In Class Question. List what topics you d like to emphasize in the quiz review: (top three)

Size: px

Start display at page:

Download "In Class Question. List what topics you d like to emphasize in the quiz review: (top three)"

Ethan Kelley
6 years ago
Views:

1 In Class Question List what topics you d like to emphasize the quiz review: (top three) Combg resistors oltage divider Identiyg ilters (high and low req) Transer unctions (magnitude, phase) Determg resonant requency Transormers PSpice

2 Electronic Instrumentation Experiment 4 * Part A: Introduction to Operational Ampliiers * Part B: oltage Followers * Part C: Integrators and Dierentiators * Part D: Ampliyg the Stra Gauge Signal

3 Part A Introduction to Operational Ampliiers Operational Ampliiers Op-Amp Circuits The Invertg Ampliier The Non-Invertg Ampliier

4 Operational Ampliiers Op-Amps are possibly the most versatile lear tegrated circuits used analog electronics. The Op-Amp is not strictly an element; it contas elements, such as resistors and transistors. However, it is a basic buildg block, just like, L, and C. We treat this complex circuit as a black box.

5 The Op-Amp Chip The op-amp is a chip, a small black box with 8 connectors or ps (only 5 are usually used). The ps any chip are numbered rom (startg at the upper let o the dent or dot) around a U to the highest p ( this case 8). 74 Op Amp or LM35 Op Amp

6 Op-Amp Input and Output The op-amp has two puts, an vertg put (-) and a non-vertg put (+), and one put. The put goes positive when the non-vertg put (+) goes more positive than the vertg (-) put, and vice versa. The symbols + and do not mean that that you have to keep one positive with respect to the other; they tell you the relative phase o the put. ( = - 2 ) A raction o a millivolt between the put termals will swg the put over its ull range.

7 Powerg the Op-Amp Sce op-amps are used as ampliiers, they need an external source o (constant DC) power. Typically, this source will supply +5 at + and -5 at -. We will use ±9. The op-amp will put a voltage range o o somewhat less because o ternal losses. The power supplied determes the put range o the op-amp. It can never put more than you put. Here the maximum range is ab 28 volts. We will use ±9 or the supply, so the maximum put range is ab 6.

8 Op-Amp Intrsic Ga Ampliiers crease the magnitude o a signal by multiplier called a ga -- A. The ternal ga o an op-amp is very high. The exact ga is oten unpredictable. We call this ga the open-loop ga or trsic ga. 5 6 Aopen loop 0 0 The put o the op-amp is this ga multiplied by the put A ol A ol 2

9 Op-Amp Saturation The huge ga causes the put to change dramatically when ( - 2 ) changes sign. However, the op-amp put is limited by the voltage that you provide to it. When the op-amp is at the maximum or mimum extreme, it is said to be saturated. i i 2 2 then then positive negative How can we keep it rom saturatg? saturation saturation

10 Feedback Negative Feedback As ormation is ed back, the put becomes more stable. Output tends to stay the lear range. The lear range is when =A( - 2 ) vs. beg saturation. Examples: cruise control, heatg/coolg systems Positive Feedback As ormation is ed back, the put destabilizes. The op-amp tends to saturate. Examples: Guitar eedback, stock market crash Positive eedback was used beore high ga circuits became available.

11 Op-Amp Circuits use Negative Feedback Negative eedback couples the put back such a way as to cancel some o the put. Ampliiers with negative eedback depend less and less on the open-loop ga and ally depend only on the properties o the values o the components the eedback network (extrsic ga) The system gives up excessive ga to improve predictability and reliability.

