Physics 310 Lecture 7b Waveform Generators & Timers

Transcription

1 Physics 0 Lecure 7b Waveform Generaors & imers Wed. /0 hurs. / Fri. / Ch 0: Oscillaors & imers - Beginning Ch 0: Oscillaors & imers es of; Lab 7: Oscillaors & imers Lab 7: Oscillaors & imers; Quiz Ch 0 HW 7: Ch0 Pr. *, 6,7,8; Lab 7 Noebook Handou: Projec Design doc Projec Proposal xample lecronics Magazines Announcemens Office Hour Swich. o he nex few weeks of he semeser will have labs begin on hursday and HW due on hursday. Wih ha in mind, would you raher move office hours o hursday morning or keep hem uesday morning? doesn maer o me. Projecs. he las few weeks of his course are dedicaed o individual projecs. By he end of nex week you ll have me mos of he basic ypes of circui componens, so you ll be prepared o conemplae a wide range of projecs. n preparaion for ha, o Monday he nd ask you o give me a projec Proposal he general idea of / parameers for wha you d like o build. o Monday he 9 h ask you o give me a projec Progress epor he specific design, ec. of wha you d like o build. o Handous. Here are wo documens one ha explains wha s expeced in a Projec Proposal and in a Projec Progress epor, and he oher (sapled o is back) is a sample Projec Proposal. o Selecing a Projec. You may already have a projec in mind, or you may be compleely uncerain abou wha you d like o do. You can creae a projec from scrach, or you can selec one from any number of sources surf around and you ll find a lo of projecs, and we ve go a lo of magazines wih lecronics projecs in hem ll bring hem ino he room when we ge going on lab oday. Waveform Shaping Comparaor (Schmi rigger is beer version) sine or riangle o square wave negraor square o riangle wave Differeniaor square wave o pulses Oscillaors (jus a few examples) Crysal oscillaors LC equivalen elaxaion oscillaors neon lamp, op-amp square-wave oscillaor, Wein bridge 555 imer Basic operaion Circui examples One-sho (monosable operaion), asable operaion Waveform Generaors CL808 is an example, exernal componens deermine frequency

2 Physics 0 Lecure 7b Waveform Generaors & imers 0- nro. Ofen you wan a circui o generae a specific waveform maybe a sine wave o help smoohly drive a moor, maybe a square wave o blink a ligh, or maybe a sawooh wave o drive sick-slip moion of a piezo. Las ime, we considered a few circuis ha shaped periodic inpu ino periodic oupu of differen forms. We also began looking a circuis ha acually generae periodic wave forms from scrach. We ll coninue wih ha oday. he UJ s a quirky componen and he 555 is a very popular one. 0-. he Unijuncion ransisor (UJ) + BB UJ mier p n Base, B Base, B B B Wired as: B B Base, B he mier is a p-ype blob wih a regular level of doping (and hus mobile charge carriers / holes). he Base, on he oher hand, is an n-ype slab wih very low doping (and low densiy of mobile charge carriers / elecrons), his means ha i has a fairly high resisance (imporan laer.) he mier probe conacs ino he Base slab a some poin, B, a fracion of he disance up from B oward B ; we ll call ha o (beween 0 and, by design i s greaer han 0.5, i.e., he emier is closer o B han o B ). ha means ha he Base bias a he poin of conac is. Similarly, hough he B o B resisance of he UJ will vary, he B B B B resisance beween B and B can be phrased as a fracion of i, B B B B (acually, will be varied, bu generally around o.) oking across he axis, we d ge small curren ou of he emier when heavily reverse biased, i.e., B ( > B ). his would die off a B. p-ype mier n-ype Base

