more_soln

# more_soln - ECE 435 Kempel Homework Set #1 Fall 2000 Due:...

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Unformatted text preview: ECE 435 Kempel Homework Set #1 Fall 2000 Due: 9H U00 All homework must be completed NEATLY! !! (Ifl can’t read it, I can’t grade it!) 1. A 4-port network has the following scattering matrix 0.14900 0.61 - 45° (16145" 0 0.61 —45° 0 0 0.6.4450 0.61—45” O 0 0.64w45" 0 0.6A4—5” 0.6-1 —4-5‘-’ 0 (a) Is this network lossless? (b) Is this network reciprocal? (c) What is the reﬂection coefficient at port 1 if a short circuit is placed at the terminal plane of pert 3 and all other ports are match loaded? leJ The scattering matrix for a two-port network is given below, what are the equivalent impedance parameters if the characteristic impedance is 500? a3+j03 jﬂﬁ jaa as—jav 3. Consider two 2—port networks, [8“] and [S3 L show that the over-all S21 of the 5333 1—sgsﬁ' 4. For a lossless 2~port network: (a) if the network is reciprocal, show [SH]2 =1 —|S“l2 and (b) if the network is nonreciprocal, show that it is impossible to have unidirectional transmission (e.g. S12 = 0 and. SN at 0). cascade network is given by S2! = au “5" Jrhis :5 310* S : 5T P m 4-HT: 1'5 inc-F 0.9145" ﬂéiﬂﬁ” G O f} o- EL-‘fS a G ‘13 £1. (E; J “1'5 " .5}. (mm? 9.455%" a”? .J agriij“ 0 a. law" a. {Mg—H5“ {Lgf‘iﬁ‘ 6‘ atria" 0. M‘Hﬁ" 6* 3 an. O 0. Egg" a. ﬁg H5" 0 _ a at am: #53” av _ a: may aim-“i=3” will. meﬂf heifwm k Eb}: KEEN] a: r-‘ 59. ? as“ + c1151 mg sf; Arm/S? Ll -a;s.. “155.3 bg‘mlﬁal W353?- 191 F 63.9“ {35313 b3, C/h'iagr '_- 19555:: £335 £14.21— F Z 13; : chin “gqﬁg‘ﬁar J ‘5“ ~j13?ﬁ.r 1 67h [+ 333 GT: -: algqo'ﬂ {at}; —La§-=1"J( DeLL-HS") Ho (I # «sign-0.3110: asﬂ'aﬂijﬂ “(50:15) u___ ‘__‘ J I | :- go I {t- Sr jfl'WSZ-‘Lj; 551-21! | ' _i_:..z_d- —— ill 5 0+ H“:?E'J JFFSH "i— h! i I “5H3”: [FSZE‘JI ' 5.11.511 anwdsﬁﬂt'gw (1* 0.3+jc.