Soi quang co bao nhiéu mode tai budéc song 1550 nm?... Bude séng 1320 nm, tinh gid tri V tan sé chudn hda va xc dinh sé mode trong soi quang.. Bao nhiéu phan tram céng suat quang 16 ri r
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DAI HOC QUOC GIA THANH PHO HO CHI MINH
DAI HOC KHOA HOC TU NHIEN KHOA DIEN TU - VIEN THONG
BO MON VIEN THONG VA MANG
Taong Neuen Hank Neuyén 9359399
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BAI TAP TRUYEN THONG QUANG
Bai 2.1
Xét mot dién trvong dugc cho boi biéu thire sau:
E = [100e°? e, 20e° e, + 40 e?!°° e, ] e™
Tir biéu thirc, tinh dién trong E tai f= 10° Hz, dua vao Phuong trinh (2-2)
PT (2-2): Ex (zt) = exExe"" *” = Re(E) = &E,xcos(wt — kz)
E= 100 cos(wt + 30°) e, + 20 cos(wt - 50°) ey + 40 cos(wt + 210°) e,
Theo dé bai, thé f10°* Hz ta dure:
E = 100 cos( 27710°t + 30°)e, + 20 cos(2710°t - 50°) e, + 40 cos(2710°t + 210°) e,
Bai 2.2
Cho m6t song duge dac trung béi phuong trinh y=8cos2m(2t—0.8z) (um)
(a) Tinh bién d6 A
(b) Tinh bude song A
(c) Tinh tan s6 géc w
(d) Tinh y, biét khi t = o thiz = 4
(b) Ta c6 yLAREQEGEALz) Ros [2n(ft—z/Hp 8e™
Trang 3Taco: X, = a, cos(wt— 6,) = a, (coswt.cos6, +sinwt.sin6,)
X, = a, cos(wt—6,) = ay (coswt.cos6, +sinwt.sin6,)
=> X, + X, = a, (coswt.cos6, +sinwt.sin6,) + a2 (coswt.cos&, +
sinwt.sind,) =coswt(a,cos6, + a,cos6,) +sinwt(a,sin6, + azsin6,)
Mat khac : X=Acos(wt—) = A(cosot.cosd+sinwt.sind) = coswt.Acosd+sinwt.Asingd
=p {Acos@=arcosn + a,cos6, (1)
Asind=a'sin&" + a*sin&* (2)
Trang 4BAI TAP TRUYEN THONG QUANG
_ {A cos @ = a,7cos?8, + a,*cos75, + 2a,a,cos5,cos6, (3)
A’sin? = a,7sin?8, + a,*sin?6, + 2a,a,sin6,sin6, (4)
(3)+(4), ta duge :
A? = a,* + a,7 + 2a,a,(cos5,cos5, + sin6,sind,)
= a,* +a," + 2a,a,c0s(6, — 52)
90° thi chiét xuat cua tam kinh 1a bao nhiéu? Tinh goc toi han cho tam kinh nay?
cos 57°
b Ta co:
Nglass SIN Oglass = Nair SIN Oair
Nhom 5n5v2
Trang 5voi Pair = 90° ya Nair = 1.0 tg duoc :
Mot tia sang phia dudi mat nudc, cach bé mat nudc la 12cm, chiét suat nude
no=1.33 Tim ban kinh cua duong tron I6n nhat trén ben mat nude ma tia sang co
Taco sin@, = n,sin@, = 1 Tt n=1.33 suy ra 0,= 48.75”
Xét gdc 0,: C6 tanO, = >— Vay r=13.7 em
Bai 2.18:
M6t soi multimode step index cd d6 khau sé 1a 0.2 c6 sé mode 1a 1000 tai bude
song 850 nm
a Xac dinh duong kinh 161
b Soi quang co bao nhiéu mode tai budéc séng 1320 nm?
c Soi quang co bao nhiéu mode tai budéc song 1550 nm?
