the well known DC-DC buck converter. In order to reduce the
stress of the semiconductor devices, voltages across the cells
have to be balanced. Therefore, the usual converter is modified
by using a controlled DC voltage source. This source is done
by a simple capacitor whose charge and discharge currents
are controlled by independent switches (S1 and S2). Each
pair formed by a switch Sk and a diode Dk is activated in a
complementary manner in such a way that when Sk is ON, Dk
is OFF and vice versa. Also, we will suppose that there exist a
phase shift of between the two command signals in order to
obtain optimum waveforms for the inductor current. Namely,
the inductor current frequency is twice the switching frequency
in this case. In order to simplify the analysis, we will consider
a passive resistive-inductive load. Note that if we consider a
capacitor filter at the output, the ripple of the output capacitor
voltage will be very small in such a way that this state variable
could be considered practically constant. In this case, we could
substitute the output parallel RC network by an equivalent
constant voltage and the value of the capacitor would have,
practically, no effect on the fast dynamics (inductor current
and flying capacitor) provided that a small ripple at the output
is guaranteed.