1. Elementary Electronic Circuits with a Diode

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1 ecture 1: truct t electrc aal crcut Elemetary Electrc Crcut wth a e Euee Paer, 2008 HE M OF HE COUSE ume lear tme-arat () electrc crcut t re ay lut t the fllw fe tak (ee F. 1), whch are ery mrtat Electrcal Eeer: 1) t mble t ctrl the crcut trafer fuct (a) by a electrcal al, ether ltae r curret. 2) t mble t mlemet a crcut wth a c a reater tha e. 3) t mble t mlemet a crcut wth a wer a reater tha e. 4) t mble t mlemet a curret urce. 5) t mble t mlemet a cllatr (crcut eerat a erc al), fr examle, a e-wae cllatr. he am f the cure t le all the abe tak by u electrc ece: e a tratr. eel a tuy electrc crcut, we tart frm elemetary crcut, aalyze them, a the mre f there a ee. 1. EEMENY EECONC CCUS WH OE Our ma am here t bul a crcut wth a a (t ecearly reater tha e) that ca be ctrlle by a electrcal al, ether ltae r curret. Namely we wul lke t bul a ltae-ctrlle ltae er a a curretctrlle curret er (hmewrk). reach th al, we frt eel hycal, mathematcal, a fally a rahcal mel f the e. Bae the rahcal mel, we f equalet electrc crcut t relace a e a electrc crcut. h wll allw u t aalyze le-e electrc crcut by aly electrc crcut thery e: ymbl, hycal tructure, aalytcal mel a rahcal charactertc he ymbl f the e a t hycal tructure are e F. 2. eel a mathematcal mel f the e we hae t ecrbe the eeece f the e curret,, the e ltae,. um that the re much mre healy e that the re, >>, we elect the e curret ue t the hle a cer ly that ue t the electr. Nelect the mall effect f the weak electrc fel wth the re the electr, whch are the mr chare carrer th re, we cclue that the e curret excluely ue t the ffu curret f electr: f (,) C > 1 P > 1 F. 1. Crcut that cat be mlemete by u cmet ly: retr, caactr, a uctace. K + Cathe K e E fr 0 E fr 0 >> hermal equlbrum ccetrat "e" elet re ( 0) / e ffu leth F. 2. Symbl f the e a t hycal tructure. ee equat (1). 0 x

2 ecture 1: truct t electrc aal crcut j (0) q q 6447 / e 448, (1) S q S / S / [10 f ] S where j the e curret ety, the e crect area, (0) the ccetrat f the electr the re at x0 (ee F. 2), the thermal-equlbrum ccetrat f the electr the re (whe the e termal are e crcute), the ffu ctat f the electr, q the chare f the electr, the ffu leth fr the electr, the thermal ltae, a S the aturat curret f the e. t wrth t, that at rm temerature S 1 m S [10 f ] 0.7 k q 300 K 26 m. (2) F. 3. he - charactertc f the e: the te a eate art f the ax hae the ame cale, the cale are fferet. k (2) the Bltzma ctat, a the ablute temerature. he tycal alue f S 10 f. ue t the tr eeece f temerature, the S curret uble t alue er a 5 creae f the e temerature. Bae (1), we raw F. 3 the e - charactertc Statc a yamc meace Nte (ee F. 4) that the charactertc f the e lear wherea that f a retr lear. a reult, a e tralate (amlfe) fferetly tatc, a, a cremetal (yamc), a, al: Oerat t (, ) G r r r G ( eeral). (3) Oerat t (, ) t bu that fr a retr G r r. (4) r G et u ete the ftely mall cremetal al a mall al. electrc crcut, tatc al uually efe erat t f electrc ece t re a requre tralat (a) fr mall al. Statc al are efe by the eer. he r f mall al uually exteral. hey eter the crcut thruh ether a atea r F. 4. Statc a yamc a fr a retr a a e. Nte that G, wherea G.