Trang 6BAI TAP TRUYEN THONG QUANG
Xét soi quang co ban kinh 16i 25 um véi chiét suat 16i nI=1,48, A=0.01
a Bude séng 1320 nm, tinh gid tri V (tan sé chudn hda) va xc dinh sé mode trong soi quang
b Bao nhiéu phan tram céng suat quang 16 ri ra lp vo (cladding)?
c Néu A=0.01, soi quang cé bao nhiéu mode va tinh ti 16 ro ri nang Ivong ra 1dp vo
b Ta co céng thire tinh ti 1¢ rd ri céng suat quang ra lép vo nhw sau, voi M
chinh 1a s6 mode truyén tai budéc song xac dinh
Trang 7Cho soi Single-mode(thudc dang Step-index) cé nl = 1,48 n2 = 1,478, budéc song
A = 1320 nm Tinh hé sé khau dé, gdc 1én nhat dé dua vao soi quang, ban kinh 16i?
Cc Tim goc dua vao cuc dai dé thoa diéu kién phan xa toan phan
NA = Sin@max => @max = arcsinNA = arcsin 0.077 = 4.4°
Bai 2.30:
Tim d6 day cua lép lang dong biét ban kinh trong va ngoai cua phéi (khuén mau duoc hinh thanh truéc) 1a 3-4mm Néu soi quang co duong kinh 16i 1a 50um va duong kinh lop boc la 125 pm
5 ym
3mm
FIBER PREFORM
Gidl:
Ching t6i muén tim ra d6 day cua Iép lang dong (3 mm - R) Diéu nay cé thé
thuc hién bang cach so sanh ti lé 10i-dén-lép boc cho khu vue mat cat ngang cua
phdi va ti 1é 16i-dén-Iép boc cho khu vue mat cat ngang cua soi quang:
Trang 8BAI TAP TRUYEN THONG QUANG
a(dB/ km )= — log eo re — log (e"" )
= 1Oce lop e= 4.343 a, (1 / kan)
Bai 3.2:
M6t soi cap quang cd hé sé suy hao 1a 0.6dB/km 6 bude séng 1300 nm va 0.3 dB/km & buéc séng 1550 nm Cé cong xuat truyén déi voi budc song 1300 nm 1a
150 pW va déi voi budéc song 1550 nm 14 100 uW Tim cong xuat cia hai tin hiéu 6
8km va 20km dé tin higu van dam bao
Gia:
Déi tir wW sang dBm la:
P(100 LW) = 10 log (100 wW/1.0 mW) = 10 log (0.10) = - 10.0 dBm
P(150 pW) = 10 log (150 uW/1.0 mW) = 10 log (0.15) =- 8.24 dBm
6 8kmcé cong xuat 1a:
Py390(8 Kin) = - 8.2 dBm — (0.6 dB/km)(8 kin) = - 13.0 dBm = 50 WW
Pisso(S km) = - 10.0 dBm — (0.3 dB’kim)(8 km) = - 12.4 dBm = 57.5 pW
Nhom 5n5v2
Trang 9“* & 20 km co cong xuat 1a:
Pi309(20 km) = - 8.2 dBm — (0.6 dB/km)(20 km) = - 20.2 dBm = 9.55 uW
Py <69(20 kim) = - 10.0 dBm — (0.3 dB/kim)(20 km) = - 16.0 dBm = 25.1 nW
Bai 3.3:
Cho mot tin hiéu quang tai mét bude séng cu thé bi mat 55 % cong suat sau khi
truyén quang soi quang dai 3.5 km Tinh dé hé s6 suy hao theo dB/km ?
Pin : cong suat sau khi truyen
Pout : cong sudt dau vao
opin 10, , 1 /
=~ a(ctB / fan) — —loo(——)=1.0dB/ km
3.5 0.45
Bai 3.4:
M6t soi cap quang dai 12 km cé hé s6 suy hao dudng truyén 1.5 dB/km
a) tim mirc céng sual téi thigu can dé dua vao truyén trén soi quang ma duy
tri duoc mire cOng suat quang 6 cudi dau nhan 1a 0.3nW ?
b) tinh mtre cong suat dé dua truyén véi hé sé suy hao 1a 2.5 dB/km ?
