Time base Generators (part-1)

Time base Generators
Part - 1

1. Time base Generators
Unit -IV

2. UNIT-IV: TIME-BASE GENERATORS
(10Periods)
•VoltageTime-BaseGenerators:GeneralfeaturesofaTimeBasesignal,
ExponentialSweepCircuit,ConstantCurrentSweepCircuit,UJTSweepCircuit,
MillerandBootstrapTime-Basegenerators-basicprinciples,TransistorMiller
Time-Basegenerator,TransistorBootstrapTime-Basegenerator.
•CurrentTime-BaseGenerators:ASimpleCurrentSweep,LinearityCorrection
throughAdjustmentofDrivingWaveform,TransistorCurrentTime-Base
generator.
Mr. M. Balaji, Dept. of ECE, SVEC 2

3. Time base Generators:
•isanelectroniccircuitwhichgeneratesanoutputvoltageorcurrent
waveform,aportionofwhichvarieslinearlywithtime.
TimebaseGeneratorsareoftwotypes:
•VoltageTimeBaseGenerators−Atimebasegeneratorthatprovidesan
outputvoltagewaveformthatvarieslinearlywithtimeiscalledasaVoltage
TimebaseGenerator.
•CurrentTimeBaseGenerator−Atimebasegeneratorthatprovidesan
outputcurrentwaveformthatvarieslinearlywithtimeiscalledasa
CurrentTimebaseGenerator.
Mr. M. Balaji, Dept. of ECE, SVEC 3

4. General features of a Time base signal:
Sweep time Restoration time
General sweep waveform Sawtoothwaveform
Mr. M. Balaji, Dept. of ECE, SVEC 4

5. •Aftergeneratingthesweepsignals,itistimetotransmitthem.The
transmittedsignalmaybesubjectedtodeviationfromlinearitywhenitis
transmittedthroughalinearnetwork.
The deviation from linearity is expressed in three most important ways.
They are −
•The Slope or Sweep Speed Error, e
s
•The Displacement Error, e
d
•The Transmission Error, e
t
Mr. M. Balaji, Dept. of ECE, SVEC 5

6. The Slope or Sweep Speed Error, e
s
•An important requirement of a sweep is that it must increase linearly with
time, i.e. the rate of change of sweep voltage with time be constant. This
deviation from linearity is defined as
Mr. M. Balaji, Dept. of ECE, SVEC 6

7. The Displacement Error, e
d
•Displacement error (ed) is the ratio of the maximum difference between the
actual sweep voltage v
s, and the linear sweep, v
s’which passes through the
initial and the end points of the sweep, to the sweep amplitude.
??????
??????=
??????
�−??????
�
′
??????
�
??????
�−??????
�
′
Mr. M. Balaji, Dept. of ECE, SVEC 7

8. The Transmission Error, e
t
•Transmission error (et): If a ramp voltage is transmitted through a
high-pass RC circuit, the output falls away from the input
•The transmission error e
tis given as:
??????
�=
??????
�
′
−????????????
??????
�′
V
s’ = input sweep
V
s= Output sweep
Mr. M. Balaji, Dept. of ECE, SVEC 8

9. Exponential Sweep Circuit
Mr. M. Balaji, Dept. of ECE, SVEC 9

10. Mr. M. Balaji, Dept. of ECE, SVEC 10

11. Mr. M. Balaji, Dept. of ECE, SVEC 11

12. Mr. M. Balaji, Dept. of ECE, SVEC 12

13. Mr. M. Balaji, Dept. of ECE, SVEC 13

14. Mr. M. Balaji, Dept. of ECE, SVEC 14

15. Mr. M. Balaji, Dept. of ECE, SVEC 15

16. Mr. M. Balaji, Dept. of ECE, SVEC 16

17. Unijunction Transistor
Mr. M. Balaji, Dept. of ECE, SVEC 17

18. UJT: Unijunction Transistor
Mr. M. Balaji, Dept. of ECE, SVEC 18

19. Mr. M. Balaji, Dept. of ECE, SVEC 19

20. Sweep circuit using UJT
Mr. M. Balaji, Dept. of ECE, SVEC 20

21. Mr. M. Balaji, Dept. of ECE, SVEC 21

22. Mr. M. Balaji, Dept. of ECE, SVEC 22

23. Mr. M. Balaji, Dept. of ECE, SVEC 23

24. •Design a relaxation oscillator using a UJT, with V
V= 3V, η=0.68 to 0.82, Ip=
2µA, I
V= 1mA, V
BB= 20V, the output frequency is to be 5KHz. Calculate the
typical peak-to –peak output voltage.
•Sol:
The given UJT has the following parameters:
Mr. M. Balaji, Dept. of ECE, SVEC 24

