ZXTape! 0Created with Ramsoft MakeTZXeh5 šq+ Ě-k(3,500):j$(3,500) electronics help tape 5  GCE Tutoring 6:6:0: !w(25,8):2000 r(10 ) t(5):9069m# Lscrhdr=9300T$:qsthdr=9350$:endsec=9400$:getans=9450$ fig2=8950":fig=9030F#:axes2=9000(#:eg=9040P#:axes=9100#:triangle=9150#:diagram=218:praise=9720% moreq=9980& electroscope=7400:parallel=7350:inc=0:triode=7700:diode=7600:series=7300:link=7250R:wiring=7000X:bulb=7050:resistor=7100:meter=7150:battery=7200  5br=8100:squrec=8850":squpar=8900" /"Electronics help eh5"::"Resonant circuits" :" GCE Tutoring March 1985" 2u:"Hello, what's your name ?":n$:n$:"OK, ";n$;",":"I'll begin by telling you how touse this electronics tape." 4]:"This tape covers 4 subjects which all come under the headingof 'resonant circuits'." :>:"Press the key marked C so I can type the next screenfull" <a$=:a$="c"62> = 60< >:z=120:z AF:"Thanks. From now on when I want you to press the C key, I'll say" D:" Hit C to continue" F4:"Here's the list of subjects on this program": Ho"capacitance time constants inductors resonance": K2:"Which subject do you want to try ?":s$: Lc$=s$ N'(s$)>3s$=s$(13) Os$="cap"100d Ps$="tim"200 Qs$="ind" 300, Rs$="res" 400 _ 70F c d f i capacitance l n"Capacitance": p"A capacitor is a device which can store electric charge. It consists of two flat electrodes separated by a very thin insula-ting layer, called a dielectric.": rt"The greater the area of the electrodes, the larger the the capacitance, i.e. more charge can be stored.": sscrhdr t"The unit of electrical capacitance is the Farad. A capacitor with a value of one farad, with one volt across itsterminals stores one coulomb of charge. The general formula relating capacitance, voltage and charge is :": v1"charge = capacitance x voltage Q = CV": x"In practice, the Farad is an inconveniently large unit, so picofarads (10^-12 Farads), nanofarads (10^-9) Farads and microfarads (10^-6) Farads are more commonly used.": yscrhdr z"There are many types of capaci- tor. They vary in the materials used to separate the two electr-odes. Thin paper or plastic is used for low values, while expensive ceramics, such as titanates, are used for higher values.": {scrhdr |N"A cheaper way of making a capac-itor with a high value than using titanates is to use a compound which electrolyses (decomposes when a current is passed through it) to form bubbles of gas. The bubbles thenform the dielectric layer, whichcan be extremely thin. This typeof capacitor is called an elect-rolytic.": }scrhdr ~`"Electrolytic capacitors can be made with extremely high values (over 100000 uF), but they do have disadvantages. The most important disadvantage is that electrolytics are 'polarised'. This means that they have a positive and negative terminal, and must not be connected the wrong way round or they may be damaged, or even explode.": y"This is a problem if the voltageacross a capacitor varies so that either terminal can at somestage be positive.": scrhdr "Another disadvantage is that electrolytic capacitors cannot be made very accurately, the tolerance often being -50%+100%.": scrhdr qsthdr "The unit of capacitance is the : 1. farad 2. coulomb 3. dielectric ? ": 4egc=3:exp=1:return=142:getans  "The insulating layer between thetwo electrodes of a capacitor iscalled the : 1. electrolytic 2. titanate 3. dielectric ?": 4egc=3:exp=3:return=148:getans  "The formula relating voltage, capacitance and charge is : 1. Q = CV 2. Q = C/V 3. Q = V/C": 4egc=3:exp=1:return=155:getans scrhdr 2n$=c$:start=100d:return=198:endsec     time constants  "Time constants": ԅ"When a potential is applied to a capacitor, the growth of the p.d. across it increases with time, as charge accumulates. ": @"A graph of voltage against time is shown on the next page.": scrhdr dgnum=1:3500 scrhdr ܱ"The p.d. rises towards the valueof the supply voltage. Notice that the voltage does not increase steadily, but slows down as the supply voltage is approached.": scrhdr J"A capacitor in series with a resistor charges in a time givenby :": "T = R x C": scrhdr 9"The time, T, is the time taken for the capacitor to charge to 69% of the supply voltage. This may seem very arbitrary, but it makes more sense if the time T is thought of as the time required for the voltage to reach the level of the supply, if it continued to charge at itsoriginal rate.": ."This is shown in the next diagram:": scrhdr:dg dgnum=2:3500 14,14;"T" scrhdr qsthdr "The formula T = RC gives the time taken for a capacitor charges to a certain value. Is it : 1. 69% 2. 59% 3. 96% ?": 4egc=3:exp=1:return=245:getans  "A graph of voltage against time for a charging capacitor is a : 1. straight line 2. curve of decreasing gradient 3. curve of increasing gradient?": 4egc=3:exp=2:return=252:getans  )2n$=c$:start=200:return=298*:endsec * + . 1 inductance 4 6"Inductance": 7"Whenever a conductor is in a magnetic field of changing strength, a voltage is induced in it. A small emf is induced ina single piece of wire, but a much larger emf is induced in a coil, which is therefore said tohave a greater 'inductance'.": 8scrhdr :~"In an A.C. circuit, the fluctua-ting current causes a varying magnetic flux, which induces an e.m.f. in the circuit.": <scrhdr @"An inductor resists the flow of alternating current, but not direct current. This is because the flow of A.C. induces an opp-osing e.m.f. in the coil, where-as D.C. induces no e.m.f.": Ascrhdr B"The amount by which an inductor resists A.C. is called its 'inductive reactance', and is measured in ohms. It is not a fixed value for a given inducta-nce, but varies with frequency:": D"X = 2fL ": FN"In this formula, L stands for inductance, which is measured inHenries.": Gscrhdr H"The greater the inductance, the larger the voltage induced by a given alternating current. For an inductance of 1 Henry, an e.m.f. of 1 volt is produced by a change in current of 1 amp persecond.": I"Induced voltage = V current change = dI time period = dT inductance = L V = dI/dT": Jscrhdr:"A simple coil has a relatively low inductance when compared to a coil wound on a former made ofa ferromagnetic material, such as iron. The increase in induct-ance depends on the relative permeability of the core, which can be over 500.": Lscrhdr Oqsthdr R"The unit of inductance is the : 1. Henry 2. amp per second 3. relative permeability ?": T4egc=3:exp=1:return=342V:getans V Y"The formula relating rate of current change and induced voltage is : 1. V = LdI/dt 2. V = Ldt/dI 3. I = dV/Ldt ?": \4egc=3:exp=1:return=350^:getans ^"A current flowing through an inductor changes at ";r(1);" amps per second. If the inductor has an inductance of ";r(2)+1;" henries, what isthe induced voltage ?": `?exp=(r(2)+1)*r(1):return=355c:getans c 2n$=c$:start=300,:return=398:endsec      resonance "Resonance": ~"A circuit involving a capacitor and an inductor has a reactance,which, like its components, var-ies with frequency. However, it does not increase with frequencylike an inductor, or decrease with frequency,like a capacitor.Instead, it increases either side of the frequency at which the individual reactances are equal. This frequency is called the resonant frequency.": scrhdr dg `"The overall resistance of the circuit is called the impedance,and is given the symbol Z.": ?"Xl = inductive reactance Xc = capacitive reactance": "Z = ((R+(Xl-Xc))": 6"At the resonant frequency, Xl-Xc=0, so Z=R.": ="The resonant frequency can be calculated as follows :": "Fr= 1/(2(LC))": scrhdr "At the resonant frequency, the voltage across the capacitor andinductor can be higher than the supply voltage. The factor by which it is greater is called the 'goodness factor', and is given the symbol Q.": scrhdr "Resonant circuits are used in radio and television receivers to select the frequency of one station, e.g. radio 1, while excluding all others. By varyingthe resonant frequency, diffe- rent stations can be received.": scrhdr n"Another use of resonant circuitsis in oscillators. If a resonantcircuit is incorporated in an amplifier, the gain can be made very high at the resonant frequ-ency, but low at all the others.The whole circuit then tends to oscillate, as any very small signal at the resonant frequencybuilds up until it reaches the limiting value of the supply voltage.": scrhdr qsthdr "The formula for the resonant frequency of a circuit involvingcapacitance and inductance is : 1. 