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Phys127AL, F21, Final exam, Form A

Write your answers in your bluebook. You don’t need to turn in either this exam sheet or your cheat sheets. I will not answer questions during the exam since that cannot be fairly applied across all stu- dents; if you think something is ambiguous, describe what you are doing fully.

1a). (5 points) Approximate to within 10% the

impedance between points A and B for a DC signal.

1b). (5 points) Approximate to within 10% the

impedance between points C and D for a DC signal.

1c). (5 points) Approximate to within 10% the

impedance between points C and D for a signal with

a frequency of 60 Hz.

2). (10 points) For each of the circuits at right, write an ex-

pression for the output voltage in terms of the input voltage.

You can leave the expressions in complex form, i.e., you

don’t need to determine the magnitudes or do any algebraic

simplication. Determine the qualitative frequency response

of each circuit, i.e., is it high-pass, low-pass, band-pass, or

notch ﬁlter. You can ﬁgure this out conceptually without

any complex calculations, or even complicated ones.

3). (20 points) Draw circuits to perform each of the following functions. Each of your circuits should have high input impedance and low output impedance.

(a) Scale the input signal by a factor of 2/3.

(b) Turn on an LED when the input signal is above 200 mV.

(d) Combine two input signals so that the output is equal to the difference between them.

(e) Remove any DC component from the input signal, and output twice the AC component with a new DC offset of 1 volt.

4). (15 points) For the circuit shown, write down at

least 4 useful equations relating the four voltages

Vin , VA , V＋, and Vout in terms of R and the four

unspeciﬁed impedances, xl through x4 . The un-

speciﬁed impedances are potentially complex, so

treat all voltages as complex and treat your equa-

tions as complex. You do not need to solve the

equations, for Vout in terms of Vin , but you should

not add any other variables, such as currents, with-

out solving for them in terms of the voltages.

More questions on the back side...

5). (20 points) Explain the output of the circuit below. Since the component values are not speciﬁed, your description should be qualitative without speciﬁc numbers.

Suppose that you built this circuit on your breadboard but found that it did not work as expected. You would then debug the circuit by doing the following: measure some aspect of its anomalous operation, list hypotheses for what problems might cause that anomalous behavior, list additional measurements you could make to test those hypotheses, then make those measurements. You would then iterate on this until you understand the problem and the solution to it.

Describe 5 potential anomalous behaviors of the circuit that you might encounter from problems in the circuit. For each of them, list two hypotheses for failures that might be the cause, and at least one addi- tional measurement you might make to test each of those hypotheses.

As an illustrative example:

Behavior: output is just a DC signal sitting at ground.

Hypothesis 1: power supply is off.

Measurement 1: look at the power supply to see if it is on.

Hypothesis 2: power supply connections are mis-wired.

Measurement 2: measure VCC and VEE at each op-amp to check if power is being delivered.

Your answer cannot include that illustrative example as one of the 5 potential anomalies, and your 5 proposed anomalies need to be clearly distinct from each other and sufﬁciently speciﬁc to make clear that you understand it.

6). (20 points) Suppose that you have two different WiFi access points that you can choose between, one of which operates at 2.6 GHz and the other at 2.2 GHz. However, the signal strength of each can vary with time, so you are tasked with designing a circuit to monitor their relative signal strength. Design a circuit that will light a red LED if the signal strength of the 2.6 GHz channel is higher than that of the 2.2 GHz signal, and a green LED if it is the other way around. Don’t worry about getting the component values exactly correct, but do explain what requirements must be satisﬁed for the component values in each part of your circuit. You also do not need to worry about bandwidth limitations of any op-amps you might use. (Hint: if you are not sure what is meant by “relative signal strength”, imagine that the same message is being sent on each channel.)