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364 Principles of Electronics14.1Sinusoidal Oscillator14.2Types of Sinusoidal Oscillations14.3Oscillatory Circuit14.4Undamped Oscillations fromTank Circuit14.5Positive Feedback Amplifier —Oscillator14.6Essentials of TransistorOscillator14.7Explanation of BarkhausenCriterion14.8Different T...

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Sinusoidal Oscillators 36514.1 Sinusoidal OscillatorAn electronic device that generates sinusoidal oscillations of desired frequency is known as a *sinu-soidal oscillator.Although we speak of an oscillator as “generating” a frequency, it should be noted that it does notcreate energy, but ...

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366 Principles of Electronics(ii) Undamped oscillations. The electrical oscillations whose amplitude remains constant withtime are called undamped oscillations. Fig. 14.1 (ii) shows waveform of undamped electrical oscil-lations. Although the electrical system in which these oscillations ...

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Sinusoidal Oscillators 367Waveform. If there were no losses in the tank circuitto consume the energy, the interchange of energy between Land C would continue indefinitely. In a practical tank cir-cuit, there are resistive and radiation losses in the coil anddielectric losses in the capacito...

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368 Principles of ElectronicsIf these conditions are fulfilled, the circuit will produce continuous undamped output as shown inFig. 14.4.14.5. Positive Feedback Amplifier — OscillatorA transistor amplifier with proper positive feedback can act as an oscillator i.e., it can generateoscilla...

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Sinusoidal Oscillators 369sinusoidal output with no external signal source. The following points may be noted carefully :(a) A transistor amplifer with proper positive feedback will work as an oscillator.(b) The circuit needs only a quick trigger signal to start the oscillations. Once the o...

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370 Principles of Electronics(i) Mathematical explanation. The voltage gain of a positive feedback amplifier is given by;Avf=1vvvAmA−If mv Av= 1,thenAvf → ∞.We know that we cannot achieve infinite gain in an amplifier. So what does this result infer inphysical terms ? It means ...

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Sinusoidal Oscillators 37114.9 Tuned Collector OscillatorFig.14.9 shows the circuit of tuned collector oscillator. It contains tuned circuit L1-C1 in the collectorand hence the name. The frequency of oscillations depends upon the values of L1 and C1 and is givenby :f =1112LCπ...(i)The feed...

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372 Principles of Electronicsreceiver makes use of an LC tuned circuit with L1 = 58.6 μH and C1 = 300 pF. Calculate thefrequency of oscillations.Solution.L1= 58.6 μH = 58.6 × 10−6 HC1= 300 pF = 300 × 10−12 FFrequency of oscillations, f =1112LCπ=6121258.61030010−−π×××H...

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Sinusoidal Oscillators 373*Note that C1 − C2 − L is also the feedback circuit that produces a phase shift of 180°.Circuit operation. When the circuit is turned on, the capaci-tors C1 and C2 are charged. The capacitors discharge through L,setting up oscillations of frequency determined...

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374 Principles of ElectronicsFig. 14.12Example 14.4. A 1 mH inductor is available. Choose the capacitor values in a Colpitts oscilla-tor so that f = 1 MHz and mv = 0.25.Solution.Feedback fraction,mv=12CCor0.25 =12CC∴ C2 = 4C1Nowf =12TLCπorCT=236 211(2)(110 ) (2110 )Lf−=π×π × × =...

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Sinusoidal Oscillators 375Fig. 14.13Circuit operation. When the circuit is turned on, the capacitoris charged. When this capacitor is fully charged, it discharges throughcoils L1 and L2 setting up oscillations of frequency determined by*exp. (i). The output voltage of the amplifier appears...

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376 Principles of ElectronicsFig. 14.15∴Operating frequency, f =12TLCπ = 612121140102010−−π××× Hz= 1052 × 103 Hz = 1052 kHz(ii)Feedback fraction, mv=211001000LHLHμ=μ = 0.1Example 14.6. A 1 pF capacitor is available. Choose the inductor values in a Hartley oscillator...

