Operating Above Resonance

Bypass capacitors, for us digital designers, are a fact of life. They may not be our favorite components, but we can't live without them. As we push designs to higher and higher speeds, it is becoming vitally important to understand how bypass capacitors will perform in the 100 MHz to 1 GHz region.Those skilled in the art of analog design may point out that this frequency range is well above the series-resonant frequency of a typical bypass component. They may say such a component will become useless, or will fail to act as a capacitor, in our target frequency range. Don't be swayed by these arguments. You can still use bypass capacitor effectively in this range. Here's why.

The purpose of a good power bypass system is to provide a very low impedance connection between Vcc and GND at all speeds. A low impedance path from Vcc to GND permits chips to draw huge surges of current from the power rails without perturbing the power voltage. The lower the impedance between Vcc and GND, the less power supply noise a system will have.

Most designers know that the Vcc-to-GND impedance has to be low, but what about the phase? Is the phase of the Vcc-to-GND connection important? For example, the impedance phase angle normally associated with a bypass capacitor is –90° (voltage lags current). What if it were 0 degrees? Would it still work?

To investigate that question, let's set up a mental experiment. First imagine an ordinary digital product laid out on an FR-4 substrate and having mounting pads for 100 surface-mounted bypass capacitors. Next, mentally replace all the bypass capacitors with 1-ohm resistors (sounds crazy, but just go ahead and do it). That would make the Vcc-GND impedance equal to 0.01 ohms, a nice, low impedance for this application. Everything looks fine except for one detail: we've shorted out the power supply with 0.01 ohms. No problem, since this is a mental experiment, we can hook up a 500-amp current source to the power terminals and—Voila! We've made a very stiff 5-volt power source with a 0.01-ohm output impedance. From the logic gates' perspective, it is near-perfect. The gates can draw huge surges of power without creating Vcc noise. Gates don't care about the impedance phase. They just care about the impedance magnitude between Vcc and GND.

From the global warming perspective, maybe it's not such a good idea. With each resistor dissipating 25 watts, the board is going to light up like the Fourth of July. Hint: this is a great experiment to try on Spice, but I wouldn't want to have to build it.

Fortunately, the premise of this column does not hinge on whether we can actually build a power system out of 1-ohm resistors. I am merely pointing out that digital logic will work with any reasonably low impedance path between Vcc and GND without regard to the phase angle associated with that impedance, whether it be –90°, 0°, or even +90°.

The reason for this discussion is simple. It's because the phase angle of a real-world capacitor changes as a function of frequency (see figure 1).

graph illustrating series-resonance of bypass capcitor

Figure 1—Magnitude and phase of real-world bypass capacitor

At low frequencies, a bypass component is essentially a perfect capacitor, and its impedance plot displays a phase angle of –90°. In the capacitive region the impedance is decreasing at a rate of –20 dB per decade. At some intermediate frequency (10 MHz for the capacitor plotted in the figure), the component's series lead frame inductance becomes significant compared to the magnitude of its capacitance, and we enter the self-resonance zone. At the precise point of self resonance, the interaction of capacitive and inductive effects exactly cancel each other out; all we see is the equivalent series resistance (ESR) of the component. As we progress above resonance, the lead frame inductance begins to dominate the behavior of the whole component, the phase angle approaches 90°, and the magnitude plot starts heading up at a rate of +20 db per decade.

As we go from low to mid-range to high frequencies, the impedance behavior changes from capacitive to resistive to inductive. Although the impedance magnitude wanders all over the map, and the phase flips polarity from –90° to +90°, it's still a useful bypass component. As plotted in the figure, over the range of 1 MHz to 100 MHz, this capacitor maintains an impedance of 1 Ω or less. That's good enough for most digital work. From 1 to 100 MHz, one hundred of these babies would give us our 0.01 ohms. Note that at 100 MHz we would be using this bypass component more than an order of magnitude above its series resonance frequency. That's okay. That's the nature of the bypass capacitor application.

Analog applications are different. In the analog design world, particularly in linear time-invariant filter designs, phase is everything. For example, in a five-pole Butterworth filter, a phase error of a couple of degrees can degrade performance noticeably. An analog designer in such an application would be very cautious about using a capacitor anywhere near resonance. Analog filtering applications often demand precise phase response. For that reason, many analog designers think of a capacitor's series resonance point as representing something akin to total circuit dysfunction. They just don't use them above resonance.

Happily, for us digital folks, we can live with the resonance, and way beyond, too. Resonance in bypass capacitors is a property to be managed and used, not avoided.