Frequency Response Analysis for Power Conversion
Products Without Small-Signal Linearization
1,2
Kasemsan Siri
The Aerospace Corporation
2350 E. El Segundo Blvd., M/S M4-179
El Segundo, CA 90245
310-336-2931
kasemsan.siri@aero.org
Calvin Truong
The Aerospace Corporation
2350 E. El Segundo Blvd., M/S M2-275
El Segundo, CA 90245
310-336-8129
calvin.h.truong@aero.org
Abstract— Presented herein is an accurate approach for
combining large signal modeling and frequency-domain
analysis of a closed-loop DC-DC converter power system
without small-signal linearization. The approach provides a
high-fidelity solution for the converter's frequency response
due to the inclusion of all non-linearity and parasitic effects
and is applicable to both pulse-by-pulse switching and
average large-signal models of DC-DC converters. In
control-oriented simulators, Fast Fourier Transformation
(FFT) is applied to the converter responses, being uniformly
sampled for one period of each injected small signal. In
circuit-oriented
simulators,
fundamental
frequency
components are extracted out of the converter time-domain
responses that are usually simulated in a variable time-step
mode. This simple, direct, and accurate analysis approach
is critically needed for performance evaluation of the
converter system frequency response and design validation
of the converter closed-loop systems for which the
linearizable large-signal models are not available. The
"virtual network analyzer" approach provides an increase in
the fidelity of non-linear and parasitic effects within the
controller and converter's power stages for which the ‘as is’
non-linear pulse-by-pulse switching model is directly
simulated. The frequency response analysis approach was
validated with a converter power system operating in solararray voltage regulation mode.
6. ANALYSIS RESULTS .......................................... 6
7. DATA FILTERING PRIOR TO FFT ......................... 7
8. CONCLUSION.................................................... 8
REFERENCES........................................................ 8
1. INTRODUCTION
Frequency response analysis techniques are among several
ways of determining performance and stability robustness
of the closed-loop DC-DC converter. These techniques can
be effectively adapted to objectively acquire a set of
frequency response functions; e.g., converter voltageregulation loop-gain, input/output impedance, and
forward/reverse audio susceptibility. Frequency response
analysis can be performed analytically through modeling
and simulation or experimentally with a network analyzer.
Currently, the ability to accurately analyze (on paper)
engineering designs of power converters and controls
provides a more flexible opportunity to identify
fundamental design flaws and prove design solutions before
proceeding to the engineering prototype phase. In such
cases, modeling and analysis tools developed for designing
DC-DC converters and their control laws are indispensable
for design validation, cost-effectiveness, and timeliness of
the power-conversion product development.
Analytical modeling of DC-DC converters and their control
laws has improved constantly through the use of more
accurate mathematical approaches, faster processing by
personal computers, and better analysis tools. Still, several
converter topologies and their control laws are classified as
“non-analyzable” items when dealing with their analytical
frequency responses. Either their mathematics is too
complex or their analytically derived small-signal average
models are so overly simplified that they fail to include
major non-linear effects. These modeling limitations cause
design engineers to avoid analytical modeling and to depend
primarily on experimental frequency/time domain
measurements of the engineering prototype. Through
TABLE OF CONTENTS
..............................................................................
1. INTRODUCTION ............................................... 1
2. FREQUENCY RESPONSE ANALYSIS WITH CIRCUIT
ORIENTED SIMULATOR..................................... 2
3. LARGE SIGNAL MODELING OF THE CLOSED-LOOP
DC-DC CONVERTER .......................................... 4
4. CONTROL-ORIENTED MODEL OF THE CLOSEDLOOP DC-DC CONVERTER ................................. 5
5. FREQUENCY RESPONSE ANALYSIS WITH FFT .... 6
1
2
0-7803-8155-6/04/$17.00© 2004 IEEE
IEEEAC paper #1001, Version 3, Updated September 30, 2003
1
engineering prototyping alone, it is much more difficult to
optimize the design and/or to identify potential root causes
(design and/or manufacturing processes) when encountering
unexpected performance deficiencies.