12 Op-Amp Circuits Op-Amps circuits can perorm mathematical operations on put signals: addition and subtraction multiplication and division dierentiation and tegration Other common uses clude: Impedance buerg Active ilters Active controllers Analog-digital teracg

13 Typical Op Amp Circuit + and - power the op-amp is the put voltage signal 2 is the eedback impedance is the put impedance 2 0k + 9dc load is the load OFF = 0 AMPL =.2 FEQ = k k 0 U ua74-9dc OS2 OUT OS load k 0 0 0

14 The Invertg Ampliier A

15 The Non-Invertg Ampliier A g g

16 Part B The oltage Follower Op-Amp Analysis oltage Followers

17 Op-Amp Analysis We assume we have an ideal op-amp: ite put impedance (no current at puts) zero put impedance (no ternal voltage losses) ite trsic ga stantaneous time response

18 Golden ules o Op-Amp Analysis ule : A = B The put attempts to do whatever is necessary to make the voltage dierence between the puts zero. The op-amp looks at its put termals and swgs its put termal around so that the external eedback network brgs the put dierential to zero. ule 2: I A = I B = 0 The puts draw no current The puts are connected to what is essentially an open circuit

19 Steps Analyzg Op-Amp Circuits ) emove the op-amp rom the circuit and draw two circuits (one or the + and one or the put termals o the op amp). 2) Write equations or the two circuits. 3) Simpliy the equations usg the rules or op amp analysis and solve or / Why can the op-amp be removed rom the circuit? There is no put current, so the connections at the puts are open circuits. The put acts like a new source. We can replace it by a source with a voltage equal to.

20 Analyzg the Invertg Ampliier ) vertg put (-): non-vertg put (+):

21 How to handle two voltage sources B B k k k B

22 : : ) Invertg Ampliier Analysis B A A B B i 0 3) 0 : : 2)

23 Analysis o Non-Invertg Ampliier Note that step 2 uses a voltage divider to d the voltage at B relative to the put voltage. ) : : 2) : : 3) A A B B g g g g g g g

24 The oltage Follower analysis ] A A B : 2] thereore, B

25 Why is it useul? In this voltage divider, we get a dierent put dependg upon the load we put on the circuit. Why?

26 We can use a voltage ollower to convert this real voltage source to an ideal voltage source. The power now comes rom the +/- 5 volts to the op amp and the load will not aect the put.

27 Part C Integrators and Dierentiators General Op-Amp Analysis Dierentiators Integrators Comparison

28 Golden ules o Op-Amp Analysis ule : A = B The put attempts to do whatever is necessary to make the voltage dierence between the puts zero. The op-amp looks at its put termals and swgs its put termal around so that the external eedback network brgs the put dierential to zero. ule 2: I A = I B = 0 The puts draw no current The puts are connected to what is essentially an open circuit

29 General Analysis Example() Assume we have the circuit above, where Z and Z represent any combation o resistors, capacitors and ductors.

30 General Analysis Example(2) We remove the op amp rom the circuit and write an equation or each put voltage. Note that the current through Z and Z is the same, because equation ] is a series circuit.

31 General Analysis Example(3) I Sce I=/Z, we can write the ollowg: I Z But A = B = 0, thereore: Z Z A A Z Z Z

32 General Analysis Conclusion For any op amp circuit where the positive put is grounded, as pictured above, the equation or the behavior is given by: Z Z

33 Ideal Dierentiator Phase shit j/2 - ± Net-/2 analysis : Z Z j C j C Amplitude changes by a actor o C

34 Analysis time doma dt d C thereore dt d C I I I I I dt d C I B A A A C C C, 0 ) ( I

35 Problem with ideal dierentiator Ideal eal Circuits will always have some kd o put resistance, even i it is just the 50 ohms or less rom the unction generator.

36 Analysis o real dierentiator I Z Z Z j C j C j C j C Low Frequencies j C ideal dierentiator High Frequencies vertg ampliier

37 Comparison o ideal and non-ideal Both dierentiate sloped region. Both curves are idealized, real put is less well behaved. A real dierentiator works at requencies below c =/ C

38 Ideal Integrator Phase shit /j-/2 - ± Net/2 analysis : Amplitude changes by a actor o / C Z Z j C j C

39 Analysis time doma ) ( 0 ) ( DC B A A A C C C dt C C dt d dt d C I I I I dt d C I I I

40 Problem with ideal tegrator () No DC oset. Works OK.

41 Problem with ideal tegrator (2) With DC oset. Saturates immediately. What is the tegration o a constant?

42 Miller (non-ideal) Integrator I we add a resistor to the eedback path, we get a device that behaves better, but does not tegrate at all requencies.

