IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: FUNDAMENTAL THEORY AND APPLICATIONS, VOL. 47, NO. 7, JULY 2000
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Describing Functions of Power Electronics Circuits
Using Progressive Analysis of Circuit Waveforms
Henry S.-H. Chung, Member, IEEE, Adrian Ioinovici, Senior Member, IEEE, and J. Zhang
Abstract—This paper presents a technique for calculating the
ac line-to-output and control-to-output transfer characteristics of
dc/dc converters, in which the time instants switching from one
topology to the next one are a priori unknown and are determined
by threshold conditions (i.e., by the time evolution of the converter
waveforms). Describing functions are defined for small perturbations in either the input voltage or the control signal. After injecting
a sinusoidal perturbation at the frequency of interest into the converter, the fundamental component of the output spectrum is determined. The describing functions are thus evaluated and provide
the required ac transfer characteristics. The proposed method is
integrated with a previously developed time-domain simulation algorithm, which is based on monitoring the switches positions, allowing the simulator to find automatically the switching instants
and topological sequence of operation. Different examples are illustrated, including a classical pulse-width-modulated (PWM) converter, a current-programmed PWM regulator, and a switchedcapacitor converter. The simulated results are compared with the
experimental measurements and the results in the available literature.
Index Terms—Circuit simulation, power electronics, switching
circuits.
I. INTRODUCTION
A. Previous Work
A
LARGE body of literature devoted to the frequency domain analysis of periodically switching circuits is available. However, they cannot be directly applied to power electronics circuits, since the switch’s operation is generally dictated
by threshold conditions. Turning a switch on or off is dependent
on the converter waveforms. In addition the topology sequence
is unknown a priori, because it depends on the behavior of the
switches that are controlled by the feedback circuit, as well as on
the behavior of the internally controlled switches. For the same
converter, different dynamic behaviors can be exhibited for different input voltage or output load. For example, depending on
the load and switching frequency, a classical pulse-width-modulated (PWM) dc/dc converter can operate in two or three topologies in one switching cycle.
Recently many analysis techniques have been developed
for studying the dynamic behaviors of power electronics
circuits. The methodologies can be classified into two main
Manuscript received November 2, 1998; revised June 18, 1999 and November
16, 1999. This paper was recommended by Associate Editor M. K. Kazimierczkuk.
H. S.-H. Chung and J. Zhang are with the Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong.
A. Ioinovici is with the Department of Electrical and Electronic Engineering,
Institute for Technological Education, Holon 58102, Israel.
Publisher Item Identifier S 1057-7122(00)05511-2.
categories, including the averaging technique and the discrete
or sampled-data modeling technique.
For the averaging technique, starting from the state-space description of each converter topology and applying small-ripple
approximation, an averaged time-invariant model is derived to
represent the time-varying circuit [1]–[4]. Then, the averaged
signals are perturbed and the equations obtained are linearized
by neglecting second- or higher order terms, such as the products of the time-dependent quantities. After separating the ac
and dc parts, various s-domain transfer functions are formulated.
Although this approach is elegant and it is possible to derive
a closed-form solution of the transfer functions, its accuracy
is limited to a predetermined operating sequence and low-frequency response [5].
Variants of the averaging technique have also been developed.
In [6] and [7], a subcircuit formed by the switches and a minimum number of other components is separated and replaced by
an averaged model. A topology-independent approach is developed in [8], in which a switched inductor formed by an inductor
and a switch is replaced by an averaged model. An averaged
model that replaces the PWM switch is another idea used in [9].
The discrete or sampled-data modeling technique [10]–[13]
also starts from the state-space equation sets for describing each
converter topology and transforms them into difference equations. Some of these models go so far as to include the threshold
conditions in a constrained equation, which is an integral part
of the system equations that characterize the circuit dynamics
[13]. However, all discrete models introduce inaccuracy either
by carrying out multivariable Taylor series expansions around
the nominal operating point and retaining the linear terms, or by
approximating the transition matrix by the first two linear terms
in the switching period of the exponential series. Another discrete-time technique is given in [14], in which numerous timedomain transient analyses of the circuit are performed. Each
analysis is started with a different initial condition, in order to
find the state-space matrices.
Therefore, both averaged and discrete or sampled-data
methods introduce two fundamental inaccuracies, including the
small-ripple approximation and the small-signal linearization.
