SIGNAL GENERATOR AND WAVEFORM-SHAPING CIRCUITS Introduction Ras Hy, the function of an oscillator (waveform generator) is to generate alternating, current or vollage waveforms. These ave two distinetly different lypes of waveform generators: © Sinusoidal oscillators, which utilize some form of resonance ¢ —Non-sinusoidal oscillators or function generators, which employ switching mechanism implemented with a multi- vibrator circuit. Sinusoidal waveform Generators A sinusoidal oscillator can be realized by placing a frequency selective network in the feedback path of an amplifier (a transistor or on op-amp). The circuit will oscillate at the frequency at which the total phase shift around the loop is zero, provided that the magnitude of the loop gain at this frequency is equal to, or slightly greater than unity. Some of the sinusoidal waveform generators, here we will discussed are Wein bridge oscillator, RC phase shitt oscillator, LC oscillators (Hartley Oscillator, Colpitt's os Clapp Oscillaor) and crystal oscillator, illators, Non-sinusoidal Waveform Generators Most digital systems require some kind of a timing waveform, far instance, a source of triggers pulses is required for all clocked sequential systems. In digital systems, a rectangular waveform most desirable (unlike analog, systems where sinusoidal signals are offen used). The generators of rectangular waveforms are (ERYR) tnsights on EE ECHRONIC VICES AND CIRCUITS ‘Scanned with CamSeannerreferred to as mulli-vibrators. Multivibrators are of three ty pes : astable (or free-running) multivibrator: monostable mnultivibrators (or one-shot) and bistable multivibrators (or flip flops): Until a few years ago, multivibratars used to be designed using giscreterdevicrs, such as vacuum triodes, bipolar junetior pansistor (BIVs), field-effect transistors (PE Ts) ete, which hav pewome obsolete now because of the availability of various ategrated circuits (ICs), The ICs used in multivibraters are opamps (ii) timers (iii) logic gates and (iv) monostable vibrator (MMV). Here, in this chapter we will be dealing with use of opamps transistors, timers, logic gates, flip-flops in non-sinusoidal waveform generators. 5.1 Basic Principles of Sinusoidal Oscillator (or Barkhausen Criteria) An oscillator is a device that generates a periodic, ac out signal without any form of input signal required. The basic structure of oscillator consists of an amplifier which forms a positive feedback (where feedback energy is in phase with the input signal) - loop & frequency selective network as shown in below: Amplifier with gain Ay (Vint BV 0) AgVint BV y) in Summing function positive feedback path with anain [Sb Fig.5.1 Basic Oscillator Configuration ‘Scanned with CamSeannerHere the upper series RC network and the lawer parallel network together produce a zero phase shift atthe fecquen Vow As (Vin BVO) of oscillation. The series RC network (Z; provides : or Vo= AniVo® Ao Vin lag and the parallel RC network (7, . amount of dynamic lead, when it frequency. a dynamic Provides an equi approaches. oscillation | i Ry | When: 1 ~ Ao 0 ie, AoB91 (Aop = loop gain) | —— Ry Hence when As and Vin-+ 0 | 7 Vo= finite value, Z (Series RC) ‘This means output voltage is produced even when no input is given. So this arrangement is called oscillator. And the condition for oscillator (Barkhausen criteria) is as follows; 1) Ao =1 ie. unity loop gain. There should be positive feedback ic. phases difference betveen input & output signal of feedback must be zero. Thus we can see block diagram of an oscillator as below: which has no input in itself & has a closed loop with no summing junction. 