Self-resonant frequency in lumped elements

Updated October 7, 2011

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New for October 2011! When you specify or purchase lumped elements such as inductors and capacitors (particularly surface mount devices), you come across the term "self-resonant frequency". What does it mean? Is it a good thing? How do you model it?

Many things in nature have self-resonances. This does not mean that they oscillate by themselves, it just means that when they are excited by applied energy they tend toward resonance at specific frequencies. If you excited a real capacitor or inductor with a voltage step function a transient oscillation would result, at the self-resonant frequency, but it will quickly die down because of parasitic resistance. You can see this phenomena on an oscilloscope, when you pulse a voltage across a component, it "rings" for a short time. Can someone send us a scope shot of that?

Inductor model

The lumped inductor model below has inductance and SRF as inputs, and it calculates the parasitic, parallel capacitor that causes the resonance. The formula for C1 has a factor of 1000 built into it so that the units come out right. In microwaves, we try to stick with pico-Farads, GHz, and nano-Henries.

In the plots below, and inductor value of 51 nH, with SRF 2.3 GHz, is shown. The self-resonance occurs, the part looks nearly like an open circuit, which might be very desirable depending on the application (think "bias tee"). Note that R2 in the model accounts for the part's DC resistance (also specified by the manufacturer, or readily measured with an accurate DC meter). Resistor R1 is part of the model, which reduces the reflection coefficient at resonance; no real part ever achieves a perfect open circuit.

Capacitor model

The model below actually has two resonances. The first SRF is the series resonance where inductor L1 and capacitor C1 cancel each other and a near short circuit is obtained. You will never get a real short circuit because of the equivalent series resistance "ESR" which is accounted for in R1. The second resonance is a parallel resonance of the capacitance C2 with the structure. This is usually undesirable, the capacitor is looking close to an open circuit.

In the plot below we have analyzed a 51 pF cap with 2.3 GHz SRF.

There is further discussion of modeling self-resonant frequency on this page, where we show you how to design a bias tee with lumped elements (also new for October 2011!)