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Self-resonant frequency of a capacitor 2009. The nonsense continues and escalates
Nonsense about so-called “self-resonant frequency” of a capacitor.
If you cut off a
capacitor’s legs at the knees, you will double its self-resonant frequency
– Ivor Catt
Martin Eccles takes
the biscuit My 1994 book Electromagnetism 1 is at http://www.ivorcatt.com/em.htm Nigel
Cook on Ivor Catt’s ideas, (London) Electronics World (was Wireless
World), aug02, pp46-49 More
nonsense is at http://www.ivorcatt.com/2605.htm Yet more nonsense
Scandals in Electromagnetic Theory http://www.ivorcatt.com/28scan.htm RIPOSTE
Ivor Catt's view of Capacitors, by Leslie Green CEng MIEE
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The amount of nonsense drifting
around the world is vast. See my 1978 article at http://www.electromagnetism.demon.co.uk/z001.htm
; “Series inductance
does not exist. Pace
the many documented values for series inductance in a capacitor, this
confirms experience that when the so-called series inductance of a
capacitor is measured it turns out to be no more than the series inductance
of the wires connected to the capacitor. No mechanism has ever been
proposed for an internal series inductance in a capacitor.” The key point in my article is that “No mechanism has ever been proposed for an internal series inductance in a capacitor.” The IEE and IEEE have helped
to cause the confusion to escalate by suppressing my 1978 article
http://www.electromagnetism.demon.co.uk/z001.htm
, which puts an end to a capacitor’s series inductance. Also, competent
experimentation will show that a capacitor has no internal series
inductance. http://www.ivorcatt.com/em_test04.htm – Ivor Catt, 30jan02
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Ivor
Catt 22apr02 In
1963 I bought the EH-125 pulse generator. This delivered a –10v step
with a 100picosecond fall time into a 50 ohm load (e.g. 50 ohm coax.). The
pulse generator could also deliver a –ve 10v spike with a width of
150psec. I decided to try to create a positive 10v spike. I cut into
the 50 ohm coax, and joined the incoming inner to the outgoing outer
via a red 1uF tantalum capacitor. I also joined the incoming outer
to the outgoing inner via another 1uF tantalum capacitor. Further
downstream I found that I had a positive 150psec spike with no discernable
degradation (in rise time or pulse width) compared with the initial
–ve spike. That is, I had a +ve 10v spike with a width of 150psec. It
is interesting to calculate the physical width of a 150 psec wide
spike travelling down normal coax, which has a dielectric with a dielectric
constant of 2. Whereas light travels one foot in vacuo in one nsec,
it would travel 8 inches in material with a dielectric constant of
2. Thus, a 150psec spike in the coax has a width of about one inch.
So I sent a TEM spike with a width of 1 inch through these 1uF capacitors.
[Note 1] Obviously, I kept their legs short. It is sad that during
the ensuing 40 years the New York IEEE and the London IEE prevented
me from informing electronic engineers that they did not have to add
“high frequency” decoupling capacitors to their logic boards, that
the 1uF would do perfectly well on its own. This obstruction has cost
the industry many millions of pounds. However, a bolshie IEEE and
a bolshie IEE cost us a lot more than that in other ways. Ivor Catt
22apr02
Note 1. Anyone who wants to play with
frequencies can be told that the fundamental of the 150psec spike
will be around 3GHz. Put that in your “self-resonant” pipe and smoke
it! IC
Note 2. As the spike passes the capacitors
placed to each side, the situation is as in http://www.ivorcatt.com/2_1.htm Figure
14. The characteristic impedance of each capacitor is very small,
less than 1% of 50 ohms. Thus, the mismatch is less than 2%, causing
a minimal reflection of less than 1%. At the same time, if the legs
of the capacitors are kept down to a total of one quarter of an inch
in length, and the two parallel legs represent a quarter inch transmission
line of characteristic impedance 150 ohms, then the mismatch will
cause a reflection of 50%, see http://www.ivorcatt.com/1_4.htm
Figure 11 and the reflection formula. This will be reduced by the
fact that the 150psec spike covers a distance of one inch and a half,
so that the reflections on entering the 150 ohms region tends to be
masked by the opposite mismatch on re-entering the 50 ohm impedance
of the next section of coax. This reduces the reflection to one sixth,
i.e. 8%.
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18may02 More drivel. Fig. 2 at http://www.ultracad.com/seminar_caps.htm Google Hit no. 7 for “self resonant frequency” + capacitor
This article high on the Google
hit list has row of capacitors, and each one decouples (digital electronic
equipment for) its particular frequency range. This farce is obvious if one
realises that a 2uF capacitor is made by glueing together two 1uF
capacitors. Thus, a supposedly “high frequency capacitor” is merely
the front little bit of a 1uF capacitor. Of course, you can ruin the
performance of either by leaving it with long legs, making a series
one-turn inductor to stifle its performance. However, the idea that
a 10pF capacitor has shorter legs than a 1uF capacitor is based on
nothing at all.