Furthermore,
limitations of test equipment may prohibit testing of
engineering prototypes within their intended operating
conditions, leading to potential premature failures, costly
redesign, and product reliability issues.
configuration of small signal acquisition, and its analysis
algorithm based on fundamental-component extractions out
of Fourier series expansion. Section 3 describes a specific
large-signal closed-loop converter system used for testing of
the analysis approach as well as its specific circuit-oriented
configuration used for time-domain signal acquisition prior
to the frequency-domain analysis. The section provides
well-correlated results obtained from two different
modeling schemes: the large-signal averaged and the nonlinear switching models. Section 4 emphasizes modeling of
the same converter system in control-oriented simulators in
which both of the modeling schemes are applicable for
validation of the frequency response analysis approach.
Section 5 outlines the FFT algorithm typically employed in
control-oriented simulators for frequency response
extraction. Section 6 compares frequency response results
obtained from the selected control-oriented simulator
(MATLAB/SIMULINK) and the selected circuit-oriented
simulator (PSPICE). Section 7 presents multi-frames and
window averaging techniques that are critical to accuracy of
subsequent frequency response analysis. Conclusions are
given in Section 8.
This paper presents a frequency response analysis approach
without small-signal linearization. The approach is
implemented in both circuit-oriented and control-oriented
simulators. The conventional small-signal linearization
approach is usually applied to over-simplified approximated
converter models that fail to include non-linear and parasitic
effects.
Furthermore, the large-signal approximated
linearizable models are not available for several converter
topologies (such as some resonant converters), and
therefore conventional small-signal analysis is not
applicable. The remaining choice of frequency response
extraction is to directly analyze the time-domain response of
the “as is” non-linear switching model of the converter
system of interest. A high-fidelity frequency response
analysis approach was first successfully developed using
control-oriented
simulators
(such
as
MATLAB/SIMULINK). However, the control-oriented
simulation requires a considerable analytical effort to
convert the circuit-oriented converter schematic diagrams
into the interconnected blocks of control-oriented models
with several derived parameters. The required effort
discourages most circuit-oriented engineers from applying
this approach, and adds risks from errors during the
derivations of the control blocks. Since the circuit-oriented
simulators (such as PSPICE) allow direct input of the
schematics and do not require conversion to a control
system format, an opportunity has been identified to reduce
the analytical overhead and associated risks through the
circuit-oriented simulators instead. As a demonstration, a
PSPICE-based circuit simulator will be used to produce
interim frequency response data that a programmable
mathematical tool (such as MATLAB) will then
numerically process to create standard frequency response
plots. Consequently, this analysis method yields a very
high-fidelity frequency response while retaining the nonlinear effects essential for circuit operation, resulting in a
more accurate measure of the system’s robustness. This
technique will be validated on a converter power system
operating in solar array voltage regulation mode by
comparing it with the results of a linearizable approximated
state-space model. The analysis approach is applicable to
any non-linear switching converter. In particular, the
approach must be used to get the simulated frequency
response whenever a linearizable approximated model of
the analyzed converter is not available.
2. FREQUENCY RESPONSE ANALYSIS
WITH CIRCUIT-ORIENTED SIMULATORS
Generic Simulation Set-up for Small-Signal Frequency
Response Acquisition
Fig. 1 represents a generic setup for frequency response
data acquisition using a circuit-oriented simulator.
Typically, a DC-DC converter power stage is controlled by
a PWM driving signal being output from the PWM circuit.
The PWM circuit converts a filtered analog input signal into
the chopped two-state switching signal that commands the
power switches in the converter power stage to either turn
on or turn off in every switching period. The converter
output voltage, Vout, is fed back to the output voltage
regulation control circuit to produce a proper error signal
that becomes the filtered analog signal feeding the PWM
circuit. In general, Vout could be any converter feedback
signal for its associated closed-loop regulation, such as
converter input voltage or output current sensed signal.
