Digital Control of Resonant Converters:
Enhancing Frequency Resolution by Dithering
Mor Mordechai Peretz and Sam Ben-Yaakov
Power Electronics Laboratory
Department of Electrical and Computer Engineering
Ben-Gurion University of the Negev
P.O. Box 653, Beer-Sheva 84105, ISRAEL.
Phone: +972-8-646-1561; Fax: +972-8-647-2949;
Emails: morp@ee.bgu.ac.il, sby@ee.bgu.ac.il ; Website: www.ee.bgu.ac.il/~pel
Abstract- Resonant converters and related systems, such as
piezoelectric transformers, may require a high-resolution
frequency drive when the quality factor of the network is high or
to avoid limit cycle oscillations. This high frequency resolution
requirement could be beyond the capabilities of low cost
microcontrollers. To remedy this problem, a frequency resolution
enhancement algorithm was developed, tested by simulations and
verified experimentally. The proposed approach is based on a
modification of the fractional-N dithering concept and includes an
adaptive dithering period and smooth DPWM frequency
transitions. The implementation of the approach on the digital
hardware is simple and requires modest additional workload
from the CPU.
Theoretical analysis was carried out to model the proposed
dithering method when applied to drive resonant network in
order to identify the causes and to quantify the expected output
signal distortion when the signal is used to drive resonant
networks. The proposed approach was tested experimentally on
two types of resonant converters: a series-resonant parallel-
loaded converter and a piezoelectric transformer. It was found
that the output signal distortion is less than 1% of the peak
amplitude of the output drive which would be acceptable in many
applications. The experimental results were found to be in
excellent agreement with the theoretical predictions, validating
the usefulness of the dithering method as a frequency resolution
enhancer for resonant network drive.
I. INTRODUCTION
In a variety of applications, variable frequency is the
preferred method for output regulation of resonant converter
(e.g. fluorescent lamp ballasts piezoelectric devices) [1-3]. In
such cases, the frequency resolution of the drive is crucial to
ensure accurate operating conditions and the desired load
performance.
At present, the control of resonant converters is mostly
dominated by analog controllers that use Voltage Controlled
Oscillator (VCO) with very high resolution capability [4]. In
digital controllers, the frequency generation is obtained by
timers that can be programmed to reset at a desired value,
while maintaining a constant duty ratio of 50%. This is
conventionally realized by the embedded Digital PWM
(DPWM) of microcontrollers and DSPs peripheral units since
they include built-in timers, period compare registers and are
capable to operate multiple channels (for synchronous bridge,
interleaving etc.) with in-phase, complementary or deadband
synchronization.
The frequency resolution and accuracy that can be attained
by the DPWM units are limited by the system’s clock
frequency. Unfortunately, to achieve a performance that is
similar to an analog VCO, very high clock frequencies are
required that translates into rather costly processors. For
example, a 50MHz DPWM clock is needed to generate a 50
KHz signal with frequency resolution of 10bit (50Hz steps).
Recent studies related to digital control of resonant
converters [5, 6] report the use of either powerful processor
with high DPWM clocks to achieve the required control
accuracy, or settle for more relaxed specifications that translate
into a modest digital hardware [7-9].
Another important aspect of the necessity for high frequency
resolution drive, emerges when resonant converters operates in
closed loop where the frequency serves as the control signal. In
this case, analogous to PWM control design, to avoid limit
cycle oscillations of the output at steady state, the frequency
resolution of the DPWM has to be made high enough such that
the output variation due to a LSB change of the DPWM will be
smaller than the ADC resolution levels (one LSB).
The conventional method for obtaining a frequency
resolution that is higher than what can be achieved by the clock
frequency division is frequency dithering. In this approach, the
DPWM output frequency is hopped between some values such
that the average frequency over time will be in between the
DPWM discrete frequencies. The main challenge of this
method is that the frequency of the DPWM can be updated
only at the beginning of a new count cycle, making this
approach impractical in applications that include a low Q
resonant tanks which respond fast to frequency changes.
The two most popular frequency dithering techniques are the
fractional-N and sigma-delta modulation [10-13]. Both
methods modulate the DPWM period between two neighboring
values, where the frac-N approach operates at a defined rate
whereas in sigma-delta the modulation rate changes arbitrarily.
It is well documented that the sigma-delta method offers a
“cleaner” spectral content of the yielded signal. However,
proper operation the sigma-delta modulation requires over-
sampling (updating the DPWM during count cycle) which is
impractical for smooth signal generation. Furthermore, since
frac-N dithering can be simply implemented on the digital
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