266
Converter Transfer Functions
models of Chapter 7. For example, the small-signal equivalent circuit model of the buck-boost converter
is illustrated in Fig. 7.17(c). This model is reproduced in Fig. 8.1, with the important inputs and terminal
impedances identified. The line-to-output transferfunction is found by setting duty cycle varia-
tions to zero, and then solving for the transfer function from
Thi s transfer function describes how variations or disturbances in the applied input voltage lead to
disturbances in the output voltage
v
(
t
). It is important in design of an output voltage regulator. For exam-
ple, in an off-line power supply, the converter input voltage contains undesired even harmonics of
the ac power line voltage. The transfer function
is
used to determine the effect of these harmonics
on the converter output voltage
v
(
t
).
The control-to-output transfer function is found by setting the input voltage variations
to zero, and then solving the equivalent circuit model for as a function of
This transfer function describes how control input variations
influence the output voltage
In an
output voltage regulator system, i s a key component of the loop gain and has a significant effect on
regulator performance.
The output impedance is found under the conditions that and variations are set
to zero. describes how variations in the load current affect the output voltage. This quantity is also
important in voltage regulator design. It may be appropriate to define either including or not
including the load resistance
R.
The converter i nput impedance plays a significant role when an electromagnetic interfer-
ence (EMI) filter is added at the converter power input. The relative magnitudes of and the EMI filter
output impedance influence whether the EMI filter disrupts the transfer function Design of input
EMI filters is the subject of Chapter 10.
An objective of this chapter is the construction of Bode plots of the important transfer functions
and terminal impedances of switching converters. For example, Fig. 8.2 illustrates the magnitude and
phase plots of
for the buck-boost converter model of Fig. 8.1. Rules for construction of magni tude
and phase asymptotes are reviewed in Section 8.1, including two types of features that often appear in
to