3 ecture 1: truct t electrc aal crcut er; they ca al be eerate by tet trumet (fuct eeratr, etc.), r by ther electrc crcut. hu, may electrc crcut are ecate t the rce f mall al. he mall-al cuctace a retace f a e ca be fu a fllw O O S / S e /. (5) / 1/ a le ' S e / S + S + S O " O tat la le γ 1 26 Ω. (6) + S 1 m, 300 K γ Nte that the mall-al (yamc) cuctace a retace,, are a fuct f the e erat t, amely, a fuct f the tatc e curret,. (c) 1.3. ltae-ctrlle ltae er bul a ltae-ctrlle ltae er that hul atteuate mall-al accr t a tatc (c) ltae, we utlze the abe eeece f a cect a e a retr [ee F. 5] mlarly t a mle rete ltae er, where e f the retr relace by a e. We the cect ere t the retr a e a tatc ltae urce,, t efe (ctrl) tether wth the e erat t, a a mall-al ltae urce. f the crcut ltae a / a a fuct f we ue the fllw ytem f equat: O γ () O S, O ( / + 1 [ ) ( + )]. (7) he ytem f equat (7) a lear e a e t ecearly hae a aalytcal lut. Hweer we ca ealy F. 5. ltae-ctrlle ltae er, rahcal lut, (c) "lare" al equalet crcut (mel) fr the e, () "lare" al equalet crcut, (e) mall-al equalet crcut, (f) mall-al equalet crcut (mel) f the e. O (e) (f)

4 ecture 1: truct t electrc aal crcut f t rahcal lut [ee F. 5], whch llutrate ery well the al tralat by the crcut. Nte F. 5 that the mall al tralate ly by the ftely mall art f the e charactertc abut the erat t. t al ery mrtat t te that the taet le t the e charactertc, raw thruh the erat t, tralate the mall al the exactly ame way. herefre, we ca ubttute the e F. 5 wth a equalet crcut [ee F. 5(c)] ha the charactertc that etcal t the taet le F. 5. a reult, the crcut F. 5 a () are equal term f the mall-al a. We wll call the crcut F. 5() "lare" al equalet crcut. he qute mea that uch a crcut tralate exactly ly tatc a yamc al. ( real lare-al equalet crcut hul exactly tralate ay al, fr examle, -ftely-mall al.) mrtat aatae f the crcut F. 5() that t a lear e a, therefre, ca be le by aly uert. Sce we are terete f mall-al a ly, we ure all the tatc al urce [ee the ahe le F. 5() that hrt-crcut the tatc al urce]. h e u equalet mall-al crcut F. 5(e). h crcut ca ealy be le by aly elemetary electrc crcut thery: r r + 1, 0,. (8) + hee equalet + 0 (c) 1. (9) < 1. (10) where the mall-al curret a, a the mallal wer a. Small-al ut a utut meace Frm the ytem-eeer t f ew, t mrtat t f a eerc mel fr a we arety f crcut. Sce electrc crcut are lear fr mall al, the hée equalet ca be che a ther eerc mall-al mel. We hall ue the cet f r t rereet the hée retace fr the mel that are ee frm the ut r the utut f a electrc crcut (ee F. 6). / ( + ) hee equalet F. 6. Small-al ut a utut meace., (c) the ral crcut,, (c) hée equalet. ()

5 ecture 1: truct t electrc aal crcut O 1 2 1/ 1 F. H1. Crcut fr the hme exerce. tat la le a le HOME EXECSE F erat t, wth the hel f a rahcal lut, fr the tw crcut F. H1. Nte that, S1 S2. F. 1. he mall-al equalet crcut f F. 5(e) a t rahcal lut. EFEENCES [1] J. Mllma a C. C. Halka, terate electrc, McGraw-Hll. [2]. S. Sera a K. C.Smth, Mcrelectrc crcut. PPENX Nte (ee F. 1) that the erat t a rahcal lut fr the mall-al equalet crcut f F. 5(e) hfte t the r f the crate ytem. h becaue we ure the mall-al equalet crcut all the urce reble fr the tatc ct, amely, a γ.