AN015 Datasheet, PDF (1/9 Pages) Analog Intergrations Corporation – DC/DC power converter

AN015
The effect of ESR on DC/DC power converter
Introduction
The capacitors, inductors, and resistors in circuit
analysis have ideal properties. Capacitors and
inductors follow precise derivative relationships. In
the real world, components do not follow such simple
models. The non-ideal behavior of energy storage
components is very important in the context of power
electronics. This article is to discuss the effect of
capacitor’s ESR (Equivalent series Resistor)
characteristics on DC/DC power converter. And now,
capacitors shall be presenting first.
Capacitors- Principles and Equivalent
Circuits
Figure 1. The Basic Parallel-Plate Capacitor
Geometry_[1]
Capacitor devices come in many forms, but nearly all
of them are composed of conducting plates or films,
also separated by an insulating layer such as air or
paper. A common parallel arrangement, shown in
figure 1, gives equation 1 as follows.
Dec 2000
C = ^εA … … … … … … … … … … … .(equ.1)
d
where is the electrical permittivity of the insulating
layer, A is the surface area, and d is the distance
between 2 plates. By definition, the magnitude of the
charge Q stored on either plates of the capacitor is
directly proportional to the potential difference V
between the plates. Therefore, we may write
Q = CV … … … … … … … … … … … . (equ.2)
where V is the applied voltage. In the arrangement of
parallel plates, the electric field is given by
E = ^V … … … … … … … … … … … . .(equ.3)
d
The time derivative of Q=CV gives the standard
property
i = C ^dv … … … … … … … … … … … . ..(equ.4)
dt
The parallel plate arrangement has provided some
challenges for years. Picture that two plates with
measurements of one square meter for both plates,
which are separated by 1um air space, form a
capacitor of less than 10µF. Nevertheless, typical
capacitors used in power converter are usually on the
order of 100µF or more. However, the permittivity of
free space or air is small, with ₀ = 8.854pF/m and
very large plates are required to give significant
values of C. But the effect of inserting the dielectric is
1