The Basics: Charge, Energy, Time, and Distance

Abstract

The concept of signal integrity begins with the basics – charge, energy, time, and distance. Electrical and computer engineering students already know a lot about these basic building blocks of electrical engineering, but a review is in order, so that the aspects relevant to signal integrity can be emphasized.

Homework

• 1. Express the speed of light in feet per second and inches per picosecond.

• 2. What is the speed of light on a circuit board with ε _r = 6?

• 3. A circuit is being designed with a risetime of 750 ps. How long is the rising edge on a circuit board with ε _r = 4.2? ε _r = 6? So, as ε _r increases, do rising edges get longer or shorter?

• 4. Consider a high-speed bus being laid out on a circuit board. The board has ε _r = 6, and the board is 40 cm by 60 cm.

  • (a) What is the longest risetime of a signal that can be considered lumped on a trace that is 5 cm long? 40 cm long?

  • (b) How long does it take a signal to propagate down a line that is 50 cm long?

• 5. Consider a signal with a risetime of 100 ps routed on a trace on a circuit board. The insulating material is FR-4 fiberglass with ε _r = 4.2.

  • (a) What is the knee frequency of the signal?

  • (b) How long does it take the signal to traverse one inch of trace? (i.e., what is the propagation speed in ps/in?)

  • (c) It is decided that the signal can be much slower and still work correctly. The source has a 3 Ω internal resistance and a 47 Ω resistor is added in series on the trace. The signal is driving a 10 pF load. What is the effective risetime of the source, after adding the resistor and taking into account the capacitance of the load?

• 6. A USB is being laid out on an FR-4 circuit board (ε _r = 4.2) with a risetime of 500 ps. The bus is being routed over a long distance from the processor to the edge of the board.

  • (a) How long is a rising edge?

  • (b) At what length would a circuit-board trace be considered distributed?

  • (c) What is the knee frequency of the USB signal?

  • (d) A designer is adding a ESD protection diode. It adds 1 Ω of resistance and 50 pF of capacitance to the signal. What is the risetime after adding the diode?

  • (e) How much faster would the source risetime need to be if adding the diode (R = 1 Ω, C = 50 pF) resulted in a risetime of 500 ps?

• 7. A circuit is being laid out on a circuit board that has good performance as high as 7 GHz and ε _r = 4.2. (Hint: the signals on the board need to have a knee frequency at or below 7 GHz to propagate well.)

  • (a) What is the minimum risetime allowable on the board?

  • (b) A signal output has a knee frequency of 10 GHz. Will it propagate well on the board or not?

  • (c) Consider the 10 GHz signal. One way to reduce the knee frequency of the signal is to add an RC filter. What value of RC will reduce the knee frequency to the maximum frequency that propagates well on the board?