Feedback Amplifier & Oscillators

256 UNIT 5 Feedback Amplifier & Oscillators 5.1 Learning Objectives Study definations of positive /negative feedback. Study the camparions of positive and negative feedback. Study the block diagram and working of negative feedback types of negative feedback. Study the conditions to get oscillations,block diagram of positive feedback,derivation over all gain of an oscillator. Study of types of oscillators working,expressions of frequency of RC Phase shift, Collector tuned,heartly,collpits oscillators. Study of comparisions of RC and LC oscillators. Study of crystal oscillators working advantages. Study of applications of oscillators.

Paper - II Electronic Devices and Circuits 257 5.0 Introduction of Feedback Amplifiers The phenomenon of feeding a portion of the output energy back to the input circuit is known as feedback. The effect results in a dependence between the output and the input and an effective control can be obtained in the working of the circuit. Feedback is of two types. 1. Positive Feedback 2. Negative Feedback Positive or regenerate feedback: When the feedback voltage or current, is in phase with the input signal, it is called positive or regenerative feedback. The positive feedback increases the amount of amplification. Negative or Degenerate feedback: When the feedback voltage or current,is out of phase to the input signal,it is called negative or degenerative feedback. Negative feedback decreases the magnitude of amplification. Its main advantage is the reduction in the distortion of the amplifier. Feedback: The process of injecting a fraction of output energy of some device back to the input is known as feedback. Depending upon whether the feedback energy aids or opposes the input signal, there are two basic types of feedbacks in amplifiers. These are. 1. Positive Feedback 2. Negative Feedback 1. Positive Feedback: In positive feedback, the feedback energy (voltage or currents), is in phase with the input signal and thus aids it. Positive feedback increases gain of the amplifier also increases distortion, noise and instability. Because of these disadvantages, positive feedback is seldom employed in amplifiers. But the positive feedback is used in oscillators. 2. Negative Feedback: In negative feedback, the feedback energy (voltage or current), is out of phase with the iput signal and thus opposes it. Negative feedback reduces gain of the amplifier. It also reduce distortion, noise and instability. This feedback increases bandwidth and improves input and output impedances. Due to these advantages, the negative feedback is frequetly used in amplifiers.

258 5.1 Comparision Between Positive and Negative Feed Back The difference between positive and negative feedback is, S.No. 1. 2. 3. 4. 5. 6. Negative Feedback Feedback energy is out phase with their input signal Gain of the amplifier decreases Gain stability increases Noise and distortion decreases. Increase the band width Used in amplifiers Positive Feedback Feedback energy is in phase with the input signal. Gain of the amplifier increases Gain stability decreases Noise and distribution increases. Decreases bandwidth Used in Oscillators 5.2 Expression for the Gain of Feedback Amplifier The configuration of the feedback amplifer in its shortest form in shown in Fig 5.1 The feedback factor of the feedback network is given by = X f / X o where X f and X o are feedback and output signals respectively. The input to the amplifier is X s. The gain of the basic amplifiers is A. Therefore, Output sigal X o = AX i where X i is the input signal to the basic amplifier which is equal to difference signal X d. Therefore X o = AX d But for negative feedback X d = X s - X f = X i Therefore X o = A(X f - X f ) We know that = X f / X o or X f = X o Substituting this value is Eqn X o = A(X s - X o ) X o + A X o = AX s X o (1+A ) = AX s

Paper - II Electronic Devices and Circuits 259 X o = AX s / 1 + A The gain of feedback amplifier is A f = X o / X s = A / 1+A Here, A f is less than A giving in reduction in gain. If positive feedback employs, in deominator is - (minus) ad therefore gain increase. Fig. 5.1 Block Diagram of Simplified Single loop Negative Feedback amplifier Effects of Negative Feedback: The following are the advantages of negative feedback in amplifies. 1. Gain Stability: An important advantage of negative feedback is that the resultant gain of the amplifier can be made independent of transistor parameters or the supply voltage variations. A f = (A) /(1+ A ) The product of A is much greater than unity. Therefore in above relation 1 can be neglected as compared to A. Then, the expression becomes. A f = (A / A = (1 / It may seen that the gain now depends only upon feedback fraction. The feedback circuit is usually resistive network. Therefore, it is uneffected by changes in temperature variations in transistor parameters ad frequency. Hence, the gain of the amplifier is extremly stable. 2. Reduces Non-Linear Distortion: The negative feedback reduces,with the non linear distortion in large signal amplifiers. It can be proved mathematically,giventhat D f = (D) / (1 + A )