The first one is due to the neglect of the terms containing
second- or higher order of the switching period. The second
one is introduced when the nonlinear terms in the perturbed
equations are neglected. A detailed comparison of different
approaches for small-signal analysis of switching power
converters can be found in [15].
An important contribution to the frequency-domain simulation of power electronics circuits is given by applying the concept of the describing function [16]–[17]. The control-to-output
1057–7122/00$10.00 © 2000 IEEE
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Fig. 1.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: FUNDAMENTAL THEORY AND APPLICATIONS, VOL. 47, NO. 7, JULY 2000
Minimal period for integrating
H for the case T
=2
T = 7T
.
describing function is defined under the condition of constant
line voltage and the line-to-output describing function is defined under the condition of constant control signal. The voltage
at the output of the modulator is expressed as a Fourier series expansion. The resulting output voltage component at the
same frequency as that of the perturbation signal is found by
calculating the amplitude and phase of the fundamental term
in the Fourier series. These values are used to determine the
transfer functions at the frequency of interest. Extending the describing function concept for resonant converters has also been
proposed in [18]–[19], in which an accurate analytical model
for small-signal analysis of resonant converters is derived. Despite the fact that the methods were developed specifically for
particular converters, they present good possibilities for generalization.
By applying Zadeh’s bifrequency transfer function and the
control-to-output describing function, a method for analyzing
power electronics circuits is developed in [20] and [21]. The approach permits accurate prediction of the magnitude and phase
of the component in the output spectrum that has the same frequency as that of the injected sinusoidal perturbation in the control signal. A general expression for the magnitude and phase
of the fundamental Fourier component in the output spectrum is
determined in terms of the system time-varying transfer function. This method requires the formulation of the state-space
equation sets for each topology and exact analytical solutions
of each set of equations, including an exact calculation of an
exponential matrix. The closed-form solution of the control-tooutput describing function is analytically determined. However,
the advantage is offset by the explicitly defined switching instants in the final formulas. This factor makes this approach
difficult for analyzing converters that have a priori unknown
switching instants and sequence of operation and calculating the
line-to-output transfer function of closed-loop regulators with
multifeedback loops, in which the switching times are affected
by the minor internal feedback loop.
B. Statement of the Goals
Determination of frequency-domain models of power electronics circuits is essential for a correct design of their feedback control. The stability can be assured only by knowing accurately the transfer functions of the switching-mode converter.
The accuracy requirements make the averaged models, the discrete models, or other methods that only keep the first two terms
in the expression of exponential series inadequate for the above
purpose.
Though accuracy is the first concern, as in any computer-aided-design tool, the algorithm speed is also of interest.
Many methods make use of state-space equation sets for each
topology. However, a modern converter might contain several
inductors and capacitors and possibly go through five, six, or
even more topologies in one switching cycle, such as quasiresonant converters with extended period operating at constant
switching frequency [22]. Hence, formulation of such a large
number of system equations is time consuming and requires
considerable computer memory. Moreover, the simulator has
to be general, i.e., applicable to any power electronics circuit
and independent of any a prior knowledge of the switches’
operation.
This paper presents a technique that meets the above requirements. It starts from the use of describing functions, in which
the fundamental component in the complex Fourier series of the
output voltage is calculated at the frequency of injected sinusoidal perturbations in either the control or line voltage. Unlike
[20] and [21], the proposed method is general and independent
of a specific circuit. No state-space equations are required. The
switching instants do not appear explicitly in the final formulas,
which open a way for applying it to complex regulators that have
many topologies in one switching cycle. The steady-state output
waveform at any time instant is obtained by a previously developed stepwise time-domain simulation algorithm [23] which
automatically determines the switching times and topological
sequence of operation.
CHUNG et al.: FUNCTIONS OF POWER ELECTRONICS CIRCUITS USING ANALYSIS OF CIRCUIT WAVEFORMS
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Fig. 2. Explanation of (14) for a generic cycle k .
Basic definitions and formulas are reviewed in Section I-C.
The methodology is presented in Section II. It can be applied
to any dc/dc converter, regardless of the type of control such
as duty-cycle control or frequency-control, single-loop or multiloop feedback, and the number of topologies in one switching
cycle. Illustrative examples are given in Section III. The simulated results are compared with the experimental measurements
and the results in the available literature.
