1. CIT 852 – Electronic Signals and Systems Chapter 4: Analogue Amplifiers 4.1 Characteristics of Analogue Amplifiers 4.2 Feedback: Gain Control and Frequency Response 1Powered by DeSiaMore

2. 2 Lecture 8 Power Amplifier (Class A) Induction of Power Amplifier Power and Efficiency Amplifier Classification Basic Class A Amplifier Transformer Coupled Class A Amplifier Powered by DeSiaMore

3. 3 Introduction Power amplifiers are used to deliver a relatively high amount of power, usually to a low resistance load. Typical load values range from 300W (for transmission antennas) to 8W (for audio speaker). Although these load values do not cover every possibility, they do illustrate the fact that power amplifiers usually drive low- resistance loads. Typical output power rating of a power amplifier will be 1W or higher. Ideal power amplifier will deliver 100% of the power it draws from the supply to load. In practice, this can never occur. The reason for this is the fact that the components in the amplifier will all dissipate some of the power that is being drawn form the supply. Powered by DeSiaMore

4. 4 Amplifier Power Dissipation The total amount of power being dissipated by the amplifier, P tot, is P tot = P 1 + P 2 + P C + P T + P E The difference between this total value and the total power being drawn from the supply is the power that actually goes to the load – i.e. output power.  Amplifier Efficiency  Powered by DeSiaMore

5. 5 Amplifier Efficiency  A figure of merit for the power amplifier is its efficiency, . Efficiency (  of an amplifier is defined as the ratio of ac output power (power delivered to load) to dc input power. By formula : As we will see, certain amplifier configurations have much higher efficiency ratings than others. This is primary consideration when deciding which type of power amplifier to use for a specific application.  Amplifier Classifications Powered by DeSiaMore

6. 6 Amplifier Classifications Power amplifiers are classified according to the percent of time that collector current is nonzero. The amount the output signal varies over one cycle of operation for a full cycle of input signal. Powered by DeSiaMore

7. 7 Efficiency Ratings The maximum theoretical efficiency ratings of class-A, B, and C amplifiers are: AmplifierMaximum Theoretical Efficiency,  max Class A25% Class B78.5% Class C99% Powered by DeSiaMore

8. 8 Class A Amplifier output waveform  same shape  input waveform +  phase shift. The collector current is nonzero 100% of the time.  inefficient, since even with zero input signal, I CQ is nonzero (i.e. transistor dissipates power in the rest, or quiescent, condition) Powered by DeSiaMore

9. 9 Basic Operation Common-emitter (voltage-divider) configuration (RC-coupled amplifier) Powered by DeSiaMore

10. 10 Typical Characteristic Curves for Class-A Operation Powered by DeSiaMore

11. 11 Typical Characteristic Previous figure shows an example of a sinusoidal input and the resulting collector current at the output. The current, I CQ, is usually set to be in the center of the ac load line. Why? (DC and AC analyses  discussed in previous sessions) Powered by DeSiaMore

12. 12 DC Input Power The total dc power, P i (dc), that an amplifier draws from the power supply : Note that this equation is valid for most amplifier power analyses. We can rewrite for the above equation for the ideal amplifier as Powered by DeSiaMore

13. 13 AC Output Power AC output (or load) power, P o (ac) Above equations can be used to calculate the maximum possible value of ac load power. HOW?? Disadvantage of using class-A amplifiers is the fact that their efficiency ratings are so low,  max  25%. Why?? A majority of the power that is drawn from the supply by a class-A amplifier is used up by the amplifier itself.  Class-B Amplifier Powered by DeSiaMore

14. 14Powered by DeSiaMore

15. 15 Limitation Powered by DeSiaMore

16. 16 Example Calculate the input power [P i (dc)], output power [P o (ac)], and efficiency [  ] of the amplifier circuit for an input voltage that results in a base current of 10mA peak. Powered by DeSiaMore

