ME 3200 Mechatronics Laboratory. Lab Exercise 8: Operational Amplifiers


 Lindsay Greene
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1 Intrductn ME 3200 Mechatrncs Labratry Lab Exercse 8: Operatnal Amplers In ths experment yu wll explre sme the basc prpertes peratnal amplers, better knwn as pamps. These electrnc devces are very useul n analg crcutry. As ther name mples, they can perrm mathematcal peratns n vltage sgnals: ncludng algebrac and calculus peratns. The Ideal OpAmp An pamp s a devce wth tw nputs and ne utput. The tw nputs are knwn as the nnnvertng nput, v+, and the nvertng nput, v. The utput the pamp s dependent upn the ptental derence between the nvertng and nnnvertng nputs. Opamps requre an external pwer surce dented cc. The pamps used n the lab use a ±cc ±12 prvded by the bench pwer supply at each statn. A smpled schematc an deal pamp s shwn n Fgure 1 belw. It s cmmn t mt the pwer cnnectn n mst pamp dagrams; therere, Fgure 1 des nt nclude these cnnectns. (a) (b) Fgure 1: (a) Smpled pamp schematc. (b) Opamp crcut dagram. The basc eatures deal pamps and ther representatn n crcut dagrams are shwn n Fgure 1 (a) and (b) respectvely. The tw nputs the pamp are cnnected thrugh a resstr wth nnte resstance that restrcts current rm lwng nt the pamp at ether termnal. The utput lead s cnnected t a dependent vltage surce thrugh a resstr zer value, thus causng the utput vltage t be equal t the vltage prvded by the dependent vltage surce. The vltage the dependent surce s prprtnal t the vltage derence between v+ and v and can be expressed as llws: D ( ) + = A v v (1) where AD s the penlp gan the ampler, whch, deally, s nnte.
2 eal Opamps In realty, hwever, nntely large resstrs, nnte penlp gans, and zervalued resstrs d nt exst. Frtunately, the characterstcs typcal mst pamps generally allw the use the equatns and assumptns that dene the deal pamp. Ths act s very useul when desgnng and analyzng pamp crcuts. The typcal nput resstance an pamp s n the rder 100 MW whch stll allws very lttle current nt the nput leads. The typcal utput resstance an pamp s n the rder 10 W. An utput resstance ths lw means that a nndeal pamp can prvde a substantal, albet nte, current and that Equatn 1 adequately apprxmates ts vltage utput. Equatn 1, hwever, s nly a gd apprxmatn the nmnal vltage derence between the nputs s small. I ths vltage derence becmes t large the pamp saturates at a vltage knwn as sat. Saturatn ccurs because the vltage derence between the nputs dctates that must be larger than the supply vltage cc accrdng t Equatn 1. Snce the pamp cannt prvde mre vltage than t s gven the utput reaches an upper r lwer lmt (±sat). The saturatn vltage an pamp s always a lttle lwer than ts supply vltage, cc. Fr example, the pamps used n ths lab cannt supply mre r less than ±12 ; the saturatn vltage r these devces s mre lke ±10. The pen lp gan, AD, the pamp s clsely related t the saturatn characterstcs a gven pamp; t denes hw large the derence between v+ and v can be bere the pamp saturates. The typcal pen lp, lwrequency gan an pamp s usually abut 105. Hwever, the penlp gan mst pamps s requency dependent and wll becme smaller and smaller dependng n the requency the nput sgnal(s). A large penlp gan drastcally restrcts the sze the ptental derence between v+ and v, but t als means that the pamp s very senstve t small changes between v+ and v. S hw des ne avd saturatn and take advantage the pamps senstvty? Saturatn s avded by dvertng a prtn the pamp s utput t ts nvertng termnal by physcally cnnectng the utput thrugh a passve electrnc devce t the nvertng nput. Ths technque s called negatve eedback and s very cmmn n almst all useul pamp crcuts. Negatve eedback ensures that the derence between v+ and v wll always be very nearly zer, but that the pamp s stll senstve t small changes between v+ and v. The precedng characterstcs real pamps allw the use the llwng assumptns n pamp crcut analyss: v = v (2) + = = 0 (3) + where + and  are the currents lwng nt the nnnvertng and nvertng nputs, respectvely. It s mprtant t nte that Equatn 2 s vald and nly negatve eedback s used n the pamp crcut and s smetmes reerred t as vrtual equalty. Wth these assumptns, the crcut can then be analyzed usng Krch s current r vltage laws (KCL and KL respectvely). Cnsder the example belw that llustrates hw these assumptns are valdated n the case the smple vltage llwer crcut. Example 1 Determne the utput vltage the pamp n Fgure 2 as a unctn the nput vltage, gven that the penlp gan AD = 105. Fgure 2: A vltage llwer crcut.
