DEPARTMENT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE MASSACHUSETTS INSTITUTE OF TECHNOLOGY CAMBRIDGE, MASSACHUSETTS 0239 6.0 Intrductry Analg Electrnics Labratry Labratry N. READING ASSIGNMENT: Review 6.002 ntes n resnance. If yu lack experience with scillscpes, yu will als need t refer t Sectins 3: Cntrls, Cnnectrs, and Indicatrs and 6: Basic Applicatins f the Tektrnix 2445 Oscillscpe Manual [available at the Stckrm windw if nt in the bag n the tp f the scpe] fr a descriptin f the peratin f the varius scillscpe cntrls. Yu shuld als read the handut Using Yur Oscillscpe Prbe [available at the Stckrm windw] and The XYZ s f Oscillscpes, available free at the Stckrm windw. Many f yu will be using ur new Tektrnix TDS30XXB Oscillscpes. These scpes cme with mini-manuals, and a full manual is lcated in the 38-60 lab space. OVERVIEW This is the first f six labs that will ccupy yu fr the first half f the term. This ne is prbably the lngest, but it is als the mst ckbk -like f all the labs. Yu will nrmally receive a new lab n Friday at 2:00 pm in class; because this lab is lnger, and yu have received it n Wednesday, yu have an extra cuple f days t cmplete it. Each subsequent lab will deal with tpics that will be presented in class and each lab will becme mre design-riented and less ckbky as time passes. In ther wrds, we want t take yu frm training wheels t bicycle racing! In Experiment, we start ut t examine the effects f resnance, especially bandwidth, using just a 475kHz transfrmer with built-in parallel capacitr, the functin generatr, and resistrs. Then we prgress t driving the transfrmer using a mre real wrld surce, a transistr, which has its wn unique value f surce resistance and is a current surce, rather than a vltage surce, in Experiment 2. We are still using a simple lad resistr n the transfrmer secndary in rder t cntrl bandwidth; the trick here is that the surce resistance f the transistr is a new factr that als affects bandwidth, alng with the lad resistr n the secndary. Then in Experiment 3, we replace the lad resistr with the dide detectr/rf filter/lad resistr cmbinatin, and we study hw the dide changes the effective value f the lad resistr and we study hw the capacitr can affect the high frequency audi respnse arund 5 khz, as well as hw the bandwidth adjustment can affect the high frequency audi respnse arund 5 khz, [due t changing the value f the lad resistr], which shuld be the main "adjustr" f the audi bandwidth. In Experiment 4, we take a lk at a simple methd f transmitting AM mdulatin that als gives us a chance t study series resnant circuit behavir. The bandwidth f the series resnant circuit can als have an effect n the high frequency audi respnse f the cmplete transmit-receive system. Lab. N. 9//03
Then, we g n in Experiment 5 t substitute a receiving antenna fr the functin generatr, which als adds a secnd tuned circuit, which if it is tuned t the same center frequency as the transfrmer is tuned, will give us a tw-resnant circuit receiver and the cmbined bandwidth f the tw resnant circuits will reduce the audi respnse arund 5kHz even mre [the Q f the ferrite rd/cil/trimmer cap arrangement is nt as high as the Q f the transfrmer, therefre the tw resnance curves are nt the same shape]. The idea is t measure a few high audi frequencies in Experiment 3, say 400, 000, 3000, 5000 Hz, and then repeat thse measurements in Experiment 5 and cmpare them t see hw the additin f the secnd tuned circuit affects the audi respnse. OBJECTIVE In this labratry yu will transmit an AM radi signal t a rudimentary AM receiver that yu will build. This is ne f many ways t achieve wireless cmmunicatin and this experience will help yu make a decisin n what kind f design prject t undertake during the secnd half f the term. The bjective f this labratry is t gain familiarity with practical series and parallel resnant circuits [tuned circuits], and with RF transmissin and demdulatin f amplitudemdulated AM signals. Yu will als learn t use the Tektrnix 2445 and TDS 30XXB series scillscpes and the Hewlett-Packard 3320A Functin Generatr/AM-FM Mdulatr. Nte that althugh we have attempted t be relatively thrugh in this write-up, there will certainly be things that yu may have t figure ut fr yurself. If yu dn't knw hw t d smething, yu wuld prbably benefit frm playing arund a bit t see if yu can figure it ut. There is very little that yu can d with the equipment required fr this labratry that can damage it, prvided yu use cmmn sense. Hwever, if yu are having truble, dn't hesitate t ask fr help. Please DO NOT USE individual banana plug-t-alligatr clip leads t cnnect frm the functin generatr t yur circuits. These wires are unshielded and unpaired and will pick up stray signals and have uncntrlled stray capacitance and inductance. DO USE the BNC [baynet nut cnnectr]-t-ez-hk r BNC-t-alligatr shielded cables that are available at the stckrm windws. Insist n them, they were purchased fr 6.0 student use. Be sure t retune yur IF transfrmer cil slug every time yu make a change t the circuit elements and/r the signal level. The large signal levels we are using tend t saturate the adjustable cre in the IF transfrmer, and this causes the inductance t change. Thus yu may have tuned the transfrmer t resnance at ne frequency and vltage level, but at the same frequency with a different vltage level, the circuit may n lnger be tuned t resnance. Check it every time! Experiment : Q and bandwidth f Parallel tuned circuits. NOTE: THIS LAB REQUIRES A CHECKOFF FOR EXPERIMENT ONE n Mnday September 8. Sign up fr yur checkff time n the list psted n the TA s ffice dr [38-544]. Lcate the 475kHz Radi-Frequency [RF] transfrmer in yur parts kit, and als a shrt purple PLASTIC adjustment screwdriver t adjust the cil slug. If yu didn t already d s when yu Lab. N. 2 9//03
