EE381 Final Review Notes Page 1 of 8 Chapter 1 Vector Algebra. R R r r. r (field position vector)

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1 81 Fia Reiew Note Page 1 of 8 Chapte 1 eto geba Saa magitude eto dietio & magitude Poitio eto poit fom oigi to a fied poit ( ) o to a oue poit ( ) itae eto uua poit fom a oue poit to a fied poit The ditae betwee the oue ad the fied poit i R R R ' ' R = Soue() (fied poitio eto) (oue poitio eto) Saa/dot podut: o( ) eto/o podut: aˆ i( ) whee a ˆ detemied b RHR. o,. Co podut hit: Remembe ode of (,, ), (,, ), ad (,, Uit eto aˆ whee the eto magitude i. Saa pojetio of eto oto i aˆ aˆ. aˆ. The eto pojetio of eto oto i Chapte Coodiate Stem ad Tafomatio & Chapte eto Cauu Retagua/Cateia Coodiate (,,) aˆ aˆ aˆ a a d d d a d d aˆ d aˆ d aˆ d d d aˆ d d d aˆ d d d aˆ d d d d aˆ aˆ aˆ aˆ ˆ ˆ a a aˆ ˆ ˆ a a

2 81 Fia Reiew Note Page of 8 d d d d d d d a a a i d a a d a i d Cidia Coodiate (, aˆ aˆ aˆ d d aˆ d aˆ d aˆ d d d aˆ d d d aˆ d d d aˆ d d d d aˆ aˆ (Note: aˆ ha depedee) 1 aˆ aˆ aˆ aˆ aˆ 1 1 aˆ Spheia Coodiate (, ) aˆ aˆ aˆ d d aˆ d aˆ i d aˆ ˆ d i d d a, d i d d a d d d aˆ d i d d d aˆ (Note: aˆ ha both & depedee) aˆ 1 1 aˆ aˆ i i i i i aˆ 1 1 aˆ i i 1 aˆ Gadiet eto epeetig magitude & dietio of maimum patia ate of hage of a aa fied iegee et outwad fu pe uit oume of a eto fied (aa) Fu of though ufae i d Cu iegee Theoem d d iuatio of a eto fied pe uit aea w/ aea oieted fo maimie (eto whoe dietio i oma to ufae b RHR Ciuatio of aoud otou i Stoke Theoem d ( ) d d eto fied aifiatio diegeee/oeoida; iotatioa & oeatie ie d ( ) d ˆ

3 81 Fia Reiew Note Page of 8 Cateia Coodiate (,,) Cidia Coodiate (,, ) Poit/aiabe oeio : o o 1 ta i i aˆ o aˆ i aˆ aˆ o aˆ i aˆ eto oeio : aˆ aˆ aˆ aˆ aˆ aˆ aˆ i aˆ o aˆ aˆ i aˆ o aˆ aˆ aˆ o i o i i o i o aˆ aˆ o aˆ aˆ i aˆ aˆ aˆ aˆ i aˆ aˆ ot Podut : o aˆ aˆ aˆ aˆ aˆ aˆ aˆ aˆ 1 Cateia Coodiate (,, ) Spheia Coodiate (, ) Poit/aiabe oeio: i o o o ta 1 i i i ta 1 o i eto oeio: aˆ ˆ ˆ ˆ ˆ ˆ a a a a a aˆ i o aˆ i i aˆ o aˆ aˆ i o aˆ o o aˆ i aˆ aˆ o o aˆ o i aˆ i aˆ aˆ i i aˆ o i aˆ o ˆ a aˆ i ˆ o ˆ a a aˆ o aˆ i aˆ i o i i o i o o o i o o o i i i i o i o i o o i ot Podut: aˆ aˆ io aˆ aˆ ii aˆ aˆ o aˆ aˆ o o aˆ aˆ o i aˆ aˆ i aˆ ˆ i ˆ ˆ o ˆ a a a a ˆ a