3 The rst step s t denty the vltage values at the nput leads. The nvertng nput s ted t the utput, and the nnnvertng nput s ted t the nput vltage. v = (4) + v = (5) The next step s t substtute these values and the gven value r the penlp gan nt Equatn 1: Ater sme algebra, Equatn 6 becmes = 10, 000( ) (6) 10, 000 = 10, 001 (7) The pamp s knwn as a vltage llwer, r buer, because the utput vltage s essentally equal t the nput vltage. The Amercan Hertage Dctnary [ denes a buer as Smethng that lessens r absrbs the shck an mpact. Based n the characterstcs a real pamp, we see that ths pamp crcut reduces the mpact the current prvded by the vltage nput s that t cannt prpagate t the utput. ecall that current cannt lw between the nput leads. Snce the nput vltage s appled t the nnnvertng nput, any current cmng rm that nput s blcked rm the utput. The utput s ted t the nvertng nput, and snce there s n current between the nput leads, there s n current n the wre cnnectng the utput t the nvertng nput (ths cnnectn s knwn as the eedback path). Any current that s requred r the devce cnnected t the utput the buer wll be prvded rm the pamp tsel. Ths eectvely separates the nput devce rm the utput devce, but stll prvdes an utput vltage that s essentally dentcal t the nput vltage. Useul Opamp Crcuts The Invertng Ampler Fgure 3: An nvertng ampler crcut. Cnsder the nvertng ampler crcut n Fgure 3. The llwng analyss shws hw t determne the utput vltage as a unctn. Wth the nnnvertng nput cnnected t grund, v + = 0, Equatn 2 states that v  = 0 as well snce the crcut has a negatve eedback lp (thrugh ). The vltage at the nvertng nput s knwn as vrtual grund. The drectns the currents assume that they run tward grund. Applyng Ohm s law results n the llwng equatns: = (8) = (9)
4 Keepng n mnd that the current rm the nvertng termnal  = 0 rm Equatn 3, KCL can be appled at the nde cntanng the nvertng nput. Substtutng Equatns 8 and 9 nt Equatn 10 yelds: Fnally, slvng Equatn 11 r yelds + = 0 (10) + = 0 (11) = (12) The mathematcal peratn perrmed by ths pamp crcut s multplcatn (.e. amplcatn the nput). Ntce that the sgn the utput s ppste the sgn the nput. Ths sgn nversn s why the crcut s called an nvertng ampler. The Actve LwPass Flter A smple mdcatn can be made t the nvertng ampler s that t can lter ut hgh requency nse a cmmn element und n mst electrnc sgnals. Hgh requency nse s cmmnly caused by external vltage r magnetc surces r rm natural mpurtes n crcut devces r cmpnents. Hgh requency nse s generally characterzed by spradc, hgh requency varatns n the vltage sgnal. The lw pass lter eectvely excludes nput requences hgher than a speced requency called the cut requency. T create an actve lw pass lter, smply cnnect a capactr n parallel wth the eedback resstr the nvertng ampler as shwn n Fgure 5. Fgure 4: An actve lw pass lter Ths crcut perrms tw peratns. Frst, t amples the nput vltage accrdng t Equatn 12 (whch s vald r lw requences), and secnd, t suppresses requences hgher than ts cut requency, where the cut requency, ω 0 n rad/sec, s dened as: 1 ω = (13) 0 C T be exact, the utput ampltude as a unctn nput requency r ths crcut s descrbed by: = ω ( ω ) 0 2 (14)
5 where ω s the requency the nput sgnal. Fgure 5 shws the requency respnse an actve lw pass lter whse resstrs have been chsen t prvde a unty gan, and where the xaxs s the nrmalzed requency, and the yaxs s the abslute value the system gan. Fgure 5: Lw pass lter requency respnse As ndcated n Fgure 5, at ω = 0 (DC vltage nput), the utput vltage s = (15) As nput requency ncreases, ampltude decreases. At the cut requency, ω = ω 0, the magntude the utput s dened by the llwng: = = (16) 2 In rder t decrease the mpact the lw pass lter n the desred utput sgnal, the cut requency s set as hgh as pssble. The trade usng a hgh cut requency s that mre nse s permtted t pass thrugh