Chapter 8 Operational Amplifier as a Black Box 8.1 General Considerations 8.2 Op-Amp-Based Circuits 8.3 Nonlinear Functions 8.4 Op-Amp Nonidealities 8.5 Design Examples

Chapter Outline CH8 Operational Amplifier as A Black Box

Basic Op Amp Op amp는 2개의 입력과 한 개의 출력으로 이루어진 회로 두 입력 차이를 증폭 CH8 Operational Amplifier as A Black Box

Inverting and Non-inverting Op Amp (-) 입력이 ground 되면, 이득은 (+). (+) 입력이 ground 되면, 이득은 (-). CH8 Operational Amplifier as A Black Box

Ideal Op Amp ∞ 이득 ∞ 입력 임피던스 0 출력 임피던스 ∞ 속도 ∞ 속도 CH8 Operational Amplifier as A Black Box

Virtual Short op amp의 ∞ 이득 때문에, Vin2 ≈ Vin1,  virtual short. CH8 Operational Amplifier as A Black Box

Ex 8.1) Unity Gain Amplifier CH8 Operational Amplifier as A Black Box

Op Amp with Supply Rails supply 전압을 보여주기 위하여, VCC 와 VEE 를 나타냄 Ex) VCC=+5V, VEE=-5V; VCC=+5V, VEE=0V (general) CH8 Operational Amplifier as A Black Box

Noninverting Amplifier (Infinite A0) 큰 Ao로, Vout/Vin 은 저항의 비에 관계하고 이는 매우 정밀함 CH8 Operational Amplifier as A Black Box

Ex 8.2) Extreme Cases of R2 (Infinite A0) R2 = 0이면, loop는 open, Vout /Vin = op amp의 intrinsic gain. R2 = ∞이면, unity-gain 증폭기가 됨 CH8 Operational Amplifier as A Black Box

Noninverting Amplifier (Finite A0) Ex 8.3 Gain error의 관점에서 closed-loop gain이 클수록, 회로는 정확도가 떨어짐 CH8 Operational Amplifier as A Black Box

Inverting Amplifier ∞ A0가 (-) 입력을 virtual ground로 만듦 I think the resistors positions in the equations should be reversed. Virtual ground: +와 –node의 전압이 같아서 ground(0V)로 보인다는 말임 ∞ A0가 (-) 입력을 virtual ground로 만듦 CH8 Operational Amplifier as A Black Box

Another View of Inverting Amplifier Noninverting CH8 Operational Amplifier as A Black Box

Gain Error Due to Finite A0 closed loop gain이 클수록, 회로는 정확도가 떨어짐 CH8 Operational Amplifier as A Black Box

Complex Impedances Around the Op Amp closed-loop gain는 두 임피던스의 비율. CH8 Operational Amplifier as A Black Box

8.2.3 Integrator The equation that defines the time domain behavior of the integrator is not correct..since Vin over R1, not Vout CH8 Operational Amplifier as A Black Box

Ex 8.5) Integrator with Pulse Input CH8 Operational Amplifier as A Black Box

Comparison of Integrator and RC Lowpass Filter The filter’s output looks like a ln() response, rather than an exponential response. RC low-pass filter는 사실 적분기의 “passive” 근사회로임. RC 시정수를 매우 크게 하면, RC filter 출력은 ramp에 근접함 CH8 Operational Amplifier as A Black Box

Ex 8.6) Lossy Integrator 유한한 op amp 이득을 고려하면, 적분기는 손실이 생기면 pole은 원점에서 -1/[(1+A0)R1C1]로 이동함 이는 A0+1 배로 증가한 C로 이루어진 RC회로로 등가가능 CH8 Operational Amplifier as A Black Box

Differentiator CH8 Operational Amplifier as A Black Box

Ex 8.7) Differentiator with Pulse Input CH8 Operational Amplifier as A Black Box

Comparison of Differentiator and High-Pass Filter RC high-pass filter는 사실 미분기에 대한 passive 근사회로임 RC 시정수가 매우 작으면, RC filter는 미분기에 근사하게 됨 CH8 Operational Amplifier as A Black Box

Lossy Differentiator Finite op amp gain의 경우, 미분기는 원점 zero에서 –(A0+1)/R1C1의 pole을 추가 RC HPF와 비교하여 R  R/(A0+1)로 근사화 가능. CH8 Operational Amplifier as A Black Box

Op Amp as non-inverting amplifiers Z1 = R1, Z2 = 1/sC2 이면, 이상적인 미분기가 아님 이 회로는 이상적인 적분기 또는 미분기로 동작하지 않음 CH8 Operational Amplifier as A Black Box

8.2.4 Voltage Adder (summer) Ao If R1 = R2=R CH8 Operational Amplifier as A Black Box

8.3 Nonlinear Functions

Precision Rectifier CH8 Operational Amplifier as A Black Box

Inverting Precision Rectifier (input=Vin,output=Vx) CH8 Operational Amplifier as A Black Box

Logarithmic Amplifier CH8 Operational Amplifier as A Black Box

Square-Root Amplifier CH8 Operational Amplifier as A Black Box

length, oxide thickness등등의 차이 8.4 Op Amp Nonidealities Wafer 제작과정에서 생길 수 있는 length, oxide thickness등등의 차이 CH8 Operational Amplifier as A Black Box

Op Amp Nonidealities: DC Offsets op amp의 입력 stage의 mismatch로 부터 발생하는 offset은 입출력 특성의 shift를 야기함. CH8 Operational Amplifier as A Black Box

Effects of DC Offsets op amp는 입력 뿐만 아니라 offset 또한 증폭하여 오차를 발생시킴. CH8 Operational Amplifier as A Black Box

