2. Electronic Circuits
1. Ideal OP amp
OP amp
OP amp 의 어떤 terminal 도 ground
에 연결되어 있지 않음 .
3 signal terminals and 2 power
terminals (Not displayed)
Ideal OP Amp
Differential input voltage, single-
ended output voltage
Infinite input impedance i i = 0
Zero output impedance
Zero common-mode gain (v2=v1
vo=0)
Infinite open-loop gain A
Infinite bandwidth : A is constant at
any frequencies.
*Differential input voltage, single-ended output voltage
2 EM Wave Lab
3. Electronic Circuits
1. Ideal OP amp
Differential and common mode
v Id = v 2 – v 1
v I cm = ½(v 1 + v 2 )
v 1 = v Icm - v Id /2
v 2 = v Icm + v Id /2
v 3 = mv d
v d = (G m v 2 – G m v 1 ) R
v 3 = mG m R (v 2 – v 1 )
Gain A = mG m R = 100·10·10
= 10 4
= 80 dB
3 EM Wave Lab
4. Electronic Circuits
2. Inverter
Closed loop gain
i2
For ideal OP amp, finite v o means v 2 -
i1 v 1 =0
v 2 – v 1 = v o /A = 0
v1
v2 v 2 ≒ v 1 : Virtual short circuit
if v 2 is grounded, v 1 is a virtual ground
i 1 = (v I – v 1 ) /R 1 = v I /R 1 terminal.
vo = v1 – i2 R2 = v1 – i1 R2 = 0 – vI R2 / R1 ∵ infinite input impedance of ideal OP
amp
vo / vI = - R2 / R1
Closed-loop gain G ≡ v o / v I = - R 2 / R 1
R2 에 의해 negative feedback 회로로 동작
(positive feedback if connected between 2 and 3)
Closed-loop gain 은 외부 수동 소자에 의해 결정
stable and predictable, but gain loss is inevitable
4 EM Wave Lab
7. Electronic Circuits
2. Inverter
Example
R 1 should be large as a input impedance, but large R 1 causes low voltage gain
7 EM Wave Lab
8. Electronic Circuits
2. Inverter
Summer
Output is a weighted sum of input
signals
v o = v 1 (R a /R 1 )·(R c /R b ) + v 2 (R a /R 2 )·(R c /R b ) –
v 3 ·(R c /R 3 ) – v 4 ·(R c /R 4 )
Different summing coefficients are
possible
8 EM Wave Lab
10. Electronic Circuits
3. Noninverter
Finite open loop gain
vo = A ( vI - vx )
i1 = - vx / R1 i 2 = ( v x – v o )/ R 2
A
1 + (R 2 / R 1 )
v o / v I = ---------------
1 + (R 2 / R 1 )
Inverting 경우
1 + ---------
A 와 분모 부분 같
음
A ≫ 1 + (R 2 / R 1 ) 이면 infinite gain 의 경우와
등가회로 같음
v I 와 v x 가 같은 값이 아니므로 (finite gain)
→ v x = R1 / (R1+ R2) · v o
v o = A ( v I - v x ) ∵ Op amp 동작 특
성
위 두식을 이용하면 같은 결과를 얻는다 .
10 EM Wave Lab
11. Electronic Circuits
3. Noninverter
Voltage follower
Non-inverting closed-loop 에서
R1=∞, R2=0 인 경우와 동일함
Ideal Op amp 의 infinite input
impedance 를 이용하여 source
inpedance 가 큰 source 에 연결할 수 있
고 , ideal Op amp 의 zero output
impedance 를 이용하여 load inpedance
가 적은 load 에 연결할 때 사용
Buffer Amp 가 Voltage Source
와 Load impedance 에 연결
11 EM Wave Lab
12. Electronic Circuits
4. Difference
Common mode rejection ratio
For practical circuits,
Common-mode voltage gain A cm ≠
0
v o = A d ·v Id + A cm ·v Icm
현재까지 두 input voltage 의 차이만 증폭된다고
가정하였음 . 하지만 , 실제로는 공통 부분도 A cm
만큼의 gain 을 가지고 증폭된다 .
|Ad |
CMRR = 20 Log
| A cm |
12 EM Wave Lab
13. Electronic Circuits
4. Difference
Difference amplifier
지금까지는 inverting/noninverting 의 경우 input
이 없는 한쪽은 GND 였지만 , difference amp 에서
는 두 input 의 차이만을 증폭하고자 함 . (why don’t
you use Op amp itself ?)