43 Behavior o Miller tegrator Low Frequencies Z Z vertg ampliier High Frequencies Z Z ideal tegrator jc The luence o the capacitor domates at higher requencies. Thereore, it acts as an tegrator at higher requencies, where it also tends to attenuate (make less) the signal.

44 Analysis o Miller tegrator Z Z Z I j C j j C j C C j C Low Frequencies vertg ampliier High Frequencies j ideal tegrator C

45 Comparison o ideal and non-ideal Both tegrate sloped region. Both curves are idealized, real put is less well behaved. A real tegrator works at requencies above c =/ C

46 Problem solved with Miller tegrator With DC oset. Still tegrates e.

47 Why use a Miller tegrator? Would the ideal tegrator work on a signal with no DC oset? Is there such a thg as a perect signal real lie? noise will always be present ideal tegrator will tegrate the noise Thereore, we use the Miller tegrator or real circuits. Miller tegrators work as tegrators at > c where c =/ C

48 Comparison Dierentiation Integration origal signal v(t)=as(t) v(t)=as(t) mathematically dv(t)/dt = Acos(t) v(t)dt = -(A/cos(t) mathematical +90 (se to cose) -90 (se to cose) phase shit mathematical / amplitude change H(j H(jjC H(jjC = j/c electronic phase shit electronic amplitude change -90 (-j) +90 (+j) C C The op amp circuit will vert the signal and multiply the mathematical amplitude by C (dierentiator) or /C (tegrator)

49 Agenda and Notes Today, durg class! 9:30 a.m. Boeg Space and Intelligence Systems (Matt and Matt) 4 extra credit assignments available at the bottom o ion/eilks.html Friday, Oct. 3 (EMPAC!), Open shop 2:00-5:00 p.m

50 Electronic Instrumentation Experiment 4 (contued) Part A. Op Amp Basics eview Part B. Adder and Dierential Op Amp Part C. Op Amp Limitations

51 What is an op amp? An expensive, versatile, tegrated circuit that is another basic buildg block to electronics (made o resistors and transistors) Ampliier that has Large open loop ga (trsic) Dierential put stage, vertg put (-) and non-vertg put (+) One put Uses components the eedback network to control the relationship between the put and put

52 What does an Op-Amp do? Perorms operations on an put signal Ampliication Buerg Integration/Dierentiation Addition/Subtraction

53 Open Loop/Closed Loop and Feedback Open loop ery high ga (trsic ga) Poor stability Open loop ga assumed to be ite or ideal op amps Closed loop Uses eedback to add stability educes ga o the ampliier Output is applied back to the vertg (-) put Most ampliiers are used this coniguration Feedback - Σ Open loop + ga

54 Golden ules o Op-Amp Analysis ule : A = B The put attempts to do whatever is necessary to make the voltage dierence between the puts zero. The op-amp looks at its put termals and swgs its put termal around so that the external eedback network brgs the put dierential to zero. ule 2: I A = I B = 0 The puts draw no current The puts are connected to what is essentially an open circuit

55 Steps Analyzg Op-Amp Circuits ) emove the op-amp rom the circuit and draw two circuits (one or the + and one or the put termals o the op amp). 2) Write equations or the two circuits. 3) Simpliy the equations usg the rules or op amp analysis and solve or / Why can the op-amp be removed rom the circuit? There is no put current, so the connections at the puts are open circuits. The put acts like a new source. We can replace it by a source with a voltage equal to.

56 The Invertg Ampliier A

57 The Non-Invertg Ampliier A g g

58 The oltage Follower High put impedance Low put impedance Buer circuit A

59 Ideal Dierentiator Time doma (like oscilloscope) C d dt analysis : Z Z j C j C Frequency doma (like AC sweep) Amplitude changes by a actor o C

60 Comparison o ideal and non-ideal Both dierentiate sloped region. Both curves are idealized, real put is less well behaved. A real dierentiator works at requencies below c =/ C

61 Ideal Integrator Time doma (like oscilloscope) dt ( DC ) C analysis : Z Z What happens to a capacitor at DC? Amplitude changes by a actor o / C j C j C Frequency doma (like AC sweep)

62 Miller (non-ideal) Integrator I we add a resistor to the eedback path, we get a device that behaves better, but does not tegrate at all requencies.

