Self-resonant frequency of a capacitor 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 Scandals in Electromagnetic Theory http://www.ivorcatt.com/28scan.htm @@@@@@@@@@@@@@@@@@@@@@ 8june03 Google Hits no. 4 and 5 (out of a total of 1,200) for "self resonant frequency" + capacitor . (My contradicting hits were 1 and 2 .) http://www.ecircuitcenter.com/Circuits/cbypass/cbypass.htm Power Supply Bypassing BYPASS CAPACITORS How can the voltage spikes be reduced? The
solution is in a statement of wishful thinking: if only the fast current
changes could be supplied to the circuit locally instead of remotely through
LS1 and LS2. This local current source can be in the form of a capacitor CB
between VCC and GND. HANDS-ON
DESIGN Add
a 0.1uF bypass capacitor by removing the comment character "*" from
the CB 3 0 0.1UF statement. Run a simulation and plot Q1
output V(12) and local supply voltage V(3). What happened to the voltage
spikes? They should be dramatically reduced. Why? Capacitor CB now supplies
the current transient; there are no fast current changes through LS1 and LS2
to create voltage spikes. Add trace I(LS1) in a new plot window to see how
the current changes in LS1 have been slowed significantly. If you increased CB from 0.1 uF to 1.0 uF,
CB supplies even more of the current demand locally, requiring even less from
VS. At first it seems too good to be true; the larger the value of CB, the
smaller the magnitude of the voltage spikes. However, real world capacitors
have some disturbing similarities to the power supply leads as will be
discussed in the next section. PRACTICAL CAPACITORS The bad news is that all real world
capacitors have parasitic components similar to the power supply leads:
inductance and resistance. What this means is that capacitors can actually be
modeled by a series RLC circuit (See Capacitor Model for a
review http://www.ecircuitcenter.com/Circuits/cmodel1/cmodel1.htm ).
The unexpected result is that the capacitor
looks inductive at high
frequencies! The switch over from capacitive to inductive behavior happens at
its self-resonant frequency.
Your circuit may perform poorly if operating above the capacitor's
self-resonant frequency. (The good news is you can usually choose a capacitor
whose reactance is still capacitive in your frequencies of interest.) @@@@@@@@@@@@@@@@@@@@@@ http://www.ecircuitcenter.com/Circuits/cbypass/cbypass.htm Power Supply Bypassing
(above) is totally wrong. It is particularly damaging because it writes about power supply decoupling, when the truth is, the bigger the capacitor, the better. As I point out below, he is drawing the reader into a trap; SMALLER IS SOMETIMES
BETTER What we need is a capacitor with a higher self-resonant frequency. And the truth about capacitors is this: for a given capacitor type, smaller capacitor values generally have higher self resonant frequencies. As I show below, the reason why a smaller value capacitor appears to be better is not because it has lower L, but because it has lower C. We need good decoupling, not a low value for C x L, which means a low value for C. 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 b and separation a. See http://www.ivorcatt.com/2_2.htm “We now calculate the
characteristic impedance Zo …..”.
The (resistive) impedance is very low because the dielectric constant is very
high indeed, and the separation b is tiny.
Ivor Catt 18may02 Practical confirmation of my assertion is given below at **** @@@@@@@@@@@@@@@@@@@@@@ Google hit no. 9 on 8june03 for "self resonant frequency" + capacitor . http://www.qsl.net/kf4trd/varactor.htm The frequency at which both impedances Here we see
the truth muddled up with old wives’ tales. The writer does not of course
realise that the primary reason why the “self resonant frequency” is lower
for a large C is that the formula includes the value of C. The “culprit” is a
larger C, not a larger L. @@@@@@@@@@@@@@@@@@@@@@ @@@@@@@@@@@@@@@@@@@@@@ Riposte Ivor Catt. 18june02 @@@@@@@@@@@@@@@@@@@@@@ The amount of nonsense
drifting around the world, of which the above are examples, 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 @@@@@@@@@@@@@@@@@@@@@@@@@@@ **** 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%. @@@@@@@@@@@@@@@@@@@@@@@@@@@ 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 @@@@@@@@@@@@@@@@@@@@@@@@@@@ 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. @@@@@@@@@@@@@@@@@@@@@@@@@@@ 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. @@@@@@@@@@@@@@@@@@@@@@@@@@@ xx |
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 |