Laboratory associate professor Radu Damian Wednesday 12-14, II.12 odd weeks L 25% final grade P 25% final grade
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1 ctur 8/9
2 C/, MDC Attndanc at mnmum 7 sssons (cours + laboratory) cturs- assocat profssor adu Daman Frday 9-,? III.34, II.3 E 5% fnal grad problms + (p attn. lct.) + (3 tsts) + (bonus actvty) 3p=+.5p all matrals/qupmnts authord aboratory assocat profssor adu Daman Wdnsday -4, II. odd wks 5% fnal grad P 5% fnal grad
3
4
5 Not customd
6 factorul andr = -p 7/8
7 COMPETENT: Car st bn nformat într-un anumt domnu; car st capabl, car st în măsură să udc un anumt lucru. [DEX]
8
9 > < 95
10 db = log (P / P ) dbm = log (P / mw) db = +. db =.3 (+.3%) + 3 db = + 5 db = 3 + db = -3 db =.5 - db =. - db =. -3 db =. dbm = mw 3 dbm = mw 5 dbm = 3 mw dbm = mw dbm = mw -3 dbm =.5 mw - dbm = W -3 dbm = W -6 dbm = nw [dbm] + [db] = [dbm] [dbm/h] + [db] = [dbm/h] [x] + [db] = [x]
11 Complx numbrs arthmtc!!!! = a + b ; = -
12
13 typcally f 3GH 3GH λ mm cm
14 Elctrcal ngth (Phas ngth) l physcal lngth E = β l lctrcal ngth Dpndncy antnna gan adar cross-scton l l l E r f l c l E, I vary ~ uslss
15 Bhavor (and dscrpton) of any crcut dpnds on hs lctrcal lngth at th partcular frquncy of ntrst E Krchhoff E> wav propagaton l E l l
16 B E t H D B J D t t J Consttutv quatons D B J E H E acuum 4 7 8,854 H m F m c, m s
17 n, S C l h S, S n, a) b) h, n n E E H H J S n n D D S B B If on of th mda s a prfct conductor (mtal) all flds ar annulld nsd
18 X X t X t X Maxwll s Equatons mor smpl g E H t f t dt f t g E E J H H J t d
19 partcular cass whr analytcal soluton xsts X harmonc sgnals, Fourr Transform, frquncy spctrum t X X X g f t t t dt f t g t d G F
20 g f t t dt
21 F t f t dt G F gt G t d
22 E E H H γ propagaton constant (known also as phas constant or wav numbr) Mdum vod of fr lctrc chargs Hlmolt quatons or Wav quatons
23 Elctrc fld only n Oy drcton, through udcous choc wav travlng aftr O drcton of th coordnat systm y E E E If w hav only th postv drcton wav E + => A y A E Harmonc Fld t y A E Ampltud Attnuaton Wav Propagaton (smultanous spac and tm varaton) Wav Propagaton Crcular Polaraton
![t y Ct E ~, E P W t y Ct E Ct Ct P P A log log ] [ P P A db 686 8. log ] [ db A 8.](/docs-images/89/97846417/images/24-0.jpg "686 ] / [ / km db A Attnuaton usually xprssd n db/km most of th tm a postv valu s usd - sgn =")
24 t y Ct E ~, E P W t y Ct E Ct Ct P P A log log ] [ P P A db log ] [ db A ] / [ / km db A Attnuaton usually xprssd n db/km most of th tm a postv valu s usd - sgn = mpld by th word usd
25 E y A Phas vlocty Group vlocty H x E H E osslss Mdum, σ = E H y x y ntrnsc mpdanc of th mdum t constant phas ponts: t const v p v g d dt d dt d d n dsprsv mda whr β = β(ω)
26 Phas vlocty vrtual spd at whch a constant phas pont travls (n crtan condtons mght b gratr than th spd of lght) Group vlocty spd at whch th sgnal (nrgy, nformaton) propagats (always lss or qual to th spd of lght n that mdum)
27 In vd 377 c f v v g c T c,9979 f 8 m s Spac prodcty Tm prodcty In mdu ndsprsv ε r c n r r rfractv ndx of a mdum T c r f c c n c f c r f r
28 wav ncdnt rflctd wav drct nvrs y E E E t y E E t y E E const t const t ponts of constant phas Elctrc fld only n Oy drcton, through udcous choc wav travlng aftr O drcton of th coordnat systm
29 wav ncdnt rflctd wav drct nvrs t t y E E E t t H H H t t t t I I I t t