Prior to feeding the composite response, VFB, back into the
control loop, the small-signal injection and data acquisition
setup is typically inserted at the output voltage node, Vout,
on which the injected AC small signal is superimposed, as
depicted in the block labeled “Fourier-Series Extraction
Model” in Fig. 1. For each given small-signal frequency, the
acquired responses, Vout (t) and VFB (t), are taken through
the process of extracting the small-signal fundamentalcomponents from their Fourier series expansions. The
small-signal frequency sample points, as well as the
extracted responses of the small-signal fundamental
components (magnitude and phase) of the acquired signals,
can then be intermediately stored in the corresponding
output file (such as a PSPICE *.out file). Later, a
programmable mathematical tool, such as MATLAB, may
This paper is organized into seven sections. Section 2
describes small-signal frequency response analysis using
circuit-oriented simulators (such as PSPICE), its generic
2
be used to read the data in the output file, post-process it
into a proper format such as magnitude and phase plots
(Bode plots), and store the final result as plot files.
fn. The tupdate#i is the time at which the simulation updates
the frequency of the injected small signal at its respective
frequency fi. Another table defines a timely sequence of
end-time data points that are synchronously used in
conjunction with the corresponding sample-point
frequencies previously defined in the former table. Each
data point defined in the end-time table is given in a format
of (tupdate#i, tend#i), where tupdate#i < tend#i ≤ tupdate#i+1. Each of
these end-time data, tend#i, is used to compare with the
simulation run-time variable called TIME (a reserved word
in a PSPICE simulator) to determine its respective active
time window (tend#i - tstart#i) for processing the fundamentalcomponent extraction algorithm on the acquired timedomain responses for each small-signal frequency. For
precise frequency response extraction, the processing time
window of each small-signal frequency is always in multiple periods of the small-signal frequency, or tend#i - tstart#i =
NTi, where N is a given integer and Ti is the small-signal
period 1/fi. From tupdate#i, tend#i, and fi, the starting time
tstart#i for an active processing time window #i must satisfy
the constraint tupdate#i < tstart#i < tend#i. In other words, tstart#i
– tupdate#i is the simulation delay time after updating the
small-signal frequency to fi prior to actually processing its
small-signal frequency response contents. Sufficient delay
time is needed for steady small-signal responses during the
processing time-window of each small-signal frequency.
Figure 1. Generic simulation set-up for acquisition of frequency response data using circuit-oriented and
MATLAB simulator
Frequency Response Extraction Algorithm
Detailed modeling of the fundamental-component extraction
out of the Fourier series expansion can be conceptualized
with the algorithm block diagram shown in Fig. 2.
Fig. 3 shows a timing diagram of the frequency samples and
the respective enable/reset pulses of the processing timewindow that are determined from both of the look-up tables.
The active duration of each enable/reset pulse (being
asserted as “active-high” pulse-width) is always in fixed
multiple periods of the injected small signal. Three
additional signals are generated from the sample frequency
look-up table: the small-signal Asinωt that is injected into
the control loop across the two nodes, Vout and VFB, and two
orthogonal sinusoidal signals, sinωt and cosωt, that are used
in tandem for extracting the two corresponding orthogonal
components of the acquired signals.
Figure 2. Algorithm block diagram of frequency response
acquisition based on fundamental-component
extraction out of Fourier series using a circuitoriented simulator
Two look-up tables are pre-defined in the extraction model.
One look-up table defines a timely sequence of the smallsignal sample frequencies that are used during the largesignal time-domain simulation of the converter system.
Each data point defined in this table is given in a format of
updating-time and its associated small-signal frequency
(tupdate#i, fi). These (tupdate#i, fi) data points may be listed in
an ascending order in both updating-time and its respective
small-signal frequency where index i=1, 2,. . n for n
frequency points from start frequency f1 to stop frequency
Figure 3. Timing diagram showing frequency samples and
their respective enable/reset signals
For any periodic signal f(t) of fundamental frequency ω, its
fundamental component f1(t) can be expressed as
3
f 1 (t ) = a cos ω t + b sin ω t
loop by superimposing the signal on the sensed array
voltage. Through a fundamental-component extraction
from Fourier series expansion, the response of loop-gain
transfer function Vin./Ve can be extracted from the timedomain simulation data Vin(t) and Ve(t) being sampled over
one or multiple periods of the injected small signal. For
validation and comparison purposes, both the large-signal
average model and the pulse-by-pulse switching model of
the converter controller and its power stage operating in the
continuous conduction mode are developed and tested
independently.