the lter. As a rule thumb, settng the cut requency t at least twce the maxmum expected nput requency and less than ne tenth the expected nse requency s best. A dmnant surce nse n the lab s AC lne nse at 60Hz. Mre sphstcated hgher rder lters can be used t create a mre deal lter. The LM324 Quad OpAmp Opamps are readly avalable as nexpensve ntegrated crcuts (ICs). The pamp IC used n the Mechatrncs lab s the LM324 quad pamp. Ths s a 14pn dual nlne package (DIP) chp that cnssts ur pamps. When plugged nt an electrcal breadbard and prvded the apprprate ± cc, the chp prvdes ur ndependent pamps that can be used t rm a wde varety useul crcuts. A schematc the LM324 s ncluded n Fgure 6. Ths type schematc s knwn as a pn ut, and t ndcates hw the pns the DIP crrespnd t the nputs and utputs the ur pamps. Whenever these types IC devces are used, t s mprtant t reer t the data sheet prvded by the chp manuacturer that descrbes the devce s characterstcs and lmtatns. The data sheet r the LM324 s avalable n the class web page n the lab handuts page.
6 Fgure 6: Schematc the LM324 quad pamp. Asde rm the applcatns dscussed n ths handut, the pamp has many ther uses n analg electrncs. Yu are encuraged t explre ther applcatns ths useul devce. Prelab Exercses 1. Determne the utput vltage the pamp n Fgure 1 as a unctn the nput vltage, the resstance, and the capactance C. The methds develped n the llwng backgrund sectn wll prvde yu wth the tls needed t perrm ths task. (ecall that the current thrugh a capactr s prprtnal t the tme dervatve the vltage acrss t.) Fgure 7: Derentatr crcut 2. Calculate the deal utput vltage,, ths crcut the nput vltage s equal t the llwng: = Asn ω t (19) where A s the ampltude the ncmng sgnal n vlts, ω s the requency the ncmng sgnal n rad/sec, and t s tme n secnds.
7 Labratry Exercse equred Materals/Equpment An Electrnc Breadbard An LM324 Quad Opamp Chp A Sgnal Generatr An Oscllscpe esstrs Capactrs The Benchtp Pwer Supply The 2_channel_scpe.v Labew I used n Lab 2 Sld Cre Wre A Wre Cutter/Strpper Banana Cables BNC t Allgatr Clp Cables Dgtal Multmeters Allgatr Clps BNC t Banana Adapters BNC Cables BNC Tees The crcuts that yu wll buld n ths lab prcedure are based n the nes descrbed n the ntrductry sectns ths lab handut. Nt nly are yu expected t buld the crcuts descrbed belw, but yu are als expected t debug them they d nt wrk apprprately the rst tme. Debuggng crcuts s a very useul skll and requres patence and attentn t detal. The mst cmmn errr n pamp crcuts s accdentally saturatng the pamp wth t large a vltage derence at ts nputs. One methd debuggng ths prblem s t use the dgtal multmeters prvded n the lab t check the vltages the nput and utput pns t trace path the crcut rm begnnng t end. Ask yur TA r help the crcut als t unctn ater yur best erts t debug the crcut. Nte: D nt turn n the bench pwer supply untl yur crcut s cmplete. In addtn, whenever any changes are made n yur crcuts turn r unplug the pwer supply rm the crcut. Ths prtects the crcutry and elmnates ptental headaches rm burned ut pamps. 1. Lcate an electrnc breadbard and an LM324 quad pamp IC and careully press the chp s pns nt the hles the breadbard s that t straddles the center dvder wthut bendng ts pns. 2. Prvde pwer t the LM324 by cnnectng the bench pwer supply 12 vlts t the cc pn and +12 vlts t the + cc pn. 3. Turn n the sgnal generatr and scllscpe, cnnect the unctn generatr utput t an scllscpe nput, and adjust the utput the sgnal generatr untl the scllscpe shws that yu have a 2 Hz, ±2vlt sne wave. Dscnnect the scllscpe nput, turn t, and set t asde. 4. Desgn an nvertng ampler that dubles the ampltude the nput sgnal. ecrd the value the resstrs that yu wll use n the space prvded. = = 5. Use a BNC tee t splt the utput the sgnal generatr, and cnnect ne end the tee t the A_CH0 nput the DAQ breakut bx yur lab statn.
