Energy and Power Engineering, 2013, 5, 1147-1152
doi:10.4236/epe.2013.54B218 Published Online July 2013 (http://www.scirp.org/journal/epe)
Variable Frequency Modulation for EMI Suppressing
in Power Converter
Zhiwen Cao, Yiming Zhang
College of Electronic Information and Control Engineering, Beijing University of Technology, Beijing
Email: czw72413@163.com
Received February, 2013
ABSTRACT
Switch mode power supply (SMPS) is good selection for power supplies of Unmanned Aerial Vehicle (UAV), which is
one of the most important interference sources of UAV. The power switches with their high dv/dt and di/dt switching
slopes are the sources of electromagnetic interference (EMI). In this paper, a variable frequency modulation technology
of the forward converter of UAV is presented, which is utilized in SMPS to improve electromagnetic compatibility
(EMC). In variable-frequency techniques, power (signal) is transmitted in power converter in wide-band mode in sev-
eral frequencies that are constantly changing, the EMI spectral performance of the SMPS can be controlled with the
modulating pattern and modulation method. The validity of the models and analyses are confirmed experimentally by
using a dc/dc forward converter.
Keywords: SMPS; Variable Frequency Modulation; EMI; EMC
1. Introduction
Recent advances made in semiconductor technology
have led to substantial increases in the current and volt-
age ratings of gate controlled devices in Switch mode
power supply (SMPS). Utility related applications of
these types of devices have captured much attention from
industry and academic communities. The reasons of the
popularity of SMPS are efficiency, size, capability to
operate at different currents and voltage levels, control
features, and price compared to other possible solutions.
An Unmanned Aerial Vehicle (UAV) is a remotely oper-
ated vehicle or autonomous aircraft, and can re-use un-
manned aircraft. UAV technology has been widely used
for aerial reconnaissance, surveillance, communications,
anti-submarine, electronic interference and other fields.
Nowadays, the UAV has become one of the latest appli-
cation technologies in the aeromagnetic field. The prob-
lem of magnetic interference of UAV must be solved to
implement high-precision aeromagnetic surveys. The
switch mode power supply (SMPS) is one of the most
important interference sources of UAV [1].
UAV platforms usually dictate that all carried compo-
nents should be light in weight, small in volume, and
energy efficient. Because the inner space of a UAV is so
confined, a smaller size of SMPS is required. The sizes
of the energy storage elements (transformers, inductors,
and capacitors) in a switch-mode power supply decrease
in an approximately linear fashion along with the in-
crease of the switching frequency. High-density power
supplies of UAVs generally demand a high switching
frequency and fast semiconductor devices.
DC-DC power converters are innate powerful sources
of electromagnetic interferences because of the large
di/dt and dv/dt. Unlike linear regulators, which operate
the power transistors in the linear mode, the Pulse Width
Modulated (PWM) power supply operates the power
transistors in both the saturated and cut-off states. SMPS
are usually implemented with the use of constant clock
frequency, so SMPS that have a periodic switching pat-
tern, have an EMI spectrum that contains switching fre-
quency and its harmonic frequencies. Electromagnetic
Interference has become the major problem of switching
mode power supplies in recent years. In order to reduce
electromagnetic interference, Variable Frequency modu-
lation is used in the paper, the EMI spectral performance
of the SMPS can be effectively controlled. The control
circuit of a pulse width modulated dc/dc converter is ex-
pected to be more complex than a control circuit used for
the conventional PWM controlled dc/dc converter.
2. Constant Pulse Width Modulation
Advanced telecommunication and computer systems of
UAV require high efficiency and power density, and dis-
tributed power supplies. Both the fly-back and forward
converter topologies are good candidates for this applica-
tion. The principal features of the supplies are a constant
Copyright © 2013 SciRes. EPE
Z. W. CAO, Y. M. ZHANG
1148
operating frequency, high efficiency and high power
density. Forward switching power is supply from the
buck converter, compared with fly back switching power
supply, it has higher efficiency, the belt load capacity
