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I am experimenting with a stripline square spiral inductor in Sonnet and the graph is showing both a positive and negative inductance.

What does it mean to have a negative inductance?

Why does it swing above and below 0?

What does it mean about the inductor that the negative spike is 2x greater than the positive spike?

square spiral inductor 144 to 148MHz

KJ7LNW
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    Negative inductance is capacitance. The trick is interpreting it in your particular setup...if it's an inductor, you're past its resonance. The above looks like a capacitor that behaves as an inductor above its resonance (around 144.7 MHz). (For more fun, figure out what reverse resistance represents.) – Cristobol Polychronopolis Jul 15 '20 at 16:11
  • It's when the coil zaps you in retaliation for disconnecting it's current source! – Hot Licks Jul 15 '20 at 21:17

3 Answers3

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In your case, the inductance is calculated from the reactance and then plotted. If the reactance is capacitive, and inductance is plotted, it appears negative.

You have an inductor with a capacitive parasitic (or vice versa), and together they form a resonant circuit.

To obtain better insight in your circuit, plot mag(Z) and angle(Z). You will see that the magnitude reaches a maximum at the resonance frequency, and the phase jumps signs there. You can also plot imag(Z), which gives you the same plot you have, only scaled by L and the frequency.

Your L_geo is theoretically determined from geometry. However, the actual impedance measurement will not yield a constant L: it is calculated from "wL = imag(Z)", but Z includes not just the "jwL" but also one or more parasitic "jwC" tems and likely one or two R terms.

Your peak difference between positive and negative reactance has to do with which effect is stronger near resonance and the value of f. The smoothness of the curve is determined from the lossy/parasitic R.

The exact shape of your curve depends on all parasitics, and it may be a more complex circuit than a simple RLC model. (It's not easy. A network analyzer will iterate through various RLC topologies and find the best match)

Here is a comparable situation (but with different R/L/C values)

enter image description here

Image from https://www.translatorscafe.com/unit-converter/en-US/calculator/parallel-rlc-impedance/

P2000
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An unbalanced RLC filter will appear inductive and capacitive (negative inductance) about the resonant frequency. This filter appears to be very underdamped series-shunt filter.

There appears to be a lot of self-capacitance from the substrate producing a low impedance series resonance at 144.7 MHz.

Tony Stewart EE75
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  • What does 'PRF' nean? – Bruce Abbott Jul 15 '20 at 00:44
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    Parallel (PRF) and series resonant (SRF) frequencies occur all Xtals and ceramic resonators. Johanson coined the new meanings with their advanced analysis of RF Caps. SRF or self-resonant freq. is still used for chokes is actually PRF ccts. Edit added – Tony Stewart EE75 Jul 15 '20 at 00:56
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Negative inductance is NOT a capacitor. Negative inductance occurs in the equivalent circuit of a real transformer. When the frequency is infinite the modulus of the impedance of a negative inductance is also infinite. On the other hand the modulus of the impedance of a capacitor when the frequency is infinite is zero.

Graeme Maditgan
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  • I agree that Capacitance and negative Inductance are different things, in wideband circuits, when created by gyrators etc. But in this very narrowband case, clearly a resonance of some kind, it's correct to call the negative reactance "capacitance". That it appears as -200 nH is just a bad choice of plot axis. – tomnexus Dec 08 '22 at 17:10