4 81 Fia Reiew Note Page 4 of 8 Chapte 4 etotati Fied pemittiit of fee pae: = F/m Couomb Law: poit hage Q Q ( ) 1 ˆ Q Q F a R1 (N) 4 R 4 1 foe o Q due to Q 1 (oppoite attat, ike epe) eti Fied F / q i oeatie (i.e., ad d ). poit hage: Q ( ) ˆ Q a R 4 R 4 (/m) Q ( ) N k k & k1 4 k (/m) ( ) d ie hage deit: (/m) 4 whee a be a futio of poitio (i.e. ). ( ) d ufae hage deit: (/m) ' 4 whee a be a futio of poitio (i.e. ). ( ) d oume hage deit: (/m) ' 4 whee a be a futio of poitio (i.e. ). eti Fu eit: poit hage: ie hage deit: (C/m ) ad eti Fu: d (C) Q Q ( ) 4R 4 ufae hage deit: oume hage deit: aˆ R (C/m ) 1 ( ) d 4 ad (C/m ) whee ( ) d 4 N k1 (C/m ) whee ' ( ) d 4 (C/m ) whee ' Qk( k) 4 k (C/m ) a be a futio of poitio (i.e. ). a be a futio of poitio (i.e. ). a be a futio of poitio (i.e. ). Gau Law: mout of eeti fu though a oed ufae i equa to amout of hage otaied withi ufae. d Q e (C). I diffeetia/poit fom etotati potetia i wok pe uit hage to moe fom poit to : To get eeti fied fom the eetotati potetia: Q Q poit hage: 4 R 4 () W q d N Qk ad () (wt to ifiit) 4 k1 d ie hage deit: () 4 whee a be a futio of poitio (i.e. ). d ufae hage deit: () ' 4 whee a be a futio of poitio (i.e. ). d oume hage deit: () ' 4 whee a be a futio of poitio (i.e. ). k

5 81 Fia Reiew Note Page 5 of 8 N k eg toed i a eeti fied: W Qkk d d C eg deit of a eeti fied: Chapte 5 eti Fied i Mateia Spae 1 1 w (J/m ) dq Codutio uet deit: J (/m ) ad eetia uet I J d = () dt Reitae: R ( ) whee i egth, i odutiit (S/m), ad S i ufae aea I S Pefet eetia oduto (PC) iide,, iide, ad fo a two poit a ad b iide. Powe diipatio: (W) ad powe deit P J d d ab w J P (J) (W/m ) Poaiatio eto: P e eate eeti fied & eeti fu deit i mateia pe P. Pemittiit: (1 e) whee e i eeti ueptibiit ad i the eatie pemittiit. oud ufae hage deit Paˆ ad boud oume hage deit p P a be ued to epeet poaied mateia. quatio of Cotiuit Chage deit i odutie mateia I out p dq dt t iide J d o J whee T / i the eaatio time. t/ T () e Q S Capaitae: Reate toed hage to potetia diffeee C (e.g., paaepate C ) d etotati ouda oditio betwee dieeti egio Tagetia,, o aˆ ( ) ad 1t t 1t t 1t t Noma = = o aˆ ( ) aˆ ( ) If, o aˆ ( ). Sufae oma aˆ poit fom egio 1 ito egio, ad poit awa fom boud whie poit towad the boud etotati ouda oditio at dieetipc itefae Tagetia,, o aˆ ad Noma = o aˆ. t t Sufae oma aˆ poit fom PC egio ito dieeti egio, i.e., poit awa PC. Regio 1 Regio, 1, 1 1t, 1t t, t, 1, 1 a 1 a 1 PC Regio,, t t i = i =, a