17. Part 1 17Powered by DeSiaMore

18. 18 Power Amplifier Small-signal approximation and models either are not applicable or must be used with care. Deliver the power to the load in efficient manner. Power dissipation is as low as possible. Powered by DeSiaMore

19. 19 Classification of Power Amplifier Power amplifiers are classified according to the collector current waveform that results when an input signal is applied. Conducting angle. Powered by DeSiaMore

20. 20 Classification of Power Amplifier Collector current waveforms for transistors operating in (a) class A, (b) class B Powered by DeSiaMore

21. 21 Classification of Power Amplifier class AB class C Powered by DeSiaMore

22. 22 Class B Output Stage  A class B output stage.  Complementary circuits.  Push-pull operation  Maximum power-conversion efficiency is 78.5% Powered by DeSiaMore

23. 23 Transfer Characteristic Powered by DeSiaMore

24. 24 Crossover Distortion Powered by DeSiaMore

25. 25 Power Dissipation The load power Maximum load power Powered by DeSiaMore

26. 26 Power Dissipation Total supply power Maximum total supply power Powered by DeSiaMore

27. 27 Power Dissipation Power-conversion efficiency Maximum power-conversion efficiency Powered by DeSiaMore

28. 28 Power Dissipation Power dissipation Maximum Power dissipation Powered by DeSiaMore

29. 29 Class AB Output Stage A bias voltage V BB is applied between the bases of Q N and Q P, giving rise to a bias current I Q. Thus, for small v I, both transistors conduct and crossover distortion is almost completely eliminated. Powered by DeSiaMore

30. 30 A Class AB Output Stage Utilizing Diodes for Biasing Powered by DeSiaMore

31. 31 A Class AB Output Stage Utilizing A V BE Multiplier for Biasing Powered by DeSiaMore

32. Part 2 32Powered by DeSiaMore

33. Control and Feedback Introduction Open-loop and Closed-loop Systems Automatic Control Systems Feedback Systems Negative Feedback The Effects of Negative Feedback Negative Feedback – A Summary Powered by DeSiaMore33

34. What is a Control System? System- a combination of components that act together and perform a certain objective. Control System- a system in which the objective is to control a process or a device or environment. Process- a progressively continuing operations/development marked by a series of gradual changes that succeed one another in a relatively fixed way and lead towards a particular result or end. 34Powered by DeSiaMore

35. Control Theory Branch of systems theory (study of interactions and behavior of a complex assemblage) Control System Manipulated Variable(s) Control Variable(s) Open Loop Control System Control System Manipulated Variable(s) Control Variable(s) Closed Loop Control System Feedback function 35Powered by DeSiaMore

36. Introduction Earlier we identified control as one of the basic functions performed by many systems – often involves regulation or command Invariably, the goal is to determine the value or state of some physical quantity – and often to maintain it at that value, despite variations in the system or the environment Powered by DeSiaMore36

37. Open-loop and Closed-loop Systems Simple control is often open-loop – user has a goal and selects an input to a system to try to achieve this Powered by DeSiaMore37

38. More sophisticated arrangements are closed- loop – user inputs the goal to the system Powered by DeSiaMore38

39. Automatic Control Systems Examples of automatic control systems: – temperature control using a room heater Powered by DeSiaMore39

40. Examples of automatic control systems: – Cruise control in a car Powered by DeSiaMore40

41. Examples of automatic control systems: – Position control in a human limb Powered by DeSiaMore41

42. Examples of automatic control systems: – Level control in a dam Powered by DeSiaMore42

43. Feedback Systems A generalised feedback system Powered by DeSiaMore43

44. By inspection of diagram we can add values or rearranging Powered by DeSiaMore44

45. Thus This the transfer function of the arrangement Terminology: A is also known as the open-loop gain G is the overall or closed-loop gain Powered by DeSiaMore45

46. Effects of the product AB – If AB is negative If AB is negative and less than 1, (1 + AB) < 1 In this situation G > A and we have positive feedback – If AB is positive If AB is positive then (1 + AB) > 1 In this situation G < A and we have negative feedback If AB is positive and AB >>1 - gain is independent of the gain of the forward path A Powered by DeSiaMore46