25. •Thus, R must be in the range of 17KΩto 2.15MΩ. If R is large, C must
be very small. Therefore Choose R such that C is not very small.
Mr. M. Balaji, Dept. of ECE, SVEC 25

26. •In the UJT sweep circuit, VBB = 20V, VYY= 50V, R= 5KΩ, C= 0.01µF, η= 0.5
and Vv= 2V. Using the UJT characteristics, find
(a) the amplitude of sweep signal
(b) the slope and displacement error
(c) duration of the sweep
(d) the recovery time
Sol:
0.6 + 0.5* 20 = 10.6V
(a)Sweep signal amplitude:
Vs= Vp-Vv= 10.6V-2V = 8.6V
Mr. M. Balaji, Dept. of ECE, SVEC 26

27. •Slope Error e
s=Vs/V
•V=peak to peak value of the sweep
•V= Vyy-Vv= 50-2=48V
•e
s=Vs/V = 8.2/48= 0.179
•Displacement Error e
d= e
s/8=0.022
•Sweep time= Ts= RC ln (Vyy-Vv/ Vyy-Vp) = 9.87µs
•Recovery time=Tr= (2+5C)Vv= 4.1µs
Mr. M. Balaji, Dept. of ECE, SVEC 27

28. Miller and Bootstrap Time base generators: basic Principles
•Asimpleexponentialsweepgeneratorisshowninfigure,essentially
producesanonlinearsweepvoltage.
Mr. M. Balaji, Dept. of ECE, SVEC 28

29. •Inanexponentialsweepgenerator,sincethecapacitorcharges
exponentially,theresultantsweepgeneratedisanon-linearone.To
getalinearsweep,thecapacitorisrequiredtochargewitha
constantcurrent.
•Letusconsiderthemethodsoflinearizinganexponentialsweep
•Introduceanauxiliarygenerator,v,asshowninFig.12.9(b).
•IfvisalwayskeptequaltothevoltageacrossC(i.e.,v=v
C),asthe
polaritiesofvandv
Careopposite,thenetvoltageintheloopisV.
Theni=V/Rwhichisaconstant.
Mr. M. Balaji, Dept. of ECE, SVEC 29

30. •Thatmeans,thecapacitor
chargingcurrentisconstant
andperfectlinearityis
achieved.
•LetusidentifythreenodesX,
YandZ.Inacircuitone
terminal,ischosenasa
referenceterminalorthe
groundterminal.
Mr. M. Balaji, Dept. of ECE, SVEC 30

31. Miller integrator sweep generator
•Now let Z be the ground terminal
•The circuit can be redrawn as Fig. 12.10(b)
Mr. M. Balaji, Dept. of ECE, SVEC 31

32. Mr. M. Balaji, Dept. of ECE, SVEC 32

33. •Sincevandv
c
areequalin
magnitudeandoppositein
polarity,vi=0.
•Hence,iftheauxiliary
generatorisreplacedbyan
amplifierwithXandZas
theinputterminalsand
YandZasoutputterminals
•thenthegainAofthe
amplifiershouldbeinfinity.
Replacingtheauxiliary
generatorbyanamplifier
withgaininfinity,thecircuit
showninFig.12.10(b)is
redrawnasthatshownin
Fig.12.10(c).
Mr. M. Balaji, Dept. of ECE, SVEC 33

34. Mr. M. Balaji, Dept. of ECE, SVEC 34

35. Mr. M. Balaji, Dept. of ECE, SVEC 35

36. Mr. M. Balaji, Dept. of ECE, SVEC 36

37. Slope error in Miller’s Sweep generator
•inwhichtheauxiliarygeneratorisreplacedbyanamplifierwithgain
infinity.
•Thévenizingthecircuitattheinput,theThéveninvoltagesourceand
itsinternalresistanceasV’andR’
Mr. M. Balaji, Dept. of ECE, SVEC 37

38. Mr. M. Balaji, Dept. of ECE, SVEC 38

39. Mr. M. Balaji, Dept. of ECE, SVEC 39

40. •Ast→∞,thecapacitorisfullycharged,hence,nocurrentflowsin
it.Thus,tocalculatetheoutputvoltage,thecapacitorcanbe
replacedbyanopencircuit.TheresultantcircuitisasshowninFig.
12.11(c).
Att=∞;v
i=V’
??????
Hencev
o=AV’
Weknowthatforanexponentialsweep,e
s=V
s/V
WhereV
sisthesweepamplitudeandVisthepeaktopeaksignalof
theoutputswing
Inthiscaseofmiller’ssweep,thetotalpeaktopeaksignalofthe
outputswing,v
o=AV’,Hence
Mr. M. Balaji, Dept. of ECE, SVEC 40

41. EvenifR
iissmall,asAislarge,theslopeerrorofamiller’ssweepis
verysmall.Hence,forallpracticalpurposesthissweepgenerator
producesanearlinearsweep.
Mr. M. Balaji, Dept. of ECE, SVEC 41

