CMPE 401 - Computer Interfacing

Assignment #6

1. Briefly describe the similarities and differences between output drivers with open collector outputs and output drivers with tri-state enable. What are appropriate situations for using each type of driver?

2. On slide 12-30 of the course notes, general forms are given for rightward and leftward-moving voltage and current waveforms on a transmission line. Recall that the voltage and current waveforms are related to each other by the characteristic impedance Zo. Show analytically that any sum of such rightward and leftward-moving voltage and current waveforms are solutions to the two first-order differential equations given on slide 12-29, as well as the two second-order differential equations given on page 12-30.
   Hint: Write down the general voltage and current waveforms, and then take the appropriate partial derivitives with respect to time and distance. Then verify that the partial differential equations are true.
   Clarification: For leftward moving waves, the current is related to the voltage by the negative of the reciprocal of the characteristic impedance. The negative sign is required to get the differential equations to work out properly.

3. Using the formulae given on slides 12-34 to 12-37 of the course notes, calculate both the characteristic impedance Zo and the speed of propagation for the following transmission line media:
   • Coaxial cable with an inner conductor of diameter 0.7 mm and a shield inner diameter of 4 mm. Assume that the dielectric has a relative permittivity of 3.2.
   • Twisted pair with conductors of diameter 0.5 mm that are separated by 2 mm. Assume that the intervening dielectric (air and plastic insulation) has the same relative permittivity as air (i.e. 1.0).
   • Microstrip in which the copper signal trace has a thickness of 0.1 mm and a width of 1.5 mm. You can assume that the ground plane lies at a distance of 2.3 mm below the bottom of the signal trace. The effective relative permittivity of the surrounding air and the epoxy glass dielectric can be assumed to be 3.5.

4. If a travelling 1-Volt voltage wavefrom encounters a sudden 10% increase in the characteristic impedance of the transmission line propagation medium, what will be the amplitude of the reflected voltage wavefront and the amplitude of the voltage wavefront that continues to propagate forward?

5. Consider a series-terminated transmission line, like the one shown in slide 12-46 of the course notes. Assume that the transmission line is 30 cm long and has a characteristic impedance of 50 ohms (the same as the total series termination resistance). Assume further that the speed of signal propagation is 50% that of the speed of light in a vacuum. Just before time t = 0, the voltage all along the line is at 0 volts (some reference potential) and there is no current flow. At time 0 ns, a voltage of 2.5 volts is suddenly applied at the left end of the termination resistance at the left end of the transmission line. The driver of this voltage signal has zero output resistance. Construct six plots of voltage versus distance along the line, and six plots of current versus distance along the line, which represent the situation at times t= 0 ns, 1 ns, 2 ns, 3 ns, 4 ns and 5 ns. Briefly explain of the evolving shapes of the waveforms that appear in your plots.