Re: [SI-LIST] : Decoupling capacitor resonance

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From: Roy Leventhal (Roy_Leventhal@mw.3com.com)
Date: Wed Jan 26 2000 - 07:29:40 PST


I disagree with this last response.

I picked up the technique of using the self resonance of a capacitor when my job
used to be RF discrete transistor amplifier design. At that time we had grid dip
meters available to us. we formed a loop of wire with (twisted the ends) the
capacitor's leads. The size of the loop plus the internal inductance in
combination with the capacitance gave a parallel resonant circuit. The grid dip
meter allowed one to tune the loop to the center frequency of interest. The
residual impedance around the loop is the ESR, basically the series resistance,
and is true either in the parallel resonant mode or the series resonant mode.
The series resonant mode acts as a notch filter. Below resonance the filter
looks capacitive. Above resonance it looks inductive - for a short while. After
the first resonance (pole-zero) there are often higher frequency resonances
(higher order pole-zeros). These are mainly influenced by structure size in the
capacitor. The smaller the package (it's wavelength and discontinuity related),
the less the problem. In RF work the object was to have this occur at
frequencies well beyond those where your circuit had any gain left. SMD
capacitors are great for RF work. Eventually, at microwave frequencies,
structure size tends to dominate and you can no longer think primarily in
discrete component/ohms law circuits/lumped filters.

When the capacitor loop is opened (cut at the point of contact of the twist) the
capacitor and its leads form a series resonant circuit. The capacitor can then
be used to bypass a power pin or as a series blocking capacitor between AC (read
analog and/or RF) amplifier stages. The technique works great. Later, when I was
designing test fixtures for high speed saturated switching transistors it
worked great there also. A large capacitor also stores more charge and all
electrical signals have a dual nature, just as matter (charge = integral of i*dt
and V = 1/C * integral of i*dt) and energy (frequency spectrum or energy at a
given frequency) are duals. For bypassing you want V to change as little as
possible for the lowest power supply bounce. The larger the C and the smaller
the current, the easier this is to accomplish. You have to think in both the
frequency (impedance / short circuit effects) and time (supplying charge) domain
effects to deal with the problem.

The larger the capacitor you can choose, the broader the minimum impedance
notch will be. The smaller the ESR, the closer to an ideal zero impedance you
will get. As noted in a different discussion, residual resistance loss can have
a damping effect on ringing. The trade-off is that they also produce residual
bounce. Ferrite beads couple loss in at high frequencies and not at DC and are
better for producing this effect. Larger capacitors tend to have larger internal
inductance and ESR and will resonate at lower frequencies all things being
equal. In using this technique it is common to bypass the large capacitor with a
smaller, higher frequency capacitor thus broadening the overall notch. It is
true that the two notches couple into each other. But, that simply tends to push
their center frequencies apart a bit. The amount of mutual coupling depends
primarily on their proximity and the loops formed by the current paths, to a
clean ground in the case of power supply bypass.

In the designs I refer to above, I often end up with 3 parallel capacitors
bypassing a power supply point because the energy of a switching pulse is spread
over a spectrum of frequencies. The usual observation is that a power supply pin
will ring or bounce at a particular frequency. That is first bypassed. Then, it
is common for it to ring at a higher frequency with less energy (amplitude).
That is then bypassed. Finally, it is common to see some residual ringing at a
lower frequency than the original and that is again bypassed. Again, I emphasize
that the technique worked great within the limits of components acting like
lumped elements.

For the designs and methods of today the challenges are several. You can't debug
on the bench. You have to model and simulate. You can't afford 3 capacitors for
every 1 you might use. You have to use one large capacitor with very low
internal inductance as a basic rolloff for bypassing with its self-resonances at
very high frequencies and limit the spectrum (edge rate) of your signal. You
have to lower the energy of the switching process by using lower voltage, lower
current technology. And, you have to make use of other ideas such as the
judicious use of small voltage regulators and ferrite beads for controlling
power bounce. Fortunately, ringing on the power pin isn't multiplied by gain of
the succeeding stage as it is in analog amplifier strings.

And you can make some use of the technique of using capacitor self resonance and
parallel combinations of them.

As long as you are bypassing to a clean ground. Otherwise, the bypass (being a
bi-directional notch filter) injects bounce on the pin.

For this, and other reasons, the power supply distribution on the RF amplifiers
I worked on often had Pi-filters between stages consisting of a series
inductance with input and output capacitors. This gives a high series impedance
and low shunt impedance for decoupling between stages.

Best Regards,

Roy

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