What is so tragic is that
the formula these clods use for self resonant frequency, 1/ sqrt LC
, means that if C is big, then the resulting calculated “self resonant
frequency” is low. This is a sensible idea if a resonant circuit is
being designed out of a discrete C and a discrete L, where L can be
varied. But if, as in our case, we (have legs of fixed length and)
can only vary the value of C, then the calculation deludes. If we
start with a pair of legs of fixed length, that is, with a fixed external
L, then the bigger the C, the lower the resonant frequency according
to the formula w = 1/ sqrt LC. These buffoons are buying capacitors for the very reason that
they have less capacitance, not that they have less L. They buy these
“high frequency capacitors” for the very reason that, lacking much
C but helping the w = 1/ sqrt LC formula, they are inferior at doing
the decoupling job that they have been bought to do. All their nonsense
is counter-productive. This was pointed out in my book more than 20
years ago. Since digital electronics took over from radio as the majority
of electronic engineering 40 years ago, it is high time the radio
men gave us at least some access to the IEEE, the London IEE and to
Cambridge and MIT. Even a single digital electronics course by someone
who understood the subject at either MIT or Cambridge University would
help a lot. I would love to give it. However, I am sure the radio
men will continue to shut me and my colleagues out, as they have done
for a number of decades, hoping that their antique radio theory will
continue to appear to address the needs of digital electronic equipment.
http://www.ivorcatt.com/em_test04.htm Ivor Catt 18may02
Since a capacitor is a two-conductor
transmission line with very low characteristic impedance, the transient
impedance that it presents to a step is resistive, not reactive. This
is the way it behaves when decoupling digital circuits; as a local
energy store for the 5v supply with a very low resistive source impedance,
not a reactive source impedance. Calculation of the impedance is made
by using the normal formula
for the characteristic impedance of a transmission line made up of
two parallel plates with width a and separation b. See p73 of my book
“Electromagnetics 1”, pub. Westfields 1975. The (resistive) impedance
is very low because the dielectric constant is very high indeed, and
the separation b is tiny. Ivor Catt 18may02
In the surreal world created with
inappropriate mathematical stunts by physically ignorant operators,
a capacitor is looked on with disdain, not because it has more L,
but because it has more C. http://www.ivorcatt.com/em_test04.htm Ivor Catt 18may02
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Recap.
Take the formula for the resonant frequency for an inductor-capacitor
tank circuit.
The
frequency (in radians per sec.) squared equals (1/ inductance x capacitance)
Thus,
either increase in inductance or increase in capacitance reduces the
resonant frequency. This has led physically ignorant mathematical
mugwumps to think, not that the best capacitor has the least capacitance,
which even they might realise is ridiculous, but that the best capacitor
has the least inductance, making it able to perform to a much higher
frequency up to its higher resonant frequency. They have failed to
realise that they would realise their dream, of a high self resonant
frequency, by reducing the capacitance just as well as by reducing
the inductance. They think that it is an accident that lo value capacitors
have the highest self resonant frequency. They think it is because
of the difference in inductance, which it is not.
However,
all this is nonsense when decoupling digital logic. What matters with
digital logic is the transient performance of a decoupling capacitor,
when some switching logic wants to grab as much charge as possible
to launch down a transmission line
towards the next logic gate. The true model, which should have
replaced the series L C R model for a capacitor, was already published
in 1978, http://www.electromagnetism.demon.co.uk/z001.htm , and has been ignored for 24 years by radio
men who continue to teach and publish the old model which is inappropriate
and damaging in digital electronics. Note that today, most capacitors
are used in DC voltage decoupling.
The
only way out of this impasse is for students to create problems during
the lecture when lecturers continue to pump out the old, wrong drivel.
Otherwise these lecturers and text book writers will continue to copy
and repeat each other from a bygone age when electronics was about
radio, and such a misconception about the physical nature of a capacitor
was not so damaging. http://www.ivorcatt.com/em_test04.htm
Students have much to gain by disrupting their
lectures. It is probably more difficult to learn and be examined in
material which is false. Ivor Catt.
18may02.
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In
1965, living in the USA, I telephoned the design engineers in Sprague,
who manufactured capacitors. They told me that they tested for the
high frequency performance of a capacitor by testing at 5kHz and 50kHz,
and deduced its performance at 1MHz and above using the series L C
R model. Thus, the published self-resonant frequency of a capacitor
is the result of lo frequency testing extrapolated using the L C R
model.
By
making this error, engineers in the capacitor manufacturers might
have doubled their companies’ sales, ensuring that a second “high
frequency” capacitor would be added to every 1uF decoupling capacitor
in every digital system.
Ivor Catt 18may02.
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| Riposte Ivor Catt. 18june02
Scandals in electromagnetic theory http://www.ivorcatt.com/28scan.htm
x |
| (Possibly we need a standard word for
this. I suggest "Riposte", or the symbol [R] .) Ivor Catt,
30june02. ivor@ivorcatt.com |