2; (Parallel RC) i bee Frequency determining network And the system will oscillate at a frequency which g.5.2(a) Wien Bridge Oscillator satisfies those above conditions i.e. Barkhausen criteria, Fig.5.2(0) Is From the circuit 2x Wi -RIN/(R= IN) Ve Von Za TV v, Lo 5.2 OP-Amp RC Oscillator Circuits ——=SS~S Wien bridge oscillator: Sinusoidal wave generator. Oscillation could also take place when the amplifier as well as the frequency determining, network, both introduces 7er0 phase shifts. This is the principle of Wien bridge oscillator. Traits an ECTRONIC DEVICES AND CIRCUF Insights on ELECTRONIC DEVICES AND CIRCUITS: ‘Scanned with CamSeanner‘At the frequency of zero phase shift ie. frequency of ‘oscillators; We have J - operator vanishes; Oo. X= +R=5, fac 7 ("3aRq Frequency of oscill ra MBE ps volgen ot should provide a voltage gain of at least 3 to n is 3. Hence the ampli produce oscillation, ‘Thus gain for non inverting op-amp (14 fp) sie ea Wien - bridge oscillator with amplitude stabilization: amplifier, Gai Ry Re Practically Rs is not exactly amplifier is not ideal too, So R. that loop gain can be 2K (Component tolerance) & s should be made adjustable so set as necessary to sustain oscillation. In practical case 'Rv' should be made adjustable so the loop gain can be set as necessary to sustain oscillation. In practice gain is made slightly larger i lc slightly larger than 3 to provide smooth continuous oscillation, Non-linear device is use in order to. form automatic gain control. (AGC) Mere, R= Composite aso Ry, Ro, Ro ogeter, & A = (1+Bps Potentiometer pis adjusted to start osilation, As oscillation grows diodes starts to conduct causing, Ru to decrease & the equilibrium will be reached at the output amplitude that sc the loop gain to be u RC phase shift oscillator: (sinusoidal wave generator) RC phase shift oscillator consists of a transistor amplifier which causes 180? phase shift in the signal passing through it & the purpose of 3 cascaded RC sections is to introduce an 1 180" (6'each RC Network) at some frequency of ‘Sxillotion (as shown in below circuit). This simple circuit has rood frequency stability and can be used for very low frequencies. additio ‘Scanned with CamSeannerBase side Collector side (shor circuited) In the above figure, the phase shift network Constant current source the collector current, (uiment is terminated into a short circuit the base current, So the current iysicand isis. The ratio of iv/i is then the amount Cf atenuation of the current when ic finally reaches back to base as is. From figure 2 we have, supplied by a And the final 0 i 1 (i) Where [x1 =555 & Eliminating is is from equation (i), (i) & @) we haves FRR) For 180° phase shift between ix i, the term containing j operation vanishes ie. (-6R?X +X) =0 or, X (OR? + X2) = Osince X20 1 X=tRV6=3556 1 slat , © foe Ja freawency of osilaton substituting X* 6R? in equation (iv) we have RS RU=SR x 6RE+O ratio is 180” out of phase between inf is, And the 29 indicates that feedback loss is 29 times. Hence current gain of 29 is 3p; The minus sign indicates that the —~ necessary from the amplifier fo ” Proper oscillation. Ifthe gai > 29 distortion occurs, aa Gains 29 oscillation can't be sustained smoothly, it decays, 53LC and Crystal Oscillators Lcoscillators (Sine wave oscillator) Hartley oscillator: Fig5.3 (a) Hartley oscillator Here two inductors Lis and Lyy are placed across Cl and formed a tank circuit. Where, Li = Lis * Lis Fig.5.3 () Feedback Circuit TESST sts os erectronic DEVICES AND cincUTTS Insights on ELECTRONIC DEVICES AND CIRCUITS. ‘Scanned with CamSeannera cuit is tumedt on, the capacitor is changed. When Asitor is lly changed, it discharges through Lyf Ey sos sting up osillations of frequency determined py la: at resonance, At resonance