30 Elctromagntc flds wth harmonc tm dpndnc Maxwll s Equatons smplfd X t X X X g t f t t dt f t g In dlmtd mda th solutons of Maxwll s Equatons must also vrfy boundary condtons solutons must rspct som supplmntal condtons t d
31 Elctrc fld must always b normal on an lctrc wall or annulld Magntc fld must always b tangnt to an lctrc wall or annulld, h C S S n l,, h, a) b) S n
32 Smlar wth Fourr Transform t g f t dt f t g E, E A Mod A E, Mod t d
33 partcular cass whr analytcal soluton xsts X harmonc sgnals, Fourr Transform, frquncy spctrum t X X X g f t t t dt f t g t d G F
34 g f t t dt
35 F t f t dt G F gt G t d
36 partcular cass whr analytcal soluton xsts wav n a sngl drcton wav ncdnt rflctd wav drct nvrs IN E E E t t y E E E OUT E E E E IN E E E E E OUT E E E E E E,
37 partcular cass whr analytcal soluton xsts mods n dlmtd mda B A E A Mod A E, Mod EIN EOUT A E, Mod IN A B A N B A E OUT B N N B Mod
38
39 TEM wav propagaton, at last two conductors I(,t) (,t)
40 TEM wav propagaton, at last two conductors I(,t) I(+Δ,t) Δ Δ (,t) G Δ C Δ (+Δ,t) Δ
41 tm doman harmonc sgnals t t t t v,,, t t v C t v G t,,, I d d C G d di K II K I d d
42 d d I d I d C G E E H H y E E E
43 Charactrstc mpdanc of th ln I I I I d d I C G C G f v f I I
44 =G= C C G C ; C C G s ral I C C v f
45 voltag rflcton coffcnt Γ l I I ral
46 voltag rflcton coffcnt sn at th nput of th ln Γ -l n Γ IN l l l l l l IN l l l l l
47 tm-avrag Powr flow along th ln I Total powr dlvrd to th load = Incdnt powr flctd powr turn oss [db]
48 th nput mpdanc sn lookng toward th load Γ -l l I l n l l n l l l l l l I n l l l l n l l n tan tan
49 th nput mpdanc sn lookng toward th load n tan tan l l
50 nput mpdanc of a lngth l of transmsson ln wth charactrstc mpdanc, loadd wth an arbtrary mpdanc Γ n tan l tan l n -l
51 nput mpdanc s frquncy dpndnt through l l n tan tan Γ -l n f v f l f v l l v f l l f f frquncy dpndnc s prodcal, mposd by th tan trgonomtrc functon
52 l = k λ/ l = λ/4 + k λ/ Γ l l k tan l tan l n n quartr-wav transformr n -l n tan l tan l
53 = purly magnary for any lngth l +/- dpndng on l valu l n tan l l n tan tan
54 = / = purly magnary for any lngth l +/- dpndng on l valu l l n tan tan l n cot
55 maxmum magntud valu for max mnmum magntud valu for SW s dfnd as th rato btwn maxmum and mnmum (oltag) Standng Wav ato SW mn max mn ral numbr SW < a masur of th msmatch (SW = mans a matchd ln)
56 l l n tan tan Γ -l n I I I l l l n
57 Impdanc Matchng wth Impdanc Transformrs (ab )
58 Sourc matchd to load? I mpdanc valus? xstnc of rflctons? E
59 Sourc matchd to load E I E I E I P E P
60 Powr dsspatd on load = 5Ω = P = = P = E P I P
61
62 Sourc matchd to load E I E I E I P E P
63 Matchng maxmum powr transmttd to th load condton? X X E E P b a b a X X E P
64 E = = 5 Ω + 5Ω P ( )? P X X E E
65
66
67 P a : Avalabl Powr X X E P 4, a P E P 4 max X X, *
68 Any mpdanc chosn as rfrnc Γ * Γ
69 * * X X X X X X X X E Γ Γ
70 E * * Γ Γ * * * * * * * *
71 * complx numbrs n th complx plan If w choos a ral Im Γ Γ * Γ Γ
72 P a P * E P r Powr rflcton Powr of th rflctd wav
73 P a P + P a P E E P * P a E P r Th sourc has th ablty to snt to th load a crtan maxmum powr (avalabl powr) P a For a partcular load th powr snt to th load s lss than th maxmum (msmatch) P < P a Th phnomnon s as f (modl) som of th powr s rflctd P r = P a P Th powr s a scalar!
