3
Introduction
General Characteristics
TPC
The real characteristics of a capacitor can be described
using conventional physical parameters and the following
equivalent electrical circuit:
C capacitance is a measure of the capacitors aptitude
to store electrical charges Q under a voltage V
(C = Q/V).
K the dielectric constant, specific to each material
(less than 500 for type I materials, from 1000 up to
10,000 for type II materials),
A the area of the electrodes, and
t the thickness of the dielectric layer are the parame-
ters determining the capacitor value
C = K A(K = er)
t
T.C. the temperature coefficient of the capacitance is
expressed in ppm/°C for stable type I dielectrics.
DC/C is used for type II dielectrics and is expressed in %
of change of the capacitance in a fixed temperature
range.
VRthe rated voltage is the maximum voltage that can
be applied to the capacitor on continuous opera-
tion. It can be constituted by:
VDC a direct current component
VRMS an alternating current component
VPthe peak voltage
VEthe test voltage
RPthe parallel resistance
IR the insulation resistance under VDC.
RSor ESR (Equivalent Series Resistance) accounts for
the conductivity of the electrodes and connections.
LSor ESL (Equivalent Series Inductance) depends on
the geometry of electrodes dielectric and connec-
tions, leads...
CPtakes into account dielectric environment of the
capacitor (coating...) but is generally neglected
except to describe very high frequency behavior of
the capacitor or for very low capacitance value.
Rp, Rs, Ls, Cp can be considered as parasitic
effects. They generate energy losses and a
dephasing
jdifference between voltage and current from 90°.
The loss angle d(90° - j) is commonly used.
tg dthe tangent of loss angle
DF the dissipation factor (same as tg d)
Q the quality factor is the ratio between the stored
energy and the dissipated energy. It measures the
quality of the capacitor and can be expressed as
Q = 1/tg dor 1/D.F.
ƒ being the frequency of the AC signal
wthe pulsation of this signal with w= 2pƒ
Z the complex impedance of the capacitor is given by
the relation (neglecting Cp):
Z = RS+ j LSw+ 1= R + j X
1 + j Cw
RP
the tangent of the loss angle tg dcan also be
expressed as tg d=R
X
so, neglecting Ls for LSw<1
C w
tg d= RSCw+1 + 1
RPCwR2
PCw
ƒRS the series resonance frequency of the capacitor is
the frequency where the capacitance reactance is
exactly equal to the inductive reactance due to LS
LSw=1 or w=1 or ƒRS =1
CwLSC2pLSC
ƒRP the parallel resonance frequency occurs when LSis
equal to CP:ƒRP =1
2pLSCP
Between ƒRS and ƒRP, the capacitor reacts as an
inductance, but still blocks DC.
The equivalent electrical circuit can be simplified
using approximations according to the frequency:
- At ƒ = ƒRS the circuit is reduced to
Z = RS
- For high frequencies but below ƒRS
Z = RS+1/jCw
tg d= RSCw
- For low frequencies Z = 1
1 + jCw
RP
tg d= 1
RPCw
IRMS is the maximum RMS current that can be transmit-
ted by the capacitor electrodes
WRis defined as the maximum reactive power and is
expressed by WR= V2RMS Cw=I2RMS
Cw
WAis the active power or dissipated power
WA= WRtg d= (2pƒCV2)(DF)