From: "Barry L. Ornitz" <ornitz@tricon.net>
Subject: Re: resistor opinion
Date: Jun 14 1997
Newsgroups: rec.audio.misc,rec.audio.opinion,rec.audio.tech,rec.audio.tubes,
	sci.electronics.repair

Dave Cigna <cigna@helios.phy.OhioU.Edu> wrote:

> Take it easy, John. All I did was report some measurements. In a later
> post I said that I would like to go back and perform them again more
> carefully (and with different equipment) but that I was pretty confident
> in the results.

If you are confident in these results, it is rather obvious that you know
nothing about how these resistors are manufactured.  One of the first
things I always teach to a technician is to NEVER trust an instrument
unless you have calibrated it.  After this comes the admonition that if the
measurement comes out looking strange, or far different from what the
theory says it should be, the proper thing to do is check your instrument
and procedure - not create a new theory.

> What got me started on this in the first place is that I repeatedly hear
> people make general statements about the relative inductance of different
> types of resistors -- and about whether or not that (entirely unquantified)
> inductance is relevant at audio frequencies -- but nobody seems to have
> any REAL idea how much inductance we're talking about. They seem perfectly
> happy spreading purely speculative and uniformed "information".

And I thought this was what "glass audio" or "high end" was really all
about!   :-)
NEVER trust measurements and science.  Trust your ears!   Who cares what
the 
inductance is?  Only the sound is important!  Sound CANNOT be measured.  
:-)

[After seeing my old friends, jj (the old curmudgeon) and Dick Pierce (who
is hopefully no longer hostile at our once common employer), posting, I
know this is not true of everyone on this group.  My apologies to those who
really do care about what is real and what is hype.]

> If you don't believe my measurements that's ok with me. If you want to
> make constructive contributions to the discussion then perform your own
> measurements (or reference someone else's *numerical* results), or at
> the very least suggest a method that can be easily performed without
> specialized equipment. Pulling numbers out of the air and plugging them
> into an equation is not all that satisfying. Especially when it's done
> with hostility. 

Ah, but it gives a perfectly good limiting value.  The actual inductance
MUST be less than this equation predicts.  Actually it is far, far less for
reasons I will explain later.
 
> If my measurements turn out to be miles off, that'll be ok with me, as
> long as this discussion led to some *real* understanding. Unfortunately,
> nobody seems interested in finding out how inductive these things really
> are when it's much easier to just share hunches and second hand 
> information.
> 
>  -- Dave Cigna

OK Dave.  How about Resistors 101 - the freshman course?

Carbon composition resistors are made by compressing a mixture of graphite
and clay into a cylindrical shape, somehow making connections to the ends,
attaching wires, and potting the mess in phenolic or epoxy.  The resistance
is determined by several things.  First is the chemical composition of the
original mixture.  Add a lot of graphite and the resistivity is low.  Add a
lot of clay or other filler material and the resistivity is high.  Note I
said resistivity and not resistance - this is important.
The second thing that determines the resistivity is how much pressure the
material is compressed under.  A lot of pressure and the resistivity goes
down.

Now resistivity is measured in ohm-cm.  You take a 1 cm cube of the
material and measure the resistance from opposite sides.  Of course you
have to have perfectly conducting electrodes on both measuring surfaces. 
The funny thing is that if you had a 1 m cube of the same material and did
the same resistance measurement, you would measure the same resistance. 
The key fact to learn here is that resistivity is a function of the
material, but resistance is also a function of the geometry of the
material.

So now you have to assume a geometry for your resistor.  This is the third
thing and the final one that determines the overall resistance.  I know you
hate equations but try to follow this one:

Resistance = Resistivity (ohm-cm) * Length (cm) / Cross Sectional Area
(cm^2)

Thus resistance is measured in ohms.  To manufacture a resistor of a given
value,
you start with a chosen chemical composition, compress it to a chosen
density in a cylindrical form, also of chosen cross sectional area.  The
only thing you have left is the length of the composition and this what is
usually adjusted slightly to trim the resistor to its desired value. 
Alternately, you could grind away a little of the center of the resistor to
adjust it too.  

This overall process is complex and not under the best control.  Thus
carbon composition resistors were originally manufactured in 20%
tolerances.  As things got better, 10% tolerances became possible and
finally 5% tolerances.  But this was really about the limit because too
many "little" things could change about the manufacturing process and upset
production.

Being essentially a straight rod of resistive material, carbon composition
resistors had minimal inductance.  A 1 Megohm resistor had approximately
the same geometry as a 1 Kohm resistor, the major change being in the
composition of the graphite mix used.  Thus inductance changed minimally
with resistor value.  Resistance did change, however, with temperature,
humidity, and time.

The film resistor was created to produce a more uniform resistor, and one
that could be manufactured to close tolerances easily.  To do this, the
design of the resistor was changed entirely.

Instead of using bulk resistivity, the surface resistivity of a thin film
of material is used to develop the resistance.  A ceramic rod is somehow
coated with this film of resistive material. [The actual process can vary: 
sputtering or chemical vapor deposition may be used, or resistive inks may
be coated on the surface and then fired, etc.]  But the same equation above
still holds.  If you want to make a higher value of resistance, make the
film thinner (reducing its cross sectional area), make it longer, or make
it out of a material with a different resistivity.  In practice, all of
three of these techniques are used.  Low value resistors use thick films of
low resistivity coatings while high value resistors use thinner films of
higher resistivity coatings.