74 Γ Γ * *
75 X X X X X X X X X X X X X X X X
76 E P a P P r a E P 4 X X E P a r X X E X X E E P P P Γ s a powr rflcton coffcnt 4 a r P X X X X E P
77 Fd ln nput ln wth charactrstc mpdanc al load mpdanc W dsr matchng th load to th fdr wth a scond ln wth th lngth λ/4 and l charactrstc mpdanc n O n l tan( l) tan( l)
78 n n n l 4 n n n In th fd ln ( ) w hav only progrssv wav In th quartr-wav ln ( ) w hav standng wavs
79 Th Multpl-flcton wpont T
80 Th Multpl-flcton wpont
81 (only) at f 4 l 4 l ) tan( ) tan( l l n tan( l) t not t t n l not
82 matchng qualty powr rflcton coffcnt sc cos sc tan t
83 w assum that th opratng frquncy s nar th dsgn frquncy (narrow bandwdth) f f l sc tan 4 cos
84 w st a maxmum valu Г m for an accptabl rflcton coffcnt magntud thn th bandwdth of th matchng transformr, θ m for TEM lns 4 4 f f f v v f l f f f f m m cos 4 4 f f f f f m m m m
85 Whn non-tem lns (such as wavguds) ar usd, th propagaton constant s no longr a lnar functon of frquncy, and th wav mpdanc wll b frquncy dpndnt, but n practc th bandwdth of th transformr s oftn small nough that ths complcatons do not substantally affct th rsult W gnord also th ffct of ractancs assocatd wth dscontnuts whn thr s a stp chang n th dmnsons of a transmsson ln ( -> ). Ths can oftn b compnsatd by makng a small adustmnt n th lngth of th matchng scton
86 Bandwdth dpnds on th ntal msmatch ncrasd bandwdth for smallr load msmatchs
87 A quartr-wav matchng transformr to match a Ω load to a 5 Ω transmsson ln at f =3GH Dtrmn th prcnt bandwdth for SW<.5
88 ADS Smulaton f. 88GH GH f f
89
90 Th quartr-wav transformr can match any ral load to any fd ln mpdanc If a gratr bandwdth for th match s rqurd w must us multpl sctons of transmsson lns transformrs: bnomal Chbyshv
91
92 T T T T T T T T 3 3 n n n n T T
93 T T 3 n n 3 n n n x n x x 3 If th dscontnuts btwn th mpdancs and ar small w can approxmat 3 3
94 W also assum that all mpdancs ncras or dcras monotoncally across th transformr Ths mpls that all rflcton coffcnts wll b ral and of th sam sgn Prvously, scton n n n n n N N N, n N 3 N N 4
95 assum that th transformr can b mad symmtrcal N, N, N Not that ths dos not mply that th mpdancs ar symmtrcal 4 N N N N N N N N4 N4 N cos N cosn cosn n last tm: N / N vn n N / cos N odd
96 Input rflcton coffcnt w can choos th coffcnts so w obtan a dsrd bhavor (of th polynomal) N N 4 x N a N x x a x a a x f
97 Th rspons s as flat as possbl nar th dsgn frquncy, also known as maxmally flat For N sctons th frst N- drvatvs of th Γ(θ) functons ar annuld ; n n d d N x A x f N A N N N N A A cos, n N 4 l l
98 A, θ, lngth sctons, th sctons dsappar Bnomal xpanson flcton coffcnt: N N N n n N N N N x C x C x C C x x f!!! n n N N C n N A A N N N N 4 n n C N A N A
99 n n C N A n n n n n n n ln ln x x x x ln ln C C A n N N N n N n n n ln ln ln C n N N n n Manual dsgn procdur A N
100 Bandwdth, Γ m maxmum accptabl valu N m N m m A cos N m m A cos N m m m A f f f f f cos 4 4
101
102
103 Dsgn a thr-scton bnomal transformr to match a 3Ω load to a Ω ln at f =3GH, Γ m =. N = 3 A N 3 ln.755 N 3! C3 3! 3! C 3 3!! 3 C3 3!!!!