received yur parts kit frm the stckrm, exchange the 475kHz RF transfrmer can that came in yur parts bx fr ne f the new transfrmers munted n a small printed circuit [PC] bard that plugs directly int yur lab kit. Build the circuit shwn in figure ne, but please nte that yu will nt need a capacitr, it is built int the transfrmer and is wired acrss [in parallel with] the full primary. Yu shuld cnnect the grund terminal [cnnected t the can, which is als a shield frm utside interference] t the grunded side f the functin generatr, and yur scpe grund clip shuld als be cnnected t the same grund. Yu will make a series f 5 measurements using varius lad and series input resistances and will enter these measurements int Table n page 6. Then yu will make sme calculatins fr the rest f the table, and then we ll ask yu t draw cnclusins abut these circuits by answering sme questins. Keep yur hands as far away frm the transfrmer assembly as yu can when making adjustments and measurements n this circuit. The stray capacity frm yur hands will affect yur readings. Als, please be aware that the lng prtbard tracks alng the tp and bttm f the prtbards, viewed with the shrt side f the kit facing yu, are nt cntinuus. They are divided int tw sectins at the screw in the middle f the lng side. Pri-Sec turns rati = 4: V S R C R LOAD Figure : Circuit fr parallel resnance, Experiment.. Yu shuld cnnect yur scillscpe acrss the utput [secndary] f the IF transfrmer. Cnnect ne side f the secndary t the same part f the circuit that the Functin Generatr [FG] grund is cnnected. Cnnect yur scpe grund clip t the same grund pint. Recrd all results fr this experiment in Table n page 6. 2. Starting with the 0kΩ series resistr in the circuit and n lad resistr n the secndary, adjust yur functin generatr t prvide abut 600 mv peak-t-peak at 475 khz measured acrss the transfrmer secndary. While bserving the vltage at the utput with yur scillscpe, slwly and carefully adjust yur transfrmer cil slug with the plastic screwdriver [NO METAL SCREWDRIVERS] until the utput peaks. [DO NOT FORCE THE SLUG. IT WILL HIT BOTTOM, AND THEN FRACTURE INTO PIECES.] Yu have just adjusted [trimmed] the value f the transfrmer primary inductance s that it resnates exactly with the built-in capacitr at 475 khz. [NOTE: it may be easier t mnitr bth the input and utput vltages paying attentin t the phase shift between the tw vltages. When they are bth exactly in phase, r exactly ut f phase by 80 degrees [depends n which secndary terminal is grunded], then resnance is achieved, since the capacitive reactance has cancelled the inductive reactance leaving nly resistance.] 3. Set yur scillscpe t measure vltage using the built-in cursrs and adjust the functin generatr utput slightly s that the wavefrm n the scpe is exactly 600 mv peak t peak. Lab. N. 3 9//03
Yu may be tempted t hk up yur HP 3440A multimeter t help yu make the fllwing measurements, but please cnsider that the input impedance f the multimeter is MΩ +/ 2% in parallel with 00 pf. This shunt capacitance will be multiplied by the transfrmer turns rati and reflected back t the primary, where it will appear in parallel with the capacitr built int the transfrmer. This will significantly change the value f primary capacitance and therefre the resnant frequency as well as the bandwidth. S dn t use it in this applicatin! 4. Nw slwly change the frequency f the functin generatr upwards and bserve that the amplitude f the wavefrm n the scpe is decreasing. Cntinue t increase the frequency until the peak-t-peak value f the wavefrm has decreased t 0.707 f the value yu recrded in step 3. This is f H r the high frequency 3dB pint. [Yu can make this jb easy by setting yur adjustable scpe cursrs t.707 X 600 mv 425 mv and then just changing the signal generatr frequency until the wavefrm just fits in between the tw cursrs.] 5. Nw slwly change the frequency f the functin generatr dwnwards and bserve that the amplitude f the wavefrm n the scpe is increasing and then decreasing again as it passes thrugh resnance. Cntinue t decrease the frequency until the peak-t-peak value f the wavefrm has decreased t 0.707 f the value yu recrded in step 3. This is f L r the lw frequency 3dB pint. 6. Nw repeat the abve prcedure first with the selectin f lad resistrs indicated in Table, and then replace the series resistr with the larger values indicated in Table, again with the same selectin f lad resistrs. Ntice that as the series resistr is increased and as the lad resistr is als increased, the sharpness f the tuning increases and the bandwidth decreases [the 3dB pints are much clser t the resnant frequency f 475 khz.] The measure f the sharpness f this resnant peak is called Q and its value is infinite fr infinite series resistance [Q. Wuld infinite series wrk? Why? ] but in the real wrld is limited by parasitic resistance and such nasty practicalities as lad resistances. [Yu will have t recheck yur utput reference levels at 475kHz each time yu change the value f either the R SOURCE r the value f R L. Be sure t set yur functin generatr back t 475kHz each time yu set yur utput reference levels. When yu get t the measurements using the MΩ series resistr and the smaller lad resistrs, yu will have t settle fr a much lwer reference vltage at 475kHz due t the large drp acrss the MΩ resistr and the lading effect f the lad resistrs. Yu shuld be able t achieve abut 80mV peak-tpeak at 475kHz measured acrss the secndary under the wrst-case cnditins. 7. When the measurements fr Table are cmpleted, use sme f the equatins belw t enter the data in the calculated data sectin f the table. Please remember that the lad resistr n the secndary is reflected t the primary accrding t the turns rati. That is t say, the secndary resistance appears in parallel with the primary but multiplied by the turns rati squared [a 2 ]. This value is R Lpri in the table n page 6. R eff is the parallel cmbinatin f the secndary lad reflected t the primary in parallel with the surce resistance. The fact that the calculated and the measured bandwidths are different is explained by the parasitic resistances in the cil and the capacitr, which we are mdeling as a resistance in parallel with R eff. The fllwing equatins will be useful in understanding the behavir f parallel resnant circuits and in calculating values fr yur table. They will be derived in a later sectin f this lab. Lab. N. 4 9//03
