in dn G.

Gc tn hao ca cht in mi tn s c nh ngha bi

= tan1G

C(2.140)

vi G v C ln lt l in dn v in dung ca ng dy. Ta vit li

G = C. tan (2.141)

Vy in dn t l vi in dung ca lp in mi theo h s tan .

biu din v mt ton hc quan h trn, ta nh ngha mt hng s in mi tng i lmt s phc.

r = r jr (2.142)

trong : r lin quan n in dung C.

V thnh phn dn np Y trong Hnh 2.2 gm in dn G mc song song vi in np C

Y = G + jC (2.143)

nn ta nhn thy thnh phn r lin quan n in dn G.

T quan h (2.142) ta suy ra tan = r/r.V G (hoc r) xc nh dng in dn, C (hoc r) xc nh dng in dch qua in mi

nn biu vector dng in tng v gc tn hao c trnh by trn Hnh 2.17.

Hnh 2.17: Gc tn hao

Ngoi cc tn hao kim loi v tn hao in mi k trn, ng dy truyn sng cn chu cc

dng tn hao khc nh tn hao do bc x in t ( tn s rt cao), tn hao do cu trc khngng nht ca ng truyn (cc im gin on, ch hn ni, vv...).


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2.3 Hin tng phn x sng trn ng dy - H s phn x

Nh chng ta phn tch trong mc 2.1.3, in p v dng in ti mt im z bt k trn

ng dy nhn chung c th c xem l tng ca mt sng ti v mt sng phn x.Sng ti xut pht t ngun tn hiu t u vo ng dy i v pha ti, cn sng phn

x i t pha ti v ngun do hin tng bt phi hp tr khng ti ti. Sng phn x lan truynvi cng vn tc ca sng ti, c bin v pha khng nhng ph thuc vo bin v pha casng ti m cn vo mi tng quan gia tr khng ti ZL v tr khng c tnh Z0 ca ngtruyn. Chng ta s xt mi tng quan ny trong cc trng hp c th. Theo ( 2.14), in pti ta z bt k c th c vit

V(z) = V+0 .ez + V0 e

z (2.144)

trong :V+0 .e

z i din cho sng ti ti z, cn V0 .ez i din cho sng phn x ti z.

Ta nh ngha: H s phn x in p v(z) ti im z l t s gia sng in p phn x vsng in p ti ti im z

v(z) =V0 .e

z

V+0 .ez =

V0V+0

e2z (2.145)

Trong biu thc trn, V0 v V+0 l cc hng s ph thuc vo iu kin ngun v ti, h s phn

x in p v(z) s bin thin theo ta z bi h s e2z .

Ti ti (z=0), h s phn x in p l

= v(0) = =V0V+0

(2.146)

Ti im ta z bt k, h s phn x in p c th c vit l

v(z) = v(0).e2z (2.147)

Nh vy ta c th suy ra v(z) ti im z bt k no trn ng dy khi bit trc v(0) titi.

Trong trng hp tng qut, ng truyn c tn hao th s l mt s phc, tc ( = + j), do v(z) cng l mt s phc. V vy, cc h s phn x in p ny c th c

biu din bi cc im trn mt phng phc = re + jim. Vit li (2.147)

v(z = ) = v(0).e2.ej2 (2.148)

trong : h s e2 l s thc ph thuc vo h s suy hao v cng gim khi tng theochiu m ca z (li xa khi ti i v pha ngun).

H s ej2 l s phc c module n v v gc pha 2 t l vi h s pha v cnggim m khi z di chuyn v pha ngun ( tng).


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http://www.ebook.edu.vn2.3. HIN TNG PHN X SNG TRN NG DY - H S PHN X 51

T nhng nhn xt trn v biu thc (2.147) ta c th rt ra: Khi di chuyn trn ng truynsng t ti v pha ngun mt khong cch , h s phn x in p v s di chuyn trn mtqu tch hnh xoy trn c trong mt phng phc (Hnh 2.18). Qu tch xut pht t im hs phn x ti ti v(0) v xoay theo chiu kim ng h (hng v ngun) mt gc 2 vi suy

gim module ca vectorv theo h s e2.

Hnh 2.18: Biu din s bin thin ca h s phn x theo v

c bit nu ng truyn sng khng tn hao ( = 0) th t (2.148) ta c

v(z) = v(0).ej2 (2.149)

Khi ny, qu tch ca v l mt vng trn tm ti gc ta v i qua im v(0). H s phnx in p v(z) ti im z bt k ch l s quay pha ca h s phn x in p ti ti v(0). Do

|v(z)| = |v(0)| (2.150)Theo (2.148), gc xoay pha khi di chuyn khong cch l 2. Theo (2.17), ta c th biu dingc xoay pha nh sau

2 = 22

= 2

/2(2.151)

Ni cch khc, gc pha ca h s phn x in p v s xoay mt lng 2 (hay quay mt vngtrn quanh gc ta trong mt phng phc khi di chuyn mt khong bng mt na bcsng (/2) ca tn hiu. Vi khong cch bt k th gc pha s xoay quanh ta mt lngt l vi theo (2.151).

Cc nhn xt trn v qu tch ca im phc v trong mt phng h s phn x in p sc p dng xy dng th Smith trong Chng 4.


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http://www.ebook.edu.vn52 CHNG 2. L TH

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