2LC 2. F = 2/(LC) 3. F = 1/2(LC) ?": 4egc=3:exp=3:return=445:getans   scrhdr:egctr=1 qsthdr "An inductor and capacitor form a resonant circuit. What is the resonant frequency if their respective values are ";r(1)*r(1);" Henries and ";r(3)*r(3);" microfarads ?": aexp=1/(2*3.14159Iρ*0.001wn*r(1)*r(3)):return=459:getans  /egctr=egctr+1:egctr<4454 scrhdr 2n$=c$:start=400:return=498:endsec     full-wave rectification  "Full-wave rectification": "The half-wave rectifier is very inefficient, making use of only half of the input waveform. It would be more efficient if both halves of the waveform were rectified. This is accomplished by a full-wave rectifier.": "The simplest full-wave rectifiernetwork is shown in the next diagram. It uses two diodes and one capacitor, but requires a centre tap in the transformer secondary coil which powers it.": dg scrhdr f"The output of the circuit has a far smaller proportion during which the capacitor discharges :":  dg  "This means that a smaller capacitor can be used to store energy between each half-cycle than is required with a half- wave rectifier.": scrhdr "An alternative full-wave recti- fication circuit is the bridge rectifier. It uses four diodes and one capacitor, and elimi- nates the need for the centre tap in the transformer powering it.": dg "There are many advantages obtained using the bridge circuit. For a given voltage, the bridge circuit uses only half the number of secondary turns than th previous circuit, and the peak reverse voltage across the diodes is half the previous value.": #:"Let's take these one by one." scrhdr  "Gain": :"Gain is defined as being the ratio of change in output signalto the change in input signal applied to an amplifier to produce that change. Written algebraically this becomes :":  "Av = Vout/Vin where means 'change in' Vout means output voltage Vin means input voltage": "="[ depends on circuit values, signal frequency etc. ]" $scrhdr &"Open loop gain": ("The gain of an operational amplifier as defined on the previous page when no feedback of any kind is applied. Often given the symbol A." ) *O[ for a good op amp, A is above 10 000, and can be over 100 000 ]" ,scrhdr ."Closed loop gain": / 0"The gain of an operational amplifier circuit in which a 'feedback' loop is connected to feed back a proportion of theoutput signal to the input.": 2"The value of the closed loop gain depends almost entirely on the circuit values, and not on the open loop gain of the opera-tional amplifier. This is true if the closed loop gain is smallin comparison with the open loopgain." 4scrhdr 6"Input impedance": 8"The input impedance is the 'load' imposed by the op amp on the circuit.An ideal operationalwould impose no load, and there-fore have an infinite input impedance.": :1"In practice, the input impedanceis around 1M." <scrhdr >"Output impedance": @"The output impedance is the electronic behaviour of the internal components connected in series with the output terminal of an op amp." A Bk"The lower the ouput impedance, the better the amplifier's ability to drive power into a load.": DV"Ideally, the value would be 0, but in practice it is around 75for a good op amp." Fscrhdr H"Frequency response": Id"The way in which the gain of an op amp circuit varies with the frequency of its input signal.": J"Frequency response is often expressed as the upper and lowerfrequncies at which the gain hasfallen to 70.7% of its maximum value.": KS"[ Depends on the characteristcs of the op amp AND the other components. ]" Lscrhdr M"Slew rate": N"The slew rate of an amplifer is the maximum rate at which the output voltage can change when an instananeous change is appiedto the input.": O*"A typical value for an op amp is1v/S." Pscrhdr U+start=500:return=598V:endsec V W X Z ] ` b"Electronics": d"Electronics differs from what has been covered so far in that it concerns active devices. An active device is one which can in some way control the flow of current, rather than merely passively impede it.": g"The first active device to be invented was the thermionic diode. A diode allows the flow of current in only one directionIt can therefore convert AC to DC.": hscrhdr je"A thermionic diode consists of a filament, a cathode and an anode. The filament is like the filament of a bulb, and heats the the cathode to such a high temperature that some electrons are liberated. These are attracted by the anode, as long as it is positive. If the anode is -ve, the electrons are repelled, and no current flows.": ln"1. The comparator This circuit compares two input signals. If the voltage at the non-inverting input of the op amp is greater than that at the inverting input, then the outputof the op amp rises to the positive supply voltage. If the signals are reversed, the outputfalls to the negative supply voltage.": mscrhdr nscrhdr p"2. Op-amp with feedback": qscrhdr:triode rw"Since A is so large, if Vout is a few volts, then Vin must be very nearly 0 (a virtual earth) since Vout/A 0.": t"The concept of a virtual earth allows the application of Kirchoff's law, which states (more or less) that current can't build up at any point." vscrhdr x"i.e. Iin + If = 0 and Vi/Ri + Vo/Rf = 0 assuming that no current flows into the inverting input": zU"re-arranging the above : Vo = - RfVi/Ri": |scrhdr ~$"3. The non-inverting amplifier": "Unlike the previous circuit, this time the gain is positive. Note that the input to the circuit is connected to the non-inverting input of the op amp.": $"The voltage gain is given by :": "Av = 1 + Rf/Ri": scrhdr &"4. The voltage follower (buffer)": "This circuit is really a specialcase of the previous one where Rf and Ri are both zero. Consequently, it has a gain of one.": D"What is the point of an amplifier with a gain of one ?": &"It's not as silly as it seems...": scrhdr "This circuit has a very high input impedance (much higher than the input impedance of the op amp), but a low output impedance. This makes it useful if a signal mustn't be loaded." 2n$=c$:start=900:return=998:endsec       " (       N T    x z     @ B H        l n t x$="": o=1̱x$ n=18 #w(o,n):x$(oo)+n-1,w(o,n) n o  H24,16,16,32 ,16,16,24,0 C24,8,8,4,8,8,24,0 F0,0,62>,64@,64@,64@,62>,0 E0,0,124|,2,2,2,124|,0 G0,66B,66B,66B,66B,66B,44,,0 G0,44,,66B,66B,66B,66B,66B,0  G0,0,60<,64@,124|,64@,60<,0 I240,8,120x,128,248,0,0,0 C0,0,0,4,126~,4,0,0 F0,0,0,126~,40(,40(,68D,0 C4,4,228,4,0,0,0,0 G240,8,240,8,240,0,0,0 E7,4,4,8,8,144,80P,32  E4,68D,228,68D,0,0,0,0 "G16,16,16,0,0,480,72H,480 %E12 ,18,18,12 ,0,0,0,0 (G28,20,16,16,8,8,40(,568 *H0,0,16,40(,68D,130,254,0 ,G32 ,32 ,32 ,16,16,16,8,4 /C32 ,16,8,8,8,4,4,4 2C4,4,4,8,8,8,16,32 4   encode screen ptr2=0 z=16384@22528X ptr=z-16383? data=z Jdata0ptr2=ptr2+1:j$(dgnum,ptr2)=(data):k(dgnum,ptr2)=z z     fetch screen pxnum=500  dgnum=1pxnum=165  z=1pxnum k(dgnum,z),(j$(dgnum,z)) z   z=31000 %v=((z^2-(z-1)^2)) u=v^0.5 C((u)-(u+0.5))<0.01z# =z;":";z-1;":";v^0.5 z  z=07 z:7-z 7x=13:"" c=110 :c x z 0::" G C E TUTORING"::" Orders"  z=025 x=14 code=(c$(xx))+z  code>"z"code=code-26 code; x::z ( X Z ]wiring ` b502,110n:0,40(:40(,0:130,150:40(,0:0,-40(:170,70F:0,-40(:-120x,0:0,40( g   bulb  170+inc,110n z=15 0,-8, z !170+inc,90Z,20     resistor  170,110n z=14 %5,-5:-5,-5 z     meter(type)  110n,150,20 3,14-1;t$ 17,0;" "    " % battery ( *502,110n ,0,-18 /8-10 ,0:20,0:-10 ,0 2502,83S 48-15,0:30,0:-15,0 60,-18 P R T Wlink Z \&90Z,150:40(,0 |   bulbs in series  '170,96`:0,-12 170,103g,7 170,77M,7 170,111o x=14 & 2,-2:-2,-2 x 170,111o-26 x=14 & 2,-2:-2,-2 x     parallel  inc=45-:bulb 9170+inc,70F:0,-40(:-inc,0 9170+inc,110n:0,40(:-inc,0  inc=0    electroscope  502,502 $502,0:0,502 &-502,0:0,-502 75K,115s 0,-45- /75K,115s-37%:4,-7 &60<,115s:30,0  V$7000X:7050:7150 X'170,150:0,40( | ~  triangle VIR  80P,80P <100d,0:-502,86V:-502,-86V 130,80P 70,43+:-25,0:502,0 9 ,12 +1;"I" '9 ,12 +1+5;"R" 4,12 +4;"V" 15,0;" "    diode  502,502 '0,80P:30,0,- 0,-80P -30,0,- 65A,145 %0,-10 :-7,0 14,0 524,43+ x=14 6,0,- x 524,43+ 0,-10 524+24,43+ 0,-10 4,11 ;"Anode" 17,11 ;"Cathode"    triode  "10 ,6;"- - - Grid"  diode D F H Kradio N P502,80P RJ502,0:0,502:-502,0:0,-502 U110n,80P XJ502,0:0,502:-502,0:0,-502 Z170,80P \J502,0:0,502:-502,0:0,-502 v  " "square + parallelogram "]27,568:75K,0:0,502:-75K,0:0,-502 "`27,568:75K,0:25,502:-75K,0:-25,-502 "#7,3;"A E D F" "!15,3;"B C" " " #K27,568:110n,0:568,41):0,557 #f15,7;"0":15,9 ;"2":15,11 ;"4":15,12 +1;"6" #E14,6;"0":12 ,6;"2":10 ,6;"4" #K27,568:110n,0:568,41):0,557 # [568+16,568+8:0,16:8,-16:-8,0 # ^56832 ,568+16:0,32 :16,-32 :-16,0 #\568-10 ,568+16:-16,0:16,8:0,-8 #11 ,9 ;"A" #9 ,12 ;"B" #11 ,4;"C" #& #' #( #2K27,41):110n,0:27,41):0,557 #:]17,3;"0":17,6;"2":17,9 ;"4":17,12 ;"6" #<17,15;"8" #>\16,2;"0":14,2;"2":12 ,2;"4":10 ,2;"6" #A #Fi579+x,513+y:20,20:-20,20:-20,-20:20,-20: #Hc72H+x,568+y:0,30:-30,0:0,-30:30,0: #P'"Here is an example of ";n$ #R #Z #\ #_noises #b #d-z=120:0.01z# =,-24:z #f #h #i&z=15:0.3,t(z):z #l #mz=15:t(z):z: #n*7,9 ,5,-7,0 # # # #axes # #_30,90Z:210,0:30,90Z:0,557:0,-110n #10 ,2;"0" #f11 ,9 ;"90":11 ,15;"180":11 ,22;"270":11 ,29;"360" #atype=09124# #atype=19130# #.4,2;"1":16,1;"-1" #07,1;".5":13 ,0;"-.5" # #.7,2;"1":13 ,1;"-1" #.4,2;"2":16,1;"-2" # # # #draw triangle # #N30,60<:100d,0:0,60<:-100d,-60< #label=09175# #15,6;"adjacent" # 8,1;"hypoteneuse" #11 ,18;"opposite" #6123{,60<:0,7:7,0 #H41),60<:0,2:-3,2:-2,0 #14,2;"A" #14,17;"B" #6,17;"C" #::::::::: # # # #"Berk ! What's ";c$;" ?": #'"Wally ! ";c$;" isn't on the tape.": ##"Moron ! Try spelling straight": #"sorry, ";n$;" ? ": #"Are you tired, ";n$;" ?": #"Don't wind me up, ";n$: $T $V scrhdr() $Y $\9900&:: $ $ qsthdr() $ $'9600%:9900&:egc=0: $ $ $endsec(start,n$) $ $7"That finishes: ":n$:"Hit r to repeat this section" $ 9900& $a$="r"start $return $ $ $getans(loop,exp) $ $?dp=0:err=0:u$:u$:(u$)>10 err=1 $(u$)=09460$ $[j=1̱(u$):(u$(jj))<45-ů(u$(jj))>579ů(u$(jj))=47/err=1 $%9480%:j:u$="-."err=1 $Cerr=1dp>1"type the answer as a number":9460$ $=ans=(u$):(exp-ans)>0.005y# ="No, the answer is ";exp $$(ans-exp)0.005y# =9720% $return $ % %$(u$(jj))=46.dp=dp+1 % ,j>1Ư(u$(jj))=45-err=1 %  %k9800H&:d1=r(1)/10 +r(2)/100d+r(3)/1000:dec=d1:int=1000*dec %& %A"See if you understand this by trying the following examples" % 9800H& % %"True or false ?" %a$ %a$ %a$"t"a$"f"9650% % %n:n;"/";:d:d: % 9630% %h"No. Don't add the numbers together. It's just the second number, so the answer is ";r(2) % %K"No, its the second number, not the first, so the answer is ";r(2) % %%9720%+((*9 )+1): % "Good": % "Correct": %"Right again": %"OK": %"That's it": %"Brilliant !": %"Well done": &"Very good": &"Genius !": &HWz=110 :r(z)=(*9 )+1:z:r(1)r(2)9800H&: &R#r(1)r(2)9800H& &\ &z "trap": & &"Hit C to continue" &a$= &a$="c"9950& &a$="r"9950& & 9920& & &z=1502:z & &Cmore=0:"More qvestions ? (y or n)":e$:e$=""9980& &?e$(11)="y"e$(11)="Y"more=1 & ' Q@@@@AAABBBBBCCCCCCDDDDDDEEEEEEFFFFFFGGGGGGG HH)H-HIHLHiHkHHHHH II)I-IIILIiIkIIIIIIIIIIIIIIIIIIII JJ)J-JIJLJiJkJJJJJJJ KK)K-KIKLKiKkKKKKKKKK LL)L,LILKLiLkLLLLLLLL M M)M,MIMKMiMjMMMMMMM N N)N,NINKNiNjNNNNNNN O O)O,OIOKOiOjOOOX&M'M(M)M,M-MIMKMMMiMjMmMMMMMMMMM N N&N'N(N)N,N-NINKNMNiNjNmNNNNNNNNNO O O O O O)O,O-OIOKOMOiOjOmOOOO@@AABBBBBBBCCCCCCCCDDDDDDDDEEEEEEEFFFFFFFFFFFFFFFFFFGGGGGG HHHH)H-H.HIHNHiHkHnHHHHHHH III%I&I'I)I,I-I.IIIKINIiIjInIIIIIIIIIIIIIIIIIIII J JJJ%J&J'J)J,J-J.JIJKJNJiJjJnJJJJJJJJ K KK%K&K'K)K,K-K.KIKKKNKiKjKnKKKKKKKKK L LLL%L&L'L)L,L.LILKLNLiLjLnLLLLLLLL M MM%M&M'M)M,M.MIMKMNMiMjMnMMMMMMMMN N N N N NN%N&N'N)N,N.NINKNNNiNjNnNNNNNNNN O OO)O,O.OIOKONOiOjOnOOOOX  `D D $( "(    `       (  ?  @ @ 8h8 ` @ @0TD   Tx    !T@    " 8T<    $0B& @ @ @"@T@ 0<   "Tx B&   $T@<@@@>||BBBBB,,BBBBB<@|@<x~~((DP DD0H0  (8(D   X5   n5StarC inductorsSindgctN inductorsU22.736A eh6 fmA*hj$(7,500,3) electronics help tape 6  GCE Tutoring 6:6:0: !w(25,8):2000 r(10 ) t(5):9069m# Lscrhdr=9300T$:qsthdr=9350$:endsec=9400$:getans=9450$ fig2=8950":fig=9030F#:axes2=9000(#:eg=9040P#:axes=9100#:triangle=9150#:diagram=218:praise=9720% moreq=9980& electroscope=7400:parallel=7350:inc=0:triode=7700:diode=7600:series=7300:link=7250R:wiring=7000X:bulb=7050:resistor=7100:meter=7150:battery=7200  5br=8100:squrec=8850":squpar=8900" -"Electronics help eh6"::"Active circuits" :" GCE Tutoring March 1985" 2u:"Hello, what's your name ?":n$:n$:"OK, ";n$;",":"I'll begin by telling you how touse this electronics tape." 4[:"This tape covers 6 subjects which all come under the headingof 'Active circuits'." :>:"Press the key marked C so I can type the next screenfull" <a$=:a$="c"62> = 60< >:z=1100d:z AF:"Thanks. From now on when I want you to press the C key, I'll say" D:" Hit C to continue" F4:"Here's the list of subjects on this program": H"transistors amplifiers common emitter amplifiers feedback operational amplifiers circuits using op. amps." K2:"Which subject do you want to try ?":s$: Lc$=s$ N'(s$)>3s$=s$(13) Os$="tra"100d Ps$="amp"200 Qs$="com" 300, Rs$="fee" 400 Ss$="ope" 500 Ts$="cir" 600X _ 70F c d f i transistors l n"The transistor": p"A transistor is a semiconductor device made up of three layers. The middle layer is called the 'base', and the outer layers the'emitter' and 'collector'": r"The layers of semiconductor are doped with impurities. The collector and emitter are given the same type of impurities, while the base is given the opposite type.": sscrhdr tdg v"The two different types of tran-sistor are called 'npn' and 'pnp'."::"These abbreviations stand for 'negative, positive, negative' and 'positive, negative, positive'. The descriptions refer to the type of doping used in the coll-ector, base and emitter."::"A circuit including an npn tran-sistor is shown on the next page."::scrhdr wWdgnum=1:3500 :12 ,18;"emitter";18,0;" ":scrhdr x"If a pnp transistor was used instead of an npn one, the circuit diagram would be identical, except that the supply connections would be reversed, and the arrow in the transistor symbol would point in the opposite direction.":scrhdr: "Transistors are normally connec-ted so that the emitter-base junction is forward biased (likea conducting diode), and the collector-base junction is reverse biased.": zscrhdr |"The current crossing the forwardbiased emitter-base junction is carried by majority charge carriers, most of which reach the collector, since the base isextremely thin, giving little space for the charge carriers torecombine.": ~"The collector current increases if a small current is passed through the emitter. This means that a transistor allows a smallinput signal to control a large output signal.": scrhdr "The ratio of change in collectorcurrent to change in base current is called current gain, an is given the symbol Hfe. Typical values are between 20 & 200.": scrhdr qsthdr "The current gain of a typical transistor is : 1. about 8 2. between 20 and 200 3. between 200 and 2000 ?": 4egc=3:exp=2:return=142:getans  scrhdr "The base-emitter junction of a transistor is : 1. forward biased 2. reverse biased 3. not biased ?": 4egc=3:exp=1:return=155:getans  scrhdr "The outer layers of a transistorare the : 1. base and emitter 2. collector and base 3. emitter and collector ?": 4egc=3:exp=3:return=165:getans  scrhdr 2n$=c$:start=100d:return=198:endsec     amplifiers  "Amplifiers": ԏ"An amplifier is a device which increases the strength of a signal without changing its other characterisics, such as waveform.":  scrhdr ܮ"The most common type of ampli- fier is the 'inverting' amplifier. Its input and output are 180 out of phase with each other, as shown in the next diagram.": scrhdr dg #dgnum=2:3500 :scrhdr n"The voltage range of the output signal is limited by the supply voltage to the amplifier, which for transistor circuits is usually less than 100 volts, and often very much less. Increasing the input signal so that the output tries to vary beyond this level causes 'clipping' of the output waveform, as shown in the next diagram.": scrhdr dg dgnum=3:3500 :10 ,20;"max. supply";14,23;"min.";15,23;"supply";18,0;" ":scrhdr #"The gain of an ideal amplifier would remain constant for diffe-rent frequencies. In the real world, though, gain tends to be lower at very high and very low frequencies."::"Some amplifiers, called DC coupled amplifiers have a constant frequency response down to DC.": scrhdr "A very common form of amplifier is called an 'operational amplifier'. It has two inputs, inverting and non-inverting. It is DC coupled, and consequently can be used in DC circuits. ": Z"Operational amplifiers are dealtwith in greater detail in another section.": scrhdr qsthdr U"An ideal amplifier changes only one characteristic of its input signal. Is it :": X"1. Its strength 2. Its waveform shape 3. Its distortion ?" 4egc=3:exp=1:return=258:getans scrhdr )2n$=c$:start=200:return=298*:endsec * + . 1 4 6"Common emitter amplifiers": 8f"One of the simplest ways to use a transistor as an amplifier is in the 'Common emitter' circuit.": :"In practice, the circuit looks much more complicated than it really is. For clarity, the extra components used in commercial designs are not shownin the following diagram." <scrhdr > diagram ?Tdgnum=1:3500 :scrhdr:"There are two resistors in the circuit. One supplies a small current to the base of the transistor, forward-biasing the base-emitter junction. The otherresistor supplies the collector current, which is changed greatly by small variations in the input signal flowing to the base.":scrhdr @"To calculate the voltage gain of this circuit multiply the collector resistance by the transconductance of the transistor.": A"The gm (transconductance) of a transistor is its conductance at a given collector current."::"For a typical silicon transistorthe gm is given by the formula :"::"gm = Ic / 26 where Ic (the collector current)is in milliamps." Bscrhdr C"The gain is given by the formula Av = gm x Rc Typical values being gm = 0.1 and Rc = 1000, giving a voltagegain of 100." Fscrhdr K L"Unfortunately, the gain changes slightly as the signal varies, so that the output signal isn't quite the same as the input, even allowing for the amplifica-tion.": Mscrhdr Nm"This effect is known as distortion, and can lessened by changing the circuit slightly." Pscrhdr R diagram S#dgnum=5:3500 :scrhdr T"The extra resistor (connected tothe emitter) makes the circuit more stable and less distorting,but at the expense of gain. The voltage gain is now given by :": V"Av = Rc / Re": X"By bypassing the AC component across Re with a capacitor, the DC operating conditions remain the same, but gain is returned to its original value.": Z$"The circuit now looks like this:" \scrhdr ^ diagram `dgnum=5:3500 a_135,65A:15,0:0,-22:150,14:0,22 bN158,36$:-16,0:158,43+:-16,0 cscrhdr hqsthdr m"The output waveform of an ampli-fier suffers clipping if : 1. the output signal tries to exceed the supply voltage 2. if the output signal exceeds the input signal 3. if the input signal has a very high frequency ?": p4egc=3:exp=1:return=370r:getans r tscrhdr w"A typical silicon transistor is connected as a common emitteramplifier. The collector currentis ";r(1);" mA and the collector resistor is ";r(2);"K." x!:"What is the value of gm ?": y@egc=3:exp=r(1)/26:return=378z:getans z9"Using the value for gm, what is the voltage gain ?": {Vegc=3:exp=r(2)*1000*r(1)/26:return=380|:getans | ~scrhdr 2n$=c$:start=300,:return=398:endsec      feedback  "Feedback": "Feedback is the process in whicha proportion of the output signal is fed back to the input.The total input to the amplifieris therefore the input signal plus a proportion of the output signal.": "If the amplifier is inverting, then the feedback will try to cancel out the input signal. This is known as NEGATIVE FEEDBACK."  