First, employing the converter-system
average model, a PSPICE AC analysis with conventional
small-signal linearization yields the array voltage regulation
loop-gain frequency response. Subsequently, using the
developed “virtual” network analyzer without small-signal
linearization as depicted in Fig. 2, another set of the
frequency response is extracted from the standard PSPICE
transient analysis run on the converter pulse-by-pulse
switching model. Finally, these two sets are plotted on the
same graph to demonstrate the excellent agreement between
the two different analysis approaches, as shown in Fig. 5.
Note that Ve and Vin shown in Fig. 4 are respectively
equivalent to VFB and Vout shown in Fig. 1.
(1a)
f1 (t ) = a 2 + b 2 sin(ωt + θ )
where θ = tan
θ=
a=
2
T
 a  or
 
b
π
(1 − sign (b) ) + tan −1  a  ⋅ sign (a ) ⋅ sign (b) (1b)
2
b
t0 +T
∫
−1
f (t ) ⋅ cosωt ⋅ dt, b =
t0
2
T
t0 +T
∫ f (t ) ⋅ sin ωt ⋅ dt
(1c)
t0
2π
(1d)
T
The fundamental components of the acquired signals, Vout(t)
and VFB(t) are similarly defined as
2
2
Vout1 (t ) = aout cos ωt + bout sin ωt = aout
sin(ωt + θ Vout ) , (2a)
+ bout
ω =
2
2
sin(ωt + θVFB )
+ bFB
VFB1 (t ) = a FB cosωt + bFB sin ωt = a FB
(2b)
From the above expressions (1a), (1b), (1c), (2a), and (2b),
the magnitude of the processed small signals at their fundamental frequency (|Vout| and |VFB| ) can be computed as
shown in expressions (3a) and (3b), respectively.
2
2
Vout = aout
+ bout
V FB =
(3a)
2
2
+ b FB
a FB
(3b)
Therefore, the voltage loop-gain in dB is computed as the
ratio |Vout| to |VFB| as shown in (4)
VOUT VFB = 20 log10( VOUT VFB
)
dB.
(4)
The phase response of small signal Vout with respect to
small signal VFB is therefore calculated from expressions
(1b), (2a), and (2b) as
θ Vout / VFB = θ Vout − θ VFB
degrees
Figure 4. Acquisition set-up for frequency response of
array-voltage regulation loop
(5)
Furthermore, integral expression (1c) can be generalized for
multiple small-signal periods NT as
a=
2
NT
t0 + NT
∫
t0
f (t ) ⋅ cosωt ⋅ dt, b =
2
NT
t0 + NT
∫ f (t ) ⋅ sinωt ⋅ dt
(6)
t0
3.LARGE-SIGNAL MODELING OF THE
CLOSED-LOOP DC-DC CONVERTER
Fig. 4 shows the block diagram of the closed-loop converter
system operating in the array voltage regulation mode [6],
consisting of a solar-array source, line-filter, current-mode
DC-DC converter power stage, output bus stabilizer, bulk
output filter capacitor, load circuit, and a solar-array clamp
error amplifier. Serving as a means to obtain the loop-gain
frequency response of the array-voltage regulation, a small
signal is injected into the array-voltage regulation control
Figure 5. Array-regulation loop-gain frequency response
acquired from the average and switching models
implemented in a circuit-oriented simulator
(PSPICE)
4
4. CONTROL-ORIENTED MODEL OF THE
CLOSED-LOOP DC-DC CONVERTER
capacitors, C5 and C0, within the converter power stage, the
large-signal state-space averaged model of the converter
output-filter can be mathematically expressed as a function
of input <Vy> and state-vector ‘x’. The power stage state
vector consists of three state variables <iL>, VC5, and VC0,
where
<f> denotes an instantaneous average over one
switching period of variable f. The instantaneous average
of the duty-ratio input d(t) controlling the power stage
response during any switching period is also written as
<d(t)>; therefore, <Vy> is the average voltage input to the
converter output filter, which is defined as a product
between <d(t)> and V2. Similarly, I2 is defined as the
average input current of the converter power stage, which is
defined as a product between <d(t)> and <iL>. Consequently, the control-oriented large-signal average model of
the converter power stage has two inputs, <d(t)> and V2,
and two outputs, I2 and Vo, where VC0 = Vo is the converter
output voltage.
