Hybrid-Modulation-Based Control Technique for Reduction of Output Voltage Ripples in Frequency-Modulated Switch-Mode Power Converters

International Journal of Power Electronics and Drive System (IJPEDS)
Vol. 9, No. 3, September 2018, pp. 1272~1284
ISSN: 2088-8694, DOI: 10.11591/ijpeds.v9.i3.pp1272-1284  1272
Journal homepage: http://iaescore.com/journals/index.php/IJPEDS
Hybrid-Modulation-Based Control Technique for Reduction of
Output Voltage Ripples in Frequency-Modulated Switch-Mode
Power Converters
Deniss Stepins1
, Jin Huang2
, Janis Audze3
1,3
Institute of Radioelectronics, Riga Technical University, Latvia
2
School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, China
Article Info ABSTRACT
Article history:
Received Apr 1, 2018
Revised Apr 24, 2018
Accepted Jul 1, 2018
In this paper a novel control technique for switching-frequency-modulated
switch-mode power converters (SMPC) operating in discontinuous
conduction mode is proposed. The use of the technique leads to significant
reduction in peak-to-peak output voltage and peak currents increased due to
straightforward application of switching frequency modulation (SFM). The
technique is based on hybrid modulation scheme in which both switching
frequency and duty ratio are modulated simultaneously by the same
modulation signal. Theoretical analysis and experimental verification of the
proposed technique are presented in details. Both computer simulations and
experiments show that switching-frequency-modulated SMPC with the
proposed control technique in comparison to SMPC without SFM has
appreciably lower conducted electromagnetic emissions, at the cost of
slightly increased peak-to-peak output voltage and peak currents.
Keyword:
Electromagnetic interference
Frequency modulation
Hybrid modulation
Ripples
Switching power converters
Copyright © 2018 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Deniss Stepins,
Institute of Radioelectronics,
Riga Technical University, 12 Azenes street, Riga, Latvia.
Email: deniss.stepins@rtu.lv
1. INTRODUCTION
With an ever increasing number of electrical and electronic devices (e.g. personal computers, TV
sets, vacuum cleaners, etc.), efficient electric power conversion has become a hot topic of research. DC/DC
or AC/DC electric power converters which are used for efficient electric power conversion in electronic
equipment are dominantly switch-mode ones. Switch-mode power converters (SMPC) have distinct
advantages over other types of power converters (e.g. linear power supplies) – mainly higher efficiency,
lower size and weight [1], [2]. However owing to rapidly switching semiconductor devices with high voltage
and current change rates they are major sources of electromagnetic interference (EMI) both conducted and
radiated [3].
Conducted EMI is usually reduced by using passive or active EMI filters, interleaving, soft-
switching techniques, spread spectrum techniques, etc. [4] – [11]. Since every conducted EMI suppression
technique has its own advantages and disadvantages, often they are used in combination with other EMI
reduction approaches. For example, it is often not enough to use spread spectrum approach alone to reduce
conducted EMI significantly and keep it within allowable limits [10]. Spread spectrum technique is often
used in combination with passive EMI filtering. In this case passive EMI filter size and weight can be
reduced noticeably [12].
This paper deals with the spread spectrum technique based on periodic switching frequency
modulation (SFM) applied to SMPC to reduce conducted EMI. In fact, the technique has gained considerable
attention during past two decades because of its easiness of implementation and ability not to increase

Int J Pow Elec & Dri Syst ISSN: 2088-8694 
Hybrid-Modulation-Based Control Technique for Reduction of Output Voltage… (Deniss Stepins)
1273
weight, size and cost of SMPC. However the main problem with the use of this technique in conventional
DC/DC or AC/DC SMPC is that peak-to-peak output voltage and power stage peak currents (e.g. power
inductor or power MOSFET currents) can increase significantly [13] – [16]. Increase in peak-to-peak output
voltage of SMPC can be very harmful to electronic equipment powered by the SMPC, but increase in peak
currents of power magnetic components can lead to increase in losses and even to saturation of a magnetic
core of transformers or inductors.
In [13] – [17] the effect of SFM on peak-to-peak output voltage and power stage peak currents of
DC/DC SMPC operating in continuous conduction mode (CCM) and discontinuous conduction mode (DCM)
was studied in details and some recommendations for proper design of DC/DC SMPC were proposed.
