Final Exam for Physics 5121, December 5, 1995

30 points - closed book - calculators allowed - show your work

1) (5 Points) Calculate the following values for the circuit in figure 1: Assume: quiescent (output) Vsat = 0, VBE = 0.6V, hfe = 100 and the operating point is 7.5V.

  1. The quiscent collector current is 5 mA. What value should Rc be?

  2. The circuit should have a gain of -10; what value should Re be?

  3. Using the values for Rc and Re previously calculated, what is the voltage at the base?

  4. Neither R1 nor R2 can exceed 20k; calculate the largest possible values for R1 and R2.

  5. What is the input impedance at In?

2. (6 Points) The op-amp circuit in figure 2 is a differential amplifier. Assume an ideal op-amp and calculate its differential gain using the superposition principle. Specifically:

  1. What type of feedback is being used in the op-amp circuit in figure 2

  2. Calculate Vout(Va) for Vb = 0.

  3. For Va = 0 and Vb != 0, (!= means "not equal") calculate V+ and V- as a function of Vb.

  4. Calculate Vout(Vb) for Va = 0. (Hint: use the information from 2.c.)

  5. Apply superposition to b and d and calculate Vout( Va, Vb).

  6. Show that the circuit has a differential gain, Vout/(Va - Vb) of: Vout/(Va - Vb) = -R2/R1.

3. (5 Points) Given a "perfect" op amp (Zin = infinity, Zout = 0,Open Loop Gain: Av = infinity and noiseless. Assume: Vcc = +15V, VEE = -15V, VEE <= Vout <= VCC) answer the following design questions:

  1. Design (give a circuit diagram) of an inverting amplifier with an input impedance of 10k and a gain of 20.
  2. Design (give a circuit diagram) of a non-inverting amplifier with infinite input impedance and 1mA maximum drain in the feedback loop and a gain of: 20.
  3. The forward current through a diode is given by: If = Is(exp(qV/kT) - 1) where Is is a device dependent constant. When exp(qV/kT)>>1 the forward current can be approximated by: If = Is exp(qV/kT). For the circuit in figure 3, find Vout as a function of Vin in the forward biased region where the approximation is valid.
  4. If Vin > 0, redraw the circuit in figure 3 with the box replaced by the appropriate diode symbol getting the polarity right so that the circuit works as calculated in part c.

4 (2 Points)

  1. Sketch how a 15k resistor and a 0.001uF capacitor can be connected to act as a high-pass filter. Show the input and output connections of the filter in your sketch. What is meant by the -3dB or "half-power" point for a high-pass filter and where is it for this filter?
  2. A square wave is applied to this circuit with a frequency 10 times less than the -3dB point. Draw the input and output waveforms.

5 (4 Points) For the circuit shown in figure 4:

  1. Describe Y in terms of A and B using Boolean algebra.
  2. Simplify this expression and determine with which single gate could you replace the circuit in figure 4?
  3. The propagation time through each gate is 25nsec and the rise and fall times are zero nsec. Describe using a timing diagram what happens at inputs to 3, 4, 5 and Y with B set LO, when A changes state from LO to HI and then returns to LO some time (>> 100nsec) later. 

6 (3 Points) For a D-type flip-flop which changes states on a negative going clock edge, the signals in figure 5 are applied at the clock and D inputs.

  1. Copy the signals and sketch the Q-output which would result from these inputs. Write out the truth table for a J-K flip-flop.
  2. The signals in figure 6 are applied to a positive edge triggered JK flip-flop, with the Q output initially low. Copy the signals and sketch the Q-output which would result from these inputs.

7 (5 Points)

In many applications 2 address lines are used to select the routing of a data line, with the unselected lines set LO. They often come with an ENABLE input which sets all outputs LO. This device is known as a demultiplexer; see figure 7. Design such a 2-address line demultiplexer with an ENABLE using the following gates: AND, NAND, OR, NOR, XOR, NOT.