Explain Inductance vs Freq....

[Milmat1]

Friends,
 Can someone put into perspective here the relationship between Inductance (L) of a coil and Frequency of the applied signal. I thought I understood this until recently...
 I understand that the reactance of a coil to the AC signal is a product of frequency and inductance, But if inductance itself changes with frequency how does this work ?  (And does it ??)

Another way of asking, If I measure the inductance of a coil with a VNA or antenna analyzer, the "L" changes dramatically with frequency. So when I use an LCR meter to measure Inductance, is there a standard frequency used ?

[owiecc]

Start with this equation: z = ωL. In ideal inductor the L is constant. If you make an air core inductor this will hold true. If you put a magnetic material in the mix things get complicated. Now your core material will dominate the inductance. Depending on its properties you will see different L at different frequencies. Your L becomes L(ω). To complicate things even more the total impedance of your inductor is modified by ESR of the wire, losses in the magnetic material and capacitances of the coil.

For grid inductors the values always refer to 50/60Hz. Beyond that there is no standard AFAIK.

[T3sl4co1l]

To the simplest possible degree, an inductor is a component were Z ~= jwL is a good fit over a useful frequency range.

If you go the opposite direction, saying that an inductor is exactly Z = jwL, you must now allow that L varies, i.e., L(w), and it takes on complex values.

In general, we express Z as a polynomial -- a formula using whole powers of w, because those powers come from ideal resistance, inductance and capacitance, added and multiplied and divided together according to circuit rules.

If instead of expressing Z as a polynomial, we express it as the single formula Z = jwL, the polynomial has to get sucked into L instead.  In that case, apparent inductance varies, and you get frequency-dependent, complex valued L.  It's simply taking a complex number and putting it on the other side of the equation.

This is normally used with core materials, where permeability is expressed as mu = mu' + j mu''.  Typically, mu' stays flat, then drops off; meanwhile, mu'' rises to a peak, then drops off.

You can take the apparent inductance of anything; a resistor has Z = R, so we can solve for its inductance as L = Z / (jw) = -j R / w.  That is, negative-imaginary inductance is resistance, and it will be inversely proportional to frequency.

Tim

[IanB]

To give a different kind of answer from the one Tim gave, consider that to magnetize a core requires magnetic work to be done (to realign magnetic domains with the imposed magnetic field). Since work has to be done the response cannot be instantaneous: the more work required, the slower the process. It follows from this that frequency is important, since if the core responds slowly it will not be able to keep up with fast changing magnetic fields (higher frequencies). If the core cannot keep up the apparent inductance will change. An outcome from this is that different core materials are chosen for different frequency ranges, and choosing the wrong core material can seriously impact the performance of the part.

[Milmat1]

Thank You all !!

And you are right, my understanding of this fell apart was when I started working with ferrite cores. 

THANK YOU...

[mikerj]

Kind of analogous to Class 2/3 ceramic caps - the capacitance on some dielectrics changes with almost every conceivable parameter.  Looking at the too hard will knock a few % off

[IanMacdonald]

Inductance does not change with frequency. At least, not in a pure inductor. It is purely a function of number of turns and core characteristics.

I think what you are referring to is impedance. Impedance is the sum of the reactance plus the DC resistance of the winding. The reactance is equal to 2Pi times the frequency, times the inductance.

[emece67]

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[G0HZU]

Real world inductors (eg a classic air wound solenoid) will have distributed capacitance so the inductance will appear to increase with frequency (when measured on an analyser) as the frequency gradually approaches the first self resonance of the solenoid. The quality factor Q (ratio of energy stored to energy dissipated) will also begin to fall rapidly in this region of rapidly climbing inductance vs frequency.