AC Equivalent Circuit Modeling
7
.
1
INTRODUCTION
Converter systems invariably require feedback. For example, in a typical dc–dc converter application, the
output voltage
v
(
t
)
must be kept constant, regardless of changes in the input voltage
or in the effec
tive load resistance
R.
This is accomplished by building a circuit that varies the converter control input
[i.e., the duty cycle
d
(
t
)]
in such a way that the output voltage
v
(
t
)
is regulated to be equal to a desired ref
erence value
In inverter systems, a feedback loop causes the output voltage to follow a sinusoidal
reference voltage. In modern lowharmonic rectifier systems, a control system causes the converter input
current to be proportional to the input voltage, such that the input port presents a resistive load to the ac
source. So feedback is commonly employed.
A typical dc–dc system incorporating a buck converter and feedback loop block diagram is
illustrated in Fig. 7.1. It is desired to design this feedback system in such a way that the output voltage is
accurately regulated, and is insensitive to disturbances in
or in the load current. In addition, the
feedback system should be stable, and properties such as transient overshoot, settling time, and steady
state regulation should meet specifications. The ac modeling and design of converters and their control
systems such as Fig. 7.1 is the subject of Part II of this book.
To design the system of Fig. 7.1, we need a dynamic model of the switching converter. How do
variations in the power input voltage, the load current, or the duty cycle affect the output voltage? What
are the smallsignal transfer functions? To answer these questions, we will extend the steadystate mod
els developed in Chapters 2 and 3 to include the dynamics introduced by the inductors and capacitors of
the converter. Dynamics of converters operating in the continuous conduction mode can be modeled
using techniques quite similar to those of Chapters 2 and 3; the resulting ac equivalent circuits bear a
strong resemblance to the dc equivalent circuits derived in Chapter 3.
Modeling is the representation of physical phenomena by mathematical means. In engineering,
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AC Equivalent Circuit Modeling
it is desired to model the important dominant behavior of a system, while neglecting other insignificant
phenomena. Simplified terminal equations of the component elements are used, and many aspects of the
system response are neglected altogether, that is, they are “unmodeled.” The resulting simplified model
yields physical insight into the system behavior, which aids the engineer in designing the system to oper
ate in a given specified manner. Thus, the modeling process involves use of approximations to neglect
small but complicating phenomena, in an attempt to understand what is most important. Once this basic
insight is gained, it may be desirable to carefully refine the model, by accounting for some of the previ
ously ignored phenomena. It is a fact of life that real, physical systems are complex, and their detailed
analysis can easily lead to an intractable and useless mathematical mess. Approximate models are an
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 Spring '09
 DariuszCzarkowski
 Alternating Current, Eqs., ac Equivalent Circuit, Equivalent Circuit Modeling

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