260 It is clear from the above equation that, a negative feedback reduces the distortion by factor 1 + A. 5.3 Types of Nagative Feedback Amplifiers The feedback amplifiers can be classified according to mixing and sampling employed to it as follows: 1. Voltage series feedback amplifier 2. Current series feedback amplifier 3. Current shunt feedback amplifier 4. Voltage shunt feedback amplifier 1. Voltage Series Feedback Amplifier: This uses output voltage sampling and series mixing. 2. Current Series Feedback Amplifier: This uses output current sampling and series mixing. 3. Current Shunt Feedback Amplifier: This uses output current sampling and shunt mixing. 4. Voltage Shunt Feedbac Amplifier: This uses output voltage sampling and shunt mixing. 5.4 Conditions of an oscillators - Barkhausen Criteron Oscillations produced by adequate positive feedback in an amplifier is called a feedback oscillator. Fig. 5.02 gives the block diagram of feedback oscillator. An amplifier is an essential part of an oscillator. Oscillations may be produced by adequate positive feedback in an amplifier. Fig. 5.2 Block diagram of an Oscillator

Paper - II Electronic Devices and Circuits 261 Consider an external signal Xs applied directly to the input terminals of the amplifier shown in Fig.5.03. This results in an output signal X o. The output of the feedback network is. X f = X o = A X s This output of the mixing network is X 1 f = -X f = -A X s Let it be so arranged that X 1 is identical with X. If now the external source f s is removed and terminal 2 is connected to terminal 1, the amplifier continues to provide the same output voltage X o as before without any exteral input signal. The system then functions as an oscillator. The condition necessary for oscillations is that X 1 = Xs. Thus the instantaneous values f X1 and X are identical at all f s times. Since X 1 = -A X implies that -A =1 i.e., the loop gain must be equal to f s unity and phase angle of -A is zero. This condition for sustained oscillations is called the Barkhausen criterion. Barkhausen Criterion: 1. Sustained oscillations are produced in a sinusoidal oscillators at a frequency for which the total phase shift introduced,as the signal travels from the input terminal through the basic amplifier, feedback network and mixing network back to the input terminals its precisely zero or a integral multiple of 2 radians. 2. Sustained oscillations are not produced if at the oscillation frequency the magnitude of the loop gain i.e., the product of the transfer gain A, of amplifer and magnitude of the feedback factor of the feedback network is less than unity. Requisites of an Oscillator 1. Tank Circuit: It consists of inductor connected in parallel with capacitor C. The frequency of oscillations in the circuit depends upon the values of inductance (L) ad capacitace (C). In RC oscillators inductor replaced by resistor(r). 2. Transistor Amplifier: The transistor amplifier receives d.c power from the battery and changes it into a.c. power for supplying to the tank circuit. The oscillations occurring in the tank circuit are applied to the input of the transistor amplifier. The amplified output of oscillations is due to the d.c. power supplied by the battery. The output of the transistor can be supplied the tank circuit to meet the losses. 3. Feedback Circuit: The feedback circuit supplies a part of collector energy

262 to the tank circuit in correct phase to aid the oscillations i.e., it provides positive feed back. In oscillator is to satisfy Barkhausen criteria has to get sustained oscillations. 5.5 Classification of Oscillators The oscillators can be classified in the following ways. 1. According to the generated waveform. (a) Sine wave oscillators. (b) Relaxation or non-sinusoidal oscillators. 2. According to the fundemental mechanism involved (a) Feedback oscillators. (b) Negative resistance oscillators. 3. According to the associated circuit components (a) RC oscillators (b) LC oscillators (c) Cyrstal oscillators 4. According to the frequency range: (a) Audio frequency (AF) oscillators (b) Radio frequency (RF) oscillators (c) VHF or microwave oscillators. 5.5.1 A > 1 When the total phase shift around a loop is 0 0 or 360 0 and A >1, then the output oscillates but the oscillations are of growing type. The amplitude of oscillations goes on increasing as shown in Fig. 5.3 Fig. 5.3 Growing type of Oscillations