As an alternative option for frequency response analysis
without small-signal linearization, the control-oriented
“virtual network analyzer” approach was also successfully
implemented by primarily performing FFT for exactly one
small-signal period on the acquired signals that must be
sampled in fixed time steps during the time-domain
simulation.
In control-oriented simulators (MATLAB/SIMULINK), the
development of a basic pulse-by-pulse non-linear switching
model or a large-signal average model of a converter system
requires some overhead mathematical conversion from
circuits to control blocks. These control blocks represent
the modeled circuits as interconnected transfer functions
and/or linked sets of state and output equations, which are
mathematically formatted in vectors and matrices. Once the
model is set up, repetitive simulation and processing can be
performed easily to obtain the frequency response. Two
SIMULINK converter system models that are developed by
two different modeling schemes are described in this
section: large-signal state-space averaging and pulse-bypulse switching techniques.
By applying the FFT to the two signals acquired from the
same converter system shown in Fig. 4, the transfer function
response, Vin./Ve, can be extracted from the time-domain
simulation data Vin(t) and Ve(t) sampled over one period of
the injected small signal.
Figure 6.
Figure 6 shows the detailed circuit of the line-filter being
excited by the array source. The figure also shows the control-oriented model of the line-filter and array source, which
is converted from the line-filter schematic. The line-filter
model is represented by a control block that is derived in
terms of a set of state and output equations having two
inputs, Ia (array current) and I2 (line-filter output current),
and two outputs, Va (array voltage) and V2 (line-filter output
voltage). The state equations [3,4] are first-order differential
equations with five state variables (four filter capacitor
voltages and one filter inductor current). The array voltage
Va, is the input excitation of the array source model that
behaves like a voltage-controlled current source. Through
the use of a look-up table, the behavioral model of the array
I-V characteristics can be represented by a piecewise-linear
function of Va.
As shown in Figure 7, a circuit-oriented pulse-by-pulse
switching model of the converter power stage operating in
the continuous conduction mode can be converted to a
large-signal control-oriented model by applying Kirchhoff’s
voltage and current laws and Middlebrook’s state-space
averaging technique [1]. Due to the existence of the main
power stage inductor L2 and the damping and filter
Conversion from circuit-oriented to controloriented models of the line-filter with an array
source
Figure 7. Large-signal average modeling of the switching
converter power stage in a control-oriented format (SIMULINK)
Figure 8 illustrates the model conversion from pulse-bypulse switching peak-current programmed control circuit to
5
5. FREQUENCY RESPONSE ANALYSIS
WITH FFT
the large-signal average model by applying Middlebrook’s
averaging technique. After combining all the derived
control-oriented models, Figs. 9 and 10 show SIMULINK
models of the converter system using the large-signal
average and pulse-by-pulse techniques. The SIMULINK
converter system models were simulated in the time-domain
and verified to function properly before proceeding to
frequency response analysis.
To obtain the open-loop frequency response of the
SIMULINK converter circuit model, time domain simulation is performed with sinusoidal signals of various frequencies injected at the summing junction (Ve in Figs. 4 and
9, V5 in Fig. 10). The FFT technique is applied on the timedomain data to extract the fundamental frequency
components (magnitude and phase). Subsequently, a singlefrequency response of Vin/Ve (gain and phase response)
was stored. The process repeats for the subsequent runs
with a different input frequency. The following algorithm is
the converter frequency response analysis that has been
coded in MATLAB [5].
Algorithm:
1) Select the frequency range of interest where f is an
array containing small-signal frequencies
2) For I=1:length(f) , where length(f) is the number of frequency points or size of the array f
a) Perform a time domain simulation of the
model and save the vin, v5, and vsine signals.
b) Pick only one small-signal cycle (N sampled
points of each acquired signal) of vin, v5 and
vsine and compute their respective FFTs for H
= FFT (v,1,N), where N is the number of timedomain samples. Let c = H(2), where c is the
complex value at fundamental frequency of
vsine, then the gain and phase of the FFTs are
• Gain = 2*abs(c )/N
• Phase = atan (imaginary (c), real (c))
c) Save the gain and phase for vin, v5, and vsine
.