However, the recommendations are not sufficiently useful to get low peak-to-peak output voltage and power
stage peak currents, especially for switching-frequency-modulated SMPC operating in DCM. This is why in
this paper a novel control technique for significant reduction of peak-to-peak output voltage and power stage
peak currents in switching-frequency-modulated SMPC is proposed. The control technique is based on
hybrid modulation scheme in which both switching frequency and duty cycle are modulated by the same
modulation signal. Along with appreciable conducted EMI reduction, the technique also decreases
significantly peak-to-peak output voltage and power stage peak currents increased due to the use of SFM. In
order to show usefulness of the proposed technique a simple analog circuit based on analog multiplier will
also be proposed and analyzed.
The proposed control technique can be applied to both classical single-switch non-isolated (e.g.
buck, boost, buck-boost) and isolated (e.g. flyback, forward) SMPC topologies operating in DCM. The
proposed method is not suitable for SMPC operating in CCM, because in this case variations of duty ratio
can lead to large low-frequency ripples in SMPC output voltage.
The paper is organized as follows. In section 2 the effect of the proposed hybrid modulation scheme
on DCM boost DC/DC SMPC peak-to-peak output voltage and power stage peak currents will be studied
analytically and by computer simulations. In section 3 thorough experimental verification of the proposed
technique will be performed. Finally, conclusions are given in Section 4.
2. THEORETICAL ANALYSIS OF THE PROPOSED CONTROL TECHNIQUE
Based on the analysis presented in our papers [15] – [17] and after analyzing expressions of output
ripple voltage for traditional switching-frequency-modulated single-switch SMPC (e.g. buck, boost, buck-
boost, forward and flyback) operating in DCM it can be shown that general expression of peak-to-peak
output voltage when SFM is enabled is as follows:
𝑉𝐹𝑀𝑝𝑝 = 𝑚𝑎𝑥{𝑣𝐿𝐹(𝑡) + 𝑣𝑒𝑛𝑣𝐻𝐹(𝑡)} − 𝑚𝑖𝑛{𝑣𝐿𝐹(𝑡) − 𝑣𝑒𝑛𝑣𝐻𝐹(𝑡)} (1)
where 𝑣𝐿𝐹(𝑡) is low-frequency (LF) ripple of output voltage caused by SFM; 𝑣𝑒𝑛𝑣𝐻𝐹(𝑡) is high-frequency
(HF) ripple envelope. The LF ripples in DCM are due to the fact that averaged inductor, diode and transistor
switch currents are switching-frequency-dependant [17]. The envelope of HF ripple in unmodulated SMPC is
constant, but in switching-frequency-modulated SMPC it is variable (because switching frequency changes in
time). Both 𝑣𝐿𝐹(𝑡) and 𝑣𝑒𝑛𝑣𝐻𝐹(𝑡) are functions of instantaneous switching frequency 𝑓𝑠𝑤(𝑡) and
instantaneous duty ratio 𝑑(𝑡):
v_LF (t)=ψ_1 [d(t),f_sw (t)]
(2)
𝑣𝑒𝑛𝑣𝐻𝐹(𝑡) = 𝜓2[𝑑(𝑡), 𝑓𝑠𝑤(𝑡)],
(3)
Where
𝑑(𝑡) = 𝐷 + 𝑑
̃(𝑡) , (4)
𝑓𝑠𝑤(𝑡) = 𝑓𝑠𝑤0 + ∆𝑓𝑠𝑤𝑚(𝑡),
(5)
where D is average duty ratio; 𝑑
̃(𝑡) is variable component of duty ratio; ∆𝑓𝑠𝑤 is switching frequency
deviation; 𝑚(𝑡) is modulation waveform with unitary amplitude; 𝑓𝑠𝑤0 is central switching frequency. Note
further in the analysis it will be assumed that 𝑚(𝑡) is periodic and 𝑓𝑚 is modulation frequency.
For frequencies 𝑓𝑚 lower than open loop gain crossover frequency (𝑓𝑐𝑟𝑜𝑠𝑠) feedback loop changes
duty ratio with the purpose to reduce the output voltage LF ripple. In order to simplify our analysis let’s
assume that 𝑓𝑚 > 𝑓𝑐𝑟𝑜𝑠𝑠. In this case 𝑑(𝑡) is almost constant and equals D approximately.

 ISSN: 2088-8694
Int J Pow Elec & Dri Syst, Vol. 9, No. 3, September 2018 : 1272 – 1284
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For quite large ∆𝑓𝑠𝑤, 𝑉𝐹𝑀𝑝𝑝 and magnetic components peak currents can increase significantly in
DCM in comparison to unmodulated case [16], [17]. Therefore it is important to propose a control technique
to reduce peak-to-peak output voltage and peak currents increased due to straightforward application of SFM.