voltage is maximum & gain = 1. The output voltage of the amplifier appears across coil Lis & feedback Voltage to amplifier across Lay From the figure of feedback circuit we soe the voltage across Liy is 180° out of phase with the voltage developed across Lis (Vou). A phase shift of 180° jg Produced by the transistor & a further phase shift of 180° jg Produced ty Lu-Ly voltage divider. In this ways circuit rovides positive feedback to produce oscillation, Colpitt's Oscillator Mc) Colpitt’s Oscillator In this, circuit components Ri, Ry Rs, Re& Cr are used to stabilize de biasing of transistor Qs. The capacitor C; is split into Cuxée Cis, And the center point is grounded so that two 1807 out of phase signals are produced TEEN) esr esrecrnonic pevices ano GINCUTTS | | Ts positive feedback is realized as in Hartley. In Colpit’s oscillator the tank resonant circuit consists of L:& ceries Cy, fe Cxz, As we see that Cu is effectively in parallel with Cee (collector to emitter junction capacitance) whereas C; effectively in parallel with Cy (base to emitter junction capacitance). Therefore at high frequencies these junction capacitances affect the frequency of oscillation. And junction capacitances change due to temperature or supply voltage variations, the frequency’ of oscillation also chanzes This kind of effect can be minimized by making Ci: and C= large compared to the transistor junction capacitances. This kind of variation is the circuit is called Clapp oscillator circuit. is if these The frequency of oscillation is given by, 1 Poe Where, Cr = Cn Ce Gata Clapp oscillator: (or Gouriet Oscillator) Fig.5.3 (d) Clapp oscillator: (or Gouriet Oscillator) Tea Trsights on ELECTRONIC DEVICES AND CIRCUITS ‘Scanned with CamSeannerLO Se lator to suit for high We can modify the Colpitt's 0s imizes the effect of Cyt anc frequency applications which nti Cis which means it also minimizes the effects of junction capacitances. [A small capacitor Cs is included in series with the inductor Ly ‘as shown in fig, I's value is usually kept smaller compared to Cu and Cys. This way the resonant frequency is mainly dependent upon the values of Li and Cs of the tank circuit ‘Therefore, very high frequency stability can be achieved in this circuit, Therefore, it may be considered as improved version of Colpitt's oscillator. The frequency oscilla ; , ; frequency oscillation; Fig5.3 () Basic crystal oscillator circuit using Clapp circuit When accuracy and stability of the oscillation frequency are required greatly, then a crystal oscillator is used. The Fesonance property of a crystal is very sharp, That means its frequency of resonance is very narrow & stable In equivalent electrical circuit, Re. Electrical equivalent of resistance; which is property of ‘mal friction or mechanical : crystal structure's inte Crystal oscillator: res Le Electrical equivalent of inductance; which is property of / R crystal structure's mass inertial in mechanics Xtal cu C= Electrical equivalent of capacitance which is property of 7 crystal structure's compliance (elasticity) => analogous c to capacitance ion Cur= Shunt capacitance equivalent to compliance produced / ‘Crystal capsule by the mechanical mounting of the crystal In this oscillator circuit, Laand Cs (of clapp circuit) is replaced Fig53(e) Basic synbo! for crystal : by the erystal module (crystal capsule). The crystal acts as @ rystal and its equivalent resonant tank circuit of oscillator. And the Cirand Ci: ai electrical circu ae the signal voltage between input and output sections. So, the feedback signal comes from a capacitive loop. A crystal module may also be regarded as a series RLC circuit as TEN agemcrcron CDEC ANDO im coms TI MELECIRONC DEES