Resnance ccurs when ωc = ; the magnitudes f the impedances are equal. Due t their ωl equal but ppsite lcatins n the imaginary axis, these impedances cancel each ther [fr ideal circuit elements nly!], leaving nly the resistive elements in the circuit at resnance. Slving fr the resnant frequency: ω = r f =. Nte that the resnant LC 2π LC frequency des nt depend n the values f any resistances in parallel with bth the L and the C; but it will vary with the value f the parasitic [series] resistance f the inductr, caused by the resistance f the fine wire used t make the cil. We shall ignre the existence f this parasitic resistance just nw. Bandwidth is defined as: BW = f = f f =. H L 2πRC f Q f the circuit is defined as Q =. With very high resistance [appraching infinity] in BW parallel with the reactive elements, the bandwidth appraches 0 Hz and the Q appraches infinity. Questins: Q.2 Parallel resnant circuits are ften presented with the R, the L, and the C all in parallel. Hwever, we are driving ur resnant circuit frm a vltage surce with a lw surce impedance, and therefre the resistance must be in series with the tw reactive elements. Explain what wuld happen if we placed the resistance in parallel with the reactive elements in this case. What is the value f the surce resistance f yur functin generatr? Q.3 What is the input impedance that the scillscpe prbe presents t the circuit? Q.4 Hw des it cmpare with the input impedance that the multimeter wuld present t the circuit? Q.5 Will it affect the primary circuit f the transfrmer in the same way as the multimeter wuld? Explain. Q.6 Review yur table f calculated and measured results. What cmbinatins f lad and surce resistances ffer the widest bandwidth? The highest Q? The lwest bandwidth? The lwest Q? Q.7 D all f yur measured and calculated values f bandwidth and Q agree? If nt, make a list f the differences and explain why they ccur. Why des the errr get wrse as the value f the resistr in series with the functin generatr gets larger, fr the case with infinite lad resistance? Q.8 Calculate the value f the parasitic resistance assciated with the transfrmer frm the data yu tk using the Meghm surce resistance and the infinite R L. Lab. N. 5 9//03
TABLE : RESONANCE DATA USING FG AND SERIES RESISTOR [C = 90 pf]; [a = 4:] MEASURED DATA [475 khz surce] CALCULATED DATA R-SERIES R-LOAD f H [khz] f L [khz] BW [khz] Q=f /BW R Lpri R eff BW [khz] f H [khz] f L [khz] Q=f /BW 0,000 Ω Open circuit 0,000 Ω 0,000 Ω 0,000 Ω 4,700 Ω 0,000 Ω,000 Ω 00,000 Ω Open circuit 00,000 Ω 0,000 Ω 00,000 Ω 4,700 Ω 00,000 Ω,000 Ω Meg Ω Open circuit Meg Ω 0,000 Ω Meg Ω 4,700 Ω Meg Ω,000 Ω Lab. N. 6 9//03
Experiment 2: Q and bandwidth f Parallel tuned circuits driven by transistr stage. Next, we will repeat sme f the previus measurements and calculatins using a real-wrld circuit. The circuit in figure tw belw is a versin f the lng tailed pair knwn as the cascde cnnectin. The lng tailed pair is a fundamental circuit that can als be used as a differential amplifier and which we will study in mre detail later in the curse. The cascde cnnectin is a cmmn-cllectr [emitter-fllwer] amplifier that drives a cmmn-base amplifier. This circuit is very useful, especially at high frequencies, because it prevents the unwanted multiplicatin f the transistr cllectr-base capacitance by the stage gain [the dreaded Miller effect ] when the cmmn-emitter transistr amplifier is used. This effect will be studied later in the term. +5 V Pri-Sec turns rati [a] = 4: R L V OUT 50Ω [Inside FG] 0.µF 2N3904 2N3904 FG V IN 5Ω [use 2-0Ω] 0 kω 0 kω 0.µF R X =5 kω -5 V Figure 2: Cascde amplifier circuit driving resnant IF transfrmer. In this new circuit, yu shuld understand that the transistr cllectr terminal is a pretty gd current surce, with a fairly high surce resistance whse value is dependent n the transistr biasing cnditins. Let s simplify figure 2 s that we can derive prperly sme f the resnance equatins that were listed abve. We will just cncern urselves with the secnd transistr and the resnant transfrmer circuit. The first transistr serves as an emitter-fllwer and prvides a relatively high input impedance and a lw utput impedance t drive the lw emitter input impedance f the cmmn-base transistr that drives the resnant tank. Yu can tell that the first transistr is an emitter-fllwer r cmmn-cllectr cnfiguratin because the cllectr is cnnected directly t the DC supply [V CC ] which is an AC grund. Yu can tell that the secnd transistr is a cmmnbase cnfiguratin because the base is cnnected t grund thrugh a capacitr. Q 2. What is the reactance [impedance] f this capacitr at the 475 khz frequency we are using? Figure 3a shws the tuned transfrmer driven by the transistr current surce, and figure 3b shws the same circuit with the secndary resistance multiplied by the primary-secndary turns rati Lab. N. 7 9//03