Similarly, by injecting a sinusoidal perturbation
The sinusoidal component at frequency
can be denoted as
in
(4)
in the output voltage
(5)
The following control-to-output describing function is defined
under constant line voltage:
C. Basic Definitions and Formulas
having a steady-state
Let us denote the input voltage by
and the control signal by
having a dc value of
value of
. For example, in PWM regulators
is one of the inputs
of the modulator. It is obtained by amplifying the difference
between the reference voltage and the actual output voltage.
The other input is the clock ramp waveform. The intersection
of these two inputs dictates the driving signal for the power
stage. In order to calculate the line-to-output transfer function,
.
a small-signal sinusoidal perturbation is introduced in
That is
(6)
The describing functions depend on the amplitude of perturbaor
). The limits of (3) and (6) are found for
tion (i.e.,
or
[16]. A general form
infinitely small amplitude in
of the component in the output spectrum of (2) and (5) is expressed as follows:
(7)
The sinusoidal component at frequency
is denoted by
(1)
in the output voltage
where
either
is either
or
or , with
and
is either
or
calculated as
, and
is
(2)
is defined as
The line-to-output describing function
the relation between the sinusoidal perturbation in the input
voltage and the sinusoidal component in the output voltage at the
same frequency under the condition of constant control signal
[16]
(3)
(8)
It is found that
(9)
In (8), it is assumed that the period
.
is a multiple of
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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: FUNDAMENTAL THEORY AND APPLICATIONS, VOL. 47, NO. 7, JULY 2000
II. ALGORITHM DESCRIPTION
A. Calculation of the AC Small-Signal Transfer Functions of
Converters
Based on the definitions in Section I-C, the major steps for
frequency-domain analysis of power electronics circuits are as
follows.
a) A small-signal sinusoidal perturbation with frequency
is injected in either the line voltage or control voltage,
under the condition of either constant control voltage or
constant line voltage, respectively.
b) In each of the above cases, the expression of
(10)
is equivalent to the
is calculated. It can be noted that
zeroth term of the time-varying transfer function as defined in [20] and [21].
, or
are
c) According to (9), the quantities
calculated as
Arg
time will be short for determining high-frequency responses because the value of becomes smaller. According to (10), is
calculated as
(13)
A power electronic circuit goes through a number of configurations in each cycle. As the switching instants and even the
number of cyclical configurations are not a priori known, it is
preferable that they do not appear explicitly in the formula used
for the calculation of . A stepwise time-domain simulation algorithm for power electronic converters is presented in the following section. It allows the simulator itself to determine a correct topology at each integration step. According to this method,
the switching interval is divided into subintervals of different
duration. The duration of each subinterval and consequently the
are determined by the
number of subintervals in each cycle
simulator. Let us denote the duration of a subinterval in cycle
by
. The output voltage has the value
within this
switching
subinterval. The integration in (13) is taken over
cycles and can be solved numerically by
(11)
d) For the frequency , the describing functions in (3) and
(6) are calculated.
e) The process is repeated for different values of for finding
the amplitude and phase characteristics of the small signal
line-to-output and control-to-output transfer functions.
The crucial step in the above algorithm is in Step b) and it
is here where the basic differences between our approach and
those available in literature reside. In order to include the complete operation of the circuit in a steady-state cycle, the integra.
tion in Step b) has to cover at least one cycle of duration
and
in (8), the integration has to cover
For calculating
at least one cycle of variation of the sinusoidal perturbation of
are independent quantities, one can
duration . As and
generally assume no relationship between these two numbers.
Therefore, , the minimum period over which the integration
must take place, has to be the least common multiple of and
(12)
and
. The least
Fig. 1 illustrates an example of
common multiple interval of periodicity for the switching fre.
quency and the perturbation frequency is
is the time interval that the perturbation signal has to
Thus,
cover two complete cycles and the switching signal has to cover
seven complete cycles.
In the actual computation, is chosen at such values as to
minimize the integration time by minimizing the value of .
kHz, it is better to avoid choosing
For example, if
kHz. If the frequency response at this value is of inkHz is the preferred choice, otherwise the
terest,
due to the incomputer will automatically determine a large
compatible numbers 43.3 and 86.5. Moreover, as the length of
integration in (10) depends on the value of , it will be shorter
for a smaller value of . Thus, as shown in (12), the simulation
(14)
This formula is exemplified in Fig. 2 for a generic cycle .
varies during the integration over a cycle . The
The step
simulator chooses a certain step at the beginning of the cycle
and diminishes the step value when the integration approaches
a switching instant. The simulator returns to the initial step value
after each switching instant. is a complex number, allowing
for the calculation of its magnitude and phase, as required by
(11).