Saturation Due to DC Offsets 3V 전원 2mV Offset은 마치 입력신호처럼 증폭되므로, 첫째 stage의 출력은 둘째 stage를 saturation (bipolar의 경우) 또는 triode (MOSFET의 경우) 영역으로 구동하게 함. CH8 Operational Amplifier as A Black Box

시간이 지나면 출력전압이 계속 커져서 전원전압까지 올라감 Offset in Integrator 시간이 지나면 출력전압이 계속 커져서 전원전압까지 올라감 CH8 Operational Amplifier as A Black Box

Offset in Integrator 출력전압이 계속 커지는 것을 막아줌 저주파 저항을 Capacitor와 병렬로 연결하여 offset을 흡수하게 함. closed-loop 전달함수는 더 이상 원점 pole은 존재하지 않고 -1/(R2C1)으로 이동함. CH8 Operational Amplifier as A Black Box

Input Bias Current bipolar base 전류의 효과는 입력에 연결된 전류원으로 모델링 가능함 CH8 Operational Amplifier as A Black Box

Effects of Input Bias Current on Noninverting Amplifier It turns out that IB1 has no effect on the output and IB2 affects the output by producing a voltage drop across R1. CH8 Operational Amplifier as A Black Box

Input Bias Current Cancellation We can cancel the effect of input bias current by inserting a correction voltage in series with the positive terminal. In order to produce a zero output, Vcorr=-IB2(R1||R2). CH8 Operational Amplifier as A Black Box

Correction for  Variation Current offset이 없는 경우에 위와 같이 전류가 흐른는 경우에도 출력으로 DC offset이 생기게 되는데, OP-AMP의 +node에서 바라본 저항과 –node에서 바라본 저항이 같아지도록 하면 제거된다. Since the correction voltage is dependent upon , and  varies with process, we insert a parallel resistor combination in series with the positive input. As long as IB1= IB2, the correction voltage can track the  variation. CH8 Operational Amplifier as A Black Box

Effects of Input Bias Currents on Integrator Input bias current will be integrated by the integrator and eventually saturate the amplifier. CH8 Operational Amplifier as A Black Box

Integrator’s Input Bias Current Cancellation 앞과 같은 방법으로 저항 추가 By placing a resistor in series with the positive input, integrator input bias current can be cancelled. However, the output still saturates due to other effects such as input mismatch, etc. CH8 Operational Amplifier as A Black Box

Open loop Gain(feedback 회로를 연결하지 않은)의 주파수 특성 Speed Limitation Open loop Gain(feedback 회로를 연결하지 않은)의 주파수 특성 Due to internal capacitances, the gain of op amps begins to roll off. CH8 Operational Amplifier as A Black Box

Continued : Gain X bandwidth = constant Closed loop Gain(feedback 회로를 연결된)의 주파수 특성 OP-AMP를 이용해서 만든 회로는 OP-AMP의 한계를 넘어서는 특성을 절대로 보일 수 없다.

Bandwidth and Gain Tradeoff Having a loop around the op amp (inverting, noninverting, etc) helps to increase its bandwidth. However, it also decreases the low frequency gain. CH8 Operational Amplifier as A Black Box

Slew Rate of Op Amp # step 입력에 대해서 출력이 step출력이 나오지 않게 됨: OP-AMP가 가지고 있는 최대 단위 시간당 전압의 변화를 slew rate라고 함. 1)step입력에 대해서 M2가 off되고, M4가 공급해 주는 전류에 의해서, Vout이 High로 올라 간다. 출력전압은 capacitor에 공급되는 전류에 의해서 High로 올라가기 때문에, linear하게 커지는 출력전압이 나온다. 2)step입력에 대해서 M1이 off되고, M2가 빼내는 전류에 의해서, Vout이 Low로 떨어진다. 출력전압은 capacitor에서 빼내는 전류에 의해서 Low로 떨어지기 때문에, linear하게 떨어지는 출력전압이 나온다. # Slew rate한계를 가지는 OP-AMP를 사용한 회로: 출력이 단위시간당 전압의 변화가 OP-AMP의 slew rate를 넘게 되는 경우에 출력 파형이 입력파형과 다르게 나옴. A) 출력 전압의 큰 변화가 생기는 경우, B) 주파수가 높은 경우 CH8 Operational Amplifier as A Black Box

Slew Rate of Op Amp: 전압의 큰 변화 In the linear region, when the input doubles, the output and the output slope also double. However, when the input is large, the op amp slews so the output slope is fixed by a constant current source charging a capacitor. This further limits the speed of the op amp. CH8 Operational Amplifier as A Black Box

Comparison of Settling with and without Slew Rate As it can be seen, the settling speed is faster without slew rate (as determined by the closed-loop time constant). CH8 Operational Amplifier as A Black Box

Slew Rate Limit on Sinusoidal Signals: 주파수가 높은 경우 As long as the output slope is less than the slew rate, the op amp can avoid slewing. However, as operating frequency and/or amplitude is increased, the slew rate becomes insufficient and the output becomes distorted. CH8 Operational Amplifier as A Black Box

Maximum Op Amp Swing To determine the maximum frequency before op amp slews, first determine the maximum swing the op amp can have and divide the slew rate by it. CH8 Operational Amplifier as A Black Box

Nonzero Output Resistance In practical op amps, the output resistance is not zero. It can be seen from the closed loop gain that the nonzero output resistance increases the gain error. CH8 Operational Amplifier as A Black Box

Design Examples Many design problems are presented at the end of the chapter to study the effects of finite loop gain, restrictions on peak to peak swing to avoid slewing, and how to design for a certain gain error. CH8 Operational Amplifier as A Black Box