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a/ Mét nguén quang LED phat ra bude song 850 nm cé dé rong pho hiéu dung 1a 45
nm D6 réng xung hiéu dung 1a bao nhiéu (ns/km) ?
Do rong xung 1a bao nhiéu khi mét Laser Diode cé dé réng phé hiéu dung 1a 2 nm ? b/ Tim tan sac vat liéu biét d6 rong xung hiéu dung la 1550nm voi dé réng phé la
Trang 11So sanh d6 trai réng trén km cho ba loai cap:
a Soi multimode step-index v6i chiét suat 1di n}=1.49 va A=1%
b Soi graded-index cé dudng parabon téi wu va co chiét suat nj=1.49 va
Gia str soi quang step-index cé chiéu dai 5km véi chiét suat 16i nj=1.49 va A=1%
a Tim d6 chénh Jéch thoi gian lan truyén giita hai mode ngan nhat va dai nhat trong soi quang
b Tim d6 trai rong xung duoc tao ra boi tan sac xuyén mode
c Tinh todn Brmax (diéu kién truyén qua soi khéng cd 16i do chéng lap
xung), Vél Br= (),.2/ostep-
Trang 12BAI TAP TRUYEN THONG QUANG
M6t LED InGaAsP co hai lép tiép xtc p-n phong xa 6 bude song dinh 1310nm cé
thoi gian tai t6 hop khi cd phong xa va khong cé phéng xa 1an luot 1a 25 va 90 ns,
voi dong chuyén 1a 35mA
a) Tim higu suat luong tu ndi va muc cong suat
b) Néu chiét sugt phan xg cya chgt ligu nguén sang 1a n=3.5, tim cng suat phat
xa cua thiét bi
P=n,_P,, = + xP = — x 0.026 = 0.00037W =0.37mW
n(n+1) 3.5(3.54+1)
Bai 4-10:
Tim hiéu suat luong tu ngoai cua lazer diode Ga;_,Al,As v6i x=0.03 va méi quan hé
cia céng suat quang va dong chuyén 1a 0.5 mW/mA (céng thitc 4-38/186)
Gidi:
n&* =0.8065A(um) Um)
Nhom 5n5v2
Trang 13(1,2) = I + (i3) = (Roo)? +5 (MRoPo)?
Voi dé nhay R, dugc cho boi céng thire (6-6)
Mot pin Photodiode InGaAs cé cac théng so nhu A= 1550 nm; [p = InA, n = 0.95,
R, = 500 Q va dong 16 ri bé mat khéng dang ké Céng suat su cé quang 14 500 nW
(-33 dBm) va bang thong nhan duoc 1a 1SOMHz So sénh dong nhiéu duge tinh bdi
Trang 14BAI TAP TRUYEN THONG QUANG
06 =2qI,B=2(1.6x107"? C)(0.593 pA)(150x 10° Hz) = 2.84 x 10-*” A? Tir cong thie (6-15) ta tinh duoc dong nhiéu:
Ofp =2qIpB=2(1.6x107'? C)(1.0 nA)(150x 10° Hz) =4.81 x 1072° A?
