1. Transistor Circuit Design Diode Approximations Heathkit EB-6002

2. Introduction Circuit components are classified as being either passive or active. Passive components cannot provide a power gain - active components can. Some examples of passive components include resistors, capacitors, inductors, transformers, and diodes. The transistor is an active device. Consequently, transistors can be used to provide a power gain. In addition, the transistor can provide a voltage and/or current gain, and function as an electronic switch. For these reasons, the transistor is a very versatile device.

3. Unit Objectives 1. Estimate the large-signal forward resistance of a semiconductor diode. 2. Estimate the bulk, junction, and small-signal AC resistance of a semiconductor diode. 3. Sketch the DC and AC equivalent circuits for a diode simultaneously driven from a large DC source, and a small AC source. 4. Sketch the DC and AC load lines for a simple diode circuit. 5. Describe the basic structure of BJTs. 6. Identify the three BJT circuit configurations.

4. Unit Objectives 7. Define the following BJT parameters: ⍺,, I CBO, I CEO, BV BCO, BV CEO, and V BE. 8. Determine when the effects of I CBO can be ignored. 9. Sketch two equivalent BJT DC models.

5. Diode Approximations The transistor is a 3-terminal, solid-state amplifying device. There are two fundamental transistor types: bipolar junction transistors (BJTs) and field-effect transistors (FETs). A transistor can be modeled as two back-to-back diodes. For this reason, we will begin our discussion of transistors by considering large- signal and small-signal diode approximations.

6. Diode Approximations Fig. 1-1A Large-Signal Diode Approximation The junction diode is formed by joining P-type and N-type semiconductors as shown in Figure 1-1A.

7. Diode Approximations Fig. 1-1B The schematic symbol and IV curve for a typical junction diode are illustrated in Figure 1-1B and Figure 1-1 C respectively.

8. Diode Approximations Fig. 1-1C In Figure 1-1 C, note the models used to represent the diode in the various regions of the curve.

9. Diode Approximations From your knowledge of passive circuit design, you should recall the following important points: 1. V T = diode’s turn-on voltage. Typically, V T = 0.3V for germanium diodes, and 0.7V for silicon diodes. 2. r F = diode’s forward resistance. Since manufacturers list the forward diode current, I F, at a specified forward voltage, V F, you can estimate r F from:

10. Diode Approximations 3. R R = diode’s reverse resistance. For values of reverse voltage, V R, less than the diodes zener voltage, V Z, you can estimate R R from: where: I R = reverse diode current.

11. Diode Approximations Incidentally, both V T and I R are temperature sensitive. As a rough guide: V T decreases by approximately 2.4mV for each °C increase in temperature. I R doubles for each 10°C increase in temperature.

12. Diode Approximations 4. V Z = diode’s zener or breakdown voltage. Normally, general-purpose and rectifier diodes are not operated in the zener region. Diodes specifically designed to operate in the zener region are called zener diodes. Manufacturers list the values of zener voltage and zener resistance, r z, on the specification sheet for the zener diode. When diode circuits are designed, component values should be chosen to mask out the nonideal effects due to V T, r F, and R R.

13. Diode Approximations As a guide, component values are selected so that: Where: V = peak voltage driving the diode R = load resistance

14. Diode Approximations Fig. 1-2A Example 1-1 The circuit in Figure 1-2A is a half-wave rectifier.

15. Diode Approximations Fig.1-2B Consequently, the output voltage ideally appears as shown in Figure 1-2B.

16. Diode Approximations Sketch the actual output voltage assuming a silicon diode is employed that has the following specifications: I F = 100mA atV F =1V lg = 0.1AatV R = -20V

17. Diode Approximations First calculate r F and R R from the given specifications.

18. Diode Approximations When the diode is forward biased, the peak current equals:

19. Diode Approximations Thus, the peak output voltage is 19.3A (1 M Ω ) or 19.3V. When the diode is reverse biased, the input voltage divides between R R and R. Thus, the peak output voltage is:

20. Diode Approximations Figure 1-2C illustrates the actual output voltage. Since the component values satisfy the inequalities given previously the real diode is an excellent approximation of an ideal diode.

21. Diode Approximations Small-Signal Diode Approximations The diode approximations introduced previously are referred to as DC, or large- signal, approximations. The term “large-signal” means that the DC or peak AC input voltage, as the case may be, is large compared to the diode’s turn-on voltage.

22. Diode Approximations Fig. 1-3A When the amplitude of the input voltage is on the same order of magnitude as, or less than, the diode's turn-on voltage, you have small-signal operation. Especially important is the case where the diode is simultaneously driven from a large DC and small AC source as shown in Figure 1-3A.

23. Diode Approximations The following is a summary of the operation of the circuit in Figure 1-3A. 1. The diode is forward biased by the DC voltage source. Assuming component values are chosen so that V 1 >> V T and R >> r F, the average diode current essentially equals V 1 /R. This establishes the diode’s quiescent operating point, Q, as shown in Figure 1-3B.