squared and referred t the primary, and labeled G fr cnductance t facilitate a simpler mathematical analysis. Pri-Sec turns rati [a] = 4: I C R I + LOAD G LOAD C L V Figure 3a: Tuned Lad n IF amplifier Figure 3b: Secndary Lad referred t Primary Nw we will use admittance ntatin t slve fr the resnance equatins. Please remember that we are adjusting the admittance f the inductr using the tuning slug s that it just cancels the admittance f the capacitr at 475kHz, s that the lad n the current generatr lks like a pure cnductance. Frm figure 3b: V G + jωc + = I; jωl I V = G + j ωc ωl r Eqn. The circuit is said t be resnant when ωc =, and the resnant frequency is given by ωl ω = r f = LC 2π LC Eqn.2 S we see that L and C must have values that will make f =475kHz and that f des nt depend n the value f G=/R. Hwever, at frequencies higher r lwer than f the values f /ωl and ωc are NOT equal, and the lad will have a net inductive r capacitive admittance in parallel that will increase the net value f admittance and thus decrease the utput vltage. Just hw fast the ttal lad admittance increases frm the peak value determines the sharpness f the tuning, ften called the selectivity f the circuit. This is a desirable quality f these circuits, fr selectivity allws us t tune t nly the statin we want and t exclude adjacent statins that wuld therwise cause interference. [Amplitude Mdulated (AM) statins in the USA have a maximum bandwidth f +/ 5kHz arund the carrier frequency, s in this case we wuld nly be interested in passing frequencies f 470kHz t 480kHz, and excluding the rest. Lab. N. 8 9//03
The bandwidth f a circuit is defined as the difference between the frequencies at which the respnse is dwn 3 db. [db=20lg 0 V 2 /V ]. A curve f Y= G + j[ωc-/ωl] is shwn in figure 4. Figure 4: Plt f Admittance vs. angular frequency, shwing bandwidth The 3 db pints f equatin abve will ccur when real equals imaginary in the denminatr: = = 0.707 + j.44 Slving fr ω 3dB : We set the real part f the denminatr in Eqn. equal t the imaginary part. G = ± ω C 3dB ω 3dB L This is rewritten as: 2 G 2 ω 3 db ± ω 3dB ω = 0 C Using the quadratic slutin: G G 2 ω 3dB = ± ± + ω Eqn.3 2C 2C But, if ω 2 is much greater than (G/2C) 2, then G ω 3 db = ω ± = ω ± 2C 2RC 2 The bandwidth is the distance between 3dB pints, s ω = 2 ; r ω = Eqn.4 2RC RC Althugh the apprximatin made in equatin 3 bscures the fact that ω is nt really quite exactly between the tw ω 3dB frequencies, the bandwidth is always /RC, regardless f the apprximatin. Lab. N. 9 9//03
Thus, we have tw majr cnsideratins in the design f this frequency-selective resnant circuit given by equatins 2 and 4 abve. Depending n which circuit elements are easily and practically varied, yu can see that resnance and bandwidth may be independently adjusted. Nte that L des nt appear in the bandwidth equatin but that C ccurs in bth the resnance equatin and the bandwidth equatin. Directins: Build the circuit shwn in figure 2. Please nte that yu are nw ging t drive the transfrmer frm the center tap. Cnnect yur functin generatr as shwn at the left f the schematic, s that the utput f the generatr is cnnected t the input f the transistr thrugh the cupling [DC blcking] capacitr. [The tw 0Ω resistrs in parallel in cmbinatin with the 50Ω surce resistance f the signal generatr frm a vltage divider t reduce the utput vltage enugh t prevent verlading this high gain stage. Yu will have t take this vltage divider int accunt when recrding the actual input vltage t yur circuit. Make sure that yur functin generatr is set fr HIGH Z befre yu take any readings fr V in. If the functin generatr is set fr 50Ω yur readings will be incrrect.] Put yur scillscpe prbe acrss the resistr R L and adjust yur input vltage t prduce an utput vltage f 2.0 vlts peak-t-peak with R L =. Retune the transfrmer fr maximum utput when yur input frequency is exactly 475 khz. Nw take the measurements required t fill in the Measured Data sectin f Table 2. [Yu will have t readjust yur input vltage at 475kHz each time yu change the lad resistr in rder t maintain the 2.0 V p-p at the utput. Als, be sure t retune yur transfrmer with the generatr set t 475kHz every time yu make a circuit change. The cres in these transfrmers can saturate easily depending n current and vltage levels, and this will change the value f the inductance. Best t recheck that the transfrmer primary is resnant at 475kHz every time yu make a change in the value f R L.] Then make the calculatins required t fill ut the Calculated Data sectin f the table. Nte that R Lpri is the value f the lad resistr reflected t the primary. A v = V ut /V in is the vltage gain. This can be calculated frm yur values recrded in Table 2. R SOURCE is the value f the transistr current generatr surce resistance, in parallel with any parasitic resistance that exists in the transfrmer, and is in parallel with R Lpri. Tgether, these tw resistances cmprise the cnductance G that we used abve t derive the resnance equatins. When yu calculate R SOURCE, use the value that yu get frm the measured data with infinite lad resistance and cpy it int the chart fr the ther values f lad resistance. Then yu can put R SOURCE in parallel with R Lpri t calculate the bandwidths fr the ther cases. These calculated bandwidths will prbably nt be exactly the same as the measured bandwidths in the left hand sectin f the chart, but they shuld be clse. [Of curse the calculated bandwidth fr the infinite lad resistr case will be the same as the measured bandwidth in rder t calculate the value f R SOURCE.] Nte: Yur DMM measures AC vltage in RMS vlts; yur scillscpe reads in peak-t-peak vlts. In rder t get an accurate gain calculatin, yu will need t cnvert ne kind f vltage unit t match the ther. Yur functin generatr can be set t read either peak-t-peak r RMS vlts. Questins: Lab. N. 0 9//03
