Some people will tell you that you can’t use a bypass capacitor above its self-resonant frequency, because above that, it no longer behaves like a capacitor. Is this really true?
No, it isn’t true.
In bypass applications, the only aspect of “behaves like a capacitor” we really care about is the magnitude of its impedance, which needs to be low in the frequencies of interest. The circuit being bypassed generally does not care about the phase angle — i.e., capacitive or inductive — associated with that impedance.
A capacitor’s impedance is at a minimum at its self-resonant frequency, and is typically “low enough” for at least an order of magnitude on either side of that frequency.
However, this does explain why it is often necessary to use several different sizes of bypass capacitors in very broadband applications. Each size keeps the power supply impedance low over a few decades of frequency.
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