Paper - II Electronic Devices and Circuits 263 5.5.2 A = 1 As stated by Barkhausen criterion, when total phase shift around a loop is 0 0 or 360 0 ensuring positive feedback and A = 1 then the oscillations are with constant frequency and amplitude called sustained oscillations. Such oscillations are shown in Fig 5.4 5.5.3 A < 1 Fig. 5.4 Sustained Oscillations When total phase shift around a loop is 0 0 or 360 0 but A < 1 then the oscillations are of decaying type i.e. such oscillation amplitude decreases exponentially and the oscillations finally cease. Thus circuit works as an amplifier without oscillations. The decaying oscillations are shown in Fig 5.5. Fig. 5.5 Exponentially decaying Oscillations

264 Classification of Oscillators As type of tank circuit employ to the amplifier circuit in positive feedback the following oscillators. 1. RC Phase Shift Oscillator 2. Collector Tuned Oscillator 3. Hartley Oscillator 4. Collpitt s Oscillator 5.6 RC Phase Shift Oscillator Fig.5.06 shows the circuit of a phase shift oscillator. It consists of a conventional single transistor amplifier and a RC Phase shift network. The phase shoft network consists of three sections R 1 C 1, R 2 C 2 and R 3 C 3. At some particular frequency f 0, the phase shift of each section is 60 0, so that the total phase-shift produced by the RC network is (3 x 60) = 180 0. The frequency of oscillations is given by f o = ( 1 ) / ( 2 RC 6) where R 1 = R 2 = R 3 = R C 1 = C 2 = C 3 = C Figure 5.6 RC Phase Shift Oscillator

Paper - II Electronic Devices and Circuits 265 With the circuit is switched ON, it produces oscillations. The output E 0 of the amplifier is feedback to RC feedback network. This network produces a phase shift of 180 0 and a voltage E 1 appears at its output which is applied to the transistor amplifier. The feedback factor = E 1 / E 0. It can be shown that the feedback factor of the RC network is = 1/29. This expression has an important significance. For self starting the oscillations we must have A >1. It means that gain A of the amplifier must be greater than 29. Only then the oscillations can start. The feedback phase is correct. A phase shift of 180 0 is produced by the transistor amplifier. A further phase shift of 180 0 is produced by the RC network. As a result, the phase around the entire loop is 360 0. Advamtages : 1. It does not require transformers or inductors. 2. It can be used to produce very low frequencies. 3. The circuit provides good frequency stability. Disadvantages : 1. It is difficult for the circuit to start oscillations as the feedback is generally small. 2. The circuit gives small output. 5.7 Tuned Collector Oscillator The tuned collector oscillator contains tuned circuit L 1 -C 1 in the collector load.the feedback coil L 2 in the base circuit is magnetically coupled to the tank circuit coil L 1.and hence the name. The frequency of oscillations depends upon the values of L 1 and C 1 and is given by f = ( 1 ) / (2 L 1 C 1 ) The figure coil L 2 in the base circuitis magnetically coupled to the tank circuit L 1. In practice L 1 and L 2 form the primary and secondary of the transformer. The biasing is provided by potential divider arrangement. The capacitor C connected in the base circuit provides low reactance path to the oscillations.

266 Circuit Operation: Fig. 5.7 When switch S is closed. Collector current starts increasing and charges the capacitor C 1. When this capacitor is fully charged, it discharges through Coil L 1, setting up oscillations of frequency. f = ( 1 ) / (2 L 1 C 1 ) These oscillations induce some voltage in coil L 2 by mutual induction. The frequency of voltage of coil L 2 is the same as that of tank circuit but its magnitude depends upon the number of turns of L 2 and coupling between L 1 and L 2. The voltage acaross L 2 is applied between base and emitter and appears in the amplified form in the collector circuit, thus overcoming the losses occurring in the tank circuit. The number of turns of L 2 and coupling between L 1 and L 2 are so adjusted that oscillations across L 2 are amplified to a level just sufficient to supply losses to the tank circuit. It may be noted that the phase of feedback is correct i.e., energy supplied to the tank circuit is in phase with the generated oscillations. A phase shift of 180 0 is created between the voltages of L 1 and L 2 due to transformer action. A further phase shift of 180 0 takes place between base-emitter and collector circuit due to transistor properties. As a result the energy feedback to the tank circuit is in phase with the generated oscillations. 5.8 Hartly Oscillator Hartly oscillator is very popular and is commonly used as a local oscillator in radio receivers. Fig.5.8 shows the circuit of Hartley oscillator. The tank circuit is made up