strongly and lower ripple factor, so it is the best choice.
2.1. PWM Control Circuit
As the DC/DC converters follow the new trend of power
generation, their switching frequencies have increased
dramatically to reduce their dimensions. The increased
switching frequency, together with the increased current
and voltage slew rates, di/dt and dv/dt, and consequently,
wide bandwidths, have detrimental effects on the EMC
performance of the power supplies. Electronic power
converters are sources of electromagnetic interference at
their input power source as well as in other neighboring
electronic equipment, and suppression of EMI is a major
issue in switch-mode power converter design.
The conventional PWM voltage control scheme is
constant pulse width modulation. In this approach, the
phase angle between the supply voltage and the current is
maintained constant. The dc output voltage is controlled
by varying the duty cycle of the conducting switches.
2.2. PWM Control Circuit
The inherent performance advantage of power MOS-
FETs makes their use very attractive in switched mode
power supplies. The fundamental advantage of the power
MOSFET is the operation at fast switching speeds and
high frequencies. Higher operating frequency allows fur-
ther reduction in the size of the filter and magnetic com-
ponents. Figure 1 shows the circuit topology of a practi-
cal forward converter, which takes into account the
non-ideal nature of a practical transformer. The control
circuit is implemented by the use of the current-mode
controller IC, UC3844 which is very popular in control-
ling power supplies. The performance of a power supply
is dependent on various factors such as layout and trans-
former construction etc. It consists of a fast switching
device ‘Q’ along with its control circuitry, and a trans-
former with its primary winding connected in series with
switch ‘Q’ to the input supply.
The circuit uses an extra tertiary winding (Nd) with a
series diode to recover the energy when the switch is
turned off. Usually, high voltage with twice the input DC
voltage is used to obtain the maximum 50% duty ratio
for resetting the transformer flux during the MOSFET’s
off period at low input DC voltage and full load. That
means the peak voltage of twice the primary DC voltage
is developed across the MOSFET during the off period.
Mechanical switches (relays and circuit breakers) have a
high inrush current (capacitive effect) at making contact
and spark-over at the breaking contact (inductive effect),
and cause wide-band emission with a continuous spec-
trum [4-5].
Switch mode power supplies are usually implemented
with the use of constant clock frequency; for example,
with traditional pulse width modulation (PWM). PWM
signal is supplied from some special chip, for example,
3842.The modulator clock and harmonic frequencies are
present in both conducted and radiated-EMI. SMPS that
have a periodic switching pattern, have an EMI spectrum
that contains switching frequency and its harmonic fre-
quencies. These periodic noise components may be very
harmful because they are repeating continuously - even if
they have low amplitude and energy content.
2.3. Frequency Spectrum Analysis of PWM
Pulse
The traditional pulse width modulation can be considered
as a periodic trapezoidal pulse train. Trapezoidal current
wave is shown in Figure 2, are defined as follows: A =
amplitude, tr = rise time, td = fall time, τ = width [9].
The rise time and fall time is not equal for the actual
control signal. According to the actual situation, a labo-
ratory prototype is constructed with the following speci-
fications: the pulse frequency f = 1/T = 10 KHz, the
turn-on time ton= tr=10 ns, the turn-off time toff= td = 20 ns,
the amplitude of the current id = A. A suitable simulation
program has been used to evaluate the variation of the
spectrum according to the values of the pulse parameters.
By means of the MATLAB program, we can derive the
spectrum at each frequency point. We can see the actual
PWM control signal contains the switching frequency
and its harmonic components from the spectrum analysis
diagram. The spectrum coefficients Cn for such a wave-
form are:
N
d
:N
p
:Ns
D2
D
1
C
L
R
L
Vo u t
D
3
Nd
V
S
PWM
modulat or
Q
Figure 1. Circuit topology of a practical forward.
t
r
t
d
Aτ
T t
Figure 2. Trapezoidal pulse wave.
Copyright © 2013 SciRes. EPE
Z. W. CAO, Y. M. ZHANG 1149
0
0
()
min 1
0
0
00
1
2
sin( )
sin( ).
on
jn ft
n
jn fjn f
j
off
dond
on off
Cje
n
e
nft
dinf tdi
dt nfdtnf