B. Time-Domain Evaluation of the Steady-State Output
Waveform (Summary of [23])
Based on progressive analysis of the switches’ positions, a
method for the time-domain analysis of cyclically switched circuits with threshold conditions has been developed in [23]. Instead of deriving state-space equations, a modified nodal approach is applied.
For the reader’s convenience, a summary of [23] is given here.
In this method, the simulator must find the switching sequence
in each cycle by validating the position of each switch at each
step. In order to illustrate the algorithm, a generic steady-state
cycle is considered. Assume that the topology has been validated at the beginning of an integration step . The capacitor
voltages and inductor currents calculated at this time are con. By
sistent initial conditions for the next interval
assuming that within the interval the nodal voltages calculated
at remain constant, the capacitor voltages and inductor curare calculated as
rents at
(15)
CHUNG et al.: FUNCTIONS OF POWER ELECTRONICS CIRCUITS USING ANALYSIS OF CIRCUIT WAVEFORMS
Fig. 3. Flowchart for the calculation of the ac transfer function at a frequency f .
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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: FUNDAMENTAL THEORY AND APPLICATIONS, VOL. 47, NO. 7, JULY 2000
where
is the voltage across the branch formed by capacand
itor and its equivalent series resistance (ESR),
is the voltage across the branch formed by inductor and its series dc resistance , both of them calculated by using the nodal
voltages determined at time . is chosen to be smaller than
in the circuit
each reactive element time constant
in order to avoid the degradation of accuracy.
, the capacitors are replaced by indepenAt the instant
and the inductors by
dent voltage sources of values
. At this point,
independent current sources of values
the dynamic circuit has been transformed into a resistive circuit
which can be analyzed by an algebraic system of modified nodal
equations, in which the feedback circuit is also included. Thus,
the nodal voltages and the output signals of the feedback circuit
are calculated. The voltages/currents across/through all
at
switches are calculated at this instant. If the output signals of the
feedback circuit point to no change in the switches’ positions
and if no contradiction in the polarity of the waveforms associated with the switches appears, the simulator will validate the
.
present topology at time
the driving signal of a switch points to a switching
If at
action, or if a contradiction between the assumed position
of the switches and their associated waveforms’ polarities
and
appears, proving that a transition took place between
, the simulator will backtrack to
in order to find the
switching instant. The process will be repeated with a reduced
is found with
step every time, until the switching moment
the desired accuracy and will then be recovered to the original
(such as
value. More sophisticated algorithms for finding
the Newton–Raphson algorithm) could be used for the same
purpose. The advantage of this elementary approach is its
guaranteed convergence for any complex converter.
The proposed method does not require solving differential
equations or performing inverse Laplace transformation. In
[24], a logical representation of Dirac impulses in the frame of
a state-space network simulation is presented. Thus, solution
of differential equations was necessary. The methods proposed
in [25] and [26] require inverse Laplace transformation.
In addition, the proposed method has the following advantages.
a) By incorporating the parasitic resistive losses of the reactive elements and switches, the simulator does not generate Dirac impulses.
b) To validate each topology, resistive circuit analyses have
to be performed, (in some other methods, dynamic circuits must be analyzed).
c) At each step, the solution is given by solving an algebraic
system of nodal equations.
According to (14), the simulator will collect the data not only
but over a period
for one steady-state cycle of duration
.
C. Interface Between the Time-Domain Simulation and
Calculation of
At each step of the time-domain integration during the peand
in (14) must be stored.
riod , the values of
is the
For the th cycle and the th step, it starts at .
