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PHYS345 Final Exam          December 10, 1999

This is a closed book exam. One 3"x5" note card is permitted; this card should be turned in with your exam papers.

Programmable calculators and graphing calculators may be used during this exam.

Since this exam booklet may be separated for grading; it is important to:

Show ALL work on problem sheet and only on that sheet.

Please read questions carefully.

Credit may be lost inadvertently if solutions are not neat and orderly.

Be careful with units, signs, and significant figures.


1.  Fun with op amps (5 points)

What does the following circuit do? That is, find an expression for the gain and give the circuit a suitable name.

Subtractor circuit


2.  Loading passive filters (15 points)

  1. Write the transfer function for this filter.

  2. Design a high-pass RC filter with a characteristic frequency of 80 Hz using a capacitor of 2.0 mF.
Passive high-pass filter
  1. What is the new characteristic frequency when the filter is loaded with 50 ohm?

  2. Sketch an active filter that will provide the same transfer function as in part a). Note that this op amp circuit will not suffer from loading effects such as encountered in part c).
Passive high-pass filter loaded with 50 ohm


3.  Digital Paranoia (20 points)

a.   You have just received a phone call from your older cousin. Pat has been working for the past few years in a small mechanical design firm. Today's crisis is a client's last minute request to add a zero-through-four counter and a digital display. They are out of time and out of money; Pat remembered that you were taking PHYS345 this semester and has phoned you for help. Design a 3-bit, 5-state counter that cycles repetitively through the states 000, 001, 010, 011, and 100.

Design constraint: Pat has an aversion to NOTted flip-flop outputs and would like you to use only Qs, not Q's.
Another constraint: Pat's boss insists that only dual-input gates be used.
Design flexibility: There are three excluded states that you may treat as you see fit to simplify your design.

Flip-flops for synchronous 3-bit counter

  Q2     Q1     Q0       D2     D1     D0  
0 0 0  
0 0 1  
0 1 0  
0 1 1  
1 0 0  
1 0 1   x x x
1 1 0   x x x
1 1 1   x x x

  D2=                                   D1=                                   D0=

b.   Indicate the behavior of the excluded states on the following state diagram.

State diagram for 5 states


4.  Too many batteries! (20 points)

A 9.0 V lithium battery (internal resistance 18 ohm) has been connected to a real inductor (inductance of 1.0 H and resistance of 27 ohm) as shown.

  1. What is the current in the inductor a long time after the circuit has been formed?

  2. What is the power delivered by the battery to the rest of the circuit?
     

Real inductor connected to real battery
A 1.5 V AA cell (internal resistance 0.6 ohm) is added in parallel to the 9.0 V battery and inductor as shown.
  1. What is the current in the inductor a long time after this circuit has been formed?

  2. How long does it take for the inductor to change to its new current value? (Use five time constants.)
Real inductor connected to two real batteries


5.  Too many resistors! (20 points)

Loaded amplifier The diagram at left shows a properly-terminated high-speed amplifier. With a 50  ohm load, the voltage across the load is exactly one-half of the open-circuit voltage of the amp.

A -6dB attenuator should reduce the voltage across the load to one-half of the voltage across the attenuator, as shown below. It should do so without changing the effective load on the amplifier, thus the effective resistance of the attenuator with the load connected across it should be identical to the load resistance. The attenuation should not depend on its orientation in the circuit, thus the tee configuration.

Amplifier with loaded attenuator Find the values of Ro and Rs for the -6dB attenuator. Show all work, including circuit reasoning and analysis.
     


6.  More digging through the past... (20 points)

Determine the numerical value of the current through the capacitor by whatever method you prefer.

Multiloop ac circuit


"http://www.physics.udel.edu/~watson/phys345/exams/fin-99f.html"
Last updated Dec. 19, 1999.
Copyright George Watson, Univ. of Delaware, 1999.