3) Plot the Gain Go and phase θ of the open-loop transfer
function, where
Figure 8. Modeling of peak-current programmed control
laws in SIMULINK
Figure 9. SIMULINK model of the converter system
shown in Fig. 4 using large-signal average
technique
Go = 20*Log [Gain(vin)/Gain(v5)] dB, and
θ = (Phase(vin) - Phase(v5))*180/π degrees.
6.
ANALYSIS RESULTS
In this section, the FFT algorithm is applied to the DC-DC
converter SIMULINK models described in Section 4,
whereas the conventional AC analysis with small-signal
linearization is independently applied in the PSPICE largesignal average model. Figure 11 shows a converter loop
gain and phase response comparison between the PSPICE
and SIMULINK large-signal average models. Note that the
results are almost identical, i.e., both showing almost 5 kHz
cross-over frequency with 63° phase margin.
The steady-state time-domain waveforms of the acquired
signals from MATLAB SIMULINK (Figure 12) were also
visually inspected and confirmed the result.
Figure 10. SIMULINK model of the converter system
shown in Fig. 1 using pulse-by-pulse technique
6
Figure 13. Converter loop-gain response acquired from
both the non-linear switching and the average
models developed in SIMULINK
Figure 11. Converter loop-gain response of the arrayvoltage regulation via PSPICE and SIMULINK
Figure 12. Time-domain steady-state responses of the loopgain input, Ve, and output, Vin
Figure 14. Time-domain steady-state responses of loop
gain input, Ve, and output, Vin , from
SIMULINK converter switching model
Figure 13 depicts the loop-gain responses individually
obtained from both the average and the non-linear switching
SIMULINK models, revealing well-correlated results.
Figure 14 shows a time response obtained from the same
SIMULINK converter system switching model, visually
confirming the same gain and phase response being
extracted from the FFT. Note that the phase discrepancy
between the average and the non-linear switching models at
upper frequencies is caused by the failure of the large-signal
average model to include non-linear and parasitic effects.
At 1 MHz switching frequency, parasitic loss across the
damping resistors within the converter model is greater.
This causes the phase to be less steep.
7. DATA FILTERING PRIOR TO FFT
In practice, the time-domain data can be corrupted by a
significant content of switching noise at the converter
switching frequency. This switching ripple is more pronounced at high frequency due to lower amplitude signals
that lead to noisier FFTs. Therefore, it is recommended that
the analysis approach without data filtering described in the
previous section be applied to data less than 2/5 of the
converter switching frequency.
As noted previously, the “virtual network analyzer”
approach is necessary for frequency response analysis of a
converter with a non-linear switching model that cannot be
linearized due to its time-variant structure. A technique
involving filtering of the acquired data prior to FFTs is also
presented in the subsequent section to reduce data noises
generated from switching ripple, thereby, further improving
the frequency response results and yielding smoother plots.
By filtering the data using a multiple-frame data-averaging
technique [7], the switching noise at the converter switching
frequency can be attenuated. Therefore, the noise contribution at any frequency is significantly reduced.
The SIMULINK converter switching model used for producing the frequency response result shown in Figure 13
7
[3] N. Balabanian and T. A. Bickart, “Electrical Network
Theory”, New York: Wiley, 1969, Chapter 4.
[4] B. C. Kuo, “Linear Networks and Systems”, New York:
McGraw-Hill, 1967, Chapter 5 and 6.
[5] D. Hanselman and B. Littlefiled, “Mastering MATLAB
5”, A Comprehensive Tutorial and Reference, Prentice
Hall, 1998.
[6] K. Siri, “Study of System Instability in Current-Mode
Converter Power Systems Operating in Solar Array
Voltage Regulation Mode,” APEC’2000, New Orleans,
Louisiana, 228-234, Vol. 1, February, 2000.