47. Negative Feedback Negative feedback can be applied in many ways – X i and X o could be temperatures, pressures, etc. – here we are mainly interested in voltages and currents Particularly important in overcoming variability – all active devices suffer from variability their gain and other characteristics vary with temperature and between devices – we noted above that using negative feedback we can produce an arrangement where the gain is independent of the gain of the forward path this gives us a way of overcoming problems of variability Powered by DeSiaMore47

48. Consider the following example below: We will base our design on our standard feedback arrangement Example: Design an arrangement with a stable voltage gain of 100 using a high-gain active amplifier. Determine the effect on the overall gain of the circuit if the voltage gain of the active amplifier varies from 100,000 to 200,000. Powered by DeSiaMore48

49. We will use our active amplifier for A and a stable feedback arrangement for B  Since we require an overall gain of 100 so we will use B = 1/100 or 0.01 Powered by DeSiaMore49

50. Now consider the gain of the circuit when the gain of the active amplifier A is 100,000 Powered by DeSiaMore50

51. Now consider the gain of the circuit when the gain of the active amplifier A is 200,000 Powered by DeSiaMore51

52. Note that a change in the gain of the active amplifier of 100% causes a change in the overall gain of just 0.05 % Thus the use of negative feedback makes the gain largely independent of the gain of the active amplifier However, it does require that B is stable – fortunately, B can be based on stable passive components Powered by DeSiaMore52

53. Implementing the passive feedback path – to get an overall gain of greater than 1 requires a feedback gain B of less than 1 – in the previous example the value of B is 0.01 – this can be achieved using a simple potential divider Powered by DeSiaMore53

54. Thus we can implement our feedback arrangement using an active amplifier and a passive feedback network to produce a stable amplifier The arrangement on the right has a gain of 100 … … but how do we implement the subtractor? Powered by DeSiaMore54

55. A differential amplifier is effectively an active amplifier combined with a subtractor. A common form is the operational amplifier or op-amp The arrangement on the right has a gain of 100. Powered by DeSiaMore55

56. In this circuit the gain is determined by the passive components and we do not need to know the gain of the op-amp – however, earlier we assumed that AB >> 1 – that is, that A >> 1/B – that is, open-loop gain >> closed-loop gain – therefore, the gain of the circuit must be much less than the gain of the op-amp – see Example 7.2 in the course text Powered by DeSiaMore56

57. The Effects of Negative Feedback Effects on Gain – negative feedback produces a gain given by – there, feedback reduces the gain by a factor of 1 + AB – this is the price we pay for the beneficial effects of negative feedback 7.6 Powered by DeSiaMore57

58. Effects on frequency response – from earlier lectures we know that all amplifiers have a limited frequency response and bandwidth – with feedback we make the overall gain largely independent of the gain of the active amplifier – this has the effect of increasing the bandwidth, since the gain of the feedback amplifier remains constant as the gain of the active amplifier falls – however, when the open-loop gain is no longer much greater than the closed-loop gain the overall gain falls Powered by DeSiaMore58

59. – therefore the bandwidth increases as the gain is reduced with feedback – in some cases the gain x bandwidth = constant Powered by DeSiaMore59

60. Effects on input and output resistance – negative feedback can either increase or decrease the input or output resistance depending on how it is used. if the output voltage is fed back this tends to make the output voltage more stable by decreasing the output resistance if the output current is fed back this tends to make the output current more stable by increasing the output resistance if a voltage related to the output is subtracted from the input voltage this increases the input resistance if a current related to the output is subtracted from the input current this decreases the input resistance the factor by which the resistance changes is (1 + AB) we will apply this to op-amps in a later lecture Powered by DeSiaMore60

61. Effects on distortion and noise – many forms of distortion are caused by a non-linear amplitude response that is, the gain varies with the amplitude of the signal – since feedback tends to stabilise the gain it also tends to reduce distortion - often by a factor of (1 + AB) – noise produced within an amplifier is also reduced by negative feedback – again by a factor of (1 + AB) note that noise already corrupting the input signal is not reduced in this way – this is amplified along with the signal Powered by DeSiaMore61

