Ground Bounce and Ringing

Abstract

We have spent the first four chapters studying the basics, including circuit boards and “lumped” parameters such as resistance, capacitance, and inductance. We also studied important consequences of these parameters, such as how return current follows the signal path. Now we are going to study two of the effects that these lumped parameters cause, ground bounce and ringing.

Homework

• 1. Estimate the ground bounce for the following situation:

  • Write down the last 3 digits of your student ID number: _____ _____ _____

  • Replace any instances of “0” with the last nonzero digit in your student ID number:

    $\begin{array}{cccc}\hfill \mathrm{Digit}:\hfill & \hfill \frac{\kern1em }{\kern1em \mathrm{R}\kern1em }\hfill & \hfill \frac{\kern1em }{\kern1em \mathrm{L}\kern1em }\hfill & \hfill \frac{\kern1em }{\kern1em \mathrm{C}\kern1em }\hfill \end{array}$

  • Voltage source rises from 0 V to 1 V with a 10–90 % risetime (T _source) of 150 ps.

  • Series resistance of 5*R Ω.

  • Series inductance of 5*L nH.

  • Circuit load is 5*C pF.

  • (a) Estimate the risetime of the circuit.

    • (i) First, compute the 10–90 % risetime of the RC constant: T _rc = 2.2RC.

    • (ii) To find the overall risetime, combine the risetime of the source with the risetime of the RC constant as follows: ${T}_{\mathrm{rise}}=\sqrt{T_{\mathrm{rc}}^2+{T}_{\mathrm{source}}^2}$.

  • (b) Estimate the amount of ground bounce using the formula

    $$ {V}_{\mathrm{gb}}=\frac{1.52LC\Delta V}{T_{\mathrm{rise}}^2}. $$

  << Note to reviewer: I can provide a spreadsheet as part of the instructor’s package that generates the correct answer for each student. Having the problem be a function of student ID numbers discourages cheating. >>

• 2. The ground bounce waveform is a “double pulse.” It is the second derivative of which waveform?

• 3. Consider the ground bounce formula ${V}_{\mathrm{gb}}=\frac{1.52LC\Delta V}{T_{\mathrm{rise}}^2}$. What four things can be done to reduce ground bounce?

• 4. Consider a circuit with an output resistance of 10 Ω and a ground-trace inductance of 10 nH driving a load of 25 pF.

  • (a) What is the Q of the circuit?

  • (b) What is the expected ringing frequency?

  • (c) If the circuit rings, what is the expected overshoot?

  • (d) How can you lower the Q of the circuit?

• 5. A circuit has an output resistance of 5 Ω, a ground-trace inductance of 10 nH, and is driving a load of 10 pF.

  • (a) What is the Q of the circuit?

  • (b) What is the expected ringing frequency?

  • (c) Will the circuit ring if the output has a risetime of 500 ps?

  • (d) What is the minimum risetime that keeps the knee frequency of the signal below the ringing frequency?

• 6. Consider a circuit that has 10 Ω source resistance, a 10 pF load, and 25 nH of inductance on the ground connection. The signal has a 1 ns risetime.

  • (a) Estimate the ground bounce as a fraction of the full logic swing. Use the formula $\frac{V_{gb}}{\Delta V}\approx \frac{1.5LC}{T_{10-90}^2}$.

  • (b) Estimate the Q of the circuit.

  • (c) Calculate the ringing frequency and knee frequency of the circuit.

• (d) Is the knee frequency above or below the ringing frequency? Will the circuit ring? Why or why not?