Q2.2 What value f lad resistance ffers the widest bandwidth? The narrwest bandwidth? Q2.3 What is the value f lad resistance that cmes clsest t giving the bandwidth discussed abve as apprpriate fr AM receptin? Q2.4 What are the high and lw 3dB frequencies yu btained with this value f R L? Q2.5 What wuld happen if we decided t vary C instead f L in rder t tune this parallel tuned circuit t 475 khz? Q2.6 Why d yu think that the gain decreases as the value f lad resistance decreases? Lab. N. 9//03
TABLE 2: RESONANCE DATA USING CASCODE AMPLIFIER AND CENTER TAP [C = 90 pf]; [a = 4:] MEASURED DATA [475 khz surce] CALCULATED DATA V in [RMS] V ut P-P R L f H [khz] f L [khz] BW [khz] Q=f /BW R Surce R Lpri R S R Lpri BW [khz] f H [khz] f L [khz] Q=f /BW Av 2.0 V p-p Open ckt. 2.0 V p-p 0,000Ω 2.0 V p-p 4,700Ω 2.0 V p-p,000ω Lab. N. 2 9//03
Experiment 3: Detectr fr Amplitude Mdulated Signals [Nte: This detectr will be cnnected t the IF transfrmer secndary in place f the lad resistr that was used in the previus experiment.] Nw we have a useful circuit that will bth amplify and select a narrw band f desired frequencies. Next we need t prepare a circuit that will demdulate r detect an AM signal. The expressin fr an amplitude-mdulated signal is: KAm v = Ac csω ct + [ cs( ω c ω m ) t + cs( ω c + ω m ) t] 2 where c subscripts refer t the carrier frequency [in this case it s 475kHz] and m subscripts refer t the mdulating frequency which is an audi frequency between 50Hz and 5kHz. K is a scaling factr. By inspecting this equatin, we can see that an AM mdulated signal cntains three frequencies: the carrier frequency and bth the sum and the difference f the carrier frequency and the audi signal. When the audi is turned ff, the carrier is the nly signal. Figure 5a shws a sketch f an AM mdulated signal, with the carrier frequency exaggerated [nrmally the carrier frequency wuld be s much larger than the audi frequency that the individual carrier wavefrms wuld blend tgether]. Figure 5b shws the frequency spectrum f the amplitude-mdulated signal. Figure 5a: Amplitude-mdulated carrier Figure 5b: Frequencies in mdulated carrier wave [nt t scale] In rder t demdulate and recapture the audi we need t remve the carrier. If we examine figure 6a we can see mre clearly hw the peaks f the carrier wave apprximate the much lwer audi frequency [again, the spacing here is exaggerated fr clarity]. Nte hw there appears t be tw cmplete audi wavefrms in figure 6a; we can dispense with ne f them, and that is exactly what the dide in the detectr circuit f figure 6b des. And the remainder f the circuit is simplicity itself: a lw pass filter! Of curse it s intuitive that t remve the carrier we need t filter ut the high frequencies and save the lw audi frequencies. Lab. N. 3 9//03
Figure 6a: The carrier peaks utline the audi frequency Figure 6b: AM detectr circuit Use a N94 r N448 fr D Until nw, we have been substituting a simple lad resistr, R L, fr the detectr circuit, and yu shuld have learned that the value f R L is reflected t the primary f the transfrmer and is the primary element in determining the circuit Q and therefre the bandwidth. Bandwidth cntrl is very imprtant in AM t reject unwanted mdulatin frm adjacent statins. Nw we must determine a methd f finding the input resistance t the detectr s that we can cntrl the bandwidth f the mdulated signal. When an AC signal is rectified and then used t charge a capacitr, we have prduced a fairly cnstant DC vltage acrss the strage device [the capacitr]. There will be sme slight ripple n tp f this DC vltage, due t the tendency f the capacitr t discharge int the resistr, but let s ignre that ripple just nw. Our task is t determine an input resistance lking int the detectr just befre the dide; let s call it R eq [fr equivalent]. We ll calculate this resistance by assuming that the DC pwer dissipated in the lad R L is equal t the AC pwer delivered by the transfrmer carrier signal int R eq. Assuming that C F charges up t the peak value f the carrier vltage, then 2 Vp PDC = ; RL The ac pwer dissipated by the transfrmer surce in the equivalent resistance f the detectr is 2 Vp 2 2 Vp PAC = = R 2R eq If we equate the input pwer with the utput pwer, then it is easy t see that R eq = R L /2. Therefre, we need t chse R L first, as it cntrls the bandwidth f the tuned circuit. Chse a value fr R L that will give a bandwidth f 0kHz [+/ 5kHz] arund the 475kHz carrier frequency, as measured acrss the IF transfrmer primary. Next, we culd chse C F frm what we knw abut lw-pass filters. Hwever, in this case we are nt sure what kind f surce resistance the eq Lab. N. 4 9//03
transfrmer secndary and the dide prvide. If we culd easily estimate r measure these values, then we culd quickly design the lw pass filter. Instead, we will design the filter empirically by first trying a value fr C F equal t 0.0 µf and then mdulating the carrier with 400 Hz at 50% mdulatin. T d this, keep yur functin generatr carrier frequency at 475kHz and then turn n the AM mdulatin functin and adjust fr a 400 Hz mdulating frequency at 50% mdulatin [cnsult the functin generatr manual, cpies available at the stckrm windw]. Put yur scpe acrss the detectr lad resistr and bserve the detected signal. Recrd the utput vltage and then increase the mdulating frequency t khz, 3 khz, and 5kHz. Recrd the level f audi utput vltage fr all fur f these test frequencies. If the utput vltage at 5 khz is nt 3 db dwn frm the vltage recrded at 400 Hz, then yu will need t increase C F until the 5kHz signal is 3dB dwn. [If yu have a great deal f truble getting the respnse at 5kHz t hld up, yu may need t chse a different R L in rder t get a wider bandwidth frm the transfrmer, especially if yu find yurself using smaller and smaller capacitrs and yu are starting