62. Negative Feedback – A Summary All negative feedback systems share some properties 1.They tend to maintain their output independent of variations in the forward path or in the environment 2.They require a forward path gain that is greater than that which would be necessary to achieve the required output in the absence of feedback 3.The overall behavior of the system is determined by the nature of the feedback path  Unfortunately, negative feedback does have implications for the stability of circuits – this is discussed in later lectures Powered by DeSiaMore62

63. Key Points Feedback is used in almost all automatic control systems Feedback can be either negative or positive If the gain of the forward path is A, the gain of the feedback path is B and the feedback is subtracted from the input then If AB is positive and much greater than 1, then G  1/B Negative feedback can be used to overcome problems of variability within active amplifiers Negative feedback can be used to increase bandwidth, and to improve other circuit characteristics. Powered by DeSiaMore63

64. Classification of Systems Classes of Systems Lumped Parameter Distributed Parameter (Partial Differential Equations, Transmission line example) Deterministic Discrete TimeContinuous Time NonlinearLinear Time Varying Stochastic Constant Coefficient Non-homogeneous Homogeneous (No External Input; system behavior depends on initial conditions) 64Powered by DeSiaMore

65. Example Control Systems Mechanical and Electo-mechanical (e.g. Turntable) Control Systems Thermal (e.g. Temperature) Control System Pneumatic Control System Fluid (Hydraulic) Control Systems Complex Control Systems Industrial Controllers – On-off Controllers – Proportional Controllers – Integral Controllers – Proportional-plus-Integral Controllers – Proportional-plus-Derivative Controllers – Proportional-plus-Integral-plus-Derivative Controllers 65Powered by DeSiaMore

66. Mathematical Background Why needed? (A system with differentials, integrals etc.) Complex variables (Cauchy-Reimann Conditions, Euler Theorem) Laplace Transformation – Definition – Standard Transforms – Inverse Laplace Transforms Z-Transforms Matrix algebra 66Powered by DeSiaMore

67. Laplace Transform Definition Condition for Existence Laplace Transforms of exponential, step, ramp, sinusoidal, pulse, and impulse functions Translation of and multiplication by Effect of Change of time scale Real and complex differentiations, initial and final value theorems, real integration, product theorem Inverse Laplace Transform 67Powered by DeSiaMore

68. Inverse Laplace Transform Definition Formula is seldom or never used; instead, Heaviside partial fraction expansion is used. Illustration with a problem: Initial conditions: y(0) = 1, y’(0) = 0, and r(t) = 1, t >= 0. Find the steady state response Multiple pole case with Use the ideas to find and 68Powered by DeSiaMore

69. Applications Spring-mass-damper- Coulomb and viscous damper cases RLC circuit, and concept of analogous variables Solution of spring-mass-damper (viscous case) DC motor- Field current and armature current controlled cases Block diagrams of the above DC-motor problems Feedback System Transfer functions and Signal flow graphs 69Powered by DeSiaMore

70. Block Diagram Reduction Combining blocks in a cascade Moving a summing point ahead of a block Moving summing point behind a block Moving splitting point ahead of a block Moving splitting point behind a block Elimination of a feedback loop G1G2G3G4 H2 H1 H3 R(s) Y(s) + - + 70Powered by DeSiaMore

71. Signal Flow Graphs Mason’s Gain Formula Solve these two equations and generalize to get Mason’s Gain Formula r1 r2 x1 x2 a21 a12 a22 a11 G1 G2G3 G4 G5 G6G7 G8 H2H3 H7H8 R(s)Y(s) Find Y(s)/R(s) using the formula 71Powered by DeSiaMore

72. Another Signal Flow Graph Problem R(s)C(s) 1 G1G2G3G4G5G6 G8 G7 -H4 -H1 -H2 -H3 72Powered by DeSiaMore