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Chapter 4 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. Sine wave Square wave Sawtooth wave Fig. 4-1: Basic oscillator concept showing three types of output waveforms. Chapter 4 If the output signal varies sinusoidally, the circuit is referred to as a sinusoidal 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. Chapter 4 Based on the waveform, oscillators are divided into following two groups: 1. Sinusoidal (or harmonic) oscillators—which produce an output having sine waveform. 2. Non-sinusoidal (or relaxation) oscillators—which produce an output having square, rectangular or sawtooth waveform or is of pulsa shape. Oscillators are widely used in most communications system as well as in digital systems, including computers, to generate required frequencies and timing signals. Chapter 4 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; Using RC circuits 2. Wien bridge oscillator; 3. Colpitts oscillator; Using LC circuits 4. Hartley oscillator; 5. Crystal oscillator; 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. Chapter 4 The requirements for oscillation are: the loop gain βA is greater than unity; the phase-shift around the feedback network is 180o (providing positive feedback). + Vi - + A + Vo = AVi - β + Vf = β(AVi) - - Fig. 2: Feedback circuit used as an oscillator. Chapter 4 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 180o. Fig. 3: Idealized phase-shift oscillator. 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. Chapter 4 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 180o to meet the requirement for oscillation of a 360o phase shift around the feed back loop. Fig. 5: Phase-shift oscillator using an op-amp. Chapter 4 The oscillation frequency in rad/sec can be calculated using the following equation: 1 0.065 f RC 2 6 RC 1 29 (4-1) Chapter 4 The Wien bridge oscillator is one of the more commonly used low-frequency RC oscillators. It contains an opamp and two feedback networks. Fig. 6: Wien bridge oscillator using an op-amp. Chapter 4 Resistors R1 and R2 and capacitors C1 and C2 form the frequency-adjustment elements. Resistors R3 and R4 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. Chapter 4 The analysis of the bridge circuit results in: R3 R1 C2 R4 R2 C1 and the resonant frequency of the Wien bridge oscillator is 1 fo 2 R1C1 R2C2 (4-2) Chapter 4 If, in particular, the values are R1 = R2 = R and C1 = C2 = C, the resulting oscillator frequency is 1 fo 2 RC and R3 2 R4 (4-3) Chapter 4 The Colpitts oscillator is a type of oscillator that uses an LC circuit in the feed-back loop. The feedback network is made up of a pair of tapped capacitors (C1 and C2) and an inductor L to produce a feedback necessary for oscillations. The output voltage is developed across C1. The feedback voltage is developed across C2. Fig. 7: Colpitts oscillator. Chapter 4 For a Colpitts configuration, the oscillator frequency is set by an LC feedback network and given as: 1 fo 2 LCeq where, C1C2 Ceq C1 C2 (4-4) Chapter 4 The Hartley oscillator is almost identical to the Colpitts oscillator. The primary difference is that the feedback network of the Hartley oscillator uses tapped inductors (L1 and L2) and a single capacitor C. Fig. 8: Hartley oscillator. Chapter 4 The oscillator frequency is given by 1 fo 2 Leq C with Leq L1 L2 (4-5) Chapter 4 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. Chapter 4 The quartz crystal is made of silicon oxide (SiO2) 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. Chapter 4 The crystal can have two resonant frequencies; R One is the series resonance frequency f1 which occurs when XL = XC. At this frequency, crystal offers a very low impedance to the external circuit where Z = R. L C The other is the parallel resonance (or antiresonance) frequency f2 which occurs when reactance of the series leg equals the reactance of CM. At this frequency, crystal offers a very high impedance to the external circuit. R Fig. 10: Crystal impedance versus frequency. CM 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. Chapter 4 The circuit was suggested by Pierce. BJT FET Fig. 11: Crystal oscillator using a crystal (XTAL) in a series-feedback path. Since, in series resonance, crystal impedance is the smallest that causes the crystal provides the largest positive feedback. Chapter 4 Resistors R1, R2, and RE provide a voltage-divider stabilized dc bias circuit. Capacitor CE provides ac bypass of the emitter resistor, RE to avoid degeneration. The RFC coil provides dc collector load and also prevents any ac signal from entering the dc supply. The coupling capacitor CC 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: 1 fo 2 LCC (4-6) Chapter 4 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. UJT Resistor RT and capacitor CT are the timing components that set the circuit oscillating rate. Fig. 12: Basic unijunction oscillator circuit. 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. The oscillating frequency is calculated as follows: Chapter 4 1 fo RT CT ln 1 / 1 (4-7) where, η = the unijunction transistor intrinsic stand- off ratio. Typically, a unijunction transistor has a stand-off ratio from 0.4 to 0.6.