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General Description
I (Ideal)
Loss
Angle
I (Actual)
f
Phase
Angle
di
The dt seen in current microprocessors can be as high as
0.3 A/ns, and up to 10A/ns. At 0.3 A/ns, 100pH of parasitic
inductance can cause a voltage spike of 30mV. While this
does not sound very drastic, with the Vcc for
microprocessors decreasing at the current rate, this can be
a fairly large percentage.
Another important, often overlooked, reason for knowing
the parasitic inductance is the calculation of the resonant
frequency. This can be important for high frequency, by-
pass capacitors, as the resonant point will give the most
IR s
V
signal attenuation. The resonant frequency is calculated
from the simple equation:
Power Factor (P.F.) = Cos f or Sine
In practice the current leads the voltage by some other phase
angle due to the series resistance R S . The complement of this
angle is called the loss angle and:
Dissipation Factor (D.F.) = tan
f res = 1
2 LC
Insulation Resistance – Insulation Resistance is the
resistance measured across the terminals of a capacitor
and consists principally of the parallel resistance R P shown
in the equivalent circuit. As capacitance values and hence
the area of dielectric increases, the I.R. decreases and
for small values of
the tan and sine are essentially equal
hence the product (C x IR or RC) is often specified in ohm
which has led to the common interchangeability of the two
terms in the industry.
Equivalent Series Resistance – The term E.S.R. or
Equivalent Series Resistance combines all losses both
series and parallel in a capacitor at a given frequency so
that the equivalent circuit is reduced to a simple R-C series
connection.
farads or more commonly megohm-microfarads. Leakage
current is determined by dividing the rated voltage by IR
(Ohm’s Law).
Dielectric Strength – Dielectric Strength is an expression
of the ability of a material to withstand an electrical stress.
Although dielectric strength is ordinarily expressed in volts, it
is actually dependent on the thickness of the dielectric and
thus is also more generically a function of volts/mil.
Dielectric Absorption – A capacitor does not discharge
instantaneously upon application of a short circuit, but
drains gradually after the capacitance proper has been
E.S.R.
C
discharged. It is common practice to measure the dielectric
absorption by determining the “reappearing voltage” which
Dissipation Factor – The DF/PF of a capacitor tells what
percent of the apparent power input will turn to heat in the
capacitor.
Dissipation Factor = E.S.R. = (2 π fC) (E.S.R.)
X C
The watts loss are:
Watts loss = (2 π fCV 2 ) (D.F.)
Very low values of dissipation factor are expressed as their
reciprocal for convenience. These are called the “Q ” or
Quality factor of capacitors.
Parasitic Inductance – The parasitic inductance of
capacitors is becoming more and more important in the
decoupling of today ’s high speed digital systems. The
relationship between the inductance and the ripple voltage
induced on the DC voltage line can be seen from the simple
inductance equation:
V = L di
dt
108
appears across a capacitor at some point in time after it has
been fully discharged under short circuit conditions.
Corona – Corona is the ionization of air or other vapors
which causes them to conduct current. It is especially
prevalent in high voltage units but can occur with low voltages
as well where high voltage gradients occur. The energy
discharged degrades the performance of the capacitor and
can in time cause catastrophic failures.
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