(a)
(b)
(c)
Fig. 4. (a) Boost PWM converter. (b) Magnitude characteristic of
the control-to-output transfer function. (c) Phase characteristic of the
control-to-output transfer function.
value of the output voltage at the beginning of this step. If the
simulator finds that no switching action took place within the
will be used as the value of
and
step
in (14) is calculated. The output
the product
in
voltage calculated at the end of the step is used as
(14) for the next step. The simulator continues the time-domain
integration for a new step by keeping constant. This value is a
.
candidate for
and
a transition
If the simulator finds that between
and repeats the process with a
took place, it backtracks to
smaller step, let’s say . This new value of the step is used in
in the product of
. The new
(14) as
CHUNG et al.: FUNCTIONS OF POWER ELECTRONICS CIRCUITS USING ANALYSIS OF CIRCUIT WAVEFORMS
1032
(a)
(b)
Fig. 5. (a) Current-programmed boost converter. (b) Magnitude characteristic of the control-to-output transfer function.
is
.
is used as
for the next step. The
simulator continues the integration with this new step, until it
comes closer to the switching instant when a further reduction
of the step value will be required.
At the end of the cycle , the sum
in (14) is determined by taking into account the partial prodcalculated for all valid steps, in which no
ucts
switching took place. A flowchart of this algorithm is given in
Fig. 3.
III. ILLUSTRATIVE EXAMPLES
In the following examples, perturbations of 1% of the steadystate values in either the line voltage or the control variable are
considered. In all examples, the magnitude and phase characteristics of the small-signal control-to-output transfer characteristics have been obtained by using three methods, including
a) the experimental measurement; b) the proposed algorithm;
and c) the state-space averaging technique. The measured results are obtained by using a gain phase analyzer HP4194A. In
the time-domain simulation of the circuits (Section II-B), if the
absolute current flowing through a switch is less than 10
A,
the computer will take the current as zero and a switching instant is assumed. This is a constant requirement in the algorithm.
Though this may introduce errors in the simulation, it has been
illustrated in [23] that the simulated results are in close agreement with the method in [26].
A. Example 1—Open-Loop Boost Converter
The same boost converter analyzed in [20] is considered. The
circuit is shown in Fig. 4(a). The component values are
V,
H,
,
F,
,
, and
kHz and the steady-state
is 0.4. The control-to-output and line-to-output
duty cycle
transfer characteristics are shown in Fig. 4(b) and (c). With
the proposed algorithm, the simulation time for determining
the characteristics at 1.0075 kHz on a 486 33-MHz PC computer was 14 s. As shown in Fig. 3, the simulation time is dependent on the frequency of interest . The simulation time
will be shorter in determining high-frequency characteristics,
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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: FUNDAMENTAL THEORY AND APPLICATIONS, VOL. 47, NO. 7, JULY 2000
(c)
(d)
(e)
Fig. 5. (Continued.) (c) Phase characteristic of the control-to-output transfer function. (d) Magnitude characteristic of the line-to-output transfer function. (e)
Phase characteristic of the line-to-output transfer function.
since the value of
in (12) is smaller. Totally 50 frequency
points are taken. The simulated curve is fitted with a simple
straight-line interpolation technique. Compared to the averaging
technique, the proposed method is slower in computation because the results of the averaging technique is based on a derived
continuous time-invariant transfer function. However, the pro-
cedures of performing the mathematical formulations are circuit-dependent and time-consuming for circuits with multiple
feedback loops and many topologies in one switching cycle. It
can be observed that the above three analysis methods give the
same results at the low-frequency range up to 15 kHz, while
the averaging technique deviates from the measured ones at the
CHUNG et al.: FUNCTIONS OF POWER ELECTRONICS CIRCUITS USING ANALYSIS OF CIRCUIT WAVEFORMS
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(a)
(b)
Fig. 6. (a) Switched-capacitor-based dc-to-dc converter. (b) Control-to-output magnitude response.
high frequency range. Beyond 15 kHz, the averaging method
gives a transfer characteristics below 20 dB, but the experimental results show that some resonant peaks appear around
the switching frequency.This is because the high-frequency information has been discarded in the averaging process. The results of the proposed method and the one in [20] show close
agreement with the measured ones over the frequency range.
However, comparing these two methods, some mathematical exbut the
pressions in [20] vanished at
proposed algorithm is still feasible to perform analysis at these
frequencies, such as at 40.3 kHz and 80.6 kHz (i.e., equals
and
, respectively). Another advantage of the proposed
method is that it is not circuit specific and does not require considerable mathematical manipulations as in [20].
