1. MULTISTAGE AMPLIFIERS
PART I - BJT AMPLIFIERS
ACKNOLEDGEMENT
The materials presented in these notes were partly taken from the original notes “MULSTISTAGE AMPLIFIERS” by ENCIK  SOHIFUL ANUAR BIN ZAINOL MURAD, School of Microelectronic

2. Many applications cannot be handled with single-transistor amplifiers in order to meet the specification of a given amplification factor, input resistance and output resistance
As a solution – transistor amplifier circuits can be connected in series or cascaded amplifiers
This can be done either to increase the overall small-signal voltage gain or provide an overall voltage gain greater than 1 with a very low output resistance

3. Multistage amplifier configuration
Cascade /RC coupling

4. Multistage amplifier configuration
Cascode

5. Multistage amplifier configuration
Darlington/Direct coupling

6. Multistage amplifier configuration
Transformer coupling

7. i) Cascade connection The most widely used method
Coupling a signal from one stage to the another stage and block dc voltage from one stage to the another stage
The signal developed across the collector resistor of each stage is coupled into the base of the next stage
The overall gain = product of the individual gain

8. Example 1
Draw the AC equivalent circuit and calculate Av, Ri and Ro.

9. Solution
DC analysis
The circuit under DC condition (stage 1 and stage 2 are identical)

10. Applying Thevenin’s theorem, the circuit becomes;

11. AC analysis
The small-signal equivalent circuit (mid-band);

13. The small-signal voltage gain;
Substituting values;

14. The input resistance;
The output resistance;

15. Example 2
Assuming 1 = 170, 2 = 150 and VBE(ON) = 0.7 V, calculate the voltage gain Av where;

16. DC analysis

17. The base-emitter loop of Q1
Substituting values;

18. For the RC1 – collector of Q1 – base of Q2 – RE2 loop
and

19. Substituting values;

21. AC analysis

23. Substituting values;

25. ii) Cascode connection
A cascode connection has one transistor on top of (in series with) another
The i/p applied to a C-E amp. (Q1) whose output is used to drive a C-B amp. (Q2)
The o/p signal current of Q1 is the i/p signal of Q2
The advantage: provides a high i/p impedance with low voltage gain to ensure the i/p Miller capacitance is at a min. with the C-B stage providing good high freq. operation

26. Cascode amplifier

27. DC analysis
May be performed using the following figure;

28. The equations are (assuming VBE = 0.7 V for both BJT’s);
The above equations may solved for the two unknown currents namely I1 and IB1.

29. AC analysis
The equivalent circuit under AC condition

30. The ac equivalent circuit using hybrid- model for BJT

31. At node E2;
Or;
Substituting in (1);

32. The small-signal voltage gain;
When 2 >> 1

33. Example 3
Compute the approximate small-signal voltage gain

34. SOLUTION
DC analysis
The circuit under DC condition

35. Substituting values;

36. Or;
Substituting values;

37. Substituting for I1 in (1)

39. AC analysis
Small-signal equivalent circuit using hybrid- model

40. At node E2;
Hence;
Substituting for v2 in (1);

41. Or;
The voltage gain;
When 2   1;

42. Substituting values;

43. iii) Darlington connection
Darlington pair
Internal connection;
Collectors of Q1 and Q2;
Emitter of Q1 and base of Q2.
Provides high current gain : IC  2IB

44. Currents in darlington pair

45. If 1 = 2 =  and assuming  is large;

46. Hybrid- model (assuming ro1 = ro2 = );

47. Darlington pair configuration
Darlington configuration provides;
Increased current;
High input resistance.
Darlington pair configuration

48. Small-signal equivalent circuit

49. Input voltage source is transformed into current source

50. The current gain is;

51. The input resistance is;
EXERCISE 1
Show that the approximate expression for the input resistance of the darlington configuration above is;
Hints: use the relationships:
&

52. Example 4 Determine the; (a) Q-point for Q1 and Q2;
(b) voltage gain vo/vs;
(c) input resistance Ris;
(d) output resistance Ro

53. (a) Determination of Q-points
Using Thevenin’s theorem;
DC equivalent circuit

54. The circuit becomes;

55. Substituting values;

56. (a) The Q-points are;

57. (b) The small-signal voltage gain (mid-band);
The equivalent circuit under AC condition

58. Using the hybrid- model of transistor, the equivalent circuit becomes;

60. Substituting for V2 in the expression for vo and simplifying;

61. Substituting for V2;
Simplifying;

62. Substituting values;

64. Substituting values;

66. Find; (a) ICQ1 and ICQ2 (b) Av = vo/vs (c) Rib and Ro
EXERCISE 2
Find; (a) ICQ1 and ICQ2 (b) Av = vo/vs (c) Rib and Ro
Answers:
(a) 2.08 mA & 69.9 mA
(b) 0.99 V/V
(c) 480 k & 