ﬂ(x—G-5 ﬂosﬁlwfj'onjM) ragga-1- ngﬁ 4—DA DE J BC: ﬁﬂﬁgﬁf'gﬂﬂﬁ' A 45' 3’5 _. .e. ' x . ' F '1 F"? c 5' ' - 1 : t +Sﬂj£ Psi?) +3115? zuhﬂﬁ [14,323 W-Jéﬁl [ + [Ed CHSE‘F)‘: H522 1ﬂ512::2_1 [LEMEQ4 Biz-EB] — --------- -—— — -—“ 2' Sm ' ﬁ—-— —H_Jr.___.—- ﬁgm 1 E'E'zr _,.. ﬂ __ _.*' a!- - a = [.1 (war. 1 "‘ # ’1‘"LMix+sﬁag._sﬁﬂ+535%1 +Lﬁﬂﬂlitﬁghﬁgﬁé‘JEElashﬁrrﬁﬂ)FSrzjﬁj J“ 252ml 15“- “ ‘2 ‘33: DC 5 CA Beg-i-Pﬁpﬁr : [é 253‘ 19; [Eat +5? +5mgigl] jr-SE)CI+3153 )‘fSFszE-j 15%] 2.5%] 2.32% EL _ an Hrrr__r______.._._ 1g: _. Jill Ear ||:'l ‘52“: \$3 a 5 1"‘(512C3'I 4. 65 Ida-work” f5 15551.:55 and 'r’rlzir'promf 5:5 [S#]£Srj:[uj and S 53‘? (5" i'l):(5” 51') % 511.:511 52' SE; 3W. 811 5 5. (3" \$13 ’5‘“ Szl _(1 a) ‘1’ if. F 3’ i322, 5|?— 352 a! 1 z 15”} +15er 5‘1”? 51' +3352 r H o (a. 53—5“ + 5333.; PSlI r 1+ L311] 1 [‘Snfi+ ISM—Ilii 19r2i1: I‘— iﬁulz EM” Siz=331 So lﬁzr 12-: I’L‘Sli‘l 6-9 {1.3: 42d =—3§[g)=-w= 43°“ -.| _. H b. H“: m3 [1- ﬁﬁ—‘J = 6:3 '{1*£"2%)=C°3 '(1-3'1'} , “51:3; “ﬂanker” “=1 : B1: m5": H1) =50“ “=2 : 3.1: Gasqfuj =1’u“ 11:3: 33 = Cu~s"{-55J= [-10% 5- Elm: {as"{i-mNdJ=CoE'(i—* mywlﬁfus—Ti—zw}; 'm=o,l,.a, - -- 1mm : 3., ::. ﬂs"{i}:g“ “=11: 9:1. = @Shilf-iJ: [3'5" 1 H1 _ _ * 3L - — d {Bin = 133 {:1 ﬁj—Jfﬂlfihr =2ﬁ3'fi~§}:2cns'HF-HEII‘J ®D=I2ﬁ¢ E. Da = 4N fﬁ) maﬁa?) =8 = ‘P-ﬂ3d13 r l J B'lg. The Fergmmended elem-Hr Spacing IE. IL d: 1+E-OEE’ I where B is the Star] (male in deerES 3.. Ba: '36” i d: L+Cn§5¢° = 0.535? wavelenij LL __ 1 I d = Fmr 1+D.’FD'?J “53-53573 “ﬁmﬂe‘ﬁﬂ 1. _ 5'— _ d= rmr my 0-55” “Whirl”- mm, 1.1 a. narrow ElEmEhT Pﬂﬂem fm'l Saha‘ﬂmea accommdaie 1a Er Spa-(inter , 1.15:1ij ‘Hn'IS rule, L311] Emma ﬂank the. a??? faith?“ “’5 “"11! WEWJE “WV- E“?ﬂ Dr.-- r'l _ 1| J" . _ _ffl_:_ -I- .f‘..-. .1 ‘|_ W110" H- -.... w.- ~-* ~ 5xr- [that 6‘28. The Excﬂ'uiinn coefﬁciem far a “Emir Emmi“! “0:? are “33" m" a, {IL-=3: {[421 B. Since the elements are plated a.th ﬁe H-axis can”: if:-if}=DE-{a1-E‘Imﬂmsﬁ+3331nasinﬁ+§aﬁsel=Smst\$¥ The am; fuchr'fnrfhig army f3. similar +0 “AH-Inf uf Problem 8.16 . The [MP4 =5 inﬁi¥ﬁina munch fasﬁalﬁ.