1. Department of Information Engineering357 Operation amplifier The tail, large impedance gives high CMRR Mirror as active load. High gain Follower as buffer amplifier Push-pull class B amp

2. Department of Information Engineering358 Operational amplifier Op-amp –Differential amp + non-linear amp + output driver Op-amp has very high gain (A) –But the gain is non-linear (because I C vs V BE is not linear) Use global feedback to build linear amplifier –Exact value of the gain of the op amp is not important, as long as it is very large

3. Department of Information Engineering359 Feedback Op amp golden rules Approximations: 1.Voltage difference between the two inputs is zero 2.Input draws no current Why? –V OUT = A V IN –If V OUT is around 10V, A=10,000, then V IN ~ 1mV, voltage difference ~ 1mV (close to zero) –FET draws virtually zero input current V IN V OUT

4. Department of Information Engineering360 Gain of this amplifier? VV

5. Department of Information Engineering361 An easier method Because A is so large that V  ~ 0 (known as virtual earth) V  ~ 0

6. Department of Information Engineering362 Inverting amplifier Input impedance (R IN )? –V  ~ 0, so R IN = R 1 Important –gain is determined by external parameters that we can control (the resistors) –gain (A) of the op amp can be non-linear, its exact value is not important, as long as it is very large

7. Department of Information Engineering363 Negative feedback Feedback MUST be applied to the –ve terminal (–ve feedback), so that V  ~ 0 (IMPORTANT) A) Works B) Doesn’t Work

8. Department of Information Engineering364 Positive feedback +ve V IN produces large +ve V OUT –+ve V OUT produces +ve V  which produces an even larger +ve output. –output reaches max +ve supply voltage very quickly useless as an amplifier (but good as a switch, small +ve signal produces large maximum output)

9. Department of Information Engineering365 Non-inverting amplifier R IN ? –infinite ! V-? –V- ~ V IN (V  ~ 0) Current through R 1 ? –I=V IN / R 1 Output voltage? – V- VV

10. Department of Information Engineering366 Voltage follower Left side circuit (work) –If output is too large, then feedback to the –ve terminal will reduce output to a equilibrium level until V  ~ 0 Right side circuit (doesn’t work) –If output is too large, then feedback to the +ve terminal will make the output even larger until saturation

11. Department of Information Engineering367 Power booster The output current of an op amp is usually small If you want larger output current, add an external push-pull follower made of discrete power transistors

12. Department of Information Engineering368 Power booster Normally push-pull follower has cross-over distortion –Not this one ! The gain of the amplifier depends on the external feedback circuit The forward gain of the internal circuit can be non- linear but must be large

13. Department of Information Engineering369 Power of feedback Can put in anything in the forward loop, still get good result

14. Department of Information Engineering370 Funny circuits What is the function of this circuit?

15. Department of Information Engineering371 Funny circuits Does this circuit work?

16. Department of Information Engineering372 Practical circuits Design an inverting amplifier with a gain of -100, to be driven by a source whose output impedance is 1M  –What is the value of R? How about 100R?

17. Department of Information Engineering373 Practical circuits A better solution

18. Department of Information Engineering374 Practical circuits Summing circuit (an adder) V IN V OUT

19. Department of Information Engineering375 V1V1 V2V2 V3V3 I

20. Department of Information Engineering376 Practical circuits (a simple digital-to-analog converter) V OUT = A+2B-3C

21. Department of Information Engineering377 Practical circuits Perfect current source using imperfect FET V + -V IN

22. Department of Information Engineering378 Active rectifier The simple passive rectifier has 0.6V drop between input and output

23. Department of Information Engineering379 Active rectifier without the diode drop (optional) The active rectifier does not have the 0.6V drop !! –V IN >0, V OUT is +ve, diode is short-circuit Feedback => V OUT = V IN (no 0.6V DC offset)

24. Department of Information Engineering380 Problem –ve input to V+, V OUT, diode is open circuit V OUT pushes to –ve extreme When input becomes +ve, takes a long time for the output to move from –ve to +ve (limited by the slew rate)

25. Department of Information Engineering381 Active rectifier (optional) This improved circuit prevents the rectifier from saturation

26. Department of Information Engineering382 Negative-impedance converter (NIC) An interesting two-terminals active device –apply a +ve voltage, you see a current flowing OUT –a negative impedance (!!) –i.e. Z IN = - Z !! –(leave the proof as exercise)

27. Department of Information Engineering383 Gyrator The following circuit is a gyrator – (leave the proof as exercise)

28. Department of Information Engineering384 Gyrator Use of gyrator –can turn a capacitor into inductor !! How? – –Z IN behaves as an inductor with L = CR 2 The use –replace bulky inductors by small gyrated capacitors –useful in integrated circuit design and small devices

29. Department of Information Engineering385 Positive feedback Apply feedback to the non-inverting (+ve) terminal –small +ve input produces a larger +ve output –output is feedback to the non-inverting input –produces an even larger output –quickly push the output to saturation Uses –Comparators –Oscillators

30. Department of Information Engineering386 Comparator – a simple switch Output = +15V if V IN < 0 Output = -15V if V IN > 0 V IN -+-+ V OUT +15V -15V

31. Department of Information Engineering387 A poor comparator because –if the input is noisy, the output makes several transitions (switching noise)

32. Department of Information Engineering388 311 op amp The output stage (emitter follower) is connected to external power supply User can choose the output voltage they like

33. Department of Information Engineering389 Schmitt trigger (an inverter switch, high V IN, low V OUT ) Hysteresis (circuit has memory) –the output switches at two separate threshold

34. Department of Information Engineering390 Analysis If V OUT = high (~5V) –V OUT ~= 5V, –Switching threshold V + = 5V When V IN > 5V –V OUT =0V –Switching threshold V + =4.76V Now if V IN drops slightly below 5V –V OUT won’t change state –Eliminate noisy switching

35. Department of Information Engineering391 Analysis V IN > 5V, V OUT =0V, V + =4.76V If V IN < 4.76V, V OUT =5V, –V + =5V (the new threshold)

36. Department of Information Engineering392 Positive feedback if phase shift = 180 o in box ‘X’ at certain frequency, then the feedback becomes +ve (unstable) !! This high frequency has sustained itself even there is no input –oscillation

37. Department of Information Engineering393 Nasty oscillators A follower driving a long cable (a common problem) –phase shift through the op amp = 180 o –cable’s capacitance adds another 90 o –The internal capacitance at high frequency adds another 90 o The follower oscillates ! (cable capacitance)

38. Department of Information Engineering394 Ways to break the oscillation Op amp oscillates at high frequency because of the additional phase shift introduced by its internal capacitor Solution –Reduce the loop gain AB at high frequency At the frequency that may cause oscillation, make A ~ 0, so that the loop gain (AB) < 1 –Op am that does this is called frequency compensated op amp Disadvantage is that the max bandwidth is reduced

39. Department of Information Engineering395 One oscillates, the other not –411 is frequency compensated, never oscillates 411 311 Never oscillates May oscillates |A| f f f occ

40. Department of Information Engineering396 Slew rate The rate that output can change Wider bandwidth  higher frequency  faster slew rate 311 has faster slew rate, good as a switch

41. Department of Information Engineering397 What is the use of these two resistors?