scrhdr:dg "Algebraically, this is :": "A is the gain of the amplifier Xi is its input Xo is its output Xs is the input to the whole circuit Xf is the signal fed back B is the proportion of Xo that Xf represents" :"From this, it follows that Xs = Xi+Xf [eq.1] Xf = BXo [eq.2] A = Xo/Xi [eq.3]" zscrhdr:"The gain of the whole circuit, i.e. the amplifier including the feedback network can be calculated :": "Af = Xo/Xs = Xo/(Xi+Xf) [subs. eq1] = Xo/(Xi+BXo) [subs. eq2] = (Xo/Xi)/((Xi/Xi)+(BXo/Xi) = A/(1+BA) [subs. eq3]": "If A is very large, then BA is also large, and the denominator can be simplified to just BA without much error (BA is very nearly the same as BA+1 if BA is large).": scrhdr U"The formula for Af now becomes : Af = A/BA = 1/B": "Which means that the voltage gain with feedback is independent of the voltage gain of the basic amplifier,providingthat A is very large.": scrhdr "But why should an amplifier of lower gain than the original be wanted ? The answer is that the gain of an amplifier with nega- tive feedback has a gain which remains constant to a higher frequency than the original, andits distortion is much lower.": scrhdr ]"Here is an example of the two formulae for Af in action."::"First the simpler one :": "An amplifier with a gain of 1000 is connected so that 10% of its output is fed back to itsinput. What is the gain of the whole circuit ?": "Given: A = 1000 B = 0.1 Af = 1/B Find: Af Af = 1/B = 1/0.1 = 10": ,scrhdr:"Now the more complex formula :": "Given: A = 1000 B = 0.1 Af = A/1+BA Find: Af Af = A/1+BA = 1000/(1+0.1x1000) = 1000/101 = 9.9": "Not very different from the first result, but harder to workout. Only use this formula if you are told to by the question,or if the gain of the amplifier without feedback is very low, eg. under 100.": scrhdr i=13 qsthdr "An inverting amplifier with a gain of ";r(1)*1000;" is connected so that ";r(2);"% of its output is fed back to its input. What is the approximate gain of the whole circuit ?": Aegc=3:exp=100d/r(2):return=458:getans scrhdr i 2n$=c$:start=400:return=498:endsec      op. amps  "Operational amplifiers": "There are a large number of definitions associated with the behaviour of operational amplif-iers. The most important ones are listed below :": "gain open loop gain closed loop gain input impedance output impedance frequency response slew rate" #:"Let's take these one by one." scrhdr  "Gain": :"Gain is defined as being the ratio of change in output signalto the change in input signal applied to an amplifier to produce that change. Written algebraically this becomes :":  "Av = Vout/Vin where means 'change in' Vout means output voltage Vin means input voltage": "="[ depends on circuit values, signal frequency etc. ]" $scrhdr &"Open loop gain": ("The gain of an operational amplifier as defined on the previous page when no feedback of any kind is applied. Often given the symbol A." ) *O"[ for a good op amp, A is above 10 000, and can be over 100 000 ]" ,scrhdr ."Closed loop gain": / 0"The gain of an operational amplifier circuit in which a 'feedback' loop is connected to feed back a proportion of theoutput signal to the input.": 2"The value of the closed loop gain depends almost entirely on the circuit values, and not on the open loop gain of the opera-tional amplifier. This is true if the closed loop gain is smallin comparison with the open loopgain." 4scrhdr 6"Input impedance": 8"The input impedance is the 'load' imposed by the op amp on the circuit.An ideal operationalwould impose no load, and there-fore have an infinite input impedance.": :2"In practice, the input impedanceis around 1M." <scrhdr >"Output impedance": @"The output impedance is the electronic behaviour of the internal components connected in series with the output terminal of an op amp." A Bk"The lower the ouput impedance, the better the amplifier's ability to drive power into a load.": DV"Ideally, the value would be 0, but in practice it is around 75for a good op amp." Fscrhdr H"Frequency response": Id"The way in which the gain of an op amp circuit varies with the frequency of its input signal.": J"Frequency response is often expressed as the upper and lowerfrequncies at which the gain hasfallen to 70.7% of its maximum value.": KS"[ Depends on the characteristcs of the op amp AND the other components. ]" Lscrhdr M"Slew rate": N"The slew rate of an amplifer is the maximum rate at which the output voltage can change when an instananeous change is appiedto the input.": O*"A typical value for an op amp is1v/uS." Pscrhdr Qr"What is the input impedance of a typical op amp ?"::egc=3:exp=1000000t$:return=594R:getans Rp"What is the output impedance of a typical op amp ?"::egc=3:exp=75K:return=595S:getans Sscrhdr U2n$=c$:start=500:return=598V:endsec V W X Z ] ` b"Circuits using op. amps": ln"1. The comparator This circuit compares two input signals. If the voltage at the non-inverting input of the op amp is greater than that at the inverting input, then the outputof the op amp rises to the positive supply voltage. If the signals are reversed, the outputfalls to the negative supply voltage.": nscrhdr p"2. Op-amp with feedback": q"The gain can be calculated usingthe following formula : Av = Rf/Ri Rf is the feedback resistor Ri is the input resistor" vscrhdr wPdgnum=6:3500 :12 ,20;"out":18,0:scrhdr x{"Since the input signal goes to the inverting input of the op amp, the circuit is that of an inverting amplifier." |scrhdr ~$"3. The non-inverting amplifier": "Unlike the previous circuit, this time the gain is positive. Note that the input to the circuit is connected to the non-inverting input of the op amp.": $"The voltage gain is given by :": "Av = 1 + Rf/Ri": scrhdr:dgnum=7:3500 :95_,95_:8,0:95_,83S:8,0:99c,79O:0,8 914,21;"Rf";18,21;"Ri":scrhdr &"4. The voltage follower (buffer)": "This circuit is really a specialcase of a previous one where Rf and Ri are both zero. Consequently, it has a gain of one.": D"What is the point of an amplifier with a gain of one ?": &"It's not as silly as it seems...": scrhdr "This circuit has a very high input impedance (much higher than the input impedance of the op amp), but a low output impedance. This makes it useful if a signal mustn't be loaded." scrhdr 2n$=c$:start=600X:return=698:endsec  x$="": o=1̱x$ n=18 #w(o,n):x$(oo)+n-1,w(o,n) n o  H0,24,36$,66B,36$,36$,102f,0 C24,8,8,4,8,8,24,0 F0,0,62>,64@,64@,64@,62>,0 E0,0,124|,2,2,2,124|,0 G0,66B,66B,66B,66B,66B,44,,0 G0,44,,66B,66B,66B,66B,66B,0  G0,0,60<,64@,124|,64@,60<,0 I240,8,120x,128,248,0,0,0 C0,0,0,4,126~,4,0,0 I248,136,136,136,0,0,0,0 C4,4,228,4,0,0,0,0 G240,8,240,8,240,0,0,0 G28,20,16,16,8,8,40(,568  E4,68D,228,68D,0,0,0,0 "G16,16,16,0,0,480,72H,480 %E12 ,18,18,12 ,0,0,0,0 (E7,4,4,8,8,144,80P,32 *H0,0,16,40(,68D,130,254,0 ,G32 ,32 ,32 ,16,16,16,8,4 /C32 ,16,8,8,8,4,4,4 2C4,4,4,8,8,8,16,32 4  encode screen ptr2=0 z=16384@22528X ptr=z-16383? data=z ̤data0ptr2=ptr2+1:j$(dgnum,ptr2,1)=(data):phi=(z/256):plo=z-256*phi:j$(dgnum,ptr2,2)=phi:j$(dgnum,ptr2,3)=plo z   fetch screen  z=1500 >addr=256*(j$(dgnum,z,2))+(j$(dgnum,z,3)) data=(j$(dgnum,z,1)) addr,data z  X Z ]wiring ` b502,110n:0,40(:40(,0:130,150:40(,0:0,-40(:170,70F:0,-40(:-120x,0:0,40( g   bulb  170+inc,110n z=15 0,-8, z !170+inc,90Z,20     resistor  170,110n z=14 %5,-5:-5,-5 z     meter(type)  110n,150,20 3,14-1;t$ 17,0;" "    " % battery ( *502,110n ,0,-18 /8-10 ,0:20,0:-10 ,0 2502,83S 48-15,0:30,0:-15,0 60,-18 P R T Wlink Z \&90Z,150:40(,0 |   bulbs in series  '170,96`:0,-12 170,103g,7 170,77M,7 170,111o x=14 & 2,-2:-2,-2 x 170,111o-26 x=14 & 2,-2:-2,-2 x     parallel  inc=45-:bulb 9170+inc,70F:0,-40(:-inc,0 9170+inc,110n:0,40(:-inc,0  inc=0  V$7000X:7050:7150 X'170,150:0,40( | ~  triangle VIR  80P,80P <100d,0:-502,86V:-502,-86V 130,80P 70,43+:-25,0:502,0 9 ,12 +1;"I" '9 ,12 +1+5;"R" 4,12 +4;"V" 15,0;" "    diode  502,502 '0,80P:30,0,- 0,-80P -30,0,- 65A,145 %0,-10 :-7,0 14,0 524,43+ x=14 6,0,- x 524,43+ 0,-10 524+24,43+ 0,-10 4,11 ;"Anode" 17,11 ;"Cathode"    triode  "10 ,6;"- - - Grid"  diode D F H Kradio N P502,80P RJ502,0:0,502:-502,0:0,-502 U110n,80P XJ502,0:0,502:-502,0:0,-502 Z170,80P \J502,0:0,502:-502,0:0,-502 v #& #' #( #2K27,41):110n,0:27,41):0,557 #:]17,3;"0":17,6;"2":17,9 ;"4":17,12 ;"6" #<17,15;"8" #>\16,2;"0":14,2;"2":12 ,2;"4":10 ,2;"6" #A #Fi579+x,513+y:20,20:-20,20:-20,-20:20,-20: #Hc72H+x,568+y:0,30:-30,0:0,-30:30,0: #P'"Here is an example of ";n$ #R #Z #\ #_noises #b #d-z=120:0.01z# =,-24:z #f #h #i&z=15:0.3,t(z):z #l #mz=15:t(z):z: #n*7,9 ,5,-7,0 # # # #axes # #_30,90Z:210,0:30,90Z:0,557:0,-110n #10 ,2;"0" #f11 ,9 ;"90":11 ,15;"180":11 ,22;"270":11 ,29;"360" #atype=09124# #atype=19130# #.4,2;"1":16,1;"-1" #07,1;".5":13 ,0;"-.5" # #.7,2;"1":13 ,1;"-1" #.4,2;"2":16,1;"-2" # # # #draw triangle # #N30,60<:100d,0:0,60<:-100d,-60< #label=09175# #15,6;"adjacent" # 8,1;"hypoteneuse" #11 ,18;"opposite" #6123{,60<:0,7:7,0 #H41),60<:0,2:-3,2:-2,0 #14,2;"A" #14,17;"B" #6,17;"C" #::::::::: # # # #"Berk ! What's ";c$;" ?": #'"Wally ! ";c$;" isn't on the tape.": ##"Moron ! Try spelling straight": #"sorry, ";n$;" ? ": #"Are you tired, ";n$;" ?": #"Don't wind me up, ";n$: $T $V scrhdr() $Y $\9900&:: $ $ qsthdr() $ $'9600%:9900&:egc=0: $ $ $endsec(start,n$) $ $7"That finishes: ":n$:"Hit r to repeat this section" $ 9900& $a$="r"start $return $ $ $getans(loop,exp) $ $?dp=0:err=0:u$:u$:(u$)>10 err=1 $(u$)=09460$ $[j=1̱(u$):(u$(jj))<45-ů(u$(jj))>579ů(u$(jj))=47/err=1 $%9480%:j:u$="-."err=1 $Cerr=1dp>1"type the answer as a number":9460$ $;ans=(u$):(exp-ans)>0.1}L"No, the answer is ";exp $"(ans-exp)0.1}L9720% $return $ % %$(u$(jj))=46.dp=dp+1 % ,j>1Ư(u$(jj))=45-err=1 %  %k9800H&:d1=r(1)/10 +r(2)/100d+r(3)/1000:dec=d1:int=1000*dec %& %D"See if you understand this by trying the following examples" % 9800H& % % % %praise % %%9720%+((*9 )+1): % "Good": % "Correct": %"Right again": %"OK": %"That's it": %"Brilliant !": %"Well done": &"Very good": &"Genius !": &HWz=110 :r(z)=(*9 )+1:z:r(1)r(2)9800H&: &R#r(1)r(2)9800H& &\ &z "trap": & &"Hit C to continue" &a$= &a$="c"9950& &a$="r"9950& & 9920& & &z=1502:z & Krp``LK(K<&D@@@~DKFHKHHKP6IDEIDErlj`dJKZKd&uvD^DvuuuKnrlf`CI\*]\!U*a\7R`in ͸y=((+[S\U"S\*a\++*I\ )@@@@Є@@@@AAAAAAAЄAA@ABBBBBBBBBBBxB8B8B8BDB8BBBBфBB@BCCCCDCDC@C0CC0CDCDCCC@CфCC@CDDDDDDDD8DDDD(DxDDD@DфDD@DEEEExEDEEEEE(E@EEE@EфEE@EFFFF@F8FxF8F F8FFD(DxDDD@DфDD@DEEEEE(E@EEE@EфEE@EFFFFFFTV(TWxTXTmTpU U@UU-U0@U1UMUP(UW@UXUmUpV V@VV-V0@V1VMVPVW@@@>||BBBBB,,BBBBB<@|@<x~(8DD0H0  P (D   X5  eh7 IS,Cj$(5,700,3) electronics help tape 7  GCE Tutoring 6:6:0: !w(25,8):2000 r(10 ) t(5):9069m# Lscrhdr=9300T$:qsthdr=9350$:endsec=9400$:getans=9450$ fig2=8950":fig=9030F#:axes2=9000(#:eg=9040P#:axes=9100#:triangle=9150#:diagram=218:praise=9720% moreq=9980& electroscope=7400:parallel=7350:inc=0:triode=7700:diode=7600:series=7300:link=7250R:wiring=7000X:bulb=7050:resistor=7100:meter=7150:battery=7200  5br=8100:squrec=8850":squpar=8900" +"Electronics help eh7"::"Rectification" :" GCE Tutoring March 1985" 2x:"Hello, what's your name ?":n$:n$:"OK, ";n$;",":"I'll begin by telling you how touse this electronics program." 4Y:"This tape covers 5 subjects which all come under the headingof 'rectification'." :>:"Press the key marked C so I can type the next screenfull" <a$=:a$="c"62> = 60< >:z=120:z AF:"Thanks. From now on when I want you to press the C key, I'll say" D:" Hit C to continue" F4:"Here's the list of subjects on this program": H"introduction rms values diodes half-wave rectification full-wave rectification" K2:"Which subject do you want to try ?":s$: Lc$=s$ N'(s$)>3s$=s$(13) Os$="int"100d Ps$="rms"200 Qs$="dio" 300, Rs$="hal" 400 Ss$="ful" 500 _ 70F c d f iintroduction l n"Introduction": p"When electrical energy is storedin batteries, or used for power-ing electronic equipment, directcurrent is required. This means that a method of converting alt-ernating current to direct current is needed, as alterna- ting current is used for trans- mitting electrical power.": qscrhdr r"The conversion of AC to DC is called rectification. It is accomplished by circuits using one or more diodes and capaci- tors.": sscrhdr tg"There are a number of different circuits for rectification. These are dealt with separately.": xscrhdr qsthdr "The conversion of AC into DC is called : 1. rectification 2. direct current 3. transmission ?":  4egc=3:exp=1:return=148:getans scrhdr "Electronic equipment needs power to operate it. Is it : 1. AC 2. DC 3. neither AC nor DC ?":  4egc=3:exp=2:return=158:getans scrhdr 2n$=c$:start=100d:return=198:endsec     rms values  "RMS values": "In an alternating current circuit, the voltage and current vary with time, so a wayof expressing the effective value is needed. The way to do this is in terms of the average power which a current can transmit.": {"At any instant, the power (p) can be found given the current (i) flowing through a circuit of resistance (R).": "p = iR": scrhdr 3"The average power over one cycleis given by :": "P = R x (mean value of i)": :"If the effective value of the current is I, then :": "P = IR": "I = (mean value of i)": scrhdr "The most important alternating voltages vary either sinusoi- dally or almost sinusoidally. For a sine wave, the instantane-ous value is given by :": "i = Im sin wt": &"so the previous quation becomes:": "I = mean value of Im sin wt = Im x (mean value of sinwt = Im/2 I = Im/2 = 0.707Im": scrhdr 3"A similar value is obtained for the voltage :": "V = Vm/2 = 0.707Vm": :"The effective value for the power is therefore :": "P = (V/2) x (I/2) = VI/2": scrhdr "Note that the r.m.s. value of voltage or current is not the same as the average value, whichfor a sine wave is given by :": "Vav = 0.636Vm": X"Which means that the r.m.s. value is about 11% greater than the average value.": "These values are compared in thefollowing diagram :":scrhdr:dgnum=1:3500 :212,79O:-115s,0:16,23;"average";17,24;"value":scrhdr scrhdr qsthdr  "What proportion of the peak value of one half cycle is the rms value of a sign wave ? 1. 63.6% 2. 50% 3. 70.7%":  4egc=3:exp=3:return=270:getans  scrhdr "The rms voltage of a sine wave is higher than its average value How much higher ? 1. 11% 2. 50% 3. 70.7%": 4egc=3:exp=1:return=280:getans  scrhdr "The rms voltage of a sine wave is measured as being ";r(1)*1.4144;" volts":"What is the peak value of one half cycle of the waveform ?":  ?egc=3:exp=2*r(1):return=290":getans " $scrhdr )2n$=c$:start=200:return=298*:endsec * + . 1 4 6 "Diodes": 8"Diodes are two terminal devices which conduct in only one direction. They consist of one thin wafer of silicon connected on each face to an electrode (the anode and cathode).": :"The semiconducting wafer is doped in the same way as a transistor. The anode area of the silicon is heavily doped with p-type impurities, and the cathode with n-type impurities.": <scrhdr @f"If a diode is connected so that its anode is positive with respect to the cathode, charge carriers are attracted by the junction opposite them. Impurities of p-type create positive charge carriers which migrate to the negative cathode,while n-type impurities generatenegative charge carriers which flow towards the positive anode.": Ascrhdr B"If a diode is reverse biased, i.e. connected so that the anodeis negative with respect to the cathode, charge carriers are repelled by the opposite junction, preventing the flow of current.": Cscrhdr D"By increasing the area of the semiconducting wafer, a larger current can be carried by the diode without overheating. This is at the expense of other important properties, such as high frequency response.": F"As well as constructing diodes from semiconductors, other methods are possible. The thermionic diode is an example.": Gscrhdr H"The thermionic diode was the first type to be invented. It consists of two electrodes inside an evacuated glass tube. One electrode (the cathode) is heated by a small coil through which current is passed. Heatingthe cathode frees electrons, which are attracted to the anodesince it is positive. Current cannot flow in the opposite direction, as the elctrons ar repelled by the cathode.": Jscrhdr Oqsthdr T"The electrodes of a diode are called the anode and the cathode. Which is positive ? 1. anode 2. cathode ": V Y4egc=3:exp=1:return=348\:getans \ :scrhdr ^"The anode of a semiconductor diode is doped with impurities. Are they : 1. p-type 2. n-type ?": `4egc=3:exp=1:return=355c:getans c fscrhdr h"A thermionic diode has an electrically heated electrode. Is it the : 1. anode 2. cathode ?": j4egc=3:exp=2:return=365m:getans m pscrhdr 2n$=c$:start=300,:return=398:endsec     half-wave rectification "Half-wave rectification": q"The simplest rectifier circuit is the half-wave rectifier. It consists of one diode and one capacitor. ": dg scrhdr:dgnum=4:3500 :14,5;"AC input";14,21;"DC output";11 ,22;"+";17,22;"-":scrhdr f"The capacitor is used to store energy between the positive halfcycles of the rectified input.": scrhdr #dgnum=3:3500 :scrhdr "There is a slight drop in voltage during the negative halfcycle, caused by the capacitor discharging. The greater the current drawn, the larger the voltage drop. The regular voltage drop superimposed on theoutput is called 'ripple'.": scrhdr W"For a half-wave rectifier, the ripple is at the same frequency as the input. Because the capac-itor is discharging for so much of the time, it has to store a considerable amount of energy, and consequently needs to be quite a high value. For heavy loads it becomes inconveniently large, and the full-wave circuitis used instead.": scrhdr qsthdr N"What is the superimposed AC on the DC output of a rectifier called ?":  a$:a$ ;a$="ripple"a$="Ripple"a$="RIPPLE""Correct":440 "No. It is called 'ripple'": scrhdr 2n$=c$:start=400:return=498:endsec     full-wave rectification  "Full-wave rectification": "The half-wave rectifier is very inefficient, making use of only half of the input waveform. It would be more efficient if both halves of the waveform were rectified. This is accomplished by a full-wave rectifier.": scrhdr "The simplest full-wave rectifiernetwork uses two diodes and one capacitor, but requires a centre tap in the transformer secondary coil which powers it.": scrhdr f"The output of the circuit has a far smaller proportion during which the capacitor discharges :": scrhdr  #dgnum=5:3500 :scrhdr  "This means that a smaller capacitor can be used to store energy between each half-cycle than is required with a half- wave rectifier.": scrhdr "An alternative