t see a lt f carrier ripple in yur audi utput.] Recrd the values f these tw circuit elements. [If the utput is mre than 3dB dwn at 5kHz, then yu will have t start ver with a smaller value f C F and then add capacitance as necessary.] NOTE: At this pint, yu may nt be able t see the mdulating [audi] frequency at the utput f the detectr. Yu may just see a distrted ghst f a wavefrm. This is due t a very imprtant characteristic f high Q [lightly damped] resnant circuits, namely: when yu stimulate a high Q resnant circuit with a pulse, a square wave, a part f a sine wave, mst anything, the resnant circuit will return a sine wave, which is its natural respnse. Therefre, in previus sectins f this lab, yu culd have been verdriving the transistr stages with a large enugh sine wave input signal t prduce clipping [a square wave] at the utput. Hwever, since the utput lad is a high Q resnant circuit, the respnse t a square wave input will be a sine wave. Almst like magic! Nw this is fine as lng as we are talking abut unmdulated signals, but when we take an amplitude-mdulated sine wave, send it at t-high a level int a transistr amplifier and clip the signal, well, we have just remved the mdulatin, the very thing we are trying t detect! Therefre, if yu d nt see any audi sine waves at the utput f yur detectr, first make sure yu are mdulating yur carrier, and then turn dwn the carrier amplitude [signal generatr utput] until yu see the prper audi utput frm the demdulatr. When yu are making yur measurements at 400 Hz, please als measure the DC vltage present at the detectr utput. Increase the mdulatin level t 80% and recrd the DC vltage again. Reduce the level f RF input t the circuit and recrd any change in DC vltage. Experiment 4: Transmitting AM signals; Series Resnant Circuits NOTE: PLEASE BRING A PORTABLE AM RADIO OR WALKMAN TO LAB FOR THIS EXPERIMENT. A FEW AM RADIOS WILL BE AVAILABLE AT THE STOCKROOM WINDOW. Yu have built and analyzed much f the circuitry required t amplify, bandwidth-limit, and detect AM radi signals. Nw it s time t transmit sme amplitude-mdulated RF [radi-frequency] signals. We will cntinue t use 475kHz in mst f ur wrk since we have designed ur receiving circuits t be sensitive t this frequency. This frequency is clse t the 455 khz used in all AM radis internally as the Intermediate Frequency [IF]. Mst current AM radi design uses the superheterdyne methd f receiving, where all the signals in the AM band [530kHz t.7mhz] are cnverted in the receiver t the IF frequency. This allws us t custmize mst f the amplifying stages in the receiver t perfrm well at nly this frequency, as yu have just dne in Experiment 2. Nrmally ne wuld nt chse t bradcast using 475kHz, as it culd nt be Lab. N. 5 9//03
received n nrmal AM radis and is clse enugh t the standard IF frequency t cause interference. Hwever, ur transmissins will be limited t 30 feet r s and als will be cntained within this building due t the shielding built int the building fr frequencies in the AM band. Antennas fr transmissin r receptin fall int tw brad categries:. physically resnant [the antenna is ¼, ½, ¾ etc. f a wavelength, depending n whether the antenna is end-fed r center fed] and 2. physically small cmpared t ne wavelength, i. e., less than 0.λ. Resnant antennae are useful at higher frequencies where the wavelengths are shrter than they are in the AM band. An antenna resnant at 475kHz wuld have t be almst 200 feet lng! Therefre we are using a physically small antenna. A physically resnant antenna lks very clse t a pure resistance when it is driven as a transmitting antenna; hwever a small antenna may lk inductive r capacitive depending n the frequency. Our antenna lks inductive at 475kHz, therefre in rder t drive a useful amunt f current int the antenna, we will have t series resnate the antenna with a series capacitr in rder t cancel ut the impedance due t the inductance. Series Resnance Analysis: Series resnant circuit analysis is identical t that f parallel resnant circuit analysis, except that we shall use impedance cncepts rather than admittance ntatin. The bandwidth curve/admittance plt f figure 4 can be cnverted int the impedance curve fr the series resnant circuit by replacing the Y s with Z s! Fr a simple series R-L-C circuit driven by a perfectly resistanceless vltage surce: V = I R + jωl + ; r jωc V I = Eqn.5 R + j ωl ωc The circuit is said t be resnant when ωl = and the resnant frequency is given by ωc ω = r f = LC 2π LC Eqn.6 The 3 db pints f equatin 5 abve will ccur when real equals imaginary in the denminatr: = = 0.707 + j.44 Slving fr ω 3dB by setting the real part f the denminatr equal t the imaginary part in Eqn. 5: R = ± ω L 3dB ω 3dBC This is rewritten as: Lab. N. 6 9//03
Using the quadratic slutin: ω R L 2 2 3 db ± ω3db ω = R R 2 ω 3dB = ± ± + ω Eqn.7 2L 2L But, if ω 2 is much greater than (R/2L) 2, then R ω 3 db = ω ± 2L The bandwidth is the distance between 3dB pints, s R R ω = 2 ; r ω = Eqn.8 2L L Althugh the apprximatin made in equatin 7 bscures the fact that ω is nt really quite exactly between the tw ω 3dB frequencies, the bandwidth is always R/L, regardless f the apprximatin. f 2πf L Since Q is still defined as Q =, in this case Q = = 2πf. Therefre, t achieve a BW R R L high Q in a series resnant circuit we will have t use a large inductr [and therefre a small capacitr]. Cntrast this with the case f parallel resnance, where we shwed that t achieve a high Q and thus a very narrw bandwidth we wuld have t use a large capacitr [and therefre a small inductr]. Frtunately, ur Agilent Functin Generatrs prvide bth AM and FM mdulatin and plenty f RF utput t drive ur antenna. If mre than ne f yu is perating at the same time in the lab at the same frequency, yu