B. Example 2—Current-Programmed Boost Converter
The next example is a current-programmed boost converter,
which has been analyzed in [4] and [8]. The circuit is shown in
Fig. 5(a), consisting of a minor current feedback loop around the
power stage and a major voltage feedback loop via the error amplifier. In order to calculate the control-to-output transfer characteristics, the external loop is open and a small perturbation is
applied to the dc control signal and the internal current loop
is not affected. The control-to-output and line-to-output transfer
characteristics are shown in Fig. 5(b)–(e). Compared to the results obtained by the averaging techniques in [4] and [8], they
give accurate results at a low-frequency range up to few hundred Hertz, but fail to determine the responses accurately at a
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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: FUNDAMENTAL THEORY AND APPLICATIONS, VOL. 47, NO. 7, JULY 2000
(c)
(d)
(e)
Fig. 6.
(Continued.) (c) Control-to-output phase response. (d) Line-to-output magnitude response. (e) Line-to-output phase response.
high frequency range. The averaging technique can predict accurately the cutoff frequency at about 10 Hz, but fails to predict the zero and pole at about 3 kHz and 12 kHz, respectively,
in both characteristics. Nevertheless, the proposed method can
predict their existences. The simulation time for getting the responses at 1 kHz is 20 s on the same computer.
C. Example 3—Switched-Capacitor Converter
A new type of switching-mode converter [27] that primarily
consists of semiconductor switches and capacitors is simulated.
The circuit diagram is shown in Fig. 6(a). The converter is operkHz. The control-to-output and line-to-output
ated at
CHUNG et al.: FUNCTIONS OF POWER ELECTRONICS CIRCUITS USING ANALYSIS OF CIRCUIT WAVEFORMS
transfer characteristics are shown in Fig. 6(b)–(e). The simulation time for getting the responses at 1 kHz is 12 s on the same
computer. Again, it can be seen that with the averaged model is
only possible to obtain responses at a relatively low frequency,
such as the cutoff frequency at 1 kHz. Starting from one third of
, the results of the averaged model show deviation from the
actual circuit responses. The existence of the zero at around 30
kHz cannot be predicted, whereas the proposed method can find
it.
Hence, the proposed method can generally give a closer prediction of the actual circuit frequency response than the averaging technique. In practice, design of the switching regulator loop gain usually has the crossover frequency at a low
frequency. It seems that the averaging technique is sufficient
for guaranteeing regulator stability. However, this is not always
true. For instance, the results of the averaging technique deviate from the actual response at one tenth of the switching frequency in Example 2 and one third of the switching frequency
in Example 3. Thus, the validity of the averaging technique at
low-frequency responses might not be guaranteed. Finally, apart
from getting high-frequency responses, the advantages of the
proposed method also lie in the generality of analysis and the
possibility of getting information in a switching cycle. It is also
possible to obtain a regulator’s large signal response by injecting
larger magnitude of perturbation, which is an adjustable parameter.
IV. CONCLUSION
A technique for simulating cyclically switching circuits with
internally controlled switches was presented. By combining
a previously developed time-domain simulation analysis
technique, the proposed method features the following characteristics.
a) It is general for analysis of dc/dc converters. It requires
no previous knowledge of the converter operation since
the switching sequence is found automatically by the
simulator. No threshold conditions have to be given.
It does not require formulating or solving state-space
equations and can be applied even for the calculation
of line-to-output transfer functions of closed-loop regulators containing minor internal feedback loops, which
affect the value of the duty-cycle in steady state (see
Example 2). The method is close in spirit to that used
in [20], but these characteristics give the superiority of
the presented algorithm. The method can also be applied
to circuits, in which ac signals are involved. However,
the side bands between the ac signal frequency or its
and
frequency components
multiples and the
or their multiples would appear in the output spectrum.
The algorithm cannot find the magnitude and phase of
the transfer functions at those frequencies, because it
cannot discern between the contributions of the ac input
signals. Therefore, this gives a
voltage and the and
limitation on the proposed method for analysis of ac-dc
or dc-ac converters.
b) It is faithful to reality. The simulator validates the correct position of the switches, ensuring that the simulated
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topology is in accordance with the actual circuit operation.
c) It is fast. In order to calculate the describing functions, the
simulator stores the steady-state data of the output waveform step by step. These data are simply found by solving
a simple algebraic system of modified nodal equations.
d) It is accurate. Unlike the averaging and discrete or sampled data approaches, no small-ripple approximations are
required. Parasitic resistance of the reactive and switching
elements is inherently included in the simulation models.
e) It is time saving for the user and memory efficient for
the computer. It does not require hand formulation of
state-space equations for each topology and solving exact
analytical solutions. The algorithm only requires solving
systems of algebraic equations.
