AN015 Datasheet, PDF (2/9 Pages) Analog Intergrations Corporation – DC/DC power converter

AN015
to increase the capacitance by a factor of dielectric
constant k.
K = ^e … … … … … … … … … … … . (equ.5)
e₀
Typical values of k are shown in table 1 as below.
Table1. Dielectric Constant and Strength
Material
Air
Paper
Glass
Paraffin
Rubber
Mica
Water
Dielectric
Constant
1.00059
3.7
4~6
2.3
2~3.5
6
80
Dielectric
Strength(10⁶V/m)
3
16
9
11
30
150
-
Although the term “dielectric” is nearly invariable
applied to insulating materials, which is somewhat a
misleading. Water, which has a high dielectric
constant, is not an insulator.
In a capacitor device, the wires and plates have
resistance and inductance. The insulation is not
perfect and has a leakage resistance. These direct
properties can be summarized in a circuit model,
shown in figure 2._[2]
numbers of important properties.
Ø The current is not exactly consistent with i=Cdv/dt
Ø Current flows even when dc voltage is applied
Ø Resonance occurred due to the combination of L
and C. The device behaves as an inductor when
operated at a frequency which is over the
resonant frequency.
Ø Extra power loss
The properties are out of consideration in general
applications. However, they play as a decisive role in
some of the applications for high operating frequency
or low voltage with high current, e.g. VRMx.x.
The inductance is expected to be in the nano-henry
( 10 ^−9 H ) range, since it represents wire inductance
and geometric effect. The leakage resistance should
be very high, and the time constant of the insulation,
τ = R_LEAK C … … … … … … … … … … … . (equ.6)
should be very long.
In many power electronics applications, a capacitor is
to be used at a specific frequency. Given a radian
frequency , the circuit model can be evaluated as
a set of impedance, then simplified. The simplified
one is shown in figure 3, the derivation starts with a
capacitor C in parallel with the leakage resistance
R_LEAK.
Figure 2. General Circuit Model for a Real
Capacitor
The properties of the model can be minimized, but
not be avoided altogether. This equivalent exhibits
Figure 3.
2