2. Chapter 4 without an external signal source Oscillator is an electronic circuit that generates a periodic waveform on its output without an external signal source. It is used to convert dc to ac. The waveform can be sine wave, square wave, triangular wave, and sawtooth wave. Fig. 4-1: Basic oscillator concept showing three types of output waveforms. Sine wave Square wave Sawtooth wave

3. Chapter 4 sinusoidal oscillator If the output signal varies sinusoidally, the circuit is referred to as a sinusoidal oscillator. pulse or square-wave oscillator If the output voltage rises quickly to one voltage level and later drops quickly to another voltage level, the circuit is referred to as a pulse or square-wave oscillator.

4. Chapter 4 Oscillators are widely used in most communications system as well as in digital systems, including computers, to generate required frequencies and timing signals. Based on the waveform, oscillators are divided into following two groups: 1.Sinusoidal (or harmonic) 1.Sinusoidal (or harmonic) oscillators—which produce an output having sine waveform. 2.Non-sinusoidal (or relaxation) 2.Non-sinusoidal (or relaxation) oscillators—which produce an output having square, rectangular or sawtooth waveform or is of pulsa shape.

5. Chapter 4 portion of the output signal is fed back to the input Feedback oscillators operation is based on the principle of positive feedback, where a portion of the output signal is fed back to the input. There are five types of feedback oscillators to produce sinusoidal outputs: 1.Phase-shift oscillator; 2.Wien bridge oscillator; 3.Colpitts oscillator; 4.Hartley oscillator; 5.Crystal oscillator; Using RC circuits Using LC circuits

6. Chapter 4 oscillation Fig. 2 illustrates the creation of a loop in which causes the signal reinforces its self and sustains a continuous output signal. This phenomenon is called oscillation. The requirements for oscillation are:  the loop gain βA is greater than unity;  the phase-shift around the feedback network is 180 o (providing positive feedback). ViVi V o = AV i A β + - V f = β(AV i ) + - + - + - Fig. 2: Feedback circuit used as an oscillator.

7. Chapter 4 Fig. 3: Idealized phase-shift oscillator. phase-shift oscillator Fig. 3 shows a circuit containing three RC circuits in its feedback network called the phase-shift oscillator. The three RC circuits combine to produce a phase shift of 180 o.

8. Chapter 4 This circuit is drawn to show clearly the amplifier and feedback network. Fig. 4: Phase-shift oscillator circuits: (a) FET version; (b) BJT version.

9. Chapter 4 an inverting amplifierthree RC circuits The IC phase-shift oscillator consist of an inverting amplifier for the required gain and three RC circuits for the feedback network. The inversion of the op-amp itself provides the additional 180 o to meet the requirement for oscillation of a 360 o phase shift around the feed back loop. Fig. 5: Phase-shift oscillator using an op-amp.

10. Chapter 4 rad/sec The oscillation frequency in rad/sec can be calculated using the following equation: (4-1)

11. Chapter 4 Fig. 6: Wien bridge oscillator using an op-amp. low-frequency RC oscillators The Wien bridge oscillator is one of the more commonly used low-frequency RC oscillators. It contains an op- amp and two feedback networks.

12. Chapter 4 frequency-adjustment elements Resistors R 1 and R 2 and capacitors C 1 and C 2 form the frequency-adjustment elements. feedback path Resistors R 3 and R 4 form part of the feedback path. The op-amp output is connected as the bridge input at points a and c. The bridge circuit output at points b and d is the input to the op-amp.

13. Chapter 4 The analysis of the bridge circuit results in: and the resonant frequency of the Wien bridge oscillator is (4-2)

14. Chapter 4 If, in particular, the values are R 1 = R 2 = R and C 1 = C 2 = C, the resulting oscillator frequency is and (4-3)

15. Chapter 4 LC circuit The Colpitts oscillator is a type of oscillator that uses an LC circuit in the feed-back loop. tapped capacitors(C 1 and C 2 ) an inductor L The feedback network is made up of a pair of tapped capacitors (C 1 and C 2 ) and an inductor L to produce a feedback necessary for oscillations. The output voltage is developed across C 1. The feedback voltage is developed across C 2. Fig. 7: Colpitts oscillator.

16. Chapter 4 For a Colpitts configuration, the oscillator frequency is set by an LC feedback network and given as: where, (4-4)

17. Chapter 4 The Hartley oscillator is almost identical to the Colpitts oscillator. tappedinductors (L 1 and L 2 )a single capacitor C The primary difference is that the feedback network of the Hartley oscillator uses tapped inductors (L 1 and L 2 ) and a single capacitor C. Fig. 8: Hartley oscillator.

18. Chapter 4 The oscillator frequency is given by with (4-5)

19. Chapter 4 extremely stable output output fluctuation Most communications and digital applications require the use of oscillators with extremely stable output. Crystal oscillators are invented to overcome the output fluctuation experienced by conventional oscillators. Crystals used in electronic applications consist of a quartz wafer held between two metal plates and housed in a a package as shown in Fig. 9 (a) and (b). Fig. 9: A quartz crystal.

20. Chapter 4 piezoelectric The quartz crystal is made of silicon oxide (SiO 2 ) and exhibits a property called the piezoelectric. When a changing an alternating voltage is applied across the crystal, it vibrates at the frequency of the applied voltage. In the other word, the frequency of the applied ac voltage is equal to the natural resonant frequency of the crystal. The thinner the crystal, higher its frequency of vibration. This phenomenon is called piezoelectric effect.

21. Chapter 4 The crystal can have two resonant frequencies; One is the series resonance frequency f 1 which occurs when X L = X C. At this frequency, crystal offers a very low impedance to the external circuit where Z = R. The other is the parallel resonance (or antiresonance) frequency f 2 which occurs when reactance of the series leg equals the reactance of C M. At this frequency, crystal offers a very high impedance to the external circuit. R L C CMCM R Fig. 10: Crystal impedance versus frequency.

22. Chapter 4 Fig. 11: Crystal oscillator using a crystal (XTAL) in a series-feedback path. BJT FET The crystal is connected as a series element in the feedback path from collector to the base so that it is excited in the series-resonance mode. Pierce The circuit was suggested by Pierce.

23. Chapter 4 Since, in series resonance, crystal impedance is the smallest that causes the crystal provides the largest positive feedback. Resistors R 1, R 2, and R E provide a voltage-divider stabilized dc bias circuit. Capacitor C E provides ac bypass of the emitter resistor, R E to avoid degeneration. The RFC coil provides dc collector load and also prevents any ac signal from entering the dc supply. The coupling capacitor C C has negligible reactance at circuit operating frequency but blocks any dc flow between collector and base. The oscillation frequency equals the series-resonance frequency of the crystal and is given by: (4-6)

24. Chapter 4 relaxation oscillator The unijunction transistor can be used in what is called a relaxation oscillator as shown by basic circuit of Fig. 12. The unijunction oscillator provides a pulse signal suitable for digital-circuit applications. Resistor R T and capacitor C T are the timing components that set the circuit oscillating rate. Fig. 12: Basic unijunction oscillator circuit. UJT

25. Chapter 4 Fig. 13 shows three waveforms that can be expected from the UJT oscillator. Sawtooth wave appears at the emitter of the transistor. This wave shows the gradual increase of capacitor voltage.

26. Chapter 4 The oscillating frequency is calculated as follows: where, η = the unijunction transistor intrinsic stand- off ratio. Typically, a unijunction transistor has a stand-off ratio from 0.4 to 0.6. (4-7)