may find that yu are interfering with ne anther. Therefre, yu may wish t turn dwn the utput f yur functin generatr t a level that will allw yu t receive yur wn signal, but which will prevent yur signal frm reaching anther s receiver. It will als be best if thse transmitting at the same time lcate themselves t distant crners f the lab! Obtain a 6.0 lp antenna frm the stckrm. This is a ne-ft square wden frm with ten turns f wire wund n it in a single layer flat cil. Yu will als need a trimmer capacitr, which is an adjustable capacitr with three legs n it. These legs will NOT fit int the prtbards, s dn't even think f trying it. Tw f the legs f the capacitr are electrically cnnected tgether and t ne plate; the third leg is the ther plate. Please slder shrt pieces f hk-up wire nt tw legs, and then insert the trimmer int the prtbard. DO NOT USE YOUR KIT PROTOBOARD, USE A FREESTANDING PROTOBOARD ON THE LAB BENCH OR SIGN ONE OUT FROM THE STOCKROOM. 2 0 Lab. N. 7 9//03
2-00 pf trimmer V S R surce C L [Antenna] 0 Ω Figure 7: Antenna tuning circuit fr transmitting AM carrier frm functin generatr. Cnnect the circuit shwn abve in figure 7. Make sure that the mdulatin n yur functin generatr is turned ff. Be sure t use shielded cable [BNC t E-Z hk r BNC t alligatr clips] between the functin generatr and the prtbard. Lk n the frame f the lp t find where the inductance f the lp is marked and calculate the required capacitance needed t achieve resnance at 540kHz, NOT 475kHz: f =. Make up this capacitance by selecting fixed 2π LC capacitrs frm yur kit r frm thse available frm the stckrm windw and placing them in parallel with the trimmer cap. Adjust the functin generatr t full utput, 20 vlts peak-t-peak at 540 khz, nt 475kHz. [Q4. Why des the functin generatr amplitude display shw a vltage value that is incrrect?] Cnnect ne channel f yur scpe acrss the 0 Ω series current-measuring resistr, making sure that the grund clip is cnnected t the side f the resistr that is cnnected t the signal generatr grund. [The scpe grund clip is permanently cnnected t electrical grund.] Adjust the scpe amplitude cntrl fr the channel acrss the resistr as required t see a signal [the signal level will be very lw until resnance is achieved]. We are trying t btain maximum current int this series resnant circuit, s yur main task will be t mnitr the vltage acrss the 0 Ω resistr as yu tune the circuit. Yu may have t add r subtract sme f the fixed capacitrs that yu have installed, but when the cmbined value f the fixed capacitrs plus the trimmer is crrect, yu will be able t tune the trimmer and bserve the vltage acrss the 0 Ω resistr pass thrugh a maximum. [Once again, it may be easier t mnitr the utput vltage f the functin generatr n ne scpe channel, and the vltage acrss the resistr n a secnd channel, and make yur adjustment until the phase angle between the tw wavefrms is either 0 r 80 degrees, depending.] When the trimmer is tuned t prduce this maximum, yu have achieved series resnance and are driving maximum current int the antenna. Once resnance is achieved, yu may remve r shrt ut the 0 Ω resistr, which will increase the current int the antenna smewhat, and lwer the bandwidth as well. Nw, adjust yur functin generatr s that yur carrier is AM mdulated with a 400Hz mdulating frequency at 00% mdulatin. Turn n yur AM radi and tune it t 540kHz while hlding it near yur transmitting antenna. Yu shuld clearly hear the mdulating tne in yur AM radi. Change the tne t different frequencies and listen again. Yu are nw bradcasting AM radi. Mve yur radi abut the lab and see hw far away frm yur antenna yu can pick up the signal. Yu will achieve maximum range with the carrier amplitude set at maximum utput and with the 0 Ω resistr shrted ut. Lab. N. 8 9//03
When yu are thrugh listening t yur test tnes ver 540kHz, tune yur functin generatr back t 475kHz. Retune yur antenna by adjusting the value f the trimmer and/r the fixed capacitrs s that the current in the antenna is nce again a maximum. Nw discnnect yur antenna while yu build the circuit fr experiment 5. Questins: Q4.2 With the 0 Ω resistr shrted ut, what is the resistance in the series resnant circuit? Q4.3 Can this resistance be adjusted r reduced t zer? Q4.4 Calculate the bandwidth f this series resnant circuit. Q4.5 What wuld be the effect n the transmitted signal if the bandwidth f the transmitter were t small [Q t high]? Q4.6 What wuld happen if we reversed the scpe leads that are cnnected acrss the 0 Ω resistr? Q4.7 Calculate the length f ne wavelength at 540kHz. Experiment 5: Receiving the signal frm yur transmitting antenna. In this last experiment, we will make sme changes t the transistr circuit yu built-in experiment 2. We will add anther parallel tuned circuit as part f a receiving antenna s that yu can pick up what yu transmit much the same way an AM radi des. Yu will be using what is knwn as a lpstick receiving antenna: a ferrite rd with an antenna cil/transfrmer wund arund it. In parallel with the large primary winding [receiving antenna] yu will again place a capacitr t resnate with the inductr and therefre prvide sensitivity t nly ne frequency at a time. If this were a real radi, instead f using a cmbinatin f fixed capacitr and trimmer fr this purpse, yu wuld be using a varactr dide r a variable capacitr that wuld have a huge adjustable range s that yu culd tune the whle AM band. The inductr yu will be using has a primary inductance f abut 723µH and a turns rati f 40: primary t secndary. This turns rati allws the high impedance primary circuit t be cupled t the lw-impedance input f the transistr stage. The step-dwn transfrmer reduces the surce impedance f the cil t nearly zer t avid lsses when driving a lw- impedance transistr