42. Transistor miller time base generator:
Mr. M. Balaji, Dept. of ECE, SVEC 42

43. Mr. M. Balaji, Dept. of ECE, SVEC 43

44. Mr. M. Balaji, Dept. of ECE, SVEC 44

45. Mr. M. Balaji, Dept. of ECE, SVEC 45

46. Mr. M. Balaji, Dept. of ECE, SVEC 46

47. Mr. M. Balaji, Dept. of ECE, SVEC 47

48. Mr. M. Balaji, Dept. of ECE, SVEC 48

49. •(vi) Calculation of the slope error: The slope error of the
Miller’s sweep generator is given by the relation:
where,R
itheresistancethroughwhichthecapacitorcharges
whentheswitchisOFF.
Tocalculatee
s,therefore,wehavetocalculateAandR
iof
thecommon-emitteramplifier.
TheCEamplifierusestheh-parametermodelasfollows
Mr. M. Balaji, Dept. of ECE, SVEC 49

50. Mr. M. Balaji, Dept. of ECE, SVEC 50

51. Mr. M. Balaji, Dept. of ECE, SVEC 51

52. R
iand A can be calculated using above equations and hence, the
value of e
s
Mr. M. Balaji, Dept. of ECE, SVEC 52

53. Bootstrap Sweep Generators:
•Alternatively,inthecircuitshowninFig.
12.9(b)letYbethegroundterminal.
•TheresultantcircuitisshowninFig.
12.13(a).
•Redrawingthiscircuitandreplacingthe
auxiliarygeneratorbyanamplifierwithX
andYasinputterminalsandZandYasthe
outputterminals,theamplifiershouldhavea
gainofunityasv=v
C,asshowninFig.
12.13(b).
Mr. M. Balaji, Dept. of ECE, SVEC 53

54. Replacingthegeneratorbyanamplifier,thecircuitshowninFig.12.13(b)isredrawnas
showninFig.12.13(c).ThesweepgeneratorrepresentedinFig.12.13(c)iscalleda
bootstrapsweepgeneratorbecausetheincreasinginputatXisaccompaniedbyan
identicalriseintheoutputatZ,asthegainoftheamplifierisunity
Mr. M. Balaji, Dept. of ECE, SVEC 54

55. Mr. M. Balaji, Dept. of ECE, SVEC 55

56. Mr. M. Balaji, Dept. of ECE, SVEC 56

57. Slope error in Bootstrap Sweep generators:
•ConsiderthebootstrapsweepgeneratorshowninFig.12.14(a)in
whichtheauxiliarygeneratorisreplacedbyanamplifierwithgain
1,whichobviouslyisanemitterfollower.
•IfinitiallythecapacitorisunchargedandifSisclosedatt=0,then
thevoltageacrossCandR
i,i.e.,v
i=0,R
iisreplacedbyashort
circuit.Asv
i=0,Av
i=0andisalsoreplacedbyashortcircuit.
Mr. M. Balaji, Dept. of ECE, SVEC 57

58. Mr. M. Balaji, Dept. of ECE, SVEC 58

59. Mr. M. Balaji, Dept. of ECE, SVEC 59

60. and as R
oof the emitter follower is very small, then v
o≈ 0.
Mr. M. Balaji, Dept. of ECE, SVEC 60

61. Mr. M. Balaji, Dept. of ECE, SVEC 61

62. Mr. M. Balaji, Dept. of ECE, SVEC 62

63. Mr. M. Balaji, Dept. of ECE, SVEC 63

64. Mr. M. Balaji, Dept. of ECE, SVEC 64

65. Transistor bootstrap time-base generator
Mr. M. Balaji, Dept. of ECE, SVEC 65

66. •ApracticalbootstraprampgeneratorisshowninFig.12.16(a).
•TherampisgeneratedacrosscapacitorC
1whichischargedfromthecurrent
throughR
1.
•ThedischargetransistorQ
1,whenON,keepsV
1atV
CE(sat)untilanegative
inputpulseisapplied.
•Q
2isanemitterfollowerwithalowoutputresistance.
•EmitterresistanceR
Eisconnectedtoanegativesupply(VEE)insteadof
referencingittothegroundtoensurethatQ2remainsconductingeven
whenitsbasevoltageV
1isclosetotheground.
•CapacitorC
3,calledthebootstrappingcapacitance,hasamuchhigher
capacitancethanC
1.
•C
3ismeanttomaintainaconstantvoltageacrossR
1andthus,maintaina
constantchargingcurrent.
Mr. M. Balaji, Dept. of ECE, SVEC 66

67. (a)Quiescentconditions:Thevoltagesunderquiescentconditions(beforethe
applicationofatrigger)arecalculatedasillustratedbelow,usingFig.12.16(b).
Mr. M. Balaji, Dept. of ECE, SVEC 67

