Ch2 Operational Amplifiers2-1 The ideal op amp1. op-amp symbol

2. op-amp 的兩種輸入

3. IC圖

4. 六大特性:

(1) input resistance

(2) output resistance

(3) open-loop gain (differential gain) A

(4) Common-Mode Rejection Ratio (CMRR)

(5) Bandwith(B.W.)

(6) no drift: op-amp 的參數值不會隨著溫度的變化而改變

1

2-2 The inverting configuration1. positive feedback and negative feedback

2. positive feedback and negative feedback的輸出

3. Virtual ground and virtual short

4. effect of finite open-loop gain

2-2 The inverting configuration1. closed-loop gain

2. weighted summer

3. Miller integrator

4. Differentiator

2

2-3 The noninverting configuration1. The closed-loop gain

2. The voltage follower

2-4 Difference Amplifier1. A difference amplifier

2. input differential resistance Rin

3.Common mode input resistance Ricm

4.Negative Impedance Converter(NIC)

3

5. General Impedance Converter (GIC)

6. GIC的兩大用途

7. Voltage-Current converter

8. noninverting integrator

[ Appendix F ]Single Time Constant (STC)1. STC網路的定義: 令輸入電源為零(電壓源—short; 電流源---open),若網路能被

表示成一個或多個的 ReqCeq或 ReqLeq則稱為 STC網路.

2. Transfer Function (T): 將網路之電壓和電流以相量表示之(VVout

in

( )( ) ) or (

IIout

in

( )( )

), 若放大器為 STC網路,則其轉移函數必為低通型或高通型.

4

3. STC低通網路轉移函數之標準型式:

4.STC高通網路轉移函數之標準型式:

5. Rapid evaluation of :(1) STC網路只有一個 C,多個 R:

(2) STC網路只有一個 R,多個 C:

(3) STC網路有多個 R,多個 C:

5

9. Frequency response of STC circuits(1) STC low pass 之振幅響應

(2) STC high pass 之振幅響應

2-5 Effect of finite open-loop gain and bandwith on circuit performance1. non-ideal

2. finite open-loop gain and bandwidth (A≠ B.W.≠ )

3. op-amp的等效模型與 transfer function表示法

6

4. Transmission frequency(fT) 又稱為 unity-gain bandwidth

5. op-amp transfer function之近似表示法

6.frequency response of closed-loop amplifier ((A≠∞ B.W.≠∞ )(1) inverting

(2) non-inverting

2-6 Large-Signal operation of op-amps1. slew rate(SR)

2. Full-Power Bandwidth(使輸出不發生傾斜失真的最大頻率)

7

2-7 DC imperfections1. offset voltage

2. Input Bias currents

3. Input offset current

8

Ch6. Single-stage Integrated-circuit Amplifiers6-2 Comparison of the MOSFET and the BJT1. The high frequency Hybrid-π model of BJT

2. The cutoff frequency: fβ(高三分貝頻率)

3. The MOSFET Unit-Gain frequency (fT) of MOSFET

6-3 IC Biasing ---- current sources, current mirrors and current-steering circuits1. current sink (判斷:從 BJT or MOS 流出之直流偏壓電路)

2. current source (判斷:從 active element流入)

9

3. current steering

6-4 High frequency response --- general considerations1. poles and zeros

2. 兩種電容效應

3. The gain function A(s)

10

4. 頻率響應分析的二種方法(1):Dominant pole approximation (主極點近似法):適用於 amplifier為 STC時Case1:若有一個主極點 (a):high frequency:可立即求得每一內部電容(Ci)兩端之等效電阻(Ri),而得到Wpi = , if 存在一個極點Wp1比其他所有極點或零點小(Smith: 4倍; Millman: 8

倍)以上則Wp1稱為主極點

(b):low frequency: 可立即求得每一耦合或旁路電容(Ci)兩端之等效電阻(Ri),而得到Wpi = , if 存在一個極點Wp1比其他所有極點或零點大 (Smith: 4倍;

