Physics 123: Homework 3: Op Amps I
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1 P123 HW 3: op amps I 1 Physics 123: Homework 3: Op Amps I Total points: 20 (plus 3 optional); due Monday, Feb. 23, 2015 REV 0 1 ; February 14, 2015 Contents 1 Bidirectional Current Source (1 point) 1 2 Odd Summing Circuit (3 points) 2 3 V to I(4 points, total) Choose An Op Amp (2 points) Design the Circuit (2 points) Bad Circuits? (5 points) 4 5 Differential Amp (4 points) Gain (1/2 point) (quasi-) differential input 1 point Hold non-inverting input (B) fixed: Hold inverting. input (A) fixed common-mode input (1 1/2 points) A question about input impedances 1 point Wien Bridge(3 points) Why is the lamp needed? (1/2 point) Why, when everything s working right, does the circuit deliver a clean sinewave? (1/2 point) Adjustments: (2 points) frequency amplitude Designing a Wien Bridge Circuit (optional: 3 points) Question: Links to Datasheets Contents Linksto Op AmpDatasheets Bidirectional Current Source (1 point) Show how to use a current-limiting diode, like the one you used in the tail of Lab 5 s difference amp (1N5294: really an FET), to make a bidirectional 2-terminal current source. Hint: a bridge circuit like the one familiar to you from power supplies can help. A sketchy data sheet describing this part appears at the end of these HW papers. Question: voltage limit With your additional circuitry, what is the minimum voltage across the bidirectional current source that will permit it to work properly? (See sketchy data sheet for the 1N5294.) 1 Revisions: cut table of recommended op amps as distracting (2/14).
2 P123 HW 3: op amps I 2 2 Odd Summing Circuit (3 points) Suppose you would like to sum the signals provided by two transducers, giving the two transducers equal full-scale weights. The summed output is to drive an A/D, and the range of that device defines the permitted output range for your summer. We will assume the transducers provide DC signals of just one polarity, as stated below. Here are the relevant specifications: A/D input range: 0 to +2.5V signal source A: signal range: 0 to +0.5V output impedance: 10MΩ signal source B: signal range: 0 to -1mA (current sink) output impedance: 10MΩ output voltage compliance: 0.1V
3 P123 HW 3: op amps I 3 3 Vto I(4 points, total) Your task, here, is to use an op amp to convert a voltage in the range 0 to +10V into a current, sourced from a +10V positive supply, in the range 0 to 100mA. You may use either an LMH6645 op amp or an LM358 (partial data sheets attached). Don t read all this data sheet material, by the way. Instead, decide first what are the few relevant specs (or one spec), then find that specification. We offer partial data sheets for two op amps but note: only one of thosetwo op amps can do the job. And here s a hint: we re proposing two single-supply op amps. In general, these devices are good at handling inputs close to the negative supply, on input and output; some can go close to the positive supply as well. Look closely at these specifications. Here are a couple of requirements: use just one supply: +10V. Let your current source work up to at least +8V (its output voltage compliance should be 0 to +8V, to say this in jargon). 3.1 Choose An Op Amp (2 points) Which op amp do you choose, and why? (You will need to sketch your circuit before you re likely to be able to answer this question.) 3.2 Design the Circuit (2 points) Design the circuit, using the op amp of your choice. Among other tasks, check whether the op amp you choose can put out 100mA. If not, provide an appropriate circuit remedy.
4 P123 HW 3: op amps I 4 4 BadCircuits? (5 points) On the next two pages you will find some bad circuits, and a few OK ones mixed in. Tell us briefly what s wrong with the bad ones, and how to fix them. Sometimes the fix itself will be a sufficient answer. Figure 1: bad circuits: I
5 P123 HW 3: op amps I 5 (More bad? circuits) Figure 2: bad circuits: II
6 P123 HW 3: op amps I 6 5 Differential Amp (4 points) Here is a standard differential amp made with an op amp. Figure 3: diff amp 5.1 Gain (1/2 point) First, what is the circuit s differential gain? Input impedances What is the input impedance at each of the circuit s input terminals (not the op amp s terminals, n.b.), for two cases 5.2 (quasi-) differential input 1 point Apply the signals to one input terminal at a time, while the other amp input sits still: Hold non-inverting input (B) fixed: Assume that you apply the signal at the R that feeds the inverting terminal, while the other input sits still (such an arrangement in fact mixes a little common-mode signal with the differential signal; you could easily figure how much, if you were so inclined!) Hold inverting. input (A) fixed :
7 P123 HW 3: op amps I common-mode input (1 1/2 points) 5.4 A question about input impedances 1 point If you got the answer we hope you got for the two input impedances differential and commonmode then you discovered a happy fact, a fact that helps a diff amp to do what it s built to do, viz., deliver good CMRR. Please explain, if you can, the relation between CMRR and the input impedances. 6 WienBridge(3 points) Here are some questions designed to help you admire this ingenious circuit: 6.1 Why is the lamp needed? (1/2 point) Why not use a fixed resistor with R R FEEDBACK 2, to set the amplifier s gain? 6.2 Why, when everything s working right, does the circuit deliver a clean sinewave? (1/2 point) Hint: Mr. Fourier knows!
8 P123 HW 3: op amps I Adjustments: (2 points) frequency To change the sine s frequency, what should you change? amplitude To change the sine s amplitude, what should you change? (This one is hard; please justify your answer briefly.) 7 Designing a Wien Bridge Circuit (optional: 3 points) Below is an I vs V plot for a particular #344 lamp. Figure 4: I vs V for #344 lamp
9 P123 HW 3: op amps I Question: What R f eedback value would you choose, to get an output amplitude of about 9V peak-to-peak? (One could answer this experimentally but we d like to see you calculate the result.) Notes: it s temperature that changes the lamp s resistance, as you know; the plot above shows DC values (Paul and I just watched I and V on two DVM s, and wrote down the pairs of readings); since the lamp responds rather slowly to heating by the sinusoidal waveform, it is the RMS I and V values that do the job: these heat the lamp the same way as the corresponding DC values we have plotted. For example, whatever I we found at 1.0V DC is the I RMS we would see for a 1.0V RMS sine wave about 1.4V peak. the relevant resistance value that we should take from the plot is not the local slope (the incremental resistance), but the average or overall relation between I and V at the operating amplitude (simpler, really). 8 Links to Datasheets 8.1 Contents Current-limiting diode LF411 op amp data LMH6645 op amp data LM358 op amp data
10 P123 HW 3: op amps I 10 Sketchy Data Sheet Figure 5: Current-limiting diode: 1N Links to Op Amp Datasheets Datasheet for 3 Op Amps We re not asking you to read through these long documents. Instead, we re hoping you ll make a quick hunt for a single specification. LF411: LMH LM358: hw3 feb15.tex; February 14, 2015
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