The illustrated examples show the superiority of the proposed
method over the classical available algorithms. Further research
will be dedicated into the analysis of resonant circuits such as
the zero-current-transition PWM converter in [28] and largesignal analysis.
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Henry S.-H. Chung (S’92–M’95) received the
B.Eng. (First Class Hons.) degree in electrical
engineering and the Ph.D. degree from The Hong
Kong Polytechnic University in 1991 and 1994,
respectively.
Since 1995 he has been with the City University
of Hong Kong, Kowloon, Hong Kong, where he is
currently an Associate Professor in the Department
of Electronic Engineering. His research interests
include time- and frequency-domain analysis of
power electronic circuits, switched-capacitor-based
converters, random-switching techniques, digital audio amplifiers, and
soft-switching converters. He has authored two research book chapters and
over 105 technical papers including 47 refereed journal papers in the current
research area.
Dr. Chung was the recipient of the China Light and Power Prize and was
awarded the Scholarship and Fellowship of the Sir Edward Youde Memorial
Fund in 1991 and 1993, respectively. He is currently Chairman of the Council
of the Sir Edward Youde Scholar’s Association and IEEE Student Branch Counselor. He was Track Chair of the technical committee on power electronics circuits and power systems of IEEE Circuits and Systems Society in 1997-1998.
He is presently an Associate Editor of the IEEE TRANSACTIONS ON CIRCUITS
AND SYSTEMS I.
Adrian Ioinovici (M’84–SM’85) received the Electrical Engineering degree in 1974 and the Doctor-Engineer degree in 1981, both in Romania.
In 1982, he joined the Holon Academic Institute
of Technology, Israel, where he is currently the
Head of the Electrical and Electronics Engineering
Department. From 1990–1995, he was Reader
and then Professor with the Electrical Engineering
Department, Hong Kong Polytechnic University.
His research interests are in simulation of power
electronics
circuits,
switched-capacitor-based
converters and inverters, and soft-switching dc power supplies. He is the author
of the book Computer-Aided Analysis of Active Circuits (New York: Marcel
Dekker, 1990). He has published more than 80 papers in circuit theory and
power electronics.
Prof. Ioinovici is Chairman of the Technical Committee on Power Systems
and Power Electronics of the IEEE Circuits and Systems Society. He has
served as an Associate Editor of the IEEE TRANSACTIONS ON CIRCUITS AND
SYSTEMS—PART I: FUNDAMENTAL THEORY AND APPLICATIONS and of the
Journal of Circuits, Systems and Computers. He is also an Overseas Advisor of
the IEICE Transactions, Japan. He was Chairman of the Israeli chapter of the
IEEE CAS Society between 1985–1990. He served as General Chairman of the
Conferences ISCSC’86, ISCSC’88 (Herzlya, Israel), SPEC’94 (Hong Kong),
organized and chaired special sessions in Power Electronics at ISCAS’91,
ISCAS’92, ISCAS’95, ISCAS’2000, and was a member of the Technical
program Committee at the Conferences ISCAS’91, ISCAS’93, ISCAS’94,
ISCAS’95. PESC’92, PESC’93, PESC’94, PESC’95, Track Chairman at
ISCAS’96, ISCAS’99, ISCAS’2000, and a Cochairman of the Special
Session’s Committee at ISCAS’97.
Jun Zhang was born in Tianjin, China in 1967. He
received the B.Eng and M.Eng degrees in mechanical
engineering from Hebei University of Technology,
Tianjin, China, in 1989 and 1995, respectively.
From 1989 to 1992, he was with the Tianjin
Automobile Industry Company Ltd., Tianjin, China,
where he was responsible for new automobile
development and technology cooperation. During
1995–1996, he was a Research Student and Teaching
Assistant at Zhejiang University, Hangzhou, China.
He is currently a Research Student in the Department
of Electronic Engineering, City University of Hong Kong, working toward the
Ph.D. degree. His research interests are in the area of power electronics, genetic
algorithm, fuzzy logic, neural network, and chaotic time series analysis and
prediction. He has authored 12 technical papers in his current research area.