line voltage, multiplier/divider in the voltage feedback loop,
and error amplifier in the current-shaping loop are eliminated.
III. NONLINEAR-CARRIER CONTROL
FOR UP–DOWN CONVERTERS
In this paper, we derive the NLC control for up–down
switching converters with the steady-state dc conversion ratio
given by
(2)
where is an arbitrary constant and is the switch duty
ratio. The constant can be 1 if the converter is inverting
the input voltage or the turns ratio if the converter has an
isolation transformer. The considered up–down converters
include buck–boost, flyback, Cuk, Sepic, and inverse Sepic ´
(Zeta) converters, with or without transformer isolation. In all
of these converters, the low-frequency portion of the switch
current is equal to the low-frequency portion of the input
current . The current-shaping objective (1) can therefore be
written as
(3)
To keep the notation simple, we assume that a switching period
always starts at . Equation (3) is the basis for one-cycle
(charge) control, which has been applied to flyback rectifiers
[5].
In the discussion that follows, we use the notation
Using (2), we find as a function of the output voltage and
the switch duty ratio
(5)
and eliminate in (3) to obtain the relation
(6)
the switch duty ratio must solve in each switching period.
is the equivalent current-sensing resistance, and the emulated
resistance
(7)
can be adjusted by the slowly-varying control signal in
the voltage feedback loop.
In each switching period, the duty ratio that solves (6)
can be obtained by comparing the voltage proportional
to the integral of the switch current (the left-hand side)
(8)
with a periodic nonlinear-carrier waveform (the righthand
side), obtained by replacing