IV. CARRIER WAVEFORM GENERATOR
The key component of the NLC controller of Fig. 1 is the
generator of the nonlinear-carrier waveform defined by
(10). We now show how this highly nonlinear periodic waveform
can be approximated in hardware without compromising
simplicity or performance of the controller.
Since the output voltage is , the converter always
operates with greater than a minimum value , at the
peak of the input-line voltage
(19)
Therefore, an accurate approximation to is only required
on the interval .
With the objective of simple hardware implementation, we
consider approximating the carrier with an exponential decay
as follows:
(20)
The time constant of the exponential decay is specified as a
fraction of the switching period using the parameter , while
Fig. 11. Small-signal model of the NLC-controlled rectifier.
is an arbitrary constant that scales the amplitude of the carrier
and therefore the emulated resistance . Fig. 5 compares the
ideal carrier waveform with the approximate exponential
carrier waveform for .
Hardware implementation of the exponential carrier is
very simple, as shown in Fig. 6. A constant-frequency clock
CK with duty ratio keeps the switch on during
. When the switch is turned off, decays
from toward zero, with the time constant .
As a result of the approximate carrier waveform, the input
current is not exactly equal to the ideal , even if
the converter operates always in the CCM. The actual can
be found from (11) by replacing the ideal carrier waveform
with the approximate waveform
(21)
Equation (5) shows how the duty ratio varies over a line
cycle
(22)
which using (20) and (21) gives the waveform in closed
form
(23)
Fig. 7 shows and waveshapes during one half of the
ac-line cycle for three values of the parameter . Using
the THD of the input current can be found for a
given value of the parameter and a given conversion ratio
. Fig. 8 shows contours of constant THD
as a function of and . The parameter has
been found to minimize the maximum THD of over the
considered four–one range of input ac-line voltages. Fig. 9
shows the THD of the ac-line current as a function of , for
the optimum value of the parameter . The maximum THD
of 3.84% is obtained for . Fig. 8 shows how the THD
stays well below 10% for wide tolerances in the time constant
of the exponential decay used to approximate the ideal
NLC waveform.