Paper - II Electronic Devices and Circuits 267 of C L 1 and L 2. The coil L 1 is inductively coupled to coil L 2, the combination functions as auto-transformer. The self bias is provided here for biasing. the capacitor C b blocks the d.c. component. When the power is ON, collector current starts rising and charges the capacitor C. When the capacitor is fully charged, it discharges through coils L 1 and L 2 setting up oscillations of frequency. f = ( 1 ) / ( 2 (L 1 +L 2 ) C) Fig. 5.8 Hartley Oscillator The oscillations across L 1 are applied to the base-emitter junction and appears in the amplified form in the collector circuit. The coil L 2 couples the collector circuit energy back into the tank circuit by means of mutual inductance between L 1 and L 2. In this way, energy is being continuously supplid to the tank circuit to overcome the losses occurring in it. It may be seen that the phase of feedback is correct. The capacitor C and L 1 - L 2 are 180 0 out of phase. A further phase shift of 180 0 is produced by transistor circuit. In this way, energy feedback to the tank circuit is in phase with oscillations. Advantages : 1. Easy to tune. 2. Adaptability to a wide range of frequencies. 5.9 Colpitt s Oscillator Fig 5.9 shows the circuits of colpitt s oscillator. The tank circuit is make up

268 of C 1 C 2 and L. The biasing is provided by self biasing. When power is ON, collector current starts rising and charges the capacitors C 1 and C 2. These capacitors discharges through coil L setting up oscillations. The frequency of oscillations is given by f = (1) / (2 LC T ) where C T = (C 1 C 2 ) / (C 1 + C 2 ) The oscillations across C 1 are applied to the base-emitter junction and appear in the amplified form in the collector circuit and supply losses to the tank circuit. The amount of feedback depends upon the relative capacitance values of C 1 and C 2. Fig. 5.9 Collpitt s Oscillator It may be noted that the phase of feedback is correct. The capacitors C 1 and C 2 act as a simple alternating voltage divider. Therefore the tank circuit of L C 1 C 2 produce 180 0 phase shift. A further 180 0 phase shift is produced by the transistor. In this way feedback is properly phased to produce continuous undamped oscillations. 5.10 Oscillators Frequency Equations as Follows a) Collector tuned oscillator frequency f = (( 1 ) / (2 C T L 1 ) b) RC Phase Shift Oscillator frequency fo = ((1) / (2 RC 6)

Paper - II Electronic Devices and Circuits 269 where R 1 = R 2 = R 3 = R C 1 = C 2 = C 3 = C c) Hartly Oscillator frequency (formula) where f o = ((1) / (2 CL 1 ) where L 1 = L 1 + L 2 + - 2M d) Colpitt s Oscillator frequency f o = ((1) / 2 CT L ) where C T = C 1 C 2 / C 1 +C 2 5.11 Comparison of LC and RC Oscillators: S.No. Particulars LC Oscillators RC Oscillators 1. Requirements of Inductor / transformer Yes No 2. Cost More Less 3. Output Frequency High Low 4. Frequency stability Poor Good 5. Output voltage More Less 5.12 Piezo Electric Crystals Certain crystalline materials, exhibit the piezo-electric effect i.e., when we apply an a.c. voltage across them, they vibrate at the frequency of the applied voltage. Conversely, if the crystals are forced mechanically to vibrate, they generate an emf at the fundamental frequency of the crystal. This nature is found in materials namely: Rochelle salt, quartz and tourmaline. Of the various piezoelectric crystals quartz is most commonly used. The advantages of quartz crystal is. 1. Optimum value of mechnical strength 2. Inexpensive 3. Readily available in nature

270 The nature shape of the quartz crystal is a hexagonal prism. The useful crystal is obtained by cutting the nature crystal. The crystal is usually mounted in an oscillator circuit to vibrate best at one of its resonant frequencies, usually the fundamental frequency. The formula of the fundamental frequency of crystal is given by. where f = k / t t = Thickness of crystal k = constant that depends o its cut and other physical factors. In order to use crystal in an electronic circuit, it is placed between two metal plates. A crystal can be conveniently replaced by an electrical equivalent circuit. When the crystal is not vibrating, it is equivalent to capacitance Cm because it has two metal plates separated by a dielectric (crystal). However when crystal is vibrating, it is equivalent to series tuned circuit RLC. Therefore, the electrical equivalent circuit of the crystal is shown in Fig.5.10. In this figure. C m = Mounting capacitance C s = Series capacitance introduced by air gap R-L-C : Electrical equivalent of vibrational characteristics of crystal. Fig. 5.10 The series resonant frequency of crystal is the resonant frequency of LCR branch is given by f s = ((1) / (2 LC s )) The parallel resonant the frequency of the crystal is the frequency at which the loop current il reaches the maximum value. Since C is in series with C m the loop capacitance C T equal to (C m C) / (C + C m ). So the parallel resonant frequency is given by f p = ((1) / 2 LC T ))