6 81 Fia Reiew Note Page 6 of 8 Chapte 6 etotati ouda aue Pobem aed o oig pobem whee the potetia at the boudaie ad mateia iide the boudaie ae kow uig Poio equatio o Lapae equatio. Q d d Capaitae C high high d d ow Reitae ad apaitae ae eated b RC ow. Reitae high d high d ow ow R I J d d Method of Image epae odutig pae with image hage o that bouda oditio ti atified. Chapte 7 Magetotati Fied pemeabiit of fee pae: = 41 7 H/m iotsaat Law: I daˆ R I d( ) Fiameta uet H ' ' (/m) 4 R 4 J ˆ d ar J d wd ( ) Sufae uet deit H ' ' ' (/m) 4 R w 4 J daˆ R J d d ( ) oume uet deit H ' ' ' (/m) 4 R 4 Fo a og taight ie uet: I H aˆ (/m) Mageti Fu eit: H (Wb/m o T) ad Mageti Fu: m d (Wb) mpee Law: Lie itega of the mageti fied aoud a oed path i equa to the amout of uet paig though the ufae eoed. H d I eoed (). iff/poit fom H J. eto Mageti Potetia : eated to mageti fu deit b m d (Wb) Fiameta uet Sufae uet deit oume uet deit I d I d 4R 4 ' w' (Wb/m) Jd Jd wd 4R 4 J d J d d 4R 4 ' ' (Wb/m) (Wb/m) ad to mageti fu b

7 81 Fia Reiew Note Page 7 of 8 Mawe quatio fo Stati Fied Itega Fom iffeetia Fom Faada' Law d mpee' Law H d J d H J Gau' Law d d d Chapte 8 Mageti Foe, Mateia, ad eie Foe of a mageti fied o a poit hage: Fm Qu ma Loet foe equatio: F F F Q u ma Foe of a mageti fied o uet eemet: fiameta uet: ufae uet deit oume uet deit e m F I d F J d d w w' F J d d ' Foe betwee two fiameta uet eemet (foe eeted b eemet o 1, F1 F1 ): fiameta uet F II d d ( ) Toque T F m (N m) whee i the momet am, F i foe, ad m I S aˆ i the mageti dipoe momet. Magetiatio eto 1 m M H eate mageti fied ad mageti fu deit i mateia pe H M H H H. m Magetotati ouda oditio betwee mageti egio Tagetia aˆ ( H H ) aˆ ( H H ) J. If J, the H H t t Noma o aˆ ( ) aˆ ( ) Sufae oma aˆ poit fom egio 1 ito, ad poit awa fom boud whie 1 1 poit towad fom boud (J) eg toed i a mageti fied: WM H d H d LI eg deit of a mageti fied: 1 1 wm H H (J/m )

8 81 Fia Reiew Note Page 8 of 8 Chapte 11 Loe Tamiio Lie I I () I L g Z g ( ) Z, u L Z L Z i (), Z i( ), 1 Phae eoit u f whee ad ae the peuitegth idutae ad apaitae 18 Phae otat (ad/m), etia egth (ad) o ( ) (deg) o ( ) u u Waeegth (m), Chaateiti impedae Z ( ) f I I Phao otage & uet ( ) e e () j j I( ) I e I e () j j bakwad taeig otage ad uet. ef ( ) Ief ( ) Zi ( ) Z Refetio Coeffiiet: () L e ( ) I ( ) Z ( ) Z Iput impedae Z L Z i i i L L Z Z ad iput Z whee,, I, ad I ae the fowad ad () Z j ( ) i () L Zi () Z ( ) ZL jz ta ( ) 1 ( ) Zi () Z Z I( ) Z jzl ta ( ) 1 ( ) ma 1 Stadig wae atio SWR 1 mi * Iput Powe P I e, of patiua iteet ae the oad j ae( ).5Re ( ) ( ) (W) (otat o a oe tamiio ie) efetio oeffiiet. The iput otage () ad uet I() I a be foud uig the equiaet iuit I Z g g Z i () Z () () ad I Z i g Z g Z i g g Zi (). Note:,.5( IZ), ad.5( IZ). 1 ()