AND CIRCUS — NEE ‘Scanned with CamSeannershown in above figure, with | Quality factor & a sinall capa frequency is almost nati Nees as well large Induct tani nce Of high Qy the resonance ied by the transistor’s junction stray capacitances, When voltage is applied on crystal module, vibrates due Pieveoclectric effect & freq depends upon size & nature, ‘Therefor ext lo icy of oscillation is high & ally a tuned circuit oscillator =? Uses piezcoelectric erystal asa resonant tank circuit ‘The crystal can have two resonant frequencies, One resonant on occurs when the reactances of the series RLC leg are equal & opposite. For this condition, the series resonant impedance is very low (equal to R). ‘The other resonant condition occurs at a higher frequency when the reaction of the seriesresonant leg equals the reactance of capacitor Cy. This is parallel resonance (also called anti-resonance) of crystal, which offers a very high impedance. w oe in f Fig.5.3(y) Crystal impedance Vs frequency 5.4 Generation of Square and Triangular \ Astablo Multi-vibrato 4 OP-Amp Square Wave Generator Jt produces a square wave (rectangular) output who frequency depends upon the charging, or discharging, time of capacitor ued. IEEE] becglts enrnncinonic pivicts ann GNCUTTS Fig.5.4 (a) OP-Amp Square Wave Generator Vefsquare wave) waft 1py, BV, Fig.5. (b) Waveform of oscillator Operation of the circuit Suppose Vo = +Vua & Ve # V" # valtage across capacitor = =f)Vaue ‘Thuy when Vo # + Vas then Vi = 4a & V" = O = Capacitor charges towards +Vsa, exponentially. When V" © Ve exceeds 4f)Vaa Vo becomes -Vuar, 0 when Vo “Ma, Vi# Vor & Vo 41iVea, capacitor discharges ter 4fiVsat towards Vas. After certain ime when Ve exces -f)Veu Vo becomes +Van, When Vo = #Vua te V" # af and V © -fiVea =» Capacitor again charges fram -PVsat towards Te Traigiis on ELECTRONIC DEVICES AND CIKCULTS ‘Scanned with CamSeannerPEELE PEL I EE Ee $PVou. Thus the eyele repeats & it continues producing, square wave output voltage. 1 # Determination of time period Let the time taken to charge the capacitor front = [Vs to [Vou be ty which és equal to & (Le. time of discharging, from 4Vc 10 -Vua), Then time period of square wave is given by Tenth 20st oS EW Zone i) For charging of capacitor using basie formula; Ye () = Vapplied - [Vapplied = Ve (initial le", Where after time ti Veit) = #BYsat; Vena * = BVsat: Vapplied = +Vsat From equation (i) +BVsat = +Vsat [+ Vsat ~(-fVsal)}eavee or, PeT— (1+ fjewite or, (1+ f)e/e= (1p) b Tine pond T= uct EN ee me enerator yrangular Wave square wave, triangular wave can be gy harging, & discharging, of 1 waveform. py integrating, ipcually the integrator the capacitor, providing a | pt Hs /., Imeggaror ere wing ‘Oran Fig.5.4(0 Triangular Wave Generator: Let the output of square wave generator circuit (V1) be Vsat- "Vs ‘Accurrent equal to net will low into resistor R & through capacitor C, causing the output ofthe integeator to Hnearly = Vsat decrease with a slope of "Rc + Because output of an OP comp integrator circuit will be either +Vax oF Vast Vidt (square wave) “LN. Vest Slope “RCs Ast Rice Fig. 5.4(dl) Waveform of oscillator Tesights on its 69 LLECIRONIC DEVICES AND CIRCUITS Teal Trsighis on ELECTRONIC DEVICES AND CIRCUITS ‘Scanned with CamSeannerie Will continue until the {nte lower threshold Vi of the cin AtOF OULPUL reAchen the WL avhich point Vy wit eh st vs ates from + Vat to = Vaal, AU this mone current through Ry C: pl Ry Co will reverse direction &¢ the sui reverse direction & the inte will start to Inerease linearly with a pte the positive threshold of the circuit Vs. At this point Vi will switches Ite state form =Vs eee ate form =Vsat lo #Vsal. And the Square wave generator using Avtable