 



 

 
 


v
0
e
(1)
Where:
,
dd
on off
on off
di di
A
A
dtt dtt
 
 
 
(2)
3. Spread Spectrum Techniques
From the discussion given in the last section, it is clear
that the measured emission is periodical with respect to
switching frequency. The emission, therefore, centers at
the switching frequency and the harmonic frequencies.
Concentration of emission power at these discrete fre-
quencies makes it harder to meet EMI regulations.
3.1. Frequency Spectrum Analysis of Spread
Spectrum
Usually, the SMPS are controlled by square switching
signal with constant frequency and duty cycle (D) ad-
justed to the response of the control loop. One of the
conventional techniques in order to reduce EMI consists
of using passive filters, which has its limitations: size,
weight, design complexity, efficiency, cost, etc. Modern
variable-frequency (VF) EMI reduction techniques have
been under intensive research to overcome the problems
faced in filter-solutions. The interleaving technique is
used to equally share the total power to be delivered the
general idea in variable-frequency spread spectrum sig-
naling is shown in Figure 3. Although the spectrum dis-
tribution of is different contained in Figures 3(a) and (b),
but the total energy is the same in both cases, the peak
level has reduced in Figure 3(b). The switching fre-
quency modulation (SFM) is an effective method to re-
duce EMI in SMPS. This technique is based on the orig-
inal spread-spectrum clock generation (SSCG) tech-
niques. Using the SFM, there is a tradeoff between the
amplitude reduction of the EMI harmonics and the gen-
eration of a set of additional side-band harmonics with
small amplitude appears.
PWM spread spectrum control principle of SMPS can
be described as below:
s
f
ff (3)
where fs is the reference frequency of the PWM switch;
f
is the additional spread spectrum signal frequency,
which is changing frequency according the time-domain
characteristics of the spread spectrum signal. As is seen
from the formula (3), The PWM spreading control is
depending on the control of the Δf. The PWM control is
the period spreading when Δf is the period signal. The
PWM control is the chaotic spreading when Δf is the
chaotic signal. As be shown in Figure 4, a pulsed proc-
ess is constituted by spreading PWM, and can be ex-
pressed as the following pulse sequence:
1
1
()( )
k
k
tAt


(4)
Where in τk represents the start time of the k-th of the
PWM waveform, A represents the amplitude of the drive
pulse, Tk is the k-th pulse interval.
Corresponding to periodic or chaotic spread spectrum
signal, the time interval Tk of the PWM pulse respec-
tively appear cycle changes or chaotic changes, the start
time τk of the k-th drive waveform is the cumulative of
the time intervals Tk, it is shown as below:
1kk k1


(5)
The period spreading can partly reduce the peak of the
power spectrum of the PWM pulse, but it is still a dis-
crete spectrum, the energy is concentrated in the nfs ± kfm
specific frequency point, and did not get full extension,
EMI can not meet the actual needs, so the article adopts
chaotic control method. Chaotic control belongs to non-
linear control techniques in power electronics. These non-
linear control techniques generate non-harmonic switch-
ing spectrum when controller parameters are correctly
chosen.
Frequency
Signal energy
Frequency
Signal energy
(a)
(b)
Figure 3. Spread spectrum signa l ing.
1k
T
k
T
1k
k
1k
A
t
Figure 4. PWM dr i ve p ul s e s.
Copyright © 2013 SciRes. EPE
Z. W. CAO, Y. M. ZHANG
1150
The advantage of the non-linear control design ap-
proach is the simplicity of the circuit: even basic switch
mode power supply control circuits, made by many IC
manufacturers, can be used with only a few additional
passive components. The main drawback of this ap-
proach is that the designer must study carefully the cir-
cuit performance at all load conditions and parameter
variations to ensure the spread spectrum operation and
system overall stability in all cases.
3.2. Quantitative Analysis of Chaos Spread
Spectrum
As is shown in Figure 5, PWM pulse interval time Tk
under the control of the chaotic spread spectrum can be
described as chaotic mapping φ:
1()
k
TT
k
(6)
The K-th PWM drive pulse start time τk is a chaotic
sequence, as is shown in equation (7):
(2)( )
11 111
()
1
() ()()
()
k
k
k
TT TT
T
 
 
(7)
Through analysis, we can get chaotic PWM pulse
power spectral densities of formula:
2
()
1
()1 ()1
11
1
() lim2()
()
cos( ())
NT
TL
K
NT NT
iK i
ii
SAEN
NET
 



