Series inductors SRF

[jmw]

I made some toroid inductors that are about the same value (+/- 10% in inductance and self-resonant frequency). In theory, placing several in series should not change the self-resonant frequency, since \$\omega_0 = 1/\sqrt{(n L) (C/n)} = 1/\sqrt{L C}\$. In practice, I'm seeing the SRF goes down. Individually they are at 55-60 MHz, and by the time I have 4 in series, it's around 35 MHz. It's about the same on different jig set-ups: dead-bug and breadboard, spaced apart or closely. What non-idealities could be affecting the circuit?

[MagicSmoker]

You're forgetting the stray inductance of the traces/wires connecting them together.

[jmw]

Is straight wire inductance going to be significant against the toroids, which are 12-13 uH each?

[MagicSmoker]

Is straight wire inductance going to be significant against the toroids, which are 12-13 uH each?

No, and you probably should have mentioned the value of the inductors in the first place. With a self-resonant frequency of 35-55MHz I was thinking the inductors were in the nH-range.  My guess is that this is more of a de-Qing type of thing that is causing the SRF to broaden out. How are you actually determining the SRF here?

[jmw]

Yeah, oops I left that out originally. I'm measuring SRF by the minimum in S21 when the inductor is connected in series to two lengths of coax+connectors hooked up to a tracking generator + spectrum analyzer. Grounds are tied together with a small sheet of copper.

[MagicSmoker]

Yeah, oops I left that out originally. I'm measuring SRF by the minimum in S21 when the inductor is connected in series to two lengths of coax+connectors hooked up to a tracking generator + spectrum analyzer. Grounds are tied together with a small sheet of copper.

Measuring scattering parameters with an SA+TG is not what I was expecting for a post in the Beginner's section... Alright, so how does the impedance peak look when you add more inductors? Does it broaden as it shifts lower in frequency or does it maintain the same sharpness?

That said, the only halfway plausible explanation I can come up with that would lower the SRF on both dead-bug and breadboard constructions is additional stray capacitance either from the ground plane on the dead-bug build or the terminal strip rows on the breadboard, but that's really stretching my imagination. You might want to delete this thread and repost it in the RF section where there are some actual RF people hanging out. I'm more of a power electronics guy that usually deals with resonance as something to be avoided, rather than studied too closely.

[jmw]

Right, well I figured there was a good chance the explanation was something basic that just escaped me... 

But for completeness here's one toroid on its lonesome:


Here's four in series:


Here's also four with 4.3k resistors across each one - that's about the average of the \$\sqrt{L/C}\$ for these. The parasitic capacitance is about .5-1 pF measured similarly by comparing the resonance frequency in parallel with a known 62p mica cap. That's where I came up with "35 MHz".

[T3sl4co1l]

If the inductors were perfectly isolated, you'd just be increasing the total impedance, correct.

Real inductors have some capacitance to their surroundings; if you include a rough model of how much is present, you should find your answer.

You should also find that it produces multiple peaks, due to the capacitance between inductors as well as to ground.

(In a perfectly reciprocal manner, one cannot connect impedances exactly in parallel, either; there is always some stray inductance between them.)

Tim