63 Comparison o ideal and non-ideal Both tegrate sloped region. Both curves are idealized, real put is less well behaved. A real tegrator works at requencies above c =/ C

64 Comparison Dierentiaion Integration origal signal v(t)=as(t) v(t)=as(t) mathematically dv(t)/dt = Acos(t) v(t)dt = -(A/cos(t) mathematical +90 (se to cose) -90 (se to cose) phase shit mathematical / amplitude change H(j H(jjC H(jjC = j/c electronic phase -90 (-j) +90 (+j) shit electronic amplitude change C C The op amp circuit will vert the signal and multiply the mathematical amplitude by C (dierentiator) or /C (tegrator)

65 In Class Problem. Which op amp below has a ga o +5? a) b) c) 2. Op amp Analysis. What are the golden rules or op amp analysis? 2. For the circuit to the right draw two circuits (one or put and one or + put) 3. Write the equation or each circuit

66 In Class Problem. Which op amp below has a ga o +5? All o them! Topology may look dierent but the unctionality is the same! 2. Op amp Analysis. What are the golden rules or op amp analysis? 2. For the circuit to the right draw two circuits (one or put and one or + put) 3. Write the equation or each circuit + Z 3 Z 2 Z Z Z

67 Op Amps to know Invertg Non-vertg oltage Follower Dierentiator Integrator Adder Dierential (Subtractg)

68 Adders i 2 then Output signal is the sum o the put signals ( and 2).

69 Weighted Adders Unlike dierential ampliiers, adders are also useul when 2. This is called a Weighted Adder A weighted adder allows you to combe several dierent signals with a dierent ga on each put. You can use weighted adders to build audio mixers and digital-to-analog converters.

70 Analysis o weighted adder I2 I I I I I I I I B A A A A A A A

71 Dierential (or Dierence) Ampliier ( 2 ) A

72 Analysis o Dierence Ampliier() ) : :

73 B A B B B B A B B or solve i : : 3) : : 2) Analysis o Dierence Ampliier(2) Note that step 2(-) here is very much like step 2(-) or the vertg ampliier and step 2(+) uses a voltage divider.

74 Op-Amp Limitations Model o a eal Op-Amp Saturation Current Limitations Slew ate

75 Internal Model o a eal Op-amp = - 2 Z Z + A ol Z is the put impedance (very large 2 MΩ) Z is the put impedance (very small 75 Ω) A ol is the open-loop ga

76 Saturation Even with eedback, any time the put tries to go above + the op-amp will saturate positive. Any time the put tries to go below - the op-amp will saturate negative. Ideally, the saturation pots or an op-amp are equal to the power voltages, reality they are -2 volts less. Ideal: -9 < < +9 eal: -8 < < +8

77 Additional Limitations Current Limits I the load on the op-amp is very small, Most o the current goes through the load Less current goes through the eedback path Op-amp cannot supply current ast enough Circuit operation starts to degrade Slew ate The op-amp has ternal current limits and ternal capacitance. There is a maximum rate that the ternal capacitance can charge, this results a maximum rate o change o the put voltage. This is called the slew rate.

78 Analog Computers (circa. 970) Analog computers use op-amp circuits to do real-time mathematical operations (solve dierential equations).

79 Usg an Analog Computer Users would hard wire adders, dierentiators, etc. usg the ternal circuits the computer to perorm whatever task they wanted real time.

80 Analog vs. Digital Computers In the 60 s and 70 s analog and digital computers competed. Analog Advantage: real time Disadvantage: hard wired Digital Advantage: more lexible, could program jobs Disadvantage: slower Digital ws they got aster they became multi-user they got even more lexible and could do more than just math

81 Now analog computers live museums with old digital computers: Md Mache Web Museum: Analog Computer Museum:

Lecture 4: Opamp Review. Inverting Amplifier (Finite A 0 )

Lecture 4: Opamp Review. Inverting Amplifier (Finite A 0 ) Lecture 4: Opamp eview Effect of fite open-loop ga, A Frequency dependence of open-loop ga Frequency dependence of closed-loop ga Output voltage and current saturation Output slew rate Offset voltage Input