Paper - II Electronic Devices and Circuits 271 5.13 Transistor Crystal Oscillator The Fig.5.11 shows the crystal oscillator. This circuit is same as Colpitt s oscillator. In this circuit the crystal is mounted to act as an inductor which forms the tuned circuit with C 1 and C 2. The positive feedback is provided by the capacitive voltage divider network. The crystal now acts as an inductor that resonants with C 1 and C 2 and the oscillating frequency of the circuit now lies in between series and parallel resonant frequencies of the crystal. The resistors R 1, R 2 for biasing and R E for stabilization. The C E configured transistor provides 180 0 phase shift where as the remaining 180 0 phase shift is provided by the feedback network. Advantages Fig. 5.11 Crystal Oscillator 1. It can produce highest oscillating frequencies. 2. The quality factor (Q) of the crystal is very high. The Q factor of the crystal may be as high as 10,000 compared to about 100 of LC tank circuit. 3. They have a high order of frequency stability. 4. Low cost. 5. Simple in construction.

272 Disadvantages : 1. They are fragile and consequently can only be used in low power circuits. 2. The frequency of oscillation cannot be changed appreciably. Summary Oscillator Circuit or Tank Circuit: A circuit which produce electrical oscillations of any desired frequency is known as an oscillatory circuit. Frequency of oscillations is given by f = (1) / (2 LC) Feedback Oscillator : Oscillations produced by adequate positive feedback in an amplifier is called a feedback oscillator. Barkhensans Condition for Sustained Oscillations: 1. A = 1 2. Phase angle of - A is zero. Colpitt s Oscillator : The tank circuit of this oscillator is made up of C 1 C 2 and L. The frequency of oscillations is given by f = (1) / (2 LC T ) where C T = (C 1 C 2 ) / (C 1 + C 2 ) Hartley Oscillator : The tank circuit of this oscillator is made up of CL 1 and L 2. The frequency of oscillations is given by f = 1 / (2 (L1+L2) C) RC Phase Shift Oscillator : The phase shift network of this oscillator consists of three identical RC sections. The phase shift of each session is 60 0. Frequency of oscillations is given by f = (1) / RC 6) Crystal Oscillator : It is used to get high frequency stability. This is possible by employing crystal in a transistor oscillator. Relaxation Oscillator : An oscillator which produces non-sinusoidal wavesl like square, sawtooth, rectangular, triangular etc., is called a relaxation oscillator.

Paper - II Electronic Devices and Circuits 273 Short Answer Type Questions 1. Define an oscillator. 2. Explain how oscillations produce in tank circuit. 3. Explain the condition for oscillation. 4. Explain the classifications of oscillators. 5. State the requisites of an oscillator. 6. Draw the circuit of a Collpitt s oscillator and explain its working? 7. With a near diagram explain the action of Hartley oscillator. 8. Draw the circuit diagram of an RC phase shift oscillator and explain. 9. Mention the advantages and disadvantages of phase shift oscillator. 10. List the applications of oscillators. 11. Draw the circuit diagram of crystal oscillator and explain its working. Also list its advantages and disadvantages. 12. Draw the circuit diagram of UJT relaxation oscillator and explain its working. 13. What are the requisites of an oscillators? Long Answer Type Questions 1. Write camparisions of negative and positive feedback. 2. Draw and explain positive feedback. 3. What are the requirements a transister amplifier works as an oscillator. Explain?. 4. Explain working of RC phase shift oscillator. 5. Explain working of tuned collector oscillator with neet diagram. 6. Explain working of Hartely oscillator. 7. Explain working of Colpitts oscillator. 8. Explain working of Crystal oscillator.

274 Practical/OJT Questions Study the oscillators-rc phase shift,hartely,colpitts,tuned collector and Crystal oscillators.