3 Physics 0 Lecure 7b Waveform Generaors & imers hen curren would sar flowing ino he emier (and on ino he base) for B B Since he mier is P-ype, he curren ha i injecs would be holes ino he valance band. here are a few imporan hings abou his: firs, since he p-ype mier is more heavily doped han is he n-ype Base, more holes flow in han elecrons flow ou hrough he p-n juncion. So, i serves o increase he ne densiy of charge carriers in he Base. Noe ha he srengh of his curren depends direcly on jus B, regardless of B B. However, once he holes are injeced, hey are free o be swep away by B B. he effec is ha he mier has dumped new charge carriers ino he boom half of he Base and hus upped is carrier densiy and hereby reduced is resisance, and hus reduced he fracion,. oking a he UJ as a volage divider, clearly B s value becomes closer o B. Wih B 0. 7, comes wih i. mier p n Base, B Base, B Like (holes in) B-B B B-B Base, B As he curren coninues o increase hough, i does so by drawing more and more curren ou of he boom half of he base, so grows and grows while does no. For a while, his is more han offse by he decreasing resisance, bu evenually ha increasing he populaion of minoriy carriers significanly increases he rae of minoriy majoriy carrier recombinaion which eliminaes boh kinds of carriers. hus he resisance increases again and B B B B acually increases again. B B (elecrons up) (elecrons up + holes down) peak = B < B everse Biased valley Carrier injecion ino base increases carrier densiy and decreases B-B = B +0.7 Forward Biased v Hole-elecron recombo reduces effec of carrier injecion, bu is sill growing wih, increasing B-B

4 Physics 0 Lecure 7b Waveform Generaors & imers Now ha we ve go an appreciaion of he srange curren-volage relaion of his device, le s see i in acion. ou = + BB peak ou B B Capacior charging Capacior discharging C valley v n his circui, say he capacior sars ou grounded and so begins charging up. For a while, he UJ is off since he emier is lower volage han he base. So he capacior charges exponenially oward BB. However, when ou = B, i s forward biased and so he UJ urns on, passes curren, and discharges he capacior hrough he UJ and. Once p is surpassed, hinks kind of snowball since passing all ha curren acually reduces he UJ s resisance beween and B, so he curren, once begun akes off. his quickly discharges he capacior and brings ou = down oward valley. Before i his here, we wan dragged below B, and so he UJ is shu off and so charging resumes. Noe: mus be chosen so ha enough curren can flow hrough i when he ou is a is peak (hus is smalles) so ha he UJ urns on, ye no so large ha i rushes o he BB peak sa ino sauraion and never urn off he ransisor, ha means ha p. Well, in a hand-wavey way, ha s how his circui works. he capacior charges wih ime consan /( C), unil i reaches peak, a which poin he UJ rapidly urns on and drains he capacior (comparaively, insananeously) unil is dragged below valley, a which poin he UJ urns off and he capacior is free o charge up again. Oscillaion Frequency Wha s he frequency / how long does i ake o charge up? n he ineres of geing a fairly simple expression ha gives us he righ ball-park, we ll make a few approximaions, bu ll flag each as we go, so you can imagine how one migh make a more exac expression. Well, if we jus wired up he lef branch, beween ground and he posiive rail, BB, he C ou BB. capacior s volage would charge up oward he rail according o ( ) ( e ) However, when he oupu volage, which is he UJ s, reaches he peak, p, he charge up ceases and discharge akes comparaively no ime a all, so we ve execued a full cycle. P BB ( e C ) 4

5 Physics 0 Lecure 7b Waveform Generaors & imers Noe: in ruh, we should analyze his jus as we did he Neon lamp oscillaor, bu if v is much less han p, we can assume ha he difference in ime o charge from 0 or from v is negligible, so we ll do alrigh ignoring ha sligh difference. Flipping his relaionship around o solve for he charge ime, we have C ln or f P BB C ln Now, we can rephrase his raio of volages P B B B B 7 P BB Here s anoher approximaion, le s jus drop ha pesky 0.7. f p is on he order of even 7, hen we migh expec ha dropping his inroduces only a 0% error in our frequency calculaion. P B B B Now, o he exen ha he inernal resisance of he UJ is far greaer han or a he ime p is achieved, hen mos of he volage drop across he righ branch of he circui occurs across he UJ / negligible drop is across or, so and 0. hus we have P P BB so ha BB And we, a long las, ge he book s expression f C ln he book noes ha, if you d raher have a wave form ha looks more like a series of righ riangles han arcs, you can charge he capacior only a small fracion of he way o is maximum, so you re operaing in a more linear region of he exponenial curve. he mos obvious way would be o use wo differen upper rails for he lef and righ branch of he circui say 00 on he lef and only 0 on he righ. B BB B 5