104 n N 3 3 ln ln C3 ln ln ln n N 3 3 ln ln C3 ln ln ln n N 3 3 ln 3 ln C3 ln ln ln
105 arccos 4 arccos 4 3 N m A f f f GH.
106 Smlarly ab. f. 69GH GH
107 Th rspons of ths multscton mpdanc transformr s qual-rppl n passband optms (ncrass) bandwdth at th xpns of passband rppl W match th Γ(θ) functon wth an dsrd Chbyshv polynomal
108 T x x T x x x T 4x 3 3x T 3 4 x 8x 8x 4 qual-rppl T x x T n x xt xt x n n n
109 4 N N T n x N cos N cosn cosn n x cos W can show that: x f x last tm: x x a a x a T n x N / N vn N / cos N odd a N x cos cosn cos narccos ( x) cosh ncosh ( x) T n x x n N
110 varabl chang so w map: m x m x x cos cos m sc cos cos x sc m
111 T T T T sc m cos sc cos sc cos sc cos m m m 3 sc cos sc cos3 3cos 3sc cos 3 m m m 4 sc cos sc cos 4 4cos 3 4sc cos 4 m m m W sarch coffcnts of Γ(θ) functon to obtan a Chbyshv polynomal N cos N cosn n cosn n N A T sc m cos last tm: N N / N vn N / cos N odd
112 A, θ, lngth sctons, th sctons dsappar m N T A sc m N T A sc ln sc T m m m N ) ( cosh cosh ) ( x n x T n m m m N N ln cosh cosh cosh cosh sc m m f f f f f 4 A m
113
114
115 A Dsgn a thr-scton Chbyshv transformr to match a 3Ω load to a Ω ln at f =3GH, Γ m =. N = cos3 cos A T sc cos m sc m 3. m cosh N A A TN sc m cosh ln m arccos.746rad scm cosh cosh 3 m A. ln 3..36
116 3 cos3 cos Asc cos3 3cos 3Asc cos m m cos3 A 3 sc m cos 3A sc m sc 747 m. 3 ; smtr:
117 n ln ln ln n ln ln ln n ln 3 ln ln
118 f f f f f m 4 m f 3. 5GH
119 Smlarly ab. f 3. 96GH GH.8GH. 995
120 G.. Mattha,. Young, and E. M. T. Jons, Mcrowav Fltrs, Impdanc-Matchng Ntworks,and Couplng Structurs, Artch Hous Books, Ddham, Mass. 98
121 Impdanc Matchng
122 Fd ln nput ln wth charactrstc mpdanc al load mpdanc W dsr matchng th load to th fdr wth a scond ln wth th lngth λ/4 and l charactrstc mpdanc n O n l tan( l) tan( l)
123 n n n l 4 n n n In th fd ln ( ) w hav only progrssv wav In th quartr-wav ln ( ) w hav standng wavs
124 Bandwdth dpnds on th ntal msmatch ncrasd bandwdth for smallr load msmatchs
125 ADS Smulaton f. 88GH GH f f
126
127 Th quartr-wav transformr can match any ral load to any fd ln mpdanc If a gratr bandwdth for th match s rqurd w must us multpl sctons of transmsson lns transformrs: bnomal Chbyshv
128 W also assum that all mpdancs ncras or dcras monotoncally across th transformr Ths mpls that all rflcton coffcnts wll b ral and of th sam sgn Prvously, scton n n n n n N N N, n N 3 N N 4
129
130 Smlarly ab. f. 69GH GH
131
132 Smlarly ab. f 3. 96GH GH.8GH. 995
133 Mcrowav and Optolctroncs aboratory
Laboratory assistant professor Radu Damian Monday II.12 even weeks Thursday 8-14 odd weeks II.12? L 25% final grade P 25% final grade
Lctur 1 017/018 C/1L, MDCR Attndanc at minimum 7 sssions (cours + laboratory) Lcturs- assistant profssor Radu Damian Monday 16-18, P E 50% final grad problms + (? 1 topic tory) + (p attn. lct.) + (3 tsts)
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