Now we are going to show some theoretical analysis in order for a reader to better understand the
idea. Assuming that 𝑓𝑚 > 𝑓𝑐𝑟𝑜𝑠𝑠, (2) and (3) can be overwritten as follows:
𝑣𝐿𝐹(𝑡) = 𝜓1[𝐷 + 𝛿(𝑡), 𝑓𝑠𝑤(𝑡)] (6)
𝑣𝑒𝑛𝑣𝐻𝐹(𝑡) = 𝜓2[𝐷 + 𝛿(𝑡), 𝑓𝑠𝑤(𝑡)] (7)
where 𝛿(𝑡)is time-dependant component of the duty ratio which should be generated and introduced into a
non-inverting input of the control block comparator so that
V_FMpp=V_pp (8)
where 𝑉
𝑝𝑝 is peak-to-peak output ripple voltage of unmodulated (without SFM) SMPC. In order to derive
𝛿(𝑡), expressions for 𝑣𝐿𝐹(𝑡) and 𝑣𝑒𝑛𝑣𝐻𝐹(𝑡) should be known and equation (8) with respect to 𝛿(𝑡) then
should be solved.
For switching frequencies up to several hundreds of kHz electrolytic capacitors are often used at
outputs of SMPC. Since for electrolytic capacitors at frequencies > 50 kHz usually equivalent series
resistance (ESR) is much higher than capacitive reactance, then in order to simplify our analysis it will be
assumed that HF ripples are due to the ESR only.
It can be proved that for single-switch SMPC (e.g. buck, boost, buck-boost, forward and flyback)
with typical output electrolytic capacitor general expression for HF ripple is as follows:
𝑣𝑒𝑛𝑣𝐻𝐹(𝑡) = 𝐾
𝑑(𝑡)
2𝑓𝑠𝑤(𝑡)
(9)
where K is SMPC-topology-dependant coefficient, which e.g. for boost SMPC is as follows [17]:
𝐾 =
𝑟𝑐𝑉𝑖𝑛
𝐿
(10)
where 𝑉𝑖𝑛 is input DC voltage; L is the power inductor’s inductance; 𝑟𝑐 is ESR of the output capacitor.
General expression for the LF ripple 𝑣𝐿𝐹(𝑡) can be found after deriving expressions for AC
component of averaged current (< 𝑖𝑒 >) before the output capacitor, applying the Laplace transform and
deriving expression for the LF ripple in s-domain [17] as follows:
𝑣𝐿𝐹(𝑠) = 𝑖𝑒
̃(𝑠)
𝐻𝑜𝑢𝑡(𝑠)
1 + 𝑇(𝑠)
(11)
where 𝐻𝑜𝑢𝑡(𝑠) is output voltage to ie transfer ratio (in case of boost SMPC, it is output voltage to diode
current transfer ratio); T(s) is open loop gain; 𝑖𝑒
̃(𝑠) is AC component of < 𝑖𝑒 > in s-domain. In general case:
< 𝑖𝑒 >= 𝐹
(𝑑(𝑡))2
𝑓𝑠𝑤(𝑡)
(12)
where F for e.g. boost SMPC [15], [17] is as follows:
𝐹 =
𝑉𝑖𝑛
2
2𝐿(𝑉𝑜𝑢𝑡 − 𝑉𝑖𝑛)
(13)
In time domain the LF ripple can be obtained by applying inverse Laplace transform of (11).
Despite the fact that optimum 𝛿(𝑡) for which 𝑉𝐹𝑀𝑝𝑝 is minimum can be found by solving equation
(8) and using (1), (9) and (11), this is, firstly, very complicated task, and secondly, it would be very difficult
to generate such a complex 𝛿(𝑡) in practice. This is why we are to derive simple approximate expression for

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𝛿(𝑡), which would give quite high reduction of 𝑉𝐹𝑀𝑝𝑝 increased due to the use of SFM. We can find the
approximate expression by solving two equations separately: one for the variable duty ratio component 𝛿1(𝑡)
to get minimum peak-to-peak HF ripple voltage and another for the variable duty ratio component 𝛿2(𝑡) to
get zero peak-to-peak LF ripple voltage. To get minimum peak-to-peak HF ripple voltage the following
equation should be solved:
𝐾
𝐷 + 𝛿1(𝑡)
2(𝑓𝑠𝑤0 + ∆𝑓𝑠𝑤𝑚(𝑡))
= 𝑣𝑒𝑛𝑣(𝑡) (14)
where 𝑣𝑒𝑛𝑣(𝑡) is envelope of output voltage ripple for unmodulated SMPC:
𝑣𝑒𝑛𝑣(𝑡) = 𝐾
𝐷
2𝑓𝑠𝑤0
(15)
After solving (14), 𝛿1(