PT



(8)
where:
()
()
limlim( )1
NT
TNT PT
 ,

NENT,
()
()
NT
PT
represents the probability of the event

() ()1NTNT
T

 ,
E represents the mathematical expectation here.
N
d
:N
p
:Ns
D
2
D
1
C
L
R
L
D
3
Nd
V
S
Q
Vout
Current
feedback
Vo l t a ge
feedback
TMS320F2812 PWM
Chaotic Modulato
r
Figure 5. Schematic diagram of PWM Control System.
As can be seen from equation (7), chaotic spread spec-
trum control PWM pulse spectrum has the continuity
characteristic, the power spectrum of chaotic spreading
spectrum drive pulse is no longer concentrated in par-
ticular spectrum, but contains various frequency spec-
trum, the energy is no longer concentrated in specific
frequency point, energy can be spread in the entire fre-
quency range, so the chaotic spread spectrum is much
better than period spread spectrum in EMI suppression. It
became effective way to solve the EMI problem of
switching converter.
3.3. PWM Control System Structure
Control schematic diagram based on TMS320F2812 is
shown in Figure 1 in the forward converter. The TMS-
320 F2812 is a low-power 32-bit fixed-point digital
signal processor. He focused on many of the outstanding
features of the digital signal processing. The C28x is a
very efficient C/C++ engine, enabling users to develop
not only their system control software in a high-level
language, but also enables math algorithms to be developed
using C/C++. The C28x is as efficient in DSP math tasks
as it is in system control tasks that typically are handled
by microcontroller devices. Add to this the fast interrupt
response with automatic context save of critical registers,
resulting in a device that is capable of servicing many
asynchronous events with minimal latency.
Chaos can be loosely defined as an apparently random
behavior in a nonlinear system. Since all switch mode
power electronic circuits are nonlinear, chaotic behavior
can be expected in power electronic circuits with some
specific component and parameter values. To achieve
chaos control, the first work is to select the chaotic sig-
nals based on need to generate chaos equation. The chaos
equation is very rich due to the long period development,
for example: Lienard equations, Van Der Pol equations.
The Lorenz equations is selected to produce chaotic sig-
nals in this paper, it is shown as below:
()xyx
y
xyxz
zxy z



(9)
3.4. Program
The powerful computing power of DSP can be helpful to
generate the chaotic signal, we usually adopt numerical
calculation method. The program flow chart is shown in
Figure 6, its core source program is shown as below:
void main()
{
int time=1;
double x=0.15;
double y=0.1;
Copyright © 2013 SciRes. EPE
Z. W. CAO, Y. M. ZHANG 1151
double z=0.1;
int i;
fori=1;i<10 000 000;i=i+timedelt //
Iteration module{
x = x + time * -16 * x + 16 * y/1000;
y = y + time * -1 * x * z +45.2 * x - y/1000;
z = z + time * x * y - 4 * z/1000;
}
}
3.5. Numerical Accuracy
Chaotic signals were generated mainly by means of po-
werful DSP computing power, what kind of numerical
methods can be used basing on the accuracy require-
ments. Usually, the higher the accuracy we demand, the
greater is the amount of computation required; the fre-
quency of the chaotic signals should be lower, so the
appropriate accuracy can be selected according to the
actual needs. The amount of computation can be directly
determined by the speed of operation, namely determined
by chaotic signal generation speed.
4. Experimental Verification
We can use a spectrum analyzer (4395A) to accept mag-
netic interference signals. The value of near-field radi-
ated emissions can be detected by a Closed Field Probe
(11945A) and a balanced loop antenna (11966B). As can
be seen from Figure 7, the spectra plotted in Figure 14
show a strong reduction of magnetic radiated emission
Choice of the parameters
and initial value
Select the chaos equation
Is it discrete
chaotic sequence?
N
Chaotic iterative
algorithm
DSP analog output
start
end
Figure 6. Program flow chart.
between 0.2 MHz and 3 MHz. Noise energy is spread
fur- there by chaotic spreading Spectrum, the noise of
lower band noise wave widened, and the peak declined
slightly; the spectrum peak of mid-frequency band
dropped significantly.
5. Conclusions
This paper has given a detail to the effects of the chaotic
control modulation schemes that are applied to dc/dc
converters operating in DCM. The chaotic control can
fully spread the discrete frequency component in the
classical PWM scheme to a continuous frequency spec-
trum. The chaotic control is a good choice because of its
effectiveness in conducted EMI suppression and of its
(a)
150 kHz 30MHz10 MHz1MHz
dBμA/m
(b)
150 kHz 30MHz10 MHz
1MHz
dB
μ
A/
m
Figure 7. Near-field emission measurement: (a) constant s
frequency (b) Chaos Spread Spectrum.
ease in practical implementation.
Copyright © 2013 SciRes. EPE
Z. W. CAO, Y. M. ZHANG
Copyright © 2013 SciRes. EPE
1152
tly by SinoProbe-09-0
development of the fixed-
6. Acknowledgements
This article is supported join
Grant No. 201011080 (the
3 and
[1] L. Beloqui and J. M. Usategui, “Vertical Differentiation
and Entry Deterrence: Reconsideration,” WP 2005-06,
Dept. Fundamentos del Analisis Economico II, Universi-
dad del Pais Vasco, 2005.
wing UAV Aeromagnetic survey system). My deepest
gratitude goes to Professor YiMing Zhang, my supervi-
sor, for his constant encouragement and guidance. I also
owe my sincere gratitude to my friends and my fellow
classmates who gave me their help.
REFERENCES
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