4.7 Decoupling Capacitors

Capacitors that are used for power decoupling in digital circuits are usually surface-mount types. This means that there are no connecting leads. The leads that must be considered are connections to pads and connecting traces. Capacitance values vary from a few hundred picofarads to 10,000 pF. Most of the capacitors that are used for decoupling use a ceramic dielectric. Manufacturers will usually provide information on the equivalent series resistance (ESR) and the equivalent series inductance (ESL), as measured at the terminals.

For high frequency sinusoids, capacitors are usually considered series resonant circuits. At their natural resonant frequency, the series impedance is a resistance. The series resistance at the resonant frequency is largely controlled by skin effect. A typical resistance is in the range 0.1–1.0 ohm. For a capacitor of 0.001 μF and a series inductance of 1 nH, the resonant frequency is 159 MHz. This is well below the frequencies involved in gigahertz operations. At frequencies above the resonant frequency of a capacitor, the impedance appears to be inductive. All of these ideas are related to sine wave analysis. In fast digital applications the transmission line view is preferred. This is the view point taken in this book. This view makes it easier to consider the response of a capacitor to step changes in load.

In designs involving high clock rates, it is customary to place many decoupling capacitors on the circuit board. To optimize performance, these capacitors are usually located close to circuits that switch the most energy. Some ICs require a cluster of capacitors. In effect, these parallel capacitors are groups of transmission lines having the same length. If the connecting traces are short, the circuit looks like one transmission line with a low characteristic impedance. This view becomes flawed when the capacitors are interconnected by a grid of transmission lines.

At 100 MHz, a clock period is 10 ns. A wave can travel in an epoxy dielectric about 150 cm in this time. This means that waves can propagate and reflect over an entire circuit board before the next clock time. This seems to imply that decoupling capacitors can supply energy to a load within one clock period. Taking energy from a decoupling capacitor requires waves to make many round trips on the connecting traces and internal to the capacitor. The resulting settling process can take more than 10 ns depending on the nature of the load and the location of the capacitor. If the power supply voltage swings, the wave action that results can cause radiation, and it can cross couple interference to nearby signal traces.

For clock rates of 1 GHz, the decoupling problems are significant. In one clock period, a wave in stripline can only travel about 15 cm.³ For this logic to function, the first energy must come from connecting traces and from the ground/power plane capacitance. As we have stressed, all of these connections are transmission lines and multiple reflections are required to move energy over these lines.

The ground/power plane capacitance was discussed in Section 2.13. This is a tapered transmission line with a distributed characteristic impedance. It takes time to obtain energy taken from this conductor geometry. Most of the time is spent in the reflections through the via at the point of connection. Fortunately, the ground/power plane is a four-terminal source of energy.

When a capacitor is placed across a transmission line, it is equivalent to placing an open-ended charged stub across that line. Even if the capacitor has a characteristic impedance of 0.1 ohm, the connecting leads are a short section of 50-ohm line. The reflections depend on location and the geometry of the capacitors. If the capacitor is multilayered, it may look like a transmission line with an added small series inductance (Section 4.6). The problem we discussed earlier still exists. The stub can provide energy but it should be remembered that it only has two terminals. Trying to move energy in and out of a two-terminal capacitor at the same time is not possible.