Millman: 8倍)以上則Wp1稱為主極點

Case2: 若有二個主極點(a):high frequency:可立即求得每一內部電容(Ci)兩端之等效電阻(Ri),而得到Wpi = , if 存在二個極點(Wp1 ,Wp2)本身很接近,但是比其他所有極點或零點小(Smith: 4倍; Millman: 8倍)以上則Wp1,Wp2稱為主極點

11

(b):low frequency: 可立即求得每一耦合或旁路電容(Ci)兩端之等效電阻(Ri),而得到Wpi = , if 存在二個極點(Wp1 ,Wp2) 本身很接近,但是比其他所有極點或零點大 (Smith: 4倍; Millman: 8倍)以上則Wp1,Wp2稱為主極點

(2):Superposition theorem (重疊定理):適用於 amplifier不為 STC時(a):high frequency:稱為 open-circuit time constant(開路時間長數法):一次只看一個內部電容,而令其他電容效應等於零,此時以為 STC網路,而可立即求得每一內部電容(Ci)兩端之等效電阻(Ri),而得到Wpi =

(b):low frequency: :稱為 short-circuit time constant(短路時間長數法):一次只看一個耦合或旁路電容,而令其他電容效應等於零,此時以為 STC網路,而可立即求得每一內部電容(Ci)兩端之等效電阻(Ri),而得到Wpi =

12

5. Miller theorem:

6-5 The common-source and common-emitter amplifier with active loads1. The CMOS CS amplifier (no Body effect)

6-6 High frequency response of the CS and CE amplifier1. CS

13

2. CE

6-7 The common-gate and common base amplifiers with active loads1. The CMOS CG amplifier (consider Body effect)

6-8 The cascode amplifier1. cascode

2. cascade

3. BiCMOS amplifier

14

4. BiCMOS double cascode

6-11 Some useful transistor parings1. CC+CE cascade

2. Darling pair (CC+CC) (cascade):可得到特性極佳之緩衝放大器

6-12 Current-mirror circuits with improved performance1. current mirror: the design of IC current source and current-steering circuit

(1) Basic circuit:由兩個 npn 組成

15

(2) 由三個 npn 組成

(3)Wilson current mirror: 可得到偏壓電流大小為mA的電流鏡

(4)Widlar current mirror: 可得到偏壓電流大小為 μA的電流鏡

16

Ch7. Differential and multistage amplifiers7-3 The BJT differential pair1. Basic circuit

2. 兩種工作方式(1) 當輸入為直流大訊號時:兩個 BJT會形成一個ON,一個OFF狀態,此時當數位電路用

(2) 當 small-signal輸入時:兩個 BJT會形成ON,此時當放大器用

3. large-signal operation of the BJT differential pair

4. small-signal operation of the BJT differential pair

(1) 共同輸入時的等效情形

(2) 互補輸入時的等效情形

17

5. differential amplifier fed in a single-end manner(1)

(2)

6. differential mode gain and common mode gain(1).differential mode gain

(2). common mode gain

(3).CMRR(common mode reject ratio)

18

7-1 The MOS differential pair1. Basic MOS differential-pair configuration

2. common-mode voltage (at pinch off)

3. operation with a differential input voltage

4. Large-signal operation

19

7-2 small-signal operation of the MOS differential pair1. differential gain

(1) if vG1= vG2=

(2) if vG1= vG2=—

7-4 (skip)7-5 The differential amplifier with active load1. The active-loaded MOS differential pair

20

2. The Bipolar differential pair with active load

7-6 Frequency response of the differential amplifier1. Basic circuit

2. the differential pair as a wideband amplifierwideband amplifier:一種單端輸入,單端輸出且 Rc1=0 之差動放大器(CC+CB)