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Sinusoidal Oscillators 377Good frequency stability and waveform can be obtained from oscillators employing resistiveand capacitive elements. Such amplifiers are called R-C or phase shift oscillators and have theadditional advantage that they can be used for very low frequencies. In a phase ...

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378 Principles of Electronicsf0=126RCπ...(i)whereR1= R2 = R3 = RC1= C2 = C3 = CCircuit operation. When the circuit is switched on, it produces oscillations of frequency deter-mined by exp. (i). The output E0 of the amplifier is fed back to RC feedback network. This networkproduc...

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Sinusoidal Oscillators 379R3, R2C2 and tungsten lamp Lp. Resistances R3 and Lp are used to stabilise the amplitude of theoutput. The transistor T1 serves as an oscillator and amplifier while the other transistor T2 serves asan inverter (i.e. to produce a phase shift of 180º). The circuit ...

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380 Principles of ElectronicsExample 14.9. In the Wien bridge oscillator shown in Fig. 14.18, R1 = R2 = 220 kΩ andC1 = C2 = 250 pF. Determine the frequency of oscillations.Solution.R1= R2 = R = 220 kΩ = 220 × 103 ΩC1= C2 = C = 250 pF = 250 × 10−12 FFrequency of oscillat...

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Sinusoidal Oscillators 381Quartz crystal. Quartz crystals are generally used in crystal oscillators because of their greatmechanical strength and simplicity of manufacture. The natural shape of quartz crystal is hexagonalas shown in Fig. 14.19. The three axes are shown : the z-axis is call...

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382 Principles of Electronics(ii) When a crystal vibrates, *it is equivalent to R –L – C series circuit. Therefore, the equivalentcircuit of a vibrating crystal is R – L – C seriescircuit shunted by the mounting capacitance Cmas shown in Fig. 14.21 (ii).Cm = mounting capacitanceR...

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Sinusoidal Oscillators 383resonant circuit. For this condition, the impedance of the crystal is very low; being equal toR. The frequency at which the vibrating crystal behaves as a series-resonant circuit is calledseries-resonant frequency fs. Its value is given by:fs=12LCπ Hzwhere L is i...

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384 Principles of Electronicsresonance caused by L and (C1 + C2), we have the parallel resonance of the crystal. At parallelresonance, the impedance of the crystal is maximum. This means that there is a maximum voltagedrop across C1. This in turn will allow the maximum energy transfer th...

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Sinusoidal Oscillators 38510. In a phase shift oscillator, the frequencydetermining elements are ...........(i) L and C(ii) R, L and C(iii) R and C(iv) none of the above11. A Wien bridge oscillator uses ...........feedback.(i) only positive(ii) only negative(iii) both positive and negative(iv...

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386 Principles of Electronics(iii) a phase shift around the feedback loopof 0º(iv) a gain around the feedback loop of lessthan 118. A second condition for oscillations is ..........(i) a gain of 1 around the feedback loop(ii) no gain around the feedback loop(iii) the attenuation of the fee...

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Sinusoidal Oscillators 387Answers to Multiple-Choice Questions1. (ii)2. (iii)3.(i)4. (iv)5. (ii)6. (i)7. (iii)8.(i)9. (ii)10. (iii)11. (iii)12. (i)13.(i)14. (iv)15. (ii)16. (ii)17. (iii)18.(i)19. (iv)20. (ii)21. (iii)22. (iii)23.(iv)24. (i)25. (ii)26. (iii)27. (iv)28.(iv)29. (i)30. (i)Chapter...

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388 Principles of Electronics4. For the Hartley oscillator shown in Fig. 14.25, C = 250 pF, L1 = 1.5 mH, L2 = 1.5 mH and M = 0.58mH. Determine the operating frequency.[159.2 kHz]Fig. 14.255. A crystal has L = 3H, C = 0.05 pF, R = 2 kΩ and Cm = 10 pF. Calculate the series-resonant andpar...