Power Distribution Network: Frequency Domain Analysis

Abstract

This chapter covers power-supply design. It turns out that power supplies source both DC and AC current. That a DC power supply sources AC current is surprising, but is a consequence of the fact that signal-value changes are an AC phenomenon. As a result, a DC power supply is actually modeled in the frequency domain.

Homework

• 1. Construct a power infrastructure for a simple design. The design as a target Xmax of 0.1 Ω, a risetime of 500 ps, and a power-and-ground-plane capacitance of 1500 pF.

  • Write down the last 4 digits of your student ID number:

    $$ \begin{array}{ccccc}\hfill \mathrm{Digit}:\hfill & \hfill \frac{}{\kern1em \mathrm{A}\kern1em }\hfill & \hfill \frac{}{\kern1em \mathrm{B}\kern1em }\hfill & \hfill \frac{}{\kern1em \mathrm{C}\kern1em }\hfill & \hfill \frac{}{\kern1em \mathrm{D}\kern1em }\hfill \end{array} $$

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

    $$ \begin{array}{ccccc}\hfill \mathrm{Digit}:\hfill & \hfill \frac{}{\kern1em \mathrm{A}\kern1em }\hfill & \hfill \frac{}{\kern1em \mathrm{B}\kern1em }\hfill & \hfill \frac{}{\kern1em \mathrm{C}\kern1em }\hfill & \hfill \frac{}{\kern1em \mathrm{D}\kern1em }\hfill \end{array} $$

  • Power-supply inductance is D*25 nH.

  • Inductance of bypass cap, L _byp, is C nH.

  • Resistance of bypass cap, R _byp, is X _max/2 = 0.05 Ω.

  • Inductance of a single array capacitor, L _cap, is B nH.

  • Resistance of a single array capacitor, R _cap, is A/10 Ω.

  • (a) Compute f _psw, the point at which the power-supply wiring has too much impedance.

  • (b) Compute C _byp, the amount of bypass capacitance needed.

  • (c) Compute f _byp, the point at which the bypass capacitance has too much impedance.

  • (d) Compute N, the number of array capacitors needed.

  • (e) Compute C _cap, the capacitance value of each array capacitor.

  • (f) Compute Rarray and Larray, the resistance and inductance of the entire capacitor array, taking into account that there are N capacitors in parallel.

  • (g) For the resonance between the capacitor array and the power and ground planes, compute the frequency of resonance and the impedance at the resonance.

• 2. Use the component values you calculated in Part 1 to construct a SPICE simulation of the power infrastructure. For the array, you can assume the parallel combination of the R, L, and C. Run an AC sweep of the structure from 1 kHz to 10 GHz. One efficient way to do this is to create a 1 Amp AC current source and measure the voltage. Under these circumstances, the voltage is equal to the impedance. Do the results match your calculations in Part 1?