input. [Anther way f lking at this is that the transfrmer steps up the lw value f input impedance f the transistr amplifier s that when it is reflected ver t the primary it is large enugh t prevent it frm lwering the bandwidth f the resnant primary circuit.] Calculate the value f capacitance yu will need t resnate the primary at 475kHz. Once again, make up this value frm a parallel cmbinatin f fixed capacitrs and a trimmer capacitr. Build the receiving antenna int yur transistr amplifier as shwn in figure 8. Be very careful with the fine wires f the antenna cil. Yu will again need t slder sme slid hkup wire t these leads in rder t insert them int the prtbard. Obtain a piece f duble-sticky fam tape abut ½ square frm the stckrm windw and stick it dwn t the panel f yur nerdkit next t the pint where the antenna cil cnnects int the circuit. Slide the ferrite rd cre int the antenna cil and stick ne end f the rd nt the duble-sticky tape. Nte that the transfrmer cil is lse Lab. N. 9 9//03
n the cre. Obtain a wden tthpick and slide it CAREFULLY between the cil and the ferrite cre t keep the cil frm sliding dwn the cre. +5 V Pri-Sec turns rati [a] = 4: D C F R L V OUT Antenna Cil White Red 0.µF 2N3904 2N3904 0 kω 0 kω 0.µF Black 2-00 pf trimmer Green R X =5 kω -5 V Figure 8: Resnant antenna/antenna cil cnnected t IF amplifier. Return t yur transmitting antenna and recnnect the functin generatr. Fr this experiment we will again use the 475kHz carrier frequency. Cnnect yur scpe acrss the secndary f the IF transfrmer just befre the detectr dide t mnitr the carrier signal strength. Adjust the functin generatr utput and watch yur scpe fr indicatin f a carrier. [Yur transmitting antenna shuld be abut 3 feet away frm yur receiving antenna at this pint.] With enugh drive int yur transmitting antenna t prvide a visible signal n the scpe, adjust yur trimmer capacitr fr a peak. If a clear peak in the carrier at the IF transfrmer primary is nt btainable, adjust the value f any fixed capacitrs yu are using t resnate the antenna cil primary. [Once again, yu may find it easier t cmpare the phase f the functin generatr utput with the phase f the transfrmer secndary signal in rder t lcate the maximum.] Once the capacitr is crrectly adjusted, remve the tthpick between the cil and the ferrite cre and GENTLY slide the cil alng the cre until yu see maximum utput n the scpe. Yu shuld readjust the trimmer cap nw, as mving the cil will change the inductance slightly. If yu dn t have a decent signal level at the primary f yur IF transfrmer, yu can btain mre gain in the IF amplifier by adjusting the value f R X. The gain f circuits f this type is primarily dependent n the value f the transistr cllectr current. If yu replace R X with a 0kΩ ptentimeter frm yur kit in series with a 5.kΩ fixed resistr, yu will be able t adjust the circuit gain by adjusting the pt. This wrks because R X is the sle current-setting resistr fr bth transistrs, which split the current thrugh R X equally. Once yu have a large enugh signal at the primary f the IF transfrmer, mve the scpe leads acrss R L [V OUT ]. With the mdulatin turned ff at the functin generatr, the nly signal yu shuld see acrss R L will be the DC vltage due t the rectificatin f the carrier. This value will Lab. N. 20 9//03
vary depending n yur signal strength. If yu nw prgram yur functin generatr t prduce a 400 Hz mdulating frequency at 80% mdulatin, yu shuld see the 400Hz audi signal riding n tp f the DC vltage at yur detectr utput. While keeping the carrier frequency utput level cnstant, and als the distance between the transmitting and receiving antennae cnstant, [in ther wrds dn t mve anything!] prgram in the fllwing audi frequencies: 400 Hz, 000 Hz, 3000 Hz, 5,000 Hz, all at 50% mdulatin. Recrd the utput levels as bserved n yur scillscpe. If the utput at 5000 Hz relative t the 400 Hz utput is n lnger dwn by 3dB, yu will have t adjust either the value f yur capacitr C F t crrect this r, if the bandwidth is nt crrect [remember that R L determines the bandwidth f the circuit], yu will need t change R L and take all the measurements abve again. Be sure nt t mve yur antenna r yur receiver while yu are making these measurements! Questins: Q5. In a previus experiment yu carefully adjusted the value f the detectr equivalent resistance t tailr the bandwidth f the IF transfrmer s that it wuld just accept 475kHz +/ 5000 Hz. Nw yu have added a secnd tuned circuit t yur receiver. If this new tuned circuit were t have exactly the same Q and bandwidth as the first tuned circuit, what wuld happen t the verall bandwidth f the receiver? Q5.2 What can yu say abut the steepness f the bandwidth respnse curve with tw tuned circuits? [A bandwidth respnse curve is just the inverse f the curve in figure 4, except that the Y- axis represents the utput vltage.] Q5.3 Fr the measurements yu made f the audi utput in the paragraph abve, recrd the utput vltage vs. audi utput frequency in a table s that yu can cmpare these values with the values frm the single tuned circuit f Experiment 3. Q5.4 Recrd the value f R X that yu ended up using. Q5.5 By nw yu shuld have nticed that the utput signal level will vary greatly depending n the distance f the receiving antenna frm that f the transmitting antenna, and als with the pwer input t the transmitting antenna. Yu have als nticed that there is a DC vltage prduced acrss the detectr lad resistance that is prprtinal t the received carrier signal strength. Given that yu have als bserved that the gain f the IF amplifier can be adjusted by varying R X in rder t vary the transistr cllectr currents, can yu think f a way that the carrier-prprtinal DC vltage can be used t autmatically adjust the gain f the IF amplifier? Lab. N. 2 9//03