Section 4: Operational Amplifiers

Transcription

1 Section 4: Operational Amplifiers Op Amps Integrated circuits Simpler to understand than transistors Get back to linear systems, but now with gain Come in various forms Comparators Full Op Amps Differential Op Amps H-Bridge Op Amps 237

2 Operational Amplifiers ( Op Amp ) Integrated Circuit (IC) complex system on a chip with simple behavior. 2 types in lab: Comparator Full Op Amp 238

3 Systems and Schematics 239

4 Input and Output Impedance Thevenin equivalent is handy here 240

5 Operational Amplifier ( Op Amp ) V "#$ =A V %&' V %&), A Properties of Ideal Op Amp 1. Infinite Input Impedance 2. Zero Output Impedance 3. Infinite Gain 241

6 Properties of Ideal Op Amp 1. Infinite Input Impedance Reads input voltage without changing it by drawing current. 2. Zero Output Impedance produce Can source infinite output current without effecting voltage. V /01 = V IR = V 3. Infinite Gain Like a battery with zero internal resistance. Equal for both inputs, so can have single variable A. V "#$ =A V %&' V %&), A 0 242

7 Comparator Simple Op Amp for comparing voltages Single-Sided Power Supply (just + and ground) Open Collector output: can only sink (pull) current, not source (push) it. 243

8 Our Comparator the LM339 Gain >10 6 practically infinite Input current 25 na practically infinite input impedance Response time 1μS very fast, generally slams all the way up or down Output 16 ma maintains desired voltage up to this current (open collector) 244

9 Comparator light-sensing circuit Wheatstone bridge Basically, comparators have a digital output. 245

10 Comparator thermoregulation circuit Example of Negative Feedback 246

11 To prevent chatter change the set point using positive feedback 247

12 Heater with transistor for current gain 248

13 Comparator powering a relay Advantage of relay Switch provides practically 0 to resistance Complete isolation between coil and switch 249

14 Weller Soldering Iron Station Thermoregulation magnet heats up, loses its magnetism, and releases (opens) switch Natural hysteresis in time to heat magnet. 250

15 Reasons for open collector Digital inputs usually have a pull-up resistor. The open collector avoids needing to specify the 1 voltage for such inputs. The 0 voltage is always ground. Sub-systems do not need to share power supplies, just grounds. Two outputs can be connected together and either can pull the input to ground. 251

16 LM339 other characteristics Power supply 2-36 V Single-sided, can be simple battery. Quiescent supply current 0.8 ma Current used within the comparator itself. Max output saturation voltage 1 V When Open Collector output transistor is fully on Max offset voltage (input + to -) 3 mv Maximum error in voltage comparison between inputs 252

17 Differential Input First stage in Comparator or Full Op Amp Two emitter follower circuits. Since V common floats, current I is split proportional to V %&' and V %&) with corresponding voltages across the two equal resistors R C. 253

18 Differential amps reject noise Twisted pair takes both wires through same noise-generating spatial field. Signal is out of phase. Noise is in-phase (common mode). If gains are equal (single gain A ) V "#$ =A V %&' V %&) then noise exactly cancels. However, in reality gains are unequal (A 5 A 7 ): V "#$ = A 1 V %&' A 2 V %&) 254

19 Common Mode Rejection Ratio How well does a real differential amp reject noise? Since noise is common-mode, the measure is called Common Mode Rejection Ratio (CMRR). V "#$ = A 1 V %&' A 2 V %&) CMRR 1 2 A 5 + A 7 A 5 A 7 Goal is to make (A 5 = A 7 ), so that CMRR = and V "#$ =A V %&' V %&) 255

20 Comparator vs. Full Op Amp faster (response time) open collector output usually just + power with ground the lowest voltage output basically digital, binary question: which input voltage is higher? slower (slew rate) push-pull output usually +/ powers with ground in the middle between them output fully analog, basis for linear systems with gain. 256

21 Push-Pull Output Stage can source and sink current speaker 257

22 Integrated Circuits (ICs) ¼ of the LM339 Comparator No resistors or capacitors. Fast, simple, basically digital. 258

23 ½ of the LM1458 Operational Amplifier Lots of resistors and even capacitors. Not as fast, subtle, analog. 259

24 Full Operational Amplifier also called a buffer 260

25 Negative Feedback If output too high, it is caused to go lower, and visa versa 261

26 Virtual Ground Inverting Amplifier Possible because we now have + and power supplies 262

27 Inverting Adder Each input has its own gain. For example: Gain a =V out V in = -R 2 R 1a 263

28 Non-Inverting Amplifier 264

29 Op Amp Circuits using Complex Impedance virtual ground 265

30 Differentiator or simply by applying the equation for the complex gain of the inverting amplifier 266

31 Integrator 267

32 268

33 269

34 270

35 271

36 272

37 Differential (Instrumentation) Amplifier Voltage followers used to provide infinite input impedance Finite gain determined by R 2 /R 1 Differential good for rejecting noise (CMRR), assuming matching resistors are used. Instead of virtual ground pivot point is set to R 2 /(R 1 +R 2 ) 273

38 274

39 275

40 Actual Instrumentation Amplifier Very high input impedance Gain controlled by a single resistor R gain Single IC with R gain only external resistor (e.g. AD623 from Analog Devices, Inc.) 276

41 Commercial Audio Power Op Amp (H-Bridge) 277

42 Audio Amp IC from Lab 4 H-Bridge 278

43 Real Op Amps: Open Loop Gain A vs. Frequency where ( ) V out = A V in+ V in

44 Square Wave Oscillator based on Hysteresis From Lab 7 capacitor charges and discharges between two thresholds. 280

45 Sinusoidal Oscillator 281

46 282

47 R 3 integrator multiply by 1 C 1 C 1 R 2 R 1 R 1 R 2 V ( t) integrator R 4 V t ( ) = d 2 V ( t) dt V ( t)dt R 1 C 1 R 1 C 1 dt = V ( t) is sinusoid ω = 1 R 1 C 1 1 R 1 C 1 2 V ( t) Amplitude of sinusoid determined by e t R 3 C 1 and e + t R 4 C 1 283

48 Why doesn t oscillators keep expanding? see movie 284

49 Laplace adds a real component σ to the phasor e F e GH = e F'GH We use a new variable, s s = σ + jω Basis function becomes e DE 285

50 Recall the Fourier Transform Applies to any finite signal (not just periodic) Fourier Transform ( ) = x t X ω + ( )e jωt dt Inverse Fourier Transform x( t) = 1 2π + X ( ω )e jωt dω 286

51 Now becomes Laplace Transform Applies to any signal (not just finite), any linear differential equation Laplace Transform 'N X s = J x t e )DE dt )N Inverse Laplace Transform x t = 1 F'GN 2πj J X s e'de ds F)GN 287

52 Exponential Amp Log Amp Because current is exponential of voltage in diode. Now can multiply signals by taking log of each, then add them and take exponential

53 R PQ Negative Resistance Circuit presents an effective negative input resistance R PQ =V R R R to signal generator V S Proof: op amp inputs are equal, V [ = V \]E Also, X Y X Y 'X Z V \]E = V [ I [ R W Combining these yields, V [ R 5 + R 7 R 5 R 5 R 5 R PQ = T U V U = R W X Y X Z = I [ R W Negative Resistance 289

54 Inductance Gyrator I in Simulates an inductor Provides inductance without large, costly inductor V in 290