68. •Whentheinputtriggersignalisnotpresent,Q
1hassufficientbasecurrent.
Therefore,Q
1isdrivenintosaturationandthevoltageV
1acrossthe
capacitorC
1isVCE(sat).V
1=VCE(sat)(pointX),typically0.2VforSi,as
showninFig.12.16(b).Q
2isanemitterfollowerforwhichinputisV
1andits
outputv
ois:
Mr. M. Balaji, Dept. of ECE, SVEC 68

69. Mr. M. Balaji, Dept. of ECE, SVEC 69

70. (b)Sweepgeneration:
•At t = 0, as the trigger is applied,
the voltage at the base of Q
1
goes negative, Q
1is OFF.
•The voltage at node K, V
K= V
CC+
V
1and D
1is OFF and is an open
circuit. The voltage at node X is
V
1.
Mr. M. Balaji, Dept. of ECE, SVEC 70

71. Mr. M. Balaji, Dept. of ECE, SVEC 71

72. FromFig.12.16(d),itisseenthat
theoutputv
ovarieslinearlyonly
whenthedurationofthegating
signal(Tg)issmallsothatinthis
periodv
odoesnotreachVCC.
However,ifTgislarge,theoutput
v
omayreachV
CCevenbeforeTg.
Whenv
o=VCC,thevoltageV
CE2of
Q
2ispracticallyzero(saturation).
Q
2nolongerbehavesasanemitter
follower.v
oandV
1thereforeremain
atV
CC.ThecurrentV
CC/R
1now
flowsthroughC
3,R
1andthrough
thebase-emitterdiodeofQ
2.
Mr. M. Balaji, Dept. of ECE, SVEC 72

73. Mr. M. Balaji, Dept. of ECE, SVEC 73

74. Mr. M. Balaji, Dept. of ECE, SVEC 74

75. Mr. M. Balaji, Dept. of ECE, SVEC 75

76. Mr. M. Balaji, Dept. of ECE, SVEC 76

77. (c) Calculation of retrace time, Tr:
•Attheendofthegatesignal,att=Tg,acurrentI
B1=(V
CC/R
B)againflows
intothebaseterminalofQ
1.Q
1onceagaintriestogointosaturation.
However,tillsuchtimeV
CEofQ
1isV
CE(sat)(Q
1isinsaturation),thecollector
current,i
C1remainsconstantat
•AsshowninFig.12.18,thecurrenti
R1throughR
1andthedischarging
currenti
dofC
1nowconstitutesi
C1,thecollectorcurrentofQ
1,neglecting
thesmallbasecurrentI
B2ofQ
2,
Mr. M. Balaji, Dept. of ECE, SVEC 77

78. Therefore V1 and vofall linearly to the initial value.
The voltage variation during the retrace time Tris:
Mr. M. Balaji, Dept. of ECE, SVEC 78

79. •Iftheretracetimeislarge,ittakesalongertimetoinitiateanew
sweepcycle.FromEq.(12.53),itisseenthatR
Bwillhavetobesmall
toreducetheretracetime.However,ifR
Bistoosmall,thenthe
collectorcurrentofQ1becomeslargeas:
ThisresultsingreaterdissipationinQ1.Duringtheperiod,T=Tg+Tr,though
C3isalargecapacitor,itmaystillloosesomecharge.Thecircuitissaidto
haverecoveredcompletelyonlywhenthechargelostbyC3isregained.The
minimumrecoverytimeT1forC3canbefoundoutasfollows:
Mr. M. Balaji, Dept. of ECE, SVEC 79

80. To reduce T
1, V
EEmay be increased. However, this increases the quiescent
current in Q
2and hence, the dissipation in it
Mr. M. Balaji, Dept. of ECE, SVEC 80

81. (d) Calculation of the slope error of a bootstrap sweep circuit:
•Theslopeerrorofthebootstrap,assumingthatthechargeonC3remains
unalteredduringthesweepduration,isgivenbytherelation:
To calculate e
s, we have to
calculate A and R
i. For a common
collector amplifier we have:
Mr. M. Balaji, Dept. of ECE, SVEC 81

82. Mr. M. Balaji, Dept. of ECE, SVEC 82

83. FortheMiller’ssweepcircuit,VCC=25V,RC2=5kΩ,RC1=10kΩ.
Thedurationofthesweepis5ms.Thesweepamplitudeis25V.
Calculate(a)thevalueofC;(b)theretracetimeand(c)theslope
error.Thetransistorhasthefollowingparameters:hfe=80,hie=1kΩ,
hoe=1/40kΩandhre=2.5×10−4.
•Sol: (a)
Mr. M. Balaji, Dept. of ECE, SVEC 83

84. Mr. M. Balaji, Dept. of ECE, SVEC 84