1. EMLAB 1 Chapter 8. Frequency response

2. EMLAB 2 1.Low-Frequency Response of the CS and CE Amplifiers 2.Internal Capacitive Effects and the High-Frequency Model of the MOSFET 3.High-Frequency Response of the CS and CE Amplifiers 4.Useful Tools for the Analysis of the High-Frequency Response of Amplifiers 5.A Closer Look at the High-Frequency Response of the CS and CE Amplifiers 6.High-Frequency Response of the CG and Cascode Amplifiers 7.High-Frequency Response of the Source and Emitter Followers 8.High-Frequency Response of Differential Amplifiers 9.Other Wideband Amplifier Configurations 10.Multistage Amplifier Examples Contents

3. EMLAB 3 Introduction Coupling capacitor Bypass capacitor High-frequency, equivalent-circuit model for the MOSFET.

4. EMLAB 4 Introduction 1.Low-frequency band 에서 coupling capacitor 또는 bypass capacitor 의 임 피던스가 커서 전압 강하 생김 → 이득 줄어듦. 2.f L : lower end frequency of the mid band. Mid-band 이득에 비해 3dB 이득 이 떨어지는 지점. IC 증폭기에서 면적을 줄이기 위해 coupling/bypass 안쓰는 경우 0 Hz. 3.High-frequency band 에서는 트랜지스터 내부의 capacitance 로 인해 이득 감소됨. 4. f H : upper end frequency of the midband. 5. f H 를 높이는 설계 방법이 주된 관심사.(source/emitter degeneration resistance, circuit configuration, …)

5. EMLAB 5 1. Low-frequency response of the CS and CE amplifiers 1.1 The CS Amplifier Mid-band gain

6. EMLAB 6 Figure 8.3 Sketch of the low-frequency magnitude response of a CS amplifier for which the three pole frequencies are sufficiently separated for their effects to appear distinct.

7. EMLAB 7 f L 을 위한 pole frequencies 를 쉽게 구하는 방법 1. V sig 를 0 V 로 바꾸고, 2. Capacitor 하나에 pole 주파수 하나씩 계산 ( 고려 대상 외 다른 capacitor 들은 short circuit 으로 대체 C→∞) 3. 개별 capacior 의 양 단자에서 관찰되는 저항 ( 다른 부품 전체에 의한 등가저항 ) 계 산. 이 저항 값을 이용해 각각의 capacitor 에 의한 time constant 가 정해짐.

8. EMLAB 8 Selecting values for the coupling and bypass capacitors 3 개의 pole frequency 중에서 f p2 가 제일 큰 값인 경우가 많음. 전체 capacitance 를 최소화하기 위해 f p2 = f L 로 다른 두 pole frequency 는 보다 5~10 배정도 낮은 값으로 정함. 너무 낮 은 값으로 하면 C C1 과 C C2 가 커지므로 너무 작게 하는 것도 피해야 함. ( 큰 capacitance 는 많은 면적 차지 )

9. EMLAB 9 1.2 The CE Amplifier

10. EMLAB 10 C C1 의 영향만 고려 (C E 와 C C2 는 무한대 또는 short 일 때 ) C E 의 영향만 고려

11. EMLAB 11 C C2 의 영향만 고려

12. EMLAB 12 Sketch of the low-frequency gain under the assumptions that C C1, C E, and C C2 do not interact and that their break (or pole) frequencies are widely separated. Low frequency gain of CE amp. 대부분의 경우 C E 에 의한 pole frequency 가 3dB 감쇄 주파수 f L 이 됨. C E 에 곱해지는 등가 저항이 가장 작은 값이기 때문

13. EMLAB 13 Selecting Values for C C1, C E, and C C2 C E 에 곱해지는 등가 저항이 가장 작은 값이므로 CE 에 의한 pole frequency 가 0.8f L 정도 되게 설정. 나머지 pole frequency 들은 0.1f L 정도 되게 설정.

14. EMLAB 14

15. EMLAB 15 2. Internal Capacitive Effects and the High-Frequency Model of the MOSFET and the BJT 2.1 The MOSFET Gate capacitance 에 의해서 gate 제어 전압에 대해 drain 전류 응답에 시간 지 연 발생. 주파수 영역에서 고주파에서 이득 감소로 나타남. MOSFET 의 capacitance 는 gate capacitance 와 source-body, drain-body 의 depletion region 에 생기는 capacitance 가 주 원인임.

16. EMLAB 16 Overlap cap. 동작 모드 Gate capacitanceJunction capacitance Cut-off Triode Saturation

17. EMLAB 17 The high-frequency MOSFET model Figure 8.6 (a) High-frequency, equivalent- circuit model for the MOSFET. (b) The equivalent circuit for the case in which the source is connected to the substrate (body). (c) The equivalent-circuit model of (b) with C db neglected (to simplify analysis).

18. EMLAB 18 The MOSFET unity-gain frequency (f T ) f T : the frequency at which the short-circuit current-gain of the common-source configuration becomes unity.

