EE40 SU2010 HW3 Due Tuesday at 2 PM in the box in 240 Cory 1. Find an expression for in terms of in Figure P14.32. Assume there is some external source driving 2. 3.4. Weird Feedback Party Consider the following problem (which some of you might recognize from Nathan Cheung’s Fall 2009 midterm. When you’re done with this homework, go work on old midterm problems! There’s a link on the course website. Any midterm 1 problem which doesn’t involve capacitors or inductors is probably fair game!)Recall that in class that I never really gave a guideline to determining whether or not we have negative feedback other than “if there is only one op-amp, and there is a path from the output to the negative terminal, you have negative feedback.” This is because it sometimes takes a little thinking to figure out what type of feedback is being applied to an op-amp. As we said in class, we have negative feedback on an op-amp whenever the output of the op-amp tends to equalize the input terminals, or in other words, when a small deviation between and generates an output which forces them to be equal. Positive feedback is the opposite, and is simply when a small deviation between and generates an output which forces them apart. The obvious way to get negative feedback is to simply wire the output port back to the port through a network of resistors, which we showed in class will result in . However there are other ways of getting negative feedback. For example, above, we have the output of one op-amp driving the positive input of the first. There are two ways to figure out what the circuit above does, the hard way, and the easy way. We’ll do both now. a. Hard way step 1: Replace the op-amps with an IDEAL op-amp (infinite input resistance and zero output resistance), and show the following: NOTE: There was a typo here, and there should NOT be a minus sign. b. Hard way step 2: From part a, what happens to as A goes to infinity? What does this mean about the overall effect of feedback on the left op-amp? c. Easy way step 1: What kind of amplifier do we have in the stage connecting and ? d. Easy way step 2: Imagine and are very close to equal. If were to suddenly get slightly larger (due to random noise, for example), think about what will happen in the next moment of time: i. How would react? Would it increase or decrease? ii. How would react? (use your answer from c) Would it increase or decrease? iii. How would react? Would it increase or decrease? Your answer to part d.iii, if you were right, basically says that minor deviations in the input terminals to the left op amp tend to drive the inputs to be equal. e. Given your answers to a through d, is it safe to use the summing point constraint? Why or why not? 5. Weird feedback party, part 2Find Vo for: b. Find Vo for: c. Find Vo and V16. Use the superposition to find a Norton equivalent to the circuit in Figure P2.79. 7. The I-V characteristic when looking into the terminals of a Thevenin equivalent circuit can be given by . Give and in terms of , , and/or . 8. Imagine a made up voltage VQ applied to terminals a and b of the circuit in Figure P2.79 above, with the positive terminal going connected to a, and the negative terminal connected to b. a. Find IQ (the current going in to terminal a) as a function of this hypothetical VQ. Plot the I-V characteristic of the circuit given your answer. (Recall that the I-V characteristic relates thecurrent flowing from the + side to the – side of the applied voltage, i.e. a resistor’s I-V characteristic has a positive slope) b. Would the I-V characteristic looking in to terminals a and c be different? c. Given the function you found in part a, and your answer to question 7, what is the Thevenin equivalent circuit? Explain how you got this answer. (Yes it should agree with your answer to #6) 9. Suppose we have an input device (for example, a portable music player) which generates a 2V output signal with internal resistance 20Ω. Suppose this device is hooked up to an amplifier with input resistance 106 Ω, output resistance 0.1Ω, and with no load attached, and the amplifier in turn drives a resistive load with resistance RL. a. How much power does the input need to supply to get its signal in to the amplifier? (Hint: Consider the equivalent circuit that the input device sees) b. What is the smallest load RL that we can attach and still get at least a 20V output across the load? (Hint: Consider the equivalent circuit the load sees) c. Suppose we can modify our amplifier and change the output resistance without changing any other parameter of the system. If our goal is to maximize power delivered to RL, what output resistance should we choose? (Hint: Draw the equivalent circuit which includes the output part of the op amp and the load resistor) Notes: Don’t forget there’s a circuit simulator that’s pretty cool, located here: http://www.falstad.com/circuit/ If you’d like to experiment with variations on the op-amp circuit from problem 4, I’ve put up the circuit in the hw directory, which you can import into Falstad’s circuit simulator using the import button. Circuit available from the link below: http://inst.eecs.berkeley.edu/~ee40/su10/assignments/hw/hw3_circuit.txt Extra problems: [not for a grade] 1.Find VO in terms of V1 and V2. You may assume all resistors are 1Ω 2. Find the Norton Equivalent between terminals A and A’ (so pretend like the resistor between those terminals is gone, and then see what circuit some other hypothetical load would see).3. Find the input resistance between terminals and assuming the resistive model. Take into account Ri and Rt. Compare your answer to the answer you got for the reading assignment. The more of these you do, the better:
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