Output port 에서 Common-mode signal 을 없애기
위해선 , inverting gain 과 noninverting gain 의
magnitude 는 같고 부호는 반대이어야 함 . (v I1 = v I2
일때 v 0 =0 이어야 함을 생각해 보면 됨 )
Inverting Noninverting
i = 0
≡
v O1 / v I 1 = - R 2 / R 1
13 EM Wave Lab
14. Electronic Circuits
4. Difference
Difference amplifier
ᅵᅵ
inverting gain ᅵᅵ ᅵᅵ
= noninverting gain ᅵᅵ
R4 R2
R2 / R1 =
R3 + R4 [1 R1
]
+
R4 R2 R2 R4
→ R3 + R4
=
R1 + R2 → R1
=
R3
R4 R2 R2
vO2 = vΙ 2
R3 + R4
[1
R1
] = vΙ 2
R1
+
R2 R2
By superposition, v O = v O1 + ( vI 2 - vI 1 ) = v Id
v O2 = R1 R1
R2
→ Ad =
R1
14 EM Wave Lab
15. Electronic Circuits
4. Difference
Difference amplifier
1 R4 1 R3
i1 =
R1
[ v Icm - v
R3 + R4 Icm ] = v Icm
R1 R3 + R4
R4 R4 R2 R3
vO = v Icm – i2R2 = v - v
R3 + R4 R3 + R4 Icm R1 R3 + R4 Icm
R4 R2 R3
=
R3 + R4
1- [ R1 R4
]v Icm
vO R4 R2 R3
For R1 = R3 , R2 = R4
Acm ≡
vΙcm = R +R 1-
3 4
[ R1 R4
]
v Id
R id ≡
iI
v Id = R 1 i I + 0 + R 1 i I ∵ vertual short
R id = 2R 1 : low input resistance for
high differential gain
15 EM Wave Lab
16. Electronic Circuits
4. Difference
Instrumentation amplifier
R2 R2
[1
R1
]
( vΙ 2 − vΙ 1 ) = 1
R1
[ ]v Ιd
+ +
R4 R2
vΟ =
R3 +
1
R1
[ ]
vΙd = Ad vΙd
R4 R2
Ad =
R3
[ 1
R1
] =
+
High input impedance and high differential
gain
Issues
A cm is equal to 1+R 2 /R 1 at the first stage.
Issues of imperfect match at the first two Op amps.
Two R 1 resistors should be simultaneously varied : Not easy job
16 EM Wave Lab
18. Electronic Circuits
5. Nonideal OP amp
Nonideal OP amp
Differential open-loop gain Noninfinite CMRR, noninfinite input
resistance, nonzero output resistance :
Closed-loop circuits 에서 Not critical
A0
A(jw) =
1+ jw/w b
For w = 0
For w ≫ w b
18 EM Wave Lab
19. Electronic Circuits
5. Nonideal OP amp
Frequency response
←
= vx
− R2 / R 1
Vo(s)/Vi(s) ≈ s
1
+ ωT / (1 + R2 / R1 )
For A0 ≫ 1+R2/R1
ωT
ω3dB = −−−−−−−−
− + R2 /
1
R1
For noninverting closed-loop case,
only DC gain (1 + R 2 /R 1 ) is different
19 EM Wave Lab
24. Electronic Circuits
6. Large signal
Full power bandwidth
Unity-gain voltage follower 의 input 에 sine wave 를 인가하고 출력 전압의 진폭이 최대
가 되도록 할 경우 , slew 현상이 발생하지 않는 입력신호의 최대 주파수
24 EM Wave Lab
26. Electronic Circuits
7. DC effect
Equivalent model
DC biasing issue
DC signal issue
Inverting Noninverting
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27. Electronic Circuits
7. DC effect
Capacitive coupling
Only for DC Only for AC
A ≠ 1 + R 2 /R 1 STC HPF
27 EM Wave Lab
28. Electronic Circuits
7. DC effect
Input bias current
두 전류 I B1 , I B2 는 거의 같은 값을 가지지만 OP amp 내부의
mismatch 로 인해 약간 차이가 남
Only for
DC
B2
28 EM Wave Lab
29. Electronic Circuits
7. DC effect
Input bias current
V O = I B1 R 2 ≈ I B R 2 limits on R 2
V O = -I B2 R 3 + R 2 (I B1 – I B2 R 3 /R 1 )
(for I B1 = I B2 = I B3 )
두 input 단자에서 본 저항 값이 같다 .
29 EM Wave Lab
30. Electronic Circuits
7. DC effect
Input bias current
For R 3 = ( R 1 ∥R 2 ) and I B1 ≠ I B2 ≠ I B3
I B1 = I B + I OS /2 I B2 = I B - I OS /2 →
V O = I OS R 2 (compare with V O = I B1 R 2 in case of without R 3 )
AC coupled inverting amp AC coupled non-inverting amp
30 EM Wave Lab
33. Electronic Circuits
8. Integrator
Miller integrator
Integrator Frequency : w int = 1/RC
Infinite DC gain : weak at DC imperfection
33 EM Wave Lab