[7] H. Li and D. S. Doermann, “Text Enhancement in
Digital Video Using Multiple frame Integration,” Proc.
AC- Multimedia 1999, Orlando, Florida, 19-22.
has a switching frequency of 1 MHz. Hence, to obtain a
valid frequency response between 1 kHz and 50 kHz, the
simulation time step was fixed at 2.5 ns (400 MHz.) with a
decimation value of 10 (the interim record of the simulated
response being sampled at 25-ns time steps). Before using
the FFT algorithm, the simulation data was conditioned with
a window averaging technique. We chose a windowaverage size of 25 (i.e., summing 25 consecutive data points
and dividing by 25). This essentially smoothed the data
within any 625 ns sampled at 40 MHz. To reduce
computation time and memory storage, the data was further
sampled at 10 MHz (the temporary record of the movingwindow average response being sampled at 100-ns time
steps). Next, a multiple-frame average technique is used.
Synchronizing with the frequency of injected signal, 4
frames of smoothed data were averaged. This further
reduced numerical noise as well as system switching noise.
Finally, the data was ready for the FFT algorithm.
BIOGRAPHY
Kasemsan Siri holds Ph.D. degrees in
electrical engineering. His experience
includes four years of teaching in
electronics, seven years of power
electronics research at the University
of Illinois at Chicago, and sixteen
years of industrial experience in
power
electronics
and
systems. Starting from the Associate Director of Research
in Power Electronics Laboratory at the UIC, a modeling
specialist at Rockwell International, Canoga Park, CA, and
a senior design engineer at Hughes Aircraft Company, El
Segundo, CA, Dr. Siri is presently an engineering specialist
at The Aerospace Corporation, El Segundo, CA, supporting
design, research, modeling and analysis of power systems
for various satellite programs. He received an Aerospace
President award in 1999 for technical rigor and leadership in
identifying a critical design flaw in a MILSTAR satellite
power system and the resolution that were adopted for four
subsequent satellites. He is the author of over 55 scientific
papers and holds eight U.S. patent inventions in zerovoltage switching DC-DC converters, maximum power
tracking architectures, current-sharing schemes, and active
power factor correction.
Note that in the lower frequency region (100 Hz To 1 kHz.),
a larger simulation time step of 25 ns and FFT time step
resolution of 1 MHz were used. This is sufficient to
maintain the accuracy of the frequency response.
8. CONCLUSION
Employing both the state-space averaged model and the
pulse-by-pulse switching model of the DC-DC converter
power system, a simple, direct, and accurate frequency
response analysis approach is demonstrated and validated
based on two fundamental-component extraction techniques. One is the variable time-step extraction from Fourier series expansion in a circuit-oriented simulator, and
another is the fixed time-step extraction through FFT. The
developed analysis tool is critical for robust design and
validation of the converter closed-loop system since more
parasitic effects within the converter power stages are
included in the model. Through applications of both circuitoriented and control-oriented simulators (such as PSPICE
and MATLAB/SIMULINK), the approach is exercised with
a converter power system operating in a solar-array voltage
regulation mode. In general, different switching converter
topologies and control schemes may produce different noise
spectra resulting from switching modulation spreading
around their switching frequencies. This may require
different data filtering techniques to smooth out the noise
prior to the FFT computation.
Calvin Truong is a senior engineer
in the Photonics and Electronics
Laboratory
at
The
Aerospace
Corporation, El Segundo, CA. He
holds M.S. and B.S. degrees in
electrical engineering. His experience
includes four years of research and
development
in
solar
power
generation and conversion in electric power utility and
fourteen years of space power electronics in the aerospace
industry. His research interest is in the areas of analytical
modeling of power conversion systems, radiation effects in
power converters, Pico-satellites development, and space
power system stability analysis.
REFERENCES
[1] R. D. Middlebrook and S. Cuk, “Advances in SwitchedMode Power Conversion”, TESLAco, Inc., Pasadena,
California, 1981.
[2] Rudolf P. Severns and Gordon E. Bloom, “Modern DCTO-DC Switch-mode Power Converter Circuits”, Van
Nostrand Reinhold, 1985.
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