Tir cong thie (6-16) ta tinh duoc dong nhiéu:
2 4kp T 4(1.38x10~23 J/K)(293 K) 6 -15 2
of = RB B= 500 0 (90 10 He? x10 A
Bai 6.7:
Xét dau nhan quang diod kiéu thac li, theo cdc théng s6 sau: dong téi(dark current)
Ip= I1nA, dong ro(leakage current) I, = InA, hiéu suat luong tu n = 0.85, dé loi M
= 100, yéu té nhiéu vuot mirc F = M"”, dién tré tai Ry = 10°Q, bang thong B = 10 kHz Gia sir tin hiéu séng sin 850 nm bién thién cé chi s6 diéu ché m = 0.85 giam
trén quang diode, nhiét dé phong T = 300K Dé so sanh dang anh huong cua nhiéu lén ty s6 signal-to-noise cho timg chi s6 set riéng, vé gidi han theo decibels [10log(S/N)] theo ham nang long quang nh4n trung binh P, Dat P, ttr -70 dén 0
Dap wng cua quang diode o budc song 850 nm la Rg = yq/hf = nqdJhe = 0.58 A/W,
tu cac cong thuc
(6-4) 1, = xP,(1-6°")(1 - Ry I, la dong photon trung binh
(6-6) R = 1,/P, = nq/hv R la dap wng cua diode
(6-11a) (i) = Opin =f i, (t) )] i, la tri so tin hiéu dong trong quang diode pin
Trang 15(6-12) [i,°()] =o) =m’ Ip /2
(6-13) (ig) = 00° = 2qI,BM°F(M) _ ig la dong nhiéu long tir ;F(M) la hé so nhiéu ctia APD; doi voi Pin photodiode thi F(M) va M = 1
(6-14) (ipg’) = opp = 2gIpM’F(M)B ing la nhiéu dong toi Ip 1a gid tri dong toi
(6-15) ins = ops =2qI;.B ips la dong surface dark
(6-17) if =o = 4kgTB/R, irla dong nhiéu nhiét; k = 1.38x10° JPK
Trang 16BAI TAP TRUYEN THONG QUANG
Protetuikty distibotions for received logical O and | signal pulses The different widths of the two
diaintbutions are caused by various aignal distortion eects
Xét phan bé xac suat trong hinh 7-5, V, 1a noi dién thé tin hiéu cho bit 1 va vin =
Mot den LED hoat d6éng 6 budc song 1300 nm, phat mot cong suat quang 25uW
vao trong soi quang Néu d6 suy hao gitra nguén LED va bé thu quang 1a 40 dB va
hé sé luong tir cua b6 thu quang 1a 0.65, tim xdc xuat cd it hon 5 cap electron-lé trong tai bd thu quang trong khoang thdi gian Ins
Gidi:
Ta su dung cac cong thie
Nhom 5n5v2
Trang 17_ n {* nE N=—] P(t)dt =—
wl, so hv
Trong do:
“N 1a sé cap electron-lé tréng trung binh
1] la hé 86 luong tir cua be thu quang
E 1a cong suat phat cua nguén quang trong khoang thoi gian t
Xét ti s6 tin hiéu trén nhiéu SNR dugc cho béi bai tap 7.29a Dua theo hinh 7.21 vé
ti so SNR theo giai dB nhu 1a mét ham biéu dién mtre céng suat nhan trong giai dBm khi dong téi Ip=10nA va x=1.0 Cho B=5MHz, m=0.8, Ro=0.5A/W, T=300K,
Req/F=10°Q, Ip= Ro.P,
Gidi:
Cong thie bai 7.29a nhu sau:
7 xin (RoPr) f Reg G7)
Trang 18BAI TAP TRUYEN THONG QUANG
Ta tién hanh vé ti s6 SNR khi P, duoc tinh theo giai dBm, tuc la 2 ee
Cac gia tri dai dién duoc cho trong bang sau:
(a) Tim d6 loi khuéch dai?
(b) Tinh cong suat bom nho nhat dé dat duoc dé loi trén?
Trang 19A a
b Psout S Psin + 2 Prin => Prin 2 (Ps.out — Poin), =
Thay cac gia tri vao voi A, bang 980nm ta duoc Pp ;, nhé nhat bang 785 mW
Bai 10.10:
Vé biéu dé cua Penalty factor F(G) duoc cho 6 Eq.(11.36) theo d6 loi, véi khoang
d6 loi tir 0 — 30 dB Gia str rang d6 suy hao cua cap 1a 0.2dB/km, vé mét truc song song voi truc dé loi dé chi khoang cach truyén twong tmg véi gid tri dé loi?
path “GA Inc
Voi G chay tu 0 dén 30, vé F path ta CO:
Trang 20BAI TAP TRUYEN THONG QUANG
G la dO loi cua ca hé thong
F path la dO tang nang lvong trung binh trén m6i tram khuéch dai trén duong truyén
Bai 11.1:
Néu mét dong 1a 100 mA,
a Tim kiém téc d6 bom Rb
b Tim dé loi lén nhat
c Mat dd photon bao hoa
d Mat dé photon néu 1Mw 6 1310 nm vao khuyét dai