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.
- Good for nothing except RF suppression (up to 1MHz if youre lucky)
- Good up to about 4 MHz
- Good up to about 30MHz
- 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.
|
note(1)
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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