Ch2 Operational Amplifiers 2-1 The ideal op amp 1. op-amp symbol 2. op-amp

2-1 The ideal op amp 1. 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. 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 configuration 1. closed-loop gain

2. weighted summer

3. Miller integrator

4. Differentiator

1. The closed-loop gain

2. The voltage follower

2-4 Difference Amplifier 1. A difference amplifier

2. input differential resistance Rin

3.Common mode input resistance Ricm

4.Negative Impedance Converter(NIC)

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(^V V

out in

( ) ( )



 ) or ( I

I

out in

( ) ( )



 ), 若放大器為 STC 網路,則其轉移函數必為低通型或高通型.

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:

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 performance 1. 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

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-amps 1. slew rate(SR)

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

2-7 DC imperfections 1. offset voltage

2. Input Bias currents

3. Input offset current

Ch6. Single-stage Integrated-circuit Amplifiers 6-2 Comparison of the MOSFET and the BJT 1. 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 circuits 1. 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)

3. current steering

6-4 High frequency response --- general considerations 1. poles and zeros

2. 兩種電容效應

3. The gain function A(s)

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 =

i iC R

1 , 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 =

i iC R

1 , 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 =

i iC R

1 , 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

(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 =

i iC R

1 , 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 =

i iC R

1

(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 =

i iC R

1

5. Miller theorem:

6-5 The common-source and common-emitter amplifier with active loads 1. The CMOS CS amplifier (no Body effect)

6-6 High frequency response of the CS and CE amplifier 1. CS

2. CE

6-7 The common-gate and common base amplifiers with active loads 1. The CMOS CG amplifier (consider Body effect)

6-8 The cascode amplifier 1. cascode

2. cascade

3. BiCMOS amplifier

4. BiCMOS double cascode

6-11 Some useful transistor parings 1. 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 performance

1. current mirror: the design of IC current source and current-steering circuit (1)Basic circuit:由兩個 npn 組成

(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

Ch7. Differential and multistage amplifiers 7-3 The BJT differential pair

1. 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

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)

7-1 The MOS differential pair

1. Basic MOS differential-pair configuration

2. common-mode voltage (at pinch off)

3. operation with a differential input voltage

4. Large-signal operation

7-2 small-signal operation of the MOS differential pair 1. differential gain

(1) if vG1= vG2= 2 vicm

(2) if vG1= 2 vid

vG2=—

2 vid

7-4 (skip)

7-5 The differential amplifier with active load 1. The active-loaded MOS differential pair

2. The Bipolar differential pair with active load

7-6 Frequency response of the differential amplifier 1. Basic circuit

2. the differential pair as a wideband amplifier

wideband amplifier:一種單端輸入,單端輸出且 Rc1=0 之差動放大器(CC+CB)

Ch8. Feedback

1. 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 structure 1. 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 feedback

1. gain desensitivity

2. bandwidth extension

3. noise reduction

4. reduction in nonlinear distortion

8-3 The four basic feedback topologies A.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=VsVf就是---串式 假設是 Ii=IsIf 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 = 0

2.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 = _1^A_A , Rif: 假設是串則為 Rif = Ri (1+ A),

假設是並則為 Rif = ^R

A

i

1

Rof:假設是串則為 Rof = Ro (1+ A), 假設是並則為 Rof = ^R

A

o

1

C.求 A, , Ri, Ro值

A  Ri Ro

串並 V

V

o s

(Av) ^V V

f o

從電壓源看入 從開路側看入

V_s (GM)

I_o

並並 V

I

o s

(RM)

I V

f o

從電流源看入 從開路側看入

並串 I

I

o s

(AI) ^I I

f o

從電流源看入 從短路側看入

D. 求 Af, Rif, Rof值

Af Rif Rof

串並 A

A 1

Ri (1+ A) R A

o

1

串串 A

A 1

Ri (1+ A) Ro (1+ A)

並並 _A

A 1

R A

i

1

R A

o

1

並串 A

A 1

R A

i

1

Ro (1+ A)

四種feedback 型態 1. voltage amplifier

2. transconductance amplifier

3. transresistance amplifier

4. current amplifier

8-4 The series-shunt feedback amplifier 1. ideal situation

2. practical situation

f.e.

8-5 The series-series feedback amplifier 1. ideal situation

2. practical situation

f.e.

8-6 The shunt-shunt and shunt-series feedback amplifier 1. shunt-shunt ideal situation

2. shunt-shunt practical situation

f.e.

3. shunt-series ideal situation

4. shunt-series practical situation

8-7 Determing the loop gain 1. 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=—

t r

V V

8-8 The stability problem

1. 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)

1. stability and pole location

2. amplifier with single-pole response

3. amplifier with to-pole response

8-10 stability study using Bode plot

1.GM:維持系統 stable 之最大迴路增益大小(∣βA│)增加值

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