6 Physics 0 Lecure 7b Waveform Generaors & imers Wih Consan Curren Source Beer ye, replace wih a consan curren source. You may recall from Lab 5 ha you used a ransisor and a couple of resisors o creae a consan curren source which essenially drew a consan curren hrough he ransisor regardless of he collecor resisor. + BB ou = A B A p B A ou C A B B C Now, looking across he capacior, Q / C d C ou cap cap / So, if he curren flowing ono he capacior is consan, hen ou rises linearly wih ime unil p is reached and he UJ is urned on o discharge he capacior. So, le s find cap and see how consan i is. cap CA CA A A CA while he UJ is off i draws negligible curren in is emier BA BB A A CA A A BA 0. 6 ( + because i s a PNP, as arrow indicaes, emier is higher volage han base) BA BB B ( BA B ) BA A /( ) Subsiuing hese back in, we find ha cap B B 0.6 B B B 0.6 So, o he exen ha he UJ isn varying he curren ha i draws, he PNP ransisor is feeding he capacior a a consan rae unil i charges o p and hus he UJ swiches on o discharge i. 6

7 Physics 0 Lecure 7b Waveform Generaors & imers 0- he 555 imer (our firs Discree gic encouner) All of he preceding oscillaors are nice o have me, bu here s one ha ges a lo of use and has some versailiy, so i s paricularly nice o undersand how o use i. he 555 imer, like an nsrumenaion Amplifier, is an inegraed circui ha iself can be hough of as buil of smaller inegraed circuis, op-amps and such. Wih jus a few exernal componens, you can wire i up o selec he frequency and even shape of he periodic oupu. nernally, he 555 imer can be hough of as build of hree resisors, wo ransisors, an inverer, wo comparaors, and a flipflop. We ll walk hrough he funcion of each. Before we do, should prepare you for a significan change in how we look a circuis. Mos of he inernal componens of he 555 have fairly discree oupus high volage (near +) or low volage (near 0), and no much in beween. So i s useful o hink of hese as logic devices making signals eiher or. ha s acually he nex phase of his course looking a (discree) logic circuis. Here will be our firs dabbling. Here are he basic rules he 555 lives by: + Lef op-amp: acs like a comparaor 8 when hresh > conrol conrol can be se hrough pin 5 or, defaul i s / + hreshold 6 when hresh < conrol igh op-amp: acs like a comparaor when rig < ½ conrol = / + if pin 5 is conneced. when hresh > ½ conrol Flip-Flop Q jus holds is value unless rese > ref hen Q if Holds regardlessof S and and Lef ransisor: When Q goes, he ransisor is on, so Discharge line is conneced sraigh o ground. nverer: Makes oupu equal opposie of Q. S S Discharge S ese Q Flip-flop ref 5 4 Conrol rigger ese Oupu Condensing his chain of reasoning as o skip he middle men of Q, S, and : 555: conrol regardless of rig Oupu if h conrol and rig conrol Holds and conrol When Oupu =, discharge swich is off When Oupu =, discharge swich is on rig conrol where conrol = / + or se hrough pin 5 Of course, he proof of his hing s usefulness is in is applicaion. 7

8 Physics 0 Lecure 7b Waveform Generaors & imers 0-. Asable Operaion You may have noiced ha Figures 0.6 and 0.7 show he differen pins geomerically disribued differenly, and neiher is in he order ha he pin s numbers sugges. he numbers do represen he acual order in which he pins are arranged around he real chip; however, for he sake of illusraing he inernal logic and exernal logic, differen orders are convenien. Le s apply he rules of operaion above o figure ou how his behaves. 0) Le s sar imagining ha he exernal capacior is charged o /+ (or above) and ou has jus become low; of course ha only happens if Q is which also means ha he inernal Discharge ransisor is making good connecion beween pin 7 and ground, hus discharging he capacior hrough. ha allows he rigger/hreshold volage o drif down oo. + /+ /+ ou c = r = h ( + )C C lo 0) ) ) 0)->)n he process, c=h=r ges down below / + and so he firs lef inernal op-amp ses ; bu S mus already be for Q o have been holding is value. ) venually c=h=r ges below even /+; now he righ inernal op-amp ses S=; his, along wih = ses Q =. ha of course shus off he discharge ransisor and sends ou =. ) -> ) Wih he discharge ransisor off, he capacior sars charging up hrough resisors + oward +. charges up, bringing r> / + herefore S goes. Wih already, Q holds is value and c ( Finding : c ( Finding : ) ) C ln() ) evenually brings h >/+ so goes and now Q goes, ou = and i sars all over again. /( ) C C ln() e e / C 8