mu (VT Relovation velar en nator (AM) An stable mullivibrator (AMV) hax no stable state, collate between two quanifable state, Thus I generates periodic waveform al output, = ye Yor ‘ i a is | vr | yA) Waveform of Onetttator 1210 oy WME MELECTHONICHIVICINANDCIMCUITN aperation when Veo is applied, collector currents start flowing in Qy awl Qs, In addition, the coupling capacitors Cy and Cy also ‘Marts chargityy up. As the characteristics of no two transistors (ie. B, Vn) are exactly alike, therefore, one transistor Qy will conduct more rapidly than the other Qs. The rising, collector current in Q) drives its collector less positive, which is applied to bone transistor Qs through Cz, Dect ALA (ie. decreasing biasing of Q) will reduce current of Q:, Their actions occur very rapidly & may be considered practically instantaneous. So initial state: Qe cut off # OFF state; Qi # saturation * ON state, So Vins + 0.7V © OV. C2 ously charged to Vec with base of Qe at negative potenti Q) is hept ON by forward bias current through Ri to is base Anal, aw a result, ity collector voltage approaches near ground potential, And Cy charges to Vee with base ney al rapidly. Qe kept OFF by vollage -Vee applied at its base ue: to charged stored In Cy, This fs unstable state, disehary ‘Afler certain time of , Cz completely ischaryes andl then reverse charges 0 40.7 V. Asa restlt, Qs becomes ON. ative pot =) Hach CE amplifier state: provides: strong feedback to ther, The transistors are driven into saturation or cut off Q) is kept ON by forward bias eur Dawe, And ay arent, ily collector voltage apy rear ground potential And Cy charges to Vee vellage With bave negative potential raphy. ‘The cha in Ci (Vex) reverse blaves Qh. Ant so, Qu ts OFF, tutable alate, Cy discharges through Ri, After certain time of te Cr completely discharges and then reverse charger to 40.7¥, Ava test, Qr becomes ONs forcing, Qe Olt. (alo fv tnltial state of op hn avext cycle bey Jon, whic fs just described pemcuns — TEN ‘Scanned with CamSeannerDetermination of time period ‘The time taken to discharge C3 from ~ following basic formula, Ver Vapplied - [Vapplied = Veyaia]e2 taken = ty where, Vea = OV; Vapplied = +Vcc, Ve initial) = ~ Vee & time 0= Vee = [Vcc = (-Vec)]e“2/% on 1 . Similarly, | And time period T= t + tz = (RiCi + R2C:) In 2if R =REG=C, &T=2RCIn2=138RC 1074 TaeRc| frequency of oscillation 5.5 Integrated Circuit Timers Astable Multivibrator (AMV) using 555 timer IC (Square wave Generator): Ri 7] ap Ri sk = EB Ssx Fig.5.5 (a) Astable Multivibrator using 555 timer IC (Square wave Generation) [EGER] Insights on ELECTRONIC DEVICES AND CIRCUITS Vee to OV is given by then it becomes square wave oscillator | operation Suppose the i state is Ve = 0 (capacitor C completely discharged), R ), $= 1. When Ve = 0, R= 0,S=1, result isQ 21, 0 = 0. So pin 7 will be open circuited due to internal transistor at cut off ie. unbiased by Q = 0, base input Go the capacitor 'C’ charges through (Ri + Rs) towards Vcc. lee When, Vo>-g. R = 0, $ = 0 = result is no change. So capacitor continues to charge. Vee When, Vez 275 (equal to V" of comparator 1) R = 1, S = 0 result is Q = 0 and Q = 1; Now pin 7 short circuited to ground due to Q = 1. Capacitor 'C’ starts to Wee discharge through R2 from’ po towards ground. When vert R= 0,$=0, result is no change capacitor continues to discharge. when vex, > R = 0,S=1 result is Q= 1, Q= 0; Now pin7 i (0 Q = 0. The capacitor starts charging again open reed de oS lessly, And the capacitor towards Vec. Ths ation continues en y charges and discharges between3 1023 9" Determination of time period: Ye clei dpe weir | | Fig5 W) Waveform mms TEST Traghis on ELECTRONIC DEVICES AND CIRCU ‘Scanned with