EMLAB 1 Chapter 8. Frequency response

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

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

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, …)

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

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.

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.

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 )

EMLAB The CE Amplifier

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

EMLAB 11 C C2 의 영향만 고려

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

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.

EMLAB 14

EMLAB 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.

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

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).

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.

EMLAB 19

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

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

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

EMLAB 23 Miller theorem :

EMLAB 24

EMLAB 25

EMLAB The Common-emitter amplifier

EMLAB 27

EMLAB 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

EMLAB 29 f H : the 3-dB frequency

EMLAB 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.

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;

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

EMLAB 33

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

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.

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

EMLAB Adapting the formulas for the case of the CE amplifier

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

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)

EMLAB 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 )

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

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.

EMLAB 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 :

EMLAB 44 (2) R sig 가 작을 때 :

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.

EMLAB 46

EMLAB 47

EMLAB High-frequency response of the Bipolar cascode amplifier

EMLAB 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.

EMLAB The emitter follower

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

EMLAB Analysis of the Active-Loaded MOS Amplifier