8 6. Buld the nvertng ampler yu desgned n the step ur use the grund lead the benchtp pwer supply as yur cmmn grund. Cnnect the utput the sgnal generatr t the nput yur ampler crcut and cnnect the utput the ampler t the A_CH1 the DAQ breakut bx yur lab statn. Nte: Yu wll need t use a BNC t Banana adapter and an allgatr clp t cnnect the utput the sgnal generatr t yur crcut. The black lead the BNC t Banana adapter shuld be cnnected t the grund the benchtp pwer supply. The red lead the BNC t Banana adapter receves the allgatr clp and s cnnected t yur crcut nput thrugh a sld cre wre jumper. When cnnectng the utput yur crcut t the DAQ breakut bx, use a BNC t Allgatr cable and jumper wres t grund (black) and the crcut utput (red). 7. Open the 2_channel_scpe.v rm the Labew lder n yur cmputer s desktp, select the run buttn rm the tlbar, under Oscllscpe Channel Selectn, type 0 and 1 n the bxes belw the ON/OFF swtches, and make sure that they are bth turned On. 8. Turn n the pwer t yur benchtp pwer supply, select apprprate values r the sample rate and the number samples n the Labew I, and press the Acqure Data buttn. 9. Examne the waverm n dsplayed n the Labew I, save yur data t a dsk by pressng the OK buttn under Save Data, and determne the amplcatn actr yur nvertng ampler usng the measurements the Labew I. ecrd ths amplcatn actr belw. Amplcatn = 10. Turn yur benchtp pwer supply. Fgure 8: Buerlteramplerderentatr crcut. 11. Desgn a buerlteramplerderentatr crcut (Fgure 8) that wll derentate a 2 Hz, ±2vlt sne wave and amply ts ampltude t a 2Hz, ±4.5vlt (9vlt peaktpeak) sne wave. eer t the prelab and the actve lwpass lter sectn ths lab r the necessary methds. Be sure t use an apprprate cut requency. ecrd the requred values r yur electrnc cmpnents n the spaces prvded. = Ω = Ω C = F C = F = Ω 12. Buld the crcut yu just desgned. eer t Fgures 6 and 8 t help wth wrng the crcut payng specal attentn t the pn ut dagram Fgure 6. Use the grund rm the bench pwer supply r the apprprate as the cmmn grund r ths crcut. As bere, all equpment and crcuts shuld be cnnected t that ne grund pnt.
9 13. Send the utput yur crcut t A_CH1 n the DAQ termnal blck and the utput the sgnal generatr t AI_CH0 and t the nput yur crcut as dne when realzng yur nvertng ampler. 14. Turn n the bench pwer supply, chse the apprprate number samples and samplng rate n the Labew I, and press the Acqure Data buttn t cllect the waverm data. Save the data t dsk and examne the waverms. 15. Determne the actual amplcatn acheved by yur buerlteramplerderentatr crcut usng the same technque as bere. Als, determne the phase sht the utput yur crcut usng the data traces n the waverm graph the Labew I. ecrd the amplcatn actr and phase sht belw. Amplcatn = Phase Sht = rad 16. Increase the requency the nput sgnal t 5Hz, chse the apprprate number samples and samplng rate, and push the Acqure Data buttn n the screen. Save the data t dsk and plt the data. Hw has the appearance the waves changed? What s the ampltude and phase derence the utput ths tme? A = Phase Sht = rad Why have the peaks been cut the snusds? (Hnt: reer t the PreLab and the Data Cllectn Labratry.) 17. Increase the requency the nput sgnal t 100Hz, chse the apprprate number samples and samplng rate, and push the Acqure Data buttn n the screen. Save the data t dsk and plt the data. Hw has the appearance the utput changed? Why des the appearance the utput wave change as the nput requency ncreases?
10 Questns 1. What s the mst ecent way t mplement a cmplex pamp crcut that requres mre than ne pamp? 2. Descrbe at least tw gd ways debuggng an peratnal ampler crcut. 3. Draw the crcut dagram r an ntegratrampler crcut that ntegrates the nput vltage. Slve r the utput vltage as a unctn tme the nput vltage s equal t Equatn 19 abve. 4. Descrbe at least tw practcal applcatns r pamps r yur rbt prject.