‘ 51:15am): 4msaf¥~smampj C- Thaw field ES obﬁiined usinj 'H'IE Pattem multiplimﬁm “11E: ﬁf (5‘5) lay Multipyi-ﬁ "Hm field 6f a single ML dipola, as a‘weﬂ l5; {4‘543' hit-PH: ‘i‘he army fnchr about. Thus I. u-kr Ca 5 n. J {tail =E = In?" - 3- 4M Hana as; Ea a.) Hrs: eJHEﬂ-‘J J'flmr gma [ (A ) 6 1H]. {FIFE E'éﬂn C03 [Emu] = at + a: magma) + £13 CaSC4LLJ =a. + altar-3311 —I) + aaESCoSm—e CaElU.‘ H) 0.. Rn‘A-DdB =4? RuEUOL'Eaje ﬁlth} =IGD Zn: 31*1‘Jj1cuzr4r\['|:;~—::+3“:—T]I'd"?[raznzw‘xfmj£4 1' = 2013243 lei-Elna. Cos u = ffﬁn (ABS = {Cu-u: +a3} + £20.;" Bdgjmsm 1-833 [1354“ = r: [1&de {2m ﬂeagxg-ﬁ 3.96 (%)+ : raga 3-134 Eﬁuaﬁrg, Mike farms yields {13:- [5-4-2?.ﬂz=4‘?.503,ﬂl= 34.0“??? GT“ in nurmall'ﬁecj for-m as“: ﬂ%3:l_lo’ d1“: ﬂ?{ﬁ-__‘L=ﬁﬂllﬁ;r {11” = ﬂﬁ3:2a?g b_ (AF); = 2.43% + 3.05Cusi£51nacqsﬁj+ﬁbﬁﬂr5inﬁfngﬁj J u=¥émamsﬁl d=3y E. f: I+0.86iﬁfﬂﬁh[1'££ask"llm}iI[=-Ik= IH-ﬁsdﬁafﬂ-MJ] = 1-3-13 2 El .1... DD : __R_T = L r. LEE? = arm/dig H-E inﬂi'rim) 1+Elﬂﬂ‘~—D [.313 Do {CUmPLL’rer Pru mm) = I-T‘TS =3.ﬂldB “it The 511de thpter}. d. HPBN = f { Eoé'ﬁtoiﬁr amﬁ) *(‘asﬂfiﬁﬁﬁaidﬁﬁJ 7135319“ = 1.323’lcosT-9443ﬁ [91-5)] — [gs—Tamt’ﬁl'fﬂ] 2:333:4133‘9 HPBW =5A3ﬂ 3-H Md =5cm, Bahamian => 3!; = 3.05.5): 163?. {1- Using Table- 9.1 km EDD -- - 2 . -= .4 j"- . it'll—4‘???“ l-MﬂFh-GAEKHM itildramwﬁm a 8 {MW} b,1fd=Eﬂﬂ 9 d =5l\$ = %i=oﬁggxmﬂh, a: 5.4??Hl53h {3, Using (9-13}? 2., =13: in [E_+_a____ Whmhﬁﬁtﬁﬁ mm? Eb: I24: ﬁn (W) =3ﬂ 5le I {5.41 (1- Uma E3~ISJ with 1.: (LUTTFL 21: = J‘ in tan£h§jl =j{3::5.Lrl}1'W&-¥, i=D-4‘WA e. Usitnj {3-24) :? an =ﬂ 22:11—21: id = Rd +_~; Ed [were acm'rd'mj +4: {4"FU. 3’54}; 8’51) Fir = 15C) {C+1nko}-C1(HJ+%SM£M} [Satzhﬂ)~281ﬁ4¥i]] +i Eﬁﬁﬂk’ﬂ] [ C +£n{%}+Ci{-1MJ*JCNHJ1E XV“ "* 5D {.2 SHMH [amt-1M2 Sim—91 {lkiﬂ — smﬂeﬂlf 1Ci[h1}-C1C1hi} 4:; (‘4‘?) J T C = D-quz 1 Rd =515124EMJJ 2 X5. 2 Sh:er REEL} 1. :1: 454% 1.15% , ﬂ = 0.4??31 H : 3-431 , lhﬁ=s.nl?2?