21

Ch8. Feedback1. negative feedback的好處

(1) stability the gain of an amplifier(2) reduce distortion (3) increase bandwidth(4) modify the input and output impedance(5) modify the input and output signal

8-1 The deneral feedback structure1. Basic feedback network

迴授放大器表示成基本迴授組態之四個假設:1. 輸入訊號必須經由放大器(A) 至輸出端,而不經由迴授網路()2. 輸出訊號必須經由迴授網路()至輸入端,而不經由放大器(A)3. 迴授網路()之值與電源電阻(Rs), 負載電阻(Rl)無關4. 放大器(A) 值與電源電阻(Rs), 負載電阻(Rl), 值無關8-2 Some properties of negative feedback1. gain desensitivity

2. bandwidth extension

3. noise reduction

22

4. reduction in nonlinear distortion

8-3 The four basic feedback topologiesA.判斷迴授網路為何種型式?1.Find 迴授網路()之右側是Vo或是 Io , 左側是Vf或是 If

2. 迴授網路()之右側(就是輸出側): 假設是Vo就是-------並式 假設是 Io 就是-------串式3. 迴授網路()之左側(就是輸入側): 假設是Vi=VsVf就是-------串式 假設是 Ii=IsIf 就是-------並式B. 如何求得迴授網路之Af, , Rif, Rof

1.將網路由迴授改為非迴授:在獲知迴授網路為何種型式後看到串就令 Io = 0 看到並就令Vo = 02.按照以前的方法求得非迴授網路之:A, , Ri, Ro

3. 迴授網路之Af = AA1

, Rif: 假設是串則為 Rif = Ri (1+ A),

假設是並則為 Rif = RA

i

1

Rof:假設是串則為 Rof = Ro (1+ A),

假設是並則為 Rof = RA

o

1

C.求A, , Ri, Ro值A Ri Ro

串並 VVo

s(Av)

VVf

o

從電壓源看入 從開路側看入

23

串串 IVo

s(GM)

VIf

o

從電壓源看入 從短路側看入並並 V

Io

s(RM)

IVf

o

從電流源看入 從開路側看入並串 I

Io

s(AI)

IIf

o

從電流源看入 從短路側看入D. 求Af, Rif, Rof值

Af Rif Rof

串並 AA1

Ri (1+ A) RA

o

1

串串 AA1

Ri (1+ A) Ro (1+ A)

並並 AA1

RA

i

1 RA

o

1

並串 AA1

RA

i

1 Ro (1+ A)

四種 feedback型態1. voltage amplifier

2. transconductance amplifier

24

3. transresistance amplifier

4. current amplifier

8-4 The series-shunt feedback amplifier1. ideal situation

25

2. practical situation

26

f.e.8-5 The series-series feedback amplifier1. ideal situation

2. practical situation

27

f.e.8-6 The shunt-shunt and shunt-series feedback amplifier1. shunt-shunt ideal situation

2. shunt-shunt practical situation

28

f.e.3. shunt-series ideal situation

29

4. shunt-series practical situation

30

f.e.8-7 Determing the loop gain1. step1.從X-X’切開

step2.從X-X’得等效組抗 Zt,再放入Vt

step3.將 Zt,放入另一端以求得Vr

step4.Loop gain:βA=—

8-8 The stability problem1. 以 loop gain判斷系統的穩定性

(1) —βA(jw)<1(2) —βA(jw)=1(3) —βA(jw)>1

2. Nyquist plot: w從 0→∞時之所有∣βA│對∠βA之極座標圖(通過負實軸之交點是否比 1大或比 1小)

31

8-9 Effect of feedback on the amplifier poles1. stability and pole location

2. amplifier with single-pole response

3. amplifier with to-pole response

8-10 stability study using Bode plot1.GM:維持系統 stable之最大迴路增益大小(∣βA│)增加值

32

2.PM: 維持系統 stable之最大迴路增益相位差大小(∠βA)之增加值

33