9 hus : Physics 0 Lecure 7b Waveform Generaors & imers C ln( ) C ln() C ln() Duy Cycle o fully characerize his wave s ime dependence, since i spends un-equal ime hi and lo, you don jus need he period bu somehing ha communicaes he fracion of he ime in one sae versus he oher. ha s ofen referred o as a device s duy cycle (you ll see a duy cycle knob on our funcion generaors). For he 555, he common definiion is ime he oupu is vs. he oal period D. C. C ln() C ln() 0-. Monosable Operaion he 555 imer is a very versaile chip, wired up in his way, i responds o pulse in he rigger line. r + 0 /+ c = h + ou C 0) Say rigger =, C is iniially discharged and ou = (hus Q = and he Discharge ransisor grounds ou pin s 7 & 6.) r s a. Noe: Qholds hr ) Pulse r from o < / + and back. he momen r drops below / +, S, bu since, Q goes. )->) ven afer r reurns high, he new value of Q = is held (see a. above). he capacior charges. ) Along he way, h crosses >/ +. When ha happens,, sending Q and urning on he discharge ransisor and sending ou iming: Of course i s prey easy o deermine how long he oupu remains. / C ( ) e C Cln() 0) ) ) 9

10 Physics 0 Lecure 7b Waveform Generaors & imers 0-6 Precision Waveform Generaer: he CL808 Lucky for us, nersil has made a chip ha makes he sandard waves and operaes over a range of frequencies 0.00 Hz o 00,000 Hz. We won even ry o peek under is hood. n he radiion of numbering he pins according o heir acual geomeric order around he chip, bu displaying hem as o minimize he number of crossed wires. n he configuraion illusraed, he load is across he square wave oupu. We are old ha he frequency of he signal i generaes is 0.5 f C Sine wave adj. Sine ou riangle ou 4 Duy cycle 5 Freq. adj FM bias NC 4 NC Sine wave adj - or ground iming Capacior 0 Square Wave Oupu 9 FM Sweep npu 8 C L Characizaion of Wave Forms A number of he circuis we ve looked a generae square waves, bu how square are hey? f we zoomed in on one of he squares, wha migh i look like? clearly can insananeously jump from one value o anoher, and i probably can perfecly hold a given value. Wha imperfecions you can eliminae, you characerize. Here s a zoom-in on a single square of a square wave oupu wih he usual imperfecions. overshoo ringing 90% Sag / il 0% ise ime decay ime he fac ha a real device will have finie rise and decay imes (can insananeously change values) has he obvious implicaion ha he oupu signal will be slighly delayed relaive o he ideal oupu. has a furher implicaion if he signal is asked o change oo frequenly, i jus doesn have he ime o come o full ampliude before i s asked o come back down again. here s a simple quaniaive relaionship ha speaks o his for a given rise ime, here s a 0

11 Physics 0 Lecure 7b Waveform Generaors & imers corresponding cu-off frequency, i.e. a frequency of signal for which he oupu would acually only make i up o / of he inended peak. he book gives r f don know abou geing exacly 0.7, bu we can easily see ha he ball-park is righ. (0.9 0.) Approximae he rise as linear, hen he slope is max. Now, if we ried o produce a periodic square wave of frequency f bu wha we go in reurn was riangle waves (never makes i o he plaue a he op, sars decaying) ha only makes i o /, i akes ¼ of he period o ge up ha high from 0, or 4 f r max / max, hen he slope is 4 f / max /(4 f ) (0.9 0.) max 0.8 quaing he wo slopes gives 4 f / max r f r + 8 hreshold Conrol olage + - rigger S Flip-flop ese Q 4 ese ref Discharge 7 Oupu