=é.oz , +eixz= [.5043 an“?! ‘—'-E-or‘i' KID—5' Can {I} = 111165;.) {:51} = Enﬂ'ﬂﬂnbcj- (1161} 2 D.E'F?.2+ Err-I # C; ij Cinta.ul?xt§‘J= D = a 5-H}. + in Emma“) 'Ciilﬁ .or‘?:< m1) 3.131351) 2 34,6|BS3 (Cr.an Lied) 9'11 (Coni’dl CiiflkﬂJfEJ-ECAfﬁﬂr‘imEé} warm 42.45325: -IL443 ICE-(«1211) = C: [3-G1}=0-[l5 ﬁnﬂhﬂ=i¥1ﬁaﬂlﬂ= Hg; 3H“) = SECS-n1] = I-Brﬁ Fm” mufﬁn—f} = Enfi-Sns} 2'. 5.40? Cifziel} =ﬂ£g.am :—0.n53 “FPEWH BI Emma}: 31mm” = 9.13.: 341521.21) : Sim-ow]: r434 Cﬁﬂﬁﬂ—TGS [3 01) =- witm R’r =Sﬂ [41. 5W2+ t. Ina—o.“ 5+ ‘L;__5_%[;.4;4._1(|_54H] _ -— (Lima —J.{c-.IIEJJ ]- =§oﬂavaj - E4 33 _ h. 1 I) Km~ 3:15 2{:.34re)-o.‘?‘il [zit-34?) ~1-424J - Naif-'1fﬂ-l15}‘—C~a.n£BJ—f-li-Mﬂﬂ Km = Eli-0.1953}: ﬁlms, I. ~ ~ . — - 64-33-— SI'TEJ:S4.|53?5-. 3; 5 4'— _ J [83? Using {3'24} m {I 5043} J Em L. 42*; Ed ___ AL £4:£EE.95}{64.6.3'FE-j3JBE'U ———_______ = 25?.na—j5-4'TJ. __—-—-——_. 2551 + it 1L64.33?5-j3,iaa?1 + 4;:er 2. ate: 1:03 2 E-lﬁxlﬁh3h(ﬁ.4‘f?xlo‘5ﬁ} =:.*‘H4xm"3).., ﬂ=ﬂ~¢TT3~ Hairuj The E’ﬁ'LLEUﬂJEHt radius ﬁe {1.31413 radqu .. 15' 2kﬂ§f£ = 2 {471\$} {Llrmxm inf/mmm} = m? m: _5 Cm Ex) 2:} = \$5?er + in ("I'Iaﬁxm—E) — C; (Wynn :55} , x: 'I'i’u‘hm Ci [zhﬂé‘ﬂ] = Emmi x155) +DI~ETW2 = — 3.3‘135 Km= 1:455, Eastman Ed 2 1- m4 {64. 350 +5 113155) = 54. 63?E+j 7. 04.355 an 2 ga- ‘z‘d : 4C4,ala.ﬁ'3}£'6fi-€3‘?5 425 “43552 :; 25l.5‘?+ ] 2.9555 23:! + R ziggqﬁgarsﬁﬂmgsaj—b4,6rB-‘T3 3. Using a = 5f: -= 3.065xm‘3’A; IL: {3.32%}. 25mm : 2 {3.u55xla3h ﬂdxrrvfupdqﬂ) = 2.4msxiﬁ4 Cm (2.454531?) to :ﬂnp4545xl54} -c; (24545;:154} warm: Gilkaﬂ3=cﬁa4ﬁ45xtﬁﬂ= Damn-1+inﬂAMSKiﬂF-THBH Xm=f|-S ; Err-54.330 Ed = I-Dcm, [54.3843 +3 lI-ISJI :64. 63151:] 1|. .3454 “+33 [ﬂrﬁ‘T‘F-E+U-4o? gm: 42ml = 4L4,61333}ca4.53'r5+3 M454} —————————— =zm.ssg +j 4.3% 234+ 3* 5215641537511; :1. 54.54} + 4,613 33 ...
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## This note was uploaded on 11/01/2009 for the course EEE 443 taught by Professor Balanis during the Spring '08 term at ASU.

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more_soln - ECE 435 Kempel Homework Set #1 Fall 2000 Due:...

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