24. Figure 1-3B

25. 2. On the positive half cycle of the AC input voltage, V 1 and v(t) are series aiding. Similarly, on the negative half cycle of the AC input voltage, V 1 and v(t) are series opposing. Thus, the AC source results in a diode current that varies between points 1 and 2, above and below the quiescent value, Q, as shown in Figure 1-3B. Diode Approximations

26. In Figure 1-3B, note that for small changes in diode current, around the Q point, a linear relationship exists between the current and voltage. Consequently, as far as the small AC source is concerned, the diode acts like a resistance. This AC or dynamic diode resistance, r AC, equals the change in diode voltage divided by the change in diode current. Stated mathematically:

27. Diode Approximations Since the graphic method suggested by Figure 1-3B and equation 1-3 is tedious, we will introduce several approximate formulas that can be used to estimate r AC. To begin, the dynamic resistance of a diode consists of two components - bulk resistance, r B, and junction resistance, r J. The bulk resistance includes the resistance of the semiconductor material and the contact resistance of the connecting leads. As a rough guide, we will assume the bulk resistance of a typical iunction diode is one ohm.

28. Diode Approximations Thus: As the name implies, the junction resistance is the effective resistance of the PN junction. The value of the junction resistance depends upon the amount of forward DC diode current.

29. Diode Approximations The theoretical value of a diode’s junction resistance is given by: Where I F = forward DC diode current.

30. Diode Approximations In practice, the actual value of r j typically varies over a 2:1 range from 26 mV/l F to 52mV/I F. Thus, for purpose of analysis and design, we will use the following “compromise formula” to calculate r j :

31. Diode Approximations Finally, combining Equation 1-4 and Equation 1-6 yields an approximate, but useful, formula for estimating the AC, or dynamic, diode resistance. Specifically:

32. Diode Approximations Example 1-2 Estimate the AC resistance of a semiconductor diode for the following values of forward DC current. 1mA, 14mA, and 200mA. When I F = 1 mA, the diode’s junction resistance is:

33. Diode Approximations Assuming the diode’s bulk resistance is 1 Q, the AC diode resistance is:

34. Diode Approximations Table 1-1 The result of similar calculations for l F = 14mA and 200mA are summarized in Table 1-1.

35. Diode Approximations Note in Table 1-1 that, for small forward currents, the AC diode resistance approximately equals the junction resistance similarly, for large forward currents, the AC diode resistance approximately equals the bulk resistance.

36. Diode Approximations DC and AC Equivalent Circuits You can analyze multi-source circuits with the superposition theorem. Recall from your study of basic circuit analysis, that, when you apply the superposition theorem, you must consider the effect of each source “acting alone”. Also recall that the actual response equals the algebraic sum of the responses produced by each source acting alone.

37. Diode Approximations DC EQUIVALENT CIRCUITS 1. Replace coupling and bypass capacitors by Open circuits. 2. Reduce AC sources to zero. 3. Replace the diode by its large-signal model.

38. Diode Approximations AC EQUIVALENT CIRCUIT 1. Replace coupling and bypass capacitors by short Circuits. 2. Reduce DC sources to zero. 3. Replace the diode by its AC, dynamic, resistance. Once you have the DC and AC equivalent circuits, you can determine the appropriate DC and AC responses. Naturally, the actual response equals the algebraic sum of the DC and AC responses.

39. Diode Approximations Example 1-3 For the circuit shown in Figure 1-4A. (a) Sketch the DC equivalent circuit. (b) Calculate the DC diode current and voltage. (c) Sketch the AC equivalent circuit. (d) Calculate the AC diode current and voltage. (e) Sketch the actual diode current and voltage.

40. Diode Approximations Fig. 1-4A (a) To obtain the DC equivalent circuit you open the coupling capacitor, reduce the AC source to zero and replace the diode by its large-signal model as shown in Figure 1-4B.

41. Diode Approximations Fig. 1-4B Here, as is usually the case, you can ignore the diode’s forward resistance, r F, since the DC resistance in series with the diode is quite large.

42. Diode Approximations Fig. 1-4B (b) In Figure 1-4B:

43. Diode Approximations (c) To obtain the AC equivalent circuit you short the coupling capacitor, reduce the DC source to zero and replace the diode by its dynamic resistance, r AC, as shown in Figure 1 -4C. The value of r AC is estimated as follows:

44. Diode Approximations (d) In Figure 1-4C the AC input voltage is connected directly across r AC. Thus:

45. Diode Approximations (e) The actual responses equal the algebraic sum of the DC and AC responses. Therefore:

46. Diode Approximations Figure 1-5A and Figure 1-5B illustrate the sketches of diode current and voltage respectively. Here, note that the AC responses “ride on” the DC levels.

47. Diode Approximations Load Lines Graphic methods, using load lines, are especially useful for analyzing and designing transistor circuits. Since the diode provides an excellent opportunity to introduce the concept of a load line, we will do so at this time.

48. Diode Approximations Fig 1-6A THE DC LOAD LINE Figure 1-6A illustrates a simple diode circuit. Here, you can obtain approximate values for the diode current and voltage by using the large-signal approximations discussed previously.

49. Diode Approximations Assuming the diode’s IV curve, Figure 1-6B, is available, it is possible theoretically to obtain exact values of the diode current and voltage.

50. Diode Approximations For an illustration of the method, consider the loop equation for the circuit in Figure 1-6A. Here: Solving for the diode voltage, V D yields:

51. Diode Approximations The variables in Equation 1-8, I D and V D, are the same variables that are displayed graphically by the diode’s IV curve. Also, since Equation 1-8 is a linear equation if I is plotted as a function of V D, the resulting graph, called the DC load line, is a straight line. “Recall that you can solve two simultaneous relationships in two unknowns by determining the point of intersection of their graphs.

52. Diode Approximations Consequently, for a particular value of Vcc and R L, the diode current and voltage correspond to the point of intersection between the DC load line and the diodes IV curve as shown in Figure 1-6C.

53. Diode Approximations Here, you should note the following: 1. The vertical intercept of the DC load line equals V CC /R L. 2, The horizontal intercept of the DC load line equals V CC. 3. The point of intersection of the DC load line and the diode's IV curve is called the Q, quiescent, point. The values of current and voltage at the Q point, I DQ and V DQ, are the theoretically exact values of the diode current and voltage. 4. The slope of the DC load line equals - 1/R L.

54. Diode Approximations Example 1-4 Work out the values of diode current and voltage for the circuit shown in Figure 1- 7A.

55. Diode Approximations With Thevenin’s Theorem, you can reduce the circuit in Figure 1-7A to a simpler single-loop equivalent circuit. Thus:

56. Diode Approximations The resulting Thevenin equivalent circuit is shown in Figure 1-8A.

57. Diode Approximations From this equivalent circuit, the intercept values of the DC load line are calculated as follows: Next, you plot the DC load line on the diode’s IV curve to determine the Q point values as shown in Figure 1-8B. Here:

58. Diode Approximations Fig. 1-8B I DQ and V DQ are the actual values of diode current and voltage respectively for the circuit in Figure 1-7A.

59. Diode Approximations THE AC LOAD LINE Figure 1-9A illustrates a diode circuit driven from a large DC, V CC, and small AC, v(t) source.

60. Diode Approximations Here, the value of capacitor C is chosen so that the capacitor provides good coupling at the frequency of the AC source. For this reason, the capacitor is effectively an AC short. Consequently, the AC load resistance as seen from the diode is: r L = R L ||R Since the capacitor acts like an open circuit for DC signals, the DC load resistance as seen from the diode is simply R L. For this reason, the DC load line and Q point values are calculated as illustrated previously.

61. Diode Approximations Fig. 1-9B By extending the DC load line concept, you can construct an AC load line as shown in Figure 1-9B.

62. Diode Approximations Here, you should note the following: 1. The AC load line crosses the DC load line at the Q point, and has a slope of -1/r L. 2. The vertical intercept of the AC load line equals l DQ + V DQ /r L. 3. The horizontal intercept of the AC load line equals V DQ + l DQ r L.

63. Diode Approximations The DC load line enables you to obtain a graphic solution for the DC diode current, I DQ, and DC diode voltage, V DQ. Similarly, the AC load line can be used to graphically determine the AC diode current. Our principle interest in the AC load line, however, lies in its application to transistor circuits. For this reason, we will not discuss the AC load line further at this time.

64. Question In AC equivalent circuits, coupling and bypass capacitors are replaced by _________ circuits.

65. Answer Short

66. Question In DC equivalent circuits, coupling and bypass capacitors are replaced by _________ circuits.

67. Answer Open

68. Question A diode driven from a large DC and small AC source acts like a _________ to the AC source.

69. Answer Resistance

70. Question As a rough guide, the bulk resistance of a semiconductor diode is approximately ____ ohm.

71. Answer One

72. Question The junction resistance of a semiconductor diode depends on the diode’s forward _________ current.

73. Answer DC

74. Question The junction resistance of a semiconductor diode typically varies over a _________ range from the theoretical value.

75. Answer 2 : 1

76. Question For any value of I F, r AC = ___________ + ___________

77. Answer r B + r j

78. Question The point of intersection of the DC load line and a diode’s IV curve establishes The __________ point.

79. Answer Q or Quiescent

80. Question The AC load line has a slope of ______________

81. Answer 1/r L where r L is the AC load resistance

82. Question The DC load line has a slope of _____________

83. Answer 1/R L where R L is the DC load resistance