In manufacturing these resistors, several things can be adjusted.  The
material coated on the ceramic form is usually not changed for every value
within a given range.  Instead its thickness is usually changed.  However
controlling this to a very narrow tolerance is not easy.  It is possible to
coat a very large number of ceramic rods uniformly in one batch, but the
next batch may be somewhat different.

This is where the spiral cutting or laser trimming is involved.  If you
ablate part of the coating, you increase the resistance.  However, this may
mean having to remove large portions of the resistive coating.  An
alternate method is to cut a spiral into the material.  What this does is
make the effective length of the resistive path longer.
The result is an increase in resistance.

Now this trimming can be done on a batch of resistors based on statistics
of the batch, or - if you are willing to pay for it - on each individual
resistor with computer controlled feedback.  The latter is used to produce
high precision resistors.  After the trimming, a conformal coating is
applied.

So now we have a ceramic rod coated with a resistive material that may be
cut in a spiral shape.  Without the spiral, the inductance of such a
resistor would be virtually the same as that of the composition resistor. 
There would be some slight differences at very high radio frequencies (UHF
and microwave) because of skin effect relationships, but you would never
see any difference in audio.  But what happens with the spiral?

This creates inductance, of course.  How much?  Well this again depends on
the geometry.  We can go back to the other poster's equations derived from
Kraus, or we can use Nagoaka's equations, or we can even go the the "bible"
of inductance, 
"Inductance Calculations" by Grover.  In all cases, however, we can see
that the inductance is proportional to the diameter and the square of the
number of turns, and inversely proportional to the overall length of the
coil.

Now this should start making sense.  In a fixed wattage of film resistor,
the overall geometry is fixed.  This means that in the same wattage, the
inductance should go up as the square of the number of turns.  Yet for a
fixed coating thickness of constant resistivity, the resistance should go
up only as the number of turns (approximately, since the cut is not
infinitely thin).

This is what I was getting at about knowing the theory.  Inductance should
approximately go up as the square of resistance, not linearly as Dave said.

But there are more details.  It is really impractical to make a very fine
spiral in these resistors as someone else pointed out.  You only have so
much space and the width of the cut must be reasonable.  The question is
really how many turns are needed in the spiral.  If you got the resistive
coating thickness perfect, you would not even need to trim the value by
cutting a spiral.  But as I said before, this is not practical.
So in reality, a spiral is usually cut to adjust the value.

In low value film resistors, the spiral may be quite minimal.  If you can
take the conformal coating off the film resistor (not so easy), you can
count the turns.
Most that I have seen have less than 5 turns for values below 1 Kohms or
so.

For very high value resistors, say 100 Kohms or more, it becomes
impractical to make the coating too thin.  Thus more turns will be needed -
but remember there are manufacturing limits.  I am sure it depends by
manufacturer, but my guess is that about 20 turns would be an upper limit. 
To get a proper feel, I am looking at a 
1 Gohm (1000 Megohm) resistor.  It is 6 inches long and 1/4 inch in
diameter.  At 12 turns per inch, it has a total of 72 turns.  The turns are
spaced such that their width is about the same as their spacing.  This is
done to maximize the voltage rating.
From geometrical scaling, 20 turns would seem to be a reasonable upper
limit in small film capacitors.

Taking 20 turns as the upper limit and the dimensions of  typical 1/4 or
1/2 watt film resistor, this places the upper limit of the inductance in
the low microhenry range.
Is this enough to do anything at audio frequencies?  Hardly.  But if I
needed a 50 ohm termination resistance at 150 MHz, I would probably not use
a film resistor.
But I might parallel a number of higher values to lower both the equivalent
resistance and inductance.
 
Now if Dave has read this far, I will publicly apologize for _my_
hostility.  It is quite normal to become a little hostile when you are
confronting an ignorant person who is unwilling to learn or listen to
reason.  The measurement of inductance with distributed series resistance
of this magnitude is extremely difficult.  The equations, however
dissatisfying they may be, are far more accurate at predicting the
inductance (if you know the geometry accurately) than all but the most
complex measurement techniques.  [For the best experimental accuracy, the
magnitude of the inductive reactance must be approximately the same as the
magnitude of the resistance.  This implies, with a 1 Megohm resistor,
measurements at very high radio frequencies.  In fact, the frequencies
needed will be high enough that secondary effects will still make the
measurements quite difficult.]

So after all of the above explanation, can I give Dave an *EXACT* value of
inductance for a 1 Megohm resistor.  No.  But give me the resistor to
remove the coating (since they will be different from one batch to another
and even more so from one manufacturer to another), allow me to count the
turns and measure the geometry, and I can come pretty damn close.  But why
is this even necessary.  It might be if I were building microwave circuits,
but this is AUDIO.

Do you want a reasonable upper limit on the inductance to judge the effects
on audio?  If so, use a value of about 1 microHenry.  Then calculate the
inductive reactance at the highest frequency you are interested in.  At a
megaHertz, this is about six ohms of inductive reactance.  Now do the
vector sum of this six ohms with the resistance value and see how much
difference it makes.

Now class, for your homework assignment in Resistors 101, show that film
resistors are perfectly suitable for virtually all audio applications -
even in feedback networks.  Class dismissed.

	Barry L. Ornitz, PhD                            ornitz@tricon.net
(not my normal signature but it is appropriate here since this was a class
after all)