CamSeanner TET ISLett = charging time of ‘© changing time of © | Ve (8) = Vagysog = [Vapptiot = Vinal 4708, IE Vapytnt~ [Vapyiat = Vaal] 8/3 For Charging: ety RC (Rr +RJCIN2 For discharging; 1. Wee=0-[o- =EERCng b+ = (Rr FIRJCIn2 ' When 2R5> Ri- then Ry + 28:= 2Re [. T=2R: Cin 2.0 TTR a Voltage controlled oscillator using IC 555: Voltage controlled oscillator is sometimes called a voltage to frequency converter because an input voltage can change the output frequency. By adjusting potentiometer, we can change control voltage Veon. TERRY incites on LecrnOnic DEVICES AND: CIRCUITS [0 Ve Ry 3 Fi 0 Output Ry ra 6 555 3 : 2 \Veon Fig.5.5(c) Voltage controlled oscillator using IC 555: ve Ve varies between +5 and + Veon. If we increase Veon, it takes capacitor longer to charge and discharge so frequency decreases, So we can change frequency of circuit by varying control voltage Let tyand tz be the time taken to charge & discharge capacitor 'C respectively. Then Ve (ti) = Vappica~ [Vapptsa ~ Ve ita] 8 & Ve (ts) = Vappia ~ [Vapptint~ Vesnnaile“a/ 2° Voor] | ig os For charging, Veon=Vec-[Vec-~3 u (te: osvean) ot Te RAC ML Vee= Veon ioc -05Vcon) or, = (R+RICINO Yeo Veon ) For discharging Yeon 2 Trsights on ELECTRONIC DEVICES AN =0-[0- Veon}e'yC parcurs Teel ‘Scanned with CamSeannerWw Sh=RCin2 ++ Total time period =m RICIn(S 05Vcor con + Ric ina ana f 5.6 Precision Rectifier Circuit Provision roster circuit considered asa special clas of wave shaping circult used in design of instrumentation systems where the need arises for rectifier circuits with very precise transfer characteristics. ae Superdiode Fig.5.6 (a) Precision Rectifier Circuit Vou Vie {eal Transfer Characteristics For positive input cycle output voltage of r ut ¢y ut voltage of op-amp will go positive & the diode will conduct, thus cstablishing closed feedback path between the op-amp's output terminal & negative input terminal. This negative feedback path will cause a virtual short circuit to appear between the two i terminals of the op-amp. eines Ve for V.20 TES] er attectnonic pevicts ann GRCULTS Note that the offset voltage half wave rectifier circui : Oo") exhibited in the simple small voltage equal to the diode drop divided by the op- famp's open-loop gain. This makes the circuit suitable for applications involving very small signals, + "Configuration obtained with an op-amp in order to have a circuit behaving an ideal diode & rectifier.” + Used for high precision signal processing. + Actual threshold of super diode is very close to zero actual threshold of diode ee gain of op-amp Describe “Barkhausen Criteria” for oscillation. Write down the general expression for the gain of a feedback amplifier, and state the condition of oscillation. illator and Draw a circuit diagram of RC sinusoidal explain its working principle. Explain the working principle of square wave generator circuit and determine its oscillation frequency Draw Wien Bridge Oscillator circuit and write the expression for frequency of oscillation. 3. Define oscillator. Explain how you can generate square wave using an op-amp. Design an oscillator for producing an output of 2 KHz frequency. 6 Draw and explain AMV circuit using IC 535 or BIT “7. Define the term multivibrator. Explain the operation chon | vibrator with the help of circuit amp based a stable mul diagram and waveform. Write the applications of tu Colpitt’s oscillator circuit an frequency of oscillation. 9%. Draw the square wave generator circuit using op-amp- scillator circuits. mned LC oscillators. Draw the dd derive the expression for 10. Draw different types of LC aann REE nRRNERBNNSINE= > coecurre mele eal cb Taights on ELECTRONIC DEVICES AND CIRCUITS & ‘Scanned with CamSeanner