full-wave recti- fication circuit is the bridge rectifier. It uses four diodes and one capacitor, and elimi- nates the need for the centre tap in the transformer powering it.": scrhdr qsthdr &"A full wave rectifier has many advantages over a half wave rectifier. Are they : 1. greater efficiency and less ripple 2. only half the original ripple frequency 3. greater reliability": (4egc=3:exp=1:return=555+:getans + .scrhdr U+start=500:return=598V:endsec V W X Z ] `    " (       N T    x z     @ B H        l n t x$="": o=1̱x$ n=18 #w(o,n):x$(oo)+n-1,w(o,n) n o  H24,16,16,32 ,16,16,24,0 C24,8,8,4,8,8,24,0 F0,0,62>,64@,64@,64@,62>,0 E0,0,124|,2,2,2,124|,0 G0,66B,66B,66B,66B,66B,44,,0 G0,44,,66B,66B,66B,66B,66B,0  G0,0,60<,64@,124|,64@,60<,0 I240,8,120x,128,248,0,0,0 C0,0,0,4,126~,4,0,0 I248,136,136,136,0,0,0,0 C4,4,228,4,0,0,0,0 G240,8,240,8,240,0,0,0 E7,4,4,8,8,144,80P,32  E4,68D,228,68D,0,0,0,0 "G16,16,16,0,0,480,72H,480 %E12 ,18,18,12 ,0,0,0,0 )G28,20,16,16,8,8,40(,568 *H0,0,16,40(,68D,130,254,0 ,G32 ,32 ,32 ,16,16,16,8,4 /C32 ,16,8,8,8,4,4,4 2C4,4,4,8,8,8,16,32 4 encode screen ptr2=0 z=16384@22528X data=z ̤data0ptr2=ptr2+1:j$(dgnum,ptr2,1)=(data):phi=(z/256):plo=z-256*phi:j$(dgnum,ptr2,2)=phi:j$(dgnum,ptr2,3)=plo z  fetch screen  z=1500 >addr=256*(j$(dgnum,z,2))+(j$(dgnum,z,3)) data=(j$(dgnum,z,1)) addr,data z   z=31000 %v=((z^2-(z-1)^2)) u=v^0.5 C((u)-(u+0.5))<0.01z# =z;":";z-1;":";v^0.5 z  z=07 z:7-z 7x=13:"" c=110 :c x z 0::" G C E TUTORING"::" Orders"  z=025 x=14 code=(c$(xx))+z  code>"z"code=code-26 code; x::z ( X Z ]wiring ` b502,110n:0,40(:40(,0:130,150:40(,0:0,-40(:170,70F:0,-40(:-120x,0:0,40( g   bulb  170+inc,110n z=15 0,-8, z !170+inc,90Z,20     resistor  170,110n z=14 %5,-5:-5,-5 z     meter(type)  110n,150,20 3,14-1;t$ 17,0;" "    " % battery ( *502,110n ,0,-18 /8-10 ,0:20,0:-10 ,0 2502,83S 48-15,0:30,0:-15,0 60,-18 P R T Wlink Z \&90Z,150:40(,0 |   bulbs in series  '170,96`:0,-12 170,103g,7 170,77M,7 170,111o x=14 & 2,-2:-2,-2 x 170,111o-26 x=14 & 2,-2:-2,-2 x     parallel  inc=45-:bulb 9170+inc,70F:0,-40(:-inc,0 9170+inc,110n:0,40(:-inc,0  inc=0    electroscope  502,502 $502,0:0,502 &-502,0:0,-502 75K,115s 0,-45- /75K,115s-37%:4,-7 &60<,115s:30,0  V$7000X:7050:7150 X'170,150:0,40( | ~  triangle VIR  80P,80P <100d,0:-502,86V:-502,-86V 130,80P 70,43+:-25,0:502,0 9 ,12 +1;"I" '9 ,12 +1+5;"R" 4,12 +4;"V" 15,0;" "    diode  502,502 '0,80P:30,0,- 0,-80P -30,0,- 65A,145 %0,-10 :-7,0 14,0 524,43+ x=14 6,0,- x 524,43+ 0,-10 524+24,43+ 0,-10 4,11 ;"Anode" 17,11 ;"Cathode"    triode  "10 ,6;"- - - Grid"  diode D F H Kradio N P502,80P RJ502,0:0,502:-502,0:0,-502 U110n,80P XJ502,0:0,502:-502,0:0,-502 Z170,80P \J502,0:0,502:-502,0:0,-502 v #( #2K27,41):110n,0:27,41):0,557 #:]17,3;"0":17,6;"2":17,9 ;"4":17,12 ;"6" #<17,15;"8" #>\16,2;"0":14,2;"2":12 ,2;"4":10 ,2;"6" #A #Fi579+x,513+y:20,20:-20,20:-20,-20:20,-20: #Hc72H+x,568+y:0,30:-30,0:0,-30:30,0: #P'"Here is an example of ";n$ #R #Z #\ #_noises #b #d-z=120:0.01z# =,-24:z #f #h #i&z=15:0.3,t(z):z #l #mz=15:t(z):z: #n*7,9 ,5,-7,0 # # # #axes # #_30,90Z:210,0:30,90Z:0,557:0,-110n #10 ,2;"0" #f11 ,9 ;"90":11 ,15;"180":11 ,22;"270":11 ,29;"360" #atype=09124# #atype=19130# #.4,2;"1":16,1;"-1" #07,1;".5":13 ,0;"-.5" # #.7,2;"1":13 ,1;"-1" #.4,2;"2":16,1;"-2" # # # #draw triangle # #N30,60<:100d,0:0,60<:-100d,-60< #label=09175# #15,6;"adjacent" # 8,1;"hypoteneuse" #11 ,18;"opposite" #6123{,60<:0,7:7,0 #H41),60<:0,2:-3,2:-2,0 #14,2;"A" #14,17;"B" #6,17;"C" #::::::::: # # # #"Berk ! What's ";c$;" ?": #'"Wally ! ";c$;" isn't on the tape.": ##"Moron ! Try spelling straight": #"sorry, ";n$;" ? ": #"Are you tired, ";n$;" ?": #"Don't wind me up, ";n$: $T $V scrhdr() $Y $\9900&:: $ $ qsthdr() $ $'9600%:9900&:egc=0: $ $ $endsec(start,n$) $ $7"That finishes: ":n$:"Hit r to repeat this section" $ 9900& $a$="r"start $return $ $ $getans(loop,exp) $ $?dp=0:err=0:u$:u$:(u$)>10 err=1 $(u$)=09460$ $[j=1̱(u$):(u$(jj))<45-ů(u$(jj))>579ů(u$(jj))=47/err=1 $%9480%:j:u$="-."err=1 $Cerr=1dp>1"type the answer as a number":9460$ $=ans=(u$):(exp-ans)>0.005y# ="No, the answer is ";exp $$(ans-exp)0.005y# =9720% $return $ % %$(u$(jj))=46.dp=dp+1 % ,j>1Ư(u$(jj))=45-err=1 %  %k9800H&:d1=r(1)/10 +r(2)/100d+r(3)/1000:dec=d1:int=1000*dec %& %A"See if you understand this by trying the following examples" % 9800H& % %"True or false ?" %a$ %a$ %a$"t"a$"f"9650% % %n:n;"/";:d:d: % 9630% %h"No. Don't add the numbers together. It's just the second number, so the answer is ";r(2) % %K"No, its the second number, not the first, so the answer is ";r(2) % %%9720%+((*9 )+1): % "Good": % "Correct": %"Right again": %"OK": %"That's it": %"Brilliant !": %"Well done": &"Very good": &"Genius !": &HWz=110 :r(z)=(*9 )+1:z:r(1)r(2)9800H&: &R#r(1)r(2)9800H& &\ &z "trap": & &"Hit C to continue" &a$= &a$="c"9950& &a$="r"9950& & 9920& & &z=1502:z & &Cmore=0:"More questions ? (y or n)":e$:e$=""9980& &?e$(11)="y"e$(11)="Y"more=1 & ' )@ @ɀ@ @@ Aq@AsAu AvA{AA AɀA AAxBn8Bo8Bp(Bq@Bs8BtBuBvBxDByBzB{8B|`BDB8BBDB8BBDB BɀBBhB8B BBDCnDCoCp0CqxCsCtCuCv CxDCy CzC{DC|CCDCCCDCDCCDC CɀC CTC@C CCDDnxDoDw DxDDy DzD{xD|D$D(DJq Js$J@JJ@JJJ JJJ@JJ JɀJ@JJ JJJ8JhJ8J K K) KI Ki@KjKkKmKoKqKs$K KK KKK KKK@KK KɀK̀KK KKKK0KTKDK L L) LI LiLjLkLmLoLqLs(L!LLL LLL LL L@L̀LL LLLLLTLxL M M) MI MiMjMkMmMoMqMs(M!MMMM MMM M M@MMM MMMMMMTM@M N N) NI!NiNl NmNo NqNs0NN NNN NNN N N@NN NN N8NTN@@@>||BBBBB,,BBBBB<@|@<x~P DD0H0  (8(D   X5   gxeturVr$ntarSCNU1A Ceh8 ɐ^Jnː6:6:0: electronics help tape 8  GCE Tutoring !w(25,8):2000 r(10 ) t(5):9069m# Lscrhdr=9300T$:qsthdr=9350$:endsec=9400$:getans=9450$ fig2=8950":fig=9030F#:axes2=9000(#:eg=9040P#:axes=9100#:triangle=9150#:diagram=218:praise=9720% #moreq=9980&:table=324D electroscope=7400:parallel=7350:inc=0:triode=7700:diode=7600:series=7300:link=7250R:wiring=7000X:bulb=7050:resistor=7100:meter=7150:battery=7200  5br=8100:squrec=8850":squpar=8900" ."Electronics help eh8"::"Special circuits" :" GCE Tutoring March 1985" 2u:"Hello, what's your name ?":n$:n$:"OK, ";n$;",":"I'll begin by telling you how touse this electronics tape." 4\:"This tape covers 5 subjects which all come under the headingof 'special circuits'." :<"Press the key marked C so I can type the next screenful." <a$=:a$="c"62> = 60< >:z=1100d:z AF:"Thanks. From now on when I want you to press the C key, I'll say" D:" Hit C to continue" F4:"Here's the list of subjects on this program": H"multivibrators logic circuits AND gates OR gates NOT gates" K2:"Which subject do you want to try ?":s$: Lc$=s$ N'(s$)>3s$=s$(13) Os$="mul"100d Ps$="log"200 Qs$="and"s$="AND" 300, Rs$="or "s$="OR " 400 Ss$="not"s$="NOT" 500 _ 70F c d f imultivibrators l n"Multivibrators": p"A multivibrator consists of two amplifier stages. The output of each amplifier is connected back to the input of the other. This connection is made by either a resistor or a capacitor, depending on the type of multivibrator.": qscrhdr r"Multivibrators operate in a digital manner, having an outputwith only two possible states. This corresponds to one transis-tor conducting with the other off, or vice versa.": sscrhdr t0"There are three types of multi- vibrator :": vP"1. bistable 2. monostable 3. astable": x"Each type has a different form of coupling between the two amplifier stages, and are used for widely differing purposes.": y""Let's take them one by one :": zscrhdr }"1. The bistable": "This circuit has two stable states : 1. a 'high' output 2. a 'low' output": "An input signal causes the output to change form its current state to the alternativestate. This action is called 'toggling'." scrhdr T"The cross-coupling components between the stages of a bistableare resistors.": scrhdr "2. The monostable": "This form of multivibrator has only one stable state. An input signal causes the output to change from its stable state (eg. a low output) to its unstable alternative state, where it remains for a short, fixed length of time determined by component values.": scrhdr R"The cross coupling components ina monostable are a capacitor anda resistor. ": "The pulse length of the output of a monostable can be calculated using the formula : T = 0.69 x R x C Where R is the resistor in series with the capacitor C.": scrhdr "3. The astable": "This type of multivibrator has no stable state. Instead, it constantly changes from one state to the other, giving the circuit an AC output.": scrhdr "The frequency of oscillation depends on the value of the resistors charging the two cross-coupling capacitors, and the capacitor's values themselves. The duration of eachcomplete cycle of oscillation isgiven by :": "T = 0.69 x (R1xC1 + R2xC2)": `"Where R1 and R2 are the series resistors, and C1 and C2 are thecross-coupling capacitors.": K"The frequency of oscillation is F = 1/T"  scrhdr qsthdr 2"A bistable multivibrator :": "1. changes constantly between two states 2. has two stable states 3. has one stable state ?": 4egc=3:exp=2:return=176:getans 3:"A astable multivibrator :": "1. changes constantly between two states 2. has two stable states 3. has one stable state ?": 4egc=3:exp=1:return=182:getans ::"A monostable has the following component values :": /"C = ";r(1);"uF R = ";r(2);"K": ?"What is the length of the outputpulse (in milliseconds) ?": Megc=3:exp=0.690 *r(1)*r(2):return=190:getans scrhdr 2n$=c$:start=100d:return=198:endsec       "Logic circuits": "A logic circuit functions in what is known as a 'binary' way.This means that the devices thatmake up a logic circuit have only two possible states, ratherthan the continuously variable output of an amplifier circuit, for instance.": scrhdr G"The most common ways of represe-nting these two states include :": S"true and false high and low one and zero": D"Within the circuit these values are represented by two voltages." scrhdr ~"Logic circuits are so called because they implement Boolean algebraic equations, which deal with the maths of logic.": ޳"This may sound very complicated,but it is really simple. To und-erstand Boolean logic you only need to know three logic equations, which are really justcommon sense.": scrhdr "The circuits that implement the equations are called gates, and it follows that since there are only three basic Boolean equations, there are three logicgates." scrhdr "The three gates are : 1. AND gates 2. OR gates 3. NOT gates": A"They are dealt with separately in the next three sections.": scrhdr qsthdr #"Logic circuits operate with :": "1. several defined voltage levels 2. two varying voltage levels 3. two defined voltage levels ?": 4egc=3:exp=3:return=252:getans b"Logic circuits use one voltage level to represent 'true' and another for 'false'. Is it :": "1. a high voltage for true and a low one for false 2. a low voltage for true and a high one for false 3. either 1. or 2. as long as it is consistent.":  4egc=3:exp=3:return=260:getans scrhdr )2n$=c$:start=200:return=298*:endsec * + . 1 4 6"The AND gate": 8"The AND gate is a circuit with two inputs and one output. Since the inputs can have one ofonly two possible values, and there two inputs, it follows that there are only four combinations of input values.": :n"This makes it possible to make a table which shows the output of the gate for each combinationof inputs." <scrhdr >Y"In the table below, the inputs are called A and B, and the output is called Q.": @ A" A B Q 0 0 0 0 1 0 1 0 0 1 1 1" B 324D C 338R D74,171-68D+25:64@,0 F@4,171-68D+25-10 :64@,0 H@4,171-68D+25-502:64@,0 J84,171-68D+25:0,-502 LA4+18,171-68D+25:0,-502 NJ4+18+24,171-68D+25:0,-502 PS4+18+24+22,171-68D+25:0,-502 Q Rr15,0;"As you can see from the table, the output of the gate is only 1when both the inputs are 1. " Tscrhdr VL"Algebraically, this is written : Q = A.B " Y \"So the four possible equations involving AND are : 0.0=0 0.1=0 1.0=0 1.1=1": ]lscrhdr:"The AND gate is represented using the following diagram :":3200 :18,0;" " ^scrhdr _k=13 `qsthdr c 3000 d#exp=r(1)r(2):b$="." e f 3100 g hk rscrhdr 2n$=c$:start=300,:return=398:endsec       "The OR gate": "The OR gate is a circuit with two inputs and one output. Since the inputs can have one ofonly two possible values, and there two inputs, it follows that there are only four combinations of input values.": n"This makes it possible to make a table which shows the output of the gate for each combinationof inputs." scrhdr Y"In the table below, the inputs are called A and B, and the output is called Q.":  " A B Q 0 0 0 0 1 1 1 0 1 1 1 1" table  438 |"These consist of a conductor wound non-inductively around an insulated former. As temperature increases, the resistance of the device also increases. Highly stable and accurate meas-urements are possible over a large range of tempertures - typically 10 to 1300K." scrhdr "3. Thermistors": "These consist of beads or rods of sintered semi-metal oxides, such as germanium. Unlike the previous type of tra-nsducers, the resistance of a thermistor drops as the tempera-ture increases.": "Thermistors are stable, and have a fast response, but are non- linear, and consequently requirean electronic circuit to converttheir output." scrhdr u15,0;"As you can see from the table, the output of the gate is only 1when either of the inputs is 1." scrhdr K"Algebraically, this is written : Q = A+B"  "So the four possible equations involving OR are : 0+0=0 0+1=1 1+0=1 1+1=1": lscrhdr:"The OR gate is represented using the following diagram :":3300 :18,0;" " scrhdr k=13 qsthdr  3000 #exp=r(1)r(2):b$="+"   3100  k scrhdr 2n$=c$:start=400:return=498:endsec       "The NOT gate": "This is the simplest gate, having only one input and one output. This makes the number ofpossible input states only two. The table showing them is on thenext page." scrhdr O"In the table below, A representsthe input and Q represents the output.":: l" A Q 0 1 1 0" table  "12 ,0;" "  5,0;" ";6,0;" ";7,0;" ";8,0;" ";9 ,0;" ";10 ,0;" ";11 ,0;" " %22,88X:44,,0 %22,88X:0,40( `"As you can see from the table, the output of a NOT gate is the opposite of its input.": scrhdr J"Algebraically, this is written : Q = A'" ! $"So the two possible equations involving NOT are : 0'=1 1'=0": %lscrhdr:"The NOT gate is represented using the following diagram :":3400H :18,0;" " &scrhdr:"If a NOT gate is placed after an AND gate, a 'NAND' gate is formed. If it is placed after an OR gate, a NOR gate is produced.":scrhdr 'k=13 (qsthdr ) + 3000 ,exp=r(1):b$="'" - . 3150N / 0k :scrhdr U+start=500:return=598V:endsec V W X Z ] ` b"Electronics": d"Electronics differs from what has been covered so far in that it concerns active devices. An active device is one which can in some way control the flow of current, rather than merely passively impede it.": g"The first active device to be invented was the thermionic diode. A diode allows the flow of current in only one directionIt can therefore convert AC to DC.": hscrhdr je"A thermionic diode consists of a filament, a cathode and an anode. The filament is like the filament of a bulb, and heats the the cathode to such a high temperature that some electrons are liberated. These are attracted by the anode, as long as it is positive. If the anode is -ve, the electrons are repelled, and no current flows.": ln"1. The comparator This circuit compares two input signals. If the voltage at the non-inverting input of the op amp is greater than that at the inverting input, then the outputof the op amp rises to the positive supply voltage. If the signals are reversed, the outputfalls to the negative supply voltage.": mscrhdr nscrhdr p"2. Op-amp with feedback": qscrhdr:triode rw"Since A is so large, if Vout is a few volts, then Vin must be very nearly 0 (a virtual earth) since Vout/A 0.": t"The concept of a virtual earth allows the application of Kirchoff's law, which states (more or less) that current can't build up at any point." vscrhdr x"i.e. Iin + If = 0 and Vi/Ri + Vo/Rf = 0 assuming that no current flows into the inverting input": zU"re-arranging the above : Vo = - RfVi/Ri": |scrhdr ~$"3. The non-inverting amplifier": "Unlike the previous circuit, this time the gain is positive. Note that the input to the circuit is connected to the non-inverting input of the op amp.": $"The voltage gain is given by :": "Av = 1 + Rf/Ri": scrhdr &"4. The voltage follower (buffer)": "This circuit is really a specialcase of the previous one where Rf and Ri are both zero. Consequently, it has a gain of one.": D"What is the point of an amplifier with a gain of one ?": &"It's not as silly as it seems...": scrhdr "This circuit has a very high input impedance (much higher than the input impedance of the op amp), but a low output impedance. This makes it useful if a signal mustn't be loaded." 2n$=c$:start=900:return=998:endsec     18,0  17,9 ;"Cathode"   " ( z;start=600X:return=898:n$="matrix arithmetic" endsec     electrostatics  "Electrostatics": "So far, current electricity has been described. It involves the flow of current through a circuit. Static electricity is the accumulation of charge on anobject:": scrhdr "Static charges can be built up by friction between insulators. Very high voltages can be produced, but the actual charge is very small.": "Static charges are detected with an electroscope. This is a device which relies on the principle that like charges repel:": scrhdr scrhdr:electroscope:scrhdr M"The greater the angle of deflection, the greater the charge.": scrhdr v"Very high voltages can be produced by a Van der Graaf generator. This consists of a vertical moving insulating belt carrying charge to a large hollow conducting sphere at the top of the generator. Charge is sprayed on at the base of the column, and is picked up by a comb-like electrode in the sphere. Voltages of 1 000 000v can be produced.": scrhdr "Charge is measured in Coulombs, and the ability of a capacitor to store it is measured in Farads. The farad is a very big unit, so the picofarad (10^-12F)is often used instead": ""Charge = capacitance x voltage"   650 qsthdr %"A diode allows current to pass:": ^"1. Both ways 2. one way 3. towards the cathode ?": 4exp=2:egc=3:return=960:getans "A triode :": V"1. amplifies signals 2. is equivalent to a transistor3. both 1. and 2.": 4exp=3:egc=3:return=968:getans "A carrier wave is": ]"1. audio frequency 2. radio frequency 3. carried by the sound": 4exp=2:egc=3:return=978:getans 2n$=c$:start=600X:return=698:endsec      N T    x z     @ B H   scalars and vectors  :"Scalars and vectors": }"Quantities such as mass, volume and length are called SCALAR quantities. Scalar quanties havesize but not direction.": z"Quantities such as velocity and acceleration have both size and direction. Thistype of quantity is called a vector.": D"The general propertyof a vector is that it has two components.": scrhdr qsthdr 1:"Which of these is a vector quantity ? " S:"1. length 2. time 3. velocity": 5exp=3:egc=3:return=1760:getans 3start=1700:return=1798:n$="vectors" endsec      vector arith. & laws  ":"Vector arithmetic and laws": ^"Vector arithmetic is very simpleand follows the laws of conventional arithmetic.": "Addition": <"Two vectors a and b add to make a vector c as follows:": ""a = 2 b = 3":" 1 4" 8i=12 :x=29:y=63?:br:x=93]:br &:"c = 2+3 = 5":" 1+4 = 5" x=101e:y=39':br  x=39':i=24:br !scrhdr $""a = 2 b = 3":" 1 4" &&:"c = 2+3 = 5":" 1+4 = 5" '9i=12 :x=29:y=151:br:x=93]:br (n:"Vector addition is commutative since it makes no difference which way round the vectors are added.": )&x=101e:y=39'+88X:br *x=39':i=24:br +"a + b = b + a = c": ."This is easy to see if you thinkof the vectors as position vectors. It makes no difference which one is taken first - the final position is the same." 0scrhdr 2"vector addition is also associative. Three vectors a, b and c add to make the same result in both of the following ways:": 54" d = a + (b + c) d = (a + b) + c" 8_:"Again, this can be easily understood if the vectors are thought of as positional." :3:"Vector subtraction is also conventional." <scrhdr ?"Vector multiplication": B/"A vector can be multiplied by a scalar:": D1" eg. a = 2 1": F:" eg. 2a = 2 x 2 = 4 2 x 1 = 2" GFi=12 :x=165:y=87W:br:x=77M:y=111o:br H(i=44,:x=85U:y=87W:br Iscrhdr Lqsthdr N/:"Is vector addition commutative ?":a$:a$ P;a$="No"a$="no""Yes it is ! Read the section again." Sa$="yes"a$="Yes"praise V(:"Is vector addition associative ?": X a$:a$ Z;a$="No"a$="no""Yes it is ! Read the section again." ]a$="yes"a$="Yes"praise b=n$="vector arithmetic":start=1800:return=1898j gendsec j k l n qvelocity triangles t v:"Velocity triangles"::"Sometimes it is necessary to know the length of a vector rather than its individual components.": x"Since the two components of a positional vector are at right angles to each other, the lengthof a vector can be calculated using Pythagoras' theorem." yscrhdr {:"For example, the length of a vector:"::" 4":" 3":::::::::"is 5. This can be seen in the triangle above." }1x=14-1:y=119w:i=12 :br ~label=0:triangle O"AB represent a the x component and BC the y component. AC is the length." scrhdr "The length of the vector can represent quantites such as speed. If an aircraft is flying at right angles to the wind its ground speed can be calculated using vectors:":  triangle q"AB represents the aircraft's airspeed, BC represents the wind velocity and AC represents the ground speed." 8,17;"air speed=150":10 ,17;"wind speed=80":12 ,17;"AC=150+80":12 +1,20;"AC=28900":14,21;"AC=170"  :::: scrhdr "Sometimes velocities will not be at right angles. In these cases Puthagorus cannot be used as the resultant triangle is not right angled." d:"The length can be calculated in these cases by drawing the triangle and measuring length." >n$="velocity triangles":start=1900l:return=1998 endsec   x$="": o=1̱x$ n=18 #w(o,n):x$(oo)+n-1,w(o,n) n o  H24,16,16,32 ,16,16,24,0 C24,8,8,4,8,8,24,0 F0,0,62>,64@,64@,64@,62>,0 E0,0,124|,2,2,2,124|,0 G0,66B,66B,66B,66B,66B,44,,0 G0,44,,66B,66B,66B,66B,66B,0  G0,0,60<,64@,124|,64@,60<,0 I240,8,120x,128,248,0,0,0 C0,0,0,4,126~,4,0,0 I248,136,136,136,0,0,0,0 H0,24,36$,66B,36$,36$,102f,0 G240,8,240,8,240,0,0,0 G28,20,16,16,8,8,40(,568  E4,68D,228,68D,0,0,0,0 "G16,16,16,0,0,480,72H,480 %E12 ,18,18,12 ,0,0,0,0 (E7,4,4,8,8,144,80P,32 *H0,0,16,40(,68D,130,254,0 ,G32 ,32 ,32 ,16,16,16,8,4 /C32 ,16,8,8,8,4,4,4 2C4,4,4,8,8,8,16,32 4 bool conv. j=16 firj=2*((r(j)/2)) r(j)=r(j)-firj j   boolqst !*"What is ";r(1);b$;r(2);" ?" +(egc=3:return=31200 :getans 0 N X"What is ";r(1);b$;" ?" ](egc=3:return=3170b :getans b gates 7,10 ;"AND gate" 100d,100d 20,0 0,-30,-1.57H -20,0 0,30 3255 3290 '100d,95_:-15,0 '100d,75K:-15,0 &127,85U:15,0 F10 ,10 ;"A";12 ,10 ;"B";11 ,18;"Q"   OR gate 7,11 ;"OR gate" 3255 397a,100d:0,-30,-1.57H 30,15,0.785H -30,15,0.785H > H NOT gate M7,10 ;"NOT gate" R 3255 \100d,100d ak30,-15:133,85U,3:130,85U:-30,-15:0,30  z=31000 %v=((z^2-(z-1)^2)) u=v^0.5 C((u)-(u+0.5))<0.01z# =z;":";z-1;":";v^0.5 z  z=07 z:7-z 7x=13:"" c=110 :c x z 0::" G C E TUTORING"::" Orders"  z=025 x=14 code=(c$(xx))+z  code>"z"code=code-26 code; x::z ( X Z ]wiring ` b502,110n:0,40(:40(,0:130,150:40(,0:0,-40(:170,70F:0,-40(:-120x,0:0,40( g   bulb  170+inc,110n z=15 0,-8, z !170+inc,90Z,20     resistor  170,110n z=14 %5,-5:-5,-5 z     meter(type)  110n,150,20 3,14-1;t$ 17,0;" "    " % battery ( *502,110n ,0,-18 /8-10 ,0:20,0:-10 ,0 2502,83S 48-15,0:30,0:-15,0 60,-18 P R T Wlink Z \&90Z,150:40(,0 |   bulbs in series  '170,96`:0,-12 170,103g,7 170,77M,7 170,111o x=14 & 2,-2:-2,-2 x 170,111o-26 x=14 & 2,-2:-2,-2 x     parallel  inc=45-:bulb 9170+inc,70F:0,-40(:-inc,0 9170+inc,110n:0,40(:-inc,0  inc=0    electroscope  502,502 $502,0:0,502 &-502,0:0,-502 75K,115s 0,-45- /75K,115s-37%:4,-7 &60<,115s:30,0  V$7000X:7050:7150 X'170,150:0,40( | ~  triangle VIR  80P,80P <100d,0:-502,86V:-502,-86V 130,80P 70,43+:-25,0:502,0 9 ,12 +1;"I" '9 ,12 +1+5;"R" 4,12 +4;"V" 15,0;" "    diode  502,502 '0,80P:30,0,- 0,-80P -30,0,- 65A,145 %0,-10 :-7,0 14,0 524,43+ x=14 6,0,- x 524,43+ 0,-10 524+24,43+ 0,-10 4,11 ;"Anode" 17,11 ;"Cathode"    triode  "10 ,6;"- - - Grid"  diode D F H Kradio N P502,80P RJ502,0:0,502:-502,0:0,-502 U110n,80P XJ502,0:0,502:-502,0:0,-502 Z170,80P \J502,0:0,502:-502,0:0,-502 v @"A geometric figure can be rotated by multiplying the individual coordinates by one ofthree different transformation matrices, depending on whether rotation through 90,180 or 270 is required.": B&"For a 90 rotation, multiply by:": E" 0 -1":" 1 0": H,"A 90 rotation is shoen in the diagram." I J:"The coordinates of the corners of the triangle are:": L&" 2 2 3":" 2 1 1": MM"which when multiplied by the matrix for a 90 rotation become:": N?" 0 -1 2 0-3 -3 1 0 3 2+0 2": O?" 0 -1 2 0-1 -1 1 0 1 2+0 2": P=" 0 -1 3 0-1 -1 1 0 1 3-0 3" R scrhdr:  Gx,y:0,16,-/3:x+i,y:0,16,/3: "There is a special matrix calledthe UNIT or identity matrix. If another matrix is multiplied by it there is no effect, rather like multiplying a number by 1 in ordinary arithmetic." $:"This is the 2x2 unit matrix:": " 1 0":" 0 1": 'x=8:i=24:y=80P:br scrhdr  " "square + rectangle "]27,568:502,0:0,502:-502,0:0,-502 "_27,568:100d,0:0,502:-100d,0:0,-502 "$7,2;"A D F" "%15,2;"B C E" " " "square + parallelogram "]27,568:75K,0:0,502:-75K,0:0,-502 "`27,568:75K,0:25,502:-75K,0:-25,-502 "#7,3;"A E D F" "!15,3;"B C" " " #K27,568:110n,0:568,41):0,557 #f15,7;"0":15,9 ;"2":15,11 ;"4":15,12 +1;"6" #E14,6;"0":12 ,6;"2":10 ,6;"4" #K27,568:110n,0:568,41):0,557 # [568+16,568+8:0,16:8,-16:-8,0 # ^568+32 ,568+16:0,32 :16,-32 :-16,0 #\568-10 ,568+16:-16,0:16,8:0,-8 #11 ,9 ;"A" #9 ,12 ;"B" #11 ,4;"C" #& #' #( #2K27,41):110n,0:27,41):0,557 #:]17,3;"0":17,6;"2":17,9 ;"4":17,12 ;"6" #<17,15;"8" #>\16,2;"0":14,2;"2":12 ,2;"4":10 ,2;"6" #A #Fi579+x,513+y:20,20:-20,20:-20,-20:20,-20: #Hc72H+x,568+y:0,30:-30,0:0,-30:30,0: #P'"Here is an example of ";n$ #R #Z #\ #_noises #b #d-z=120:0.01z# =,-24:z #f #h #i&z=15:0.3,t(z):z #l #mz=15:t(z):z: #n*7,9 ,5,-7,0 # # # #axes # #_30,90Z:210,0:30,90Z:0,557:0,-110n #10 ,2;"0" #f11 ,9 ;"90":11 ,15;"180":11 ,22;"270":11 ,29;"360" #atype=09124# #atype=19130# #.4,2;"1":16,1;"-1" #07,1;".5":13 ,0;"-.5" # #.7,2;"1":13 ,1;"-1" #.4,2;"2":16,1;"-2" # # # #draw triangle # #N30,60<:100d,0:0,60<:-100d,-60< #label=09175# #15,6;"adjacent" # 8,1;"hypoteneuse" #11 ,18;"opposite" #6123{,60<:0,7:7,0 #H41),60<:0,2:-3,2:-2,0 #14,2;"A" #14,17;"B" #6,17;"C" #::::::::: # # # #"Berk ! What's ";c$;" ?": #'"Wally ! ";c$;" isn't on the tape.": ##"Moron ! Try spelling straight": #"sorry, ";n$;" ? ": #"Are you tired, ";n$;" ?": #"Don't wind me up, ";n$: $T $V scrhdr() $Y $\9900&:: $ $ qsthdr() $ $'9600%:9900&:egc=0: $ $ $endsec(start,n$) $ $7"That finishes: ":n$:"Hit r to repeat this section" $ 9900& $a$="r"start $return $ $ $getans(loop,exp) $ $?dp=0:err=0:u$:u$:(u$)>10 err=1 $(u$)=09460$ $[j=1̱(u$):(u$(jj))<45-ů(u$(jj))>579ů(u$(jj))=47/err=1 $%9480%:j:u$="-."err=1 $Cerr=1dp>1"type the answer as a number":9460$ $=ans=(u$):(exp-ans)>0.005y# ="No, the answer is ";exp $$(ans-exp)0.005y# =9720% $return $ % %$(u$(jj))=46.dp=dp+1 % ,j>1Ư(u$(jj))=45-err=1 %  %k9800H&:d1=r(1)/10 +r(2)/100d+r(3)/1000:dec=d1:int=1000*dec %& %A"See if you understand this by trying the following examples" % 9800H& % %"True or false ?" %a$ %a$ %a$"t"a$"f"9650% % %n:n;"/";:d:d: % 9630% %h"No. Don't add the numbers together. It's just the second number, so the answer is ";r(2) % %K"No, its the second number, not the first, so the answer is ";r(2) % %%9720%+((*9 )+1): % "Good": % "Correct": %"Right again": %"OK": %"That's it": %"Brilliant !": %"Well done": &"Very good": &"Genius !": &HWz=110 :r(z)=(*9 )+1:z:r(1)r(2)9800H&: &R#r(1)r(2)9800H& &\ &z "trap": & &"Hit C to continue" &a$= &a$="c"9950& &a$="r"9950& & 9920& & &z=1502:z & &Cmore=0:"More questions ? (y or n)":e$:e$=""9980& &?e$(11)="y"e$(11)="Y"more=1 & '  >@@@>||BBBBB,,BBBBB<@|@<x~$B$$f(8DD0H0  P (D   X 5      H&crhdT$sthd$ndse$etan$ig"iF#xes(#P#xe#riangl#iagrarais%ore&ablDlectroscoparallenriodioderieinRirinXulesistoeteatter qure"qupa"tareturb gxr$nir'vu{7B'U0NNickCmultivibratorsSmulA R