19. EMLAB 19

20. EMLAB 20 2.2 The BJT The Base-Charging or Diffusion Capacitance C de The Base–Emitter Junction Capacitance C je The Collector–Base Junction Capacitance C μ

21. EMLAB 21 BJT unity-gain frequency (f T ) Figure 8.10 Bode plot for |h fe | Figure 8.11 Variation of fT with IC.

22. EMLAB 22 3. High-frequency response of the CS and CE amplifiers 3.1 The Common-Source Amplifier

23. EMLAB 23 Miller theorem :

24. EMLAB 24

25. EMLAB 25

26. EMLAB 26 3.2 The Common-emitter amplifier

27. EMLAB 27

28. EMLAB 28 4. Useful tools for the analysis of the high-frequency response of amplifiers 4.1 The High-Frequency Gain Function 4.2 Determining the 3-dB frequency f H (1) Dominant-pole response : pole 주파수 중에 하나가 특히 낮을 때 (2) Dominant-pole 이 없을 때 : Bode plot 보고 결정, 또는 근사식

29. EMLAB 29 f H : the 3-dB frequency

30. EMLAB 30 4.3 Using Open-Circuit time constants for the approximate determination of f H f H 를 위한 pole frequencies 를 쉽게 구하는 방법 1. V sig 를 0 V 로 바꾸고, 2. Capacitor 하나에 pole 주파수 하나씩 계산 ( 고려 대상 외 다른 capacitor 들은 open circuit 으로 대체 C→0) 3. 개별 capacior 의 양 단자에서 관찰되는 저항 ( 다른 부품 전체에 의한 등가저항 ) 계 산. 이 저항 값을 이용해 각각의 capacitor 에 의한 time constant 가 정해짐.

31. EMLAB 31 Example 8.6 Find the mid band gain A M = V o /V sig and the upper 3-dB frequency (f H ). (a) high-frequency equivalent circuit of a MOSFET amplifier; (b) the equivalent circuit at mid band frequencies;

32. EMLAB 32 (c) circuit for determining the resistance seen by C gs ; (d) circuit for determining the resistance seen by C gd.

33. EMLAB 33

34. EMLAB 34 4.4 Miller’s theorem General linear network with V 2 = K V 1 Y General linear network with V 2 = K V 1 Y1Y1 Y2Y2

35. EMLAB 35 Example 8.7 Find the Miller equivalent circuit when Z is (a) a 1-MΩ resistance and (b) a 1-pF capacitance. In each case, use the equivalent circuit to determine V o /V sig.

36. EMLAB 36 5. A closer look at the high-frequency response of the CS and CE amplifiers 5.2 Analysis Using Miller’s Theorem

37. EMLAB 37 5.5 Adapting the formulas for the case of the CE amplifier

38. EMLAB 38 5.6 The situation when R sig is low R sig 이 작으면 C gs 에 의한 time constant 가 작아짐.

39. EMLAB 39 Example 8.8 Consider an IC CS amplifier for which g m = 1.25mA/V 2, C gs = 20fF, C gd = 5fF, C L =25fF, R’ sig = 10kΩ, and R L = 10k Ω. Assume that C L includes C db. Determine f H using (a) the Miller approximation and (b) Use the method of open-circuit time constants to obtain another estimate of f H. (a) (b)

40. EMLAB 40 6. High-frequency response of the common-gate and cascode amplifiers Figure 8.26 (a) The common-gate amplifier with the transistor internal capacitances shown. A load capacitance C L is also included. (b) Equivalent circuit for the case in which r o is neglected. f P1 과 f P2 가 Common-Source amp 보다 훨씬 높음. ( r o 무시한 경우임 )

41. EMLAB 41 Figure 8.27 Circuits for determining R gs and R gd. (IC 증폭기에서 r o 효과 포함시켜야 함 )

42. EMLAB 42 Example 8.12 Consider a CG amplifier with g m = 1.25mA/V 2, r o = 20kΩ, C gs = 20fF, C gd = 5fF, C L =15fF, R’ sig = 10kΩ, and R L = 20k Ω. Assume that C L includes C db. Determine the input resistance, the mid-band gain and the upper 3-dB frequency f H.

43. EMLAB 43 6.2 High-Frequency Response of the MOS Cascode Amplifier 다시 정리하면, Cascode transistor Q 2 가 CG type 이어서 R in2 가 작아져서 Miller effect 작음. (1) R sig 가 클 때 :

44. EMLAB 44 (2) R sig 가 작을 때 :

45. EMLAB 45 Example 8.13 This example illustrates the advantages of cascoding by comparing the performance of a cascode amplifier with that of a common-source amplifier in two cases: (a) R sig 이 클 때 (R sig = 10kΩ) (b) R sig 이 작을 때. Assume all MOSFETs have g m = 1.25mA/V 2, r o = 20kΩ, C gs = 20fF, C gd = 5fF, C db = 5fF, C L =10fF, and C L (excluding C db )=10 fF. For case (a), let R L = r o = 20kΩ for both amplifiers. For case (b), let R L = r o = 20kΩ for the CS amplifiers and R L = r o for the cascode amplifier For all cases, determine the input resistance, the mid-band gain and the upper 3-dB frequency f H.

46. EMLAB 46

47. EMLAB 47

48. EMLAB 48 6.3 High-frequency response of the Bipolar cascode amplifier

49. EMLAB 49 7. High-frequency response of the source and emitter followers Figure 8.32 Analysis of the high-frequency response of the source follower: (a) equivalent circuit; (b) simplified equivalent circuit; (c) determining the resistance R gs seen by C gs. Source follower 는 drain 이 접지되어 있어 Miller 효과가 없으므로 높은 주파수까 지 동작함.

50. EMLAB 50 7.2 The emitter follower

51. EMLAB 51 8. High-frequency response of differential amplifiers Common mode 이득 증가로 CMRR 이 낮아짐.

52. EMLAB 52 8.2 Analysis of the Active-Loaded MOS Amplifier