some thoughts about the practical measurement of inductance for the  radio amateur

abstract:  a simple ,classical and reproducible method for quickly and accurately indicating Q and measuring inductance in unknown coils and cores over the range of most interest to  radio Hams from 0.1uH to 100+ uH.  A method for quickly characterizing ferrite cores is presented.

January 2010 by ralph klimek
over many years I have been trying to measure inductance in a way that is usefull, accurate and meaningfully.
An inductor as a practical circuit element using real physical materials suddenly assumes a character and identity and behaviour that is challenging and confusing.  The real motivation for this article is the  accumulated frustration of many years with the specification of inductances in various amateur radio journals,  particularly the excellent ARRL articles in QST and the ubiquitous ARRL Handbook.  It always make me very cross when an inductor is specified as so many turns on an Amidon blah-blah core, or in older days, a Miller coil type blah.  These devices were rarely available as retail items in Australia and if they were,  very prohibitively marked up in price, with never a full range being available.  The writers of the articles allmost never specified a design  in inductance....Henries,  only as X turns on an Amidon blah core !  This oversight  has thwarted the starting of many small projects. I refuse to pay the silly prices demanded for proprietary cores!

Real inductors made with real materials exhibit a strong dependence on the desired frequency of operation. The very wide choice of ferrite or iron dust core materials  merely adds to the confusion.  Then there exists  now, the widespread availability of assorted unmarked and un specified ferrite cores available as surplus. Cores exhibit basically four distinct operational types.

  1. Good for nothing except RF suppression (up to 1MHz if youre lucky)
  2. Good up to about 4 MHz
  3. Good up to about 30MHz
  4. Good up to about 100MHz

type 1  can be found in all modern electronic equipment. Never attempt to use one of these as the basis of an inductor, allthough they may still  exhibit usefull properties at 1.8MHz
type 2  are generally found in switchmode power supplies  in large quantities
type 3  are what Hams really want and they are relatively rare
type 4  are generally rare, found in TV baluns and have a permiability so low, that an air core inductor works better.

At issue here is the coil Q.  A ferrite core inductor invariably has lower Q then any air core coil. (note1)   It is true that a toriod core is inherently self shielding, but so is an air core coil bent into a torus !  I notice that the Indian Ham radio journals actually specifiy their coils wound on plastic washers ! They get self shielding, self supporting and no Amidon tax and higher Q into the bargain!

So here was my problem. My junkbox was brimming over with mystery coils and cores salvaged from long dead consumer durables. What were they good for ?

I have tried assorted methods to quickly characterise a mystery coil.  My first attempts used the Maxwell Bridge, a charming design, given that first order theory suggests that it is not frequency Dependant.  This is practically true but only under the conditions that stray capacitance is negligible and the frequency of measurement is below 100kHz.  The maxwell bridge can also easily measure Q.  The inductances of interest to Hams, typically 100uH to 0.1uH  are beyond the usefull range of physcially realizable bridges.  The maximum frequency that is usefull with a maxwell bridge is about 5MHz,  but the bridge null  seems to be only loosely related to the inductance under measurement!

My other method has been to use my noise bridge.  It quickly reveals the maximum useable frequency of a mystery core. The method here is to wind a few bifilar turns as a 4:1 balun and measure the impedance when a 200ohm resistor is connected to the balun.  A useless core cannot translate this impedance to 50ohms real + 0ohms reactive.  If its not 50 ohms and has significant reactive component then the core is useless for rf  , and particularly useless for balun cores.  However, it is distincly difficult to measure inductance by this method, because I have to calibrate the reactive scale of the noise bridge, and this is a tedious procedure; nor do I necessarily believe in my calibrations!

Commercial direct reading inductance meters give up below 100uH.  Professional automatic LCR bridges are another matter, at least one might specify  the frequency of measurement and then be confident in the result.  They are utterly beyond my budget and they dont make it to Ham fests.

Another method I have tried with some success is to use a two terminal oscillator, like the MC1628 ecl oscillator, with a 100pF variable capacitor and just measure the frequency at which the mystery inductor oscillates.  The method cannot reveal the Q of the inductor. It can measure very small inductances, down to 0.1uH quite reliably. At this low value, they are invariably air core and have "high" Q. The MC1628 ecl oscillator  does not always start oscillating with all possible combinations of L and C.  The method generally is reliable with all air cored or slug tuned inductors between about 200uH to 0.1uH.  The uncertainties in the measurement are the result of stray impedances.
Toroid ferrite cored inductors are still troublesome. sometimes the oscillator starts, often it does not. There is still no Q indication. It may appear to work at your frequency of interest but the Q could be so low that its use in filters would be impossible.

So what to do.

It is ferrite cores I care about here so I really need accurate inductance and a reliable indication of Q.

This method does actually work because we are measuring the parallel resonance frequency of the mystery inductor and a capacitor in whom I have faith !  The circuit is ridiculously simple, it is hardly worth the effort of drawing the circuit.  The mystery inductor is placed in parallel with a 2700pF silver mica capacitor, that is all !   I recommend the usage of silver mica capacitors for this application. They have very high Q and  very low drift and none of the pathology that ceramic capacitors can have.  Do not use "audio" capacitors like "greencaps"
and avoid ceramic capacitors if possible. If you must use a ceramic use one rated for high voltage as these will have good Q and absence of piezzo electric parasitic phenonema  that low voltage ceramics can exhibit.

A wide range function generator that can sweep from DC to 5MHz is used as the measurement source. A CRO is used to quickly indicate the amplitude across the coil. The generator and the CRO feed the coil and capacitor through 10pF silver mica capacitors.     There is nothing sacred about 2700pF. Its just that my function generator goes up to 5MHz and 2700pF  seems to resonate with the inductance range of interest >100uh to 0.1uH.  This method even reveals the self inductance of the test probes and capacitor.  The low 10pF source and scope coupling capacitors give us the illusion that the source is a perfect high impedance current source, and the scope input is effectively an open circuit.  The worst case stray shunt capacitance of 20pF is totally swamped out by using such a high test capacitance (2700pf) that there is only a few percent error in measured inductance.  This is accurate enough for all but the most demanding filter or resonator applications.

On a high Q air core coil  the cro trace will quickly indicate resonance when manually sweeping the generator.  Move the generator off frequency to find where the amplitude is 70% down.  This is a measurement of Q.    A large freq differance is indicative of low Q.  The maximum amplitude scope display directly gives a feel for Q.  It is possible  to rapidly sort mystery ferrite cores according to my simple forementioned scheme .  A type 1  (as above) core is quickly revealled when NO resonance peak is apparent. It is correctly doing its job by eating up all the RF but an "inductor" it is not!

The measured inductance is quickly revealed by using the simple parallel resonance formula. (and a calculator!)

I specify silver mica capacitors over ceramic because sm caps have the highest Q and the least parametric variation. You can actually trust the capacitance value printed on the device.  Beware the really ancient mica capacitors that are moulded in Bakelite (phenolic resin), use only the more modern epoxy dipped varieties. Nearly all my stock of the older type have now got significant resistive leakage and uncertain capacitance. If your mica capacitor has less than a giga-ohm of resistance, just discard it.

In practice, we can measure with this technique ferrite pot core inductors up to 10Henries (!) if your function generator gets down to low kilohertz range.  Iron core inductors cannot be reliably measured with this method because their core loss is very high and resonance is very hard to find.

Now then,  we are still only measuring the effective inductance to about 5MHz. What about higher ?  If the inductor has a high Q at 5MHz then it will still have "useable" Q at 20MHz.  Any RF coil for use above , say, 20 MHz should be air cored, anyway.  Any ferrite core at 20MHz and above just has a lousy Q.  If you MUST use a ferrite toroid core here check it first with a noise bridge to avoid disappointment. What about cores for baluns ?  This is a special case.  The net magnetic flux in a perfectly operating  balun core is zero!  If there is no net flux, then, do we still need a core ?  In reality, with real wire and real windings and real source and load impedances the net core flux in not zero so core loss  still matters. Only it does not matter that much , compared to a core that might be the inductive element in a resonator.  You have to judge how much core loss is acceptible.  Interstage broadband amplifier  coupling is an application that can cope with lossy cores.  The balun core feeding a dipole antenna, say, most emphatically cannot cope with core loss because real antennas are never perfect resistive loads! (and on recieve every dB is precious). An antenna balun core should always require the use of the best ferrite core you can afford.  Always test your balun with a noise bridge (at the frequency of interest) to avoid disappointment.

What about coils for 30MHz and above?  Use a ferrite toroid...go to jail....its the law !

the "standard" inductance formulas are based on rules of thumb and are crude approximations at best. The assumptions they make are exposed when the number of turns goes below about 10.  The inductance then is given by applying the Biot-Savart law which involves the numerical integration of a path integral which for most "coil" geometries is intractable. The inductance of such small coils is now very strongly Dependant on wire size, conductor elemental composition, winding pitch and the effect of nearby objects that intersect some of the "coil's" magnetic flux.  At VHF and above, the coil behaves more like a coiled transmission line or delay line than an "inductor".  For these small coils I suggest the usage of either a small grid dip oscillator, or better still, make a model prototype of the proposed circuit using identical materials and objects and perform a frequency sweep. The results may disappoint your expectations. Small coils seem to have more inductance then you may suspect, or the common formulas suggest.   There is no such thing as a UHF coil. Think of them only as RF chokes or delay (transmission)  lines of arbitrary shape.

Here is another Law.  Never use a ferrite cored inductor as a resonator for an oscillator.  You will get extreme temperature sensitivity and sensitivy to external magnetic fields. Why ?  a ferrite's permeability  is a strong function of the net average magnetic flux.  Your carefully crafted oscillator will be heavily frequency modulated by stray  Mains Power magnetic fields ! Hum fields are notoriously difficult to shield against.


Is is strictly true that a inductor wound on a ferrite core has invariably lower Q ?  The correct answer is "depends".
On what though ?   The input parameters to this question are  desired inductance, target frequency, core material,  the volume to be occupied by the inductor  which directly determines  the wire size to be wound.  The wire  size determines  its series inductance (DC)  and skin depth AC dependence.

For any ferromagnetic  core  the inductors loss  scales as the  fixed loss (DC resistance) PLUS the first power of frequency (skin effect copper loss)  PLUS  the second power of frequency (core loss).   This is a quadratic relationship  which  has a local minimum !   There IS a range over which copper loss dominates core loss for a given frequency.  Your design choice totally depends on on the physical volume at your disposal. A huge toroidal solenoid wound with 1cm2 copper bus bar for say 10milliHenries will have a nice high Q  but will fill up a small warehouse !  The equivalent ferrite cored coil  will occupy about 10cm3 volume , have a Q of about 50  at 20kHz..hey....not too bad.   Small air cored multi-layer Solenoids that I have wound for the same volume have measured Q values of only 10 to 20.

It is still my assertion that any ferrite coil inductor  for resonator application  will always have a lower Q still applies for applications  in the 3 to 30 megahertz HF band and beyond.   As always, dont trust your inductor untill you have measured (and Q)  it at the intended frequency of operation ! The results can be perplexing and often dont agree with formulas, tables and rules-o-thumb.

This assertion is not valid  for transfomer application provided that the coefficient of coupling k   is nearly  "one".

 This exploration was prompted by a small time signal VLF reciever project that I am scoping .  Inductors for resonators are hard to make and big for below 30kHz.


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page created Dec-22-2009
Fri Jan 15 18:56:58 EST 2010,  Fri Jan 12 12:25:23 AEDT 2018

added schematic (not much there, hardly worth the effort, but you might actually want to see one!)
I was surprised and delighted to discover that this humble and inadequate offering was recently quoted in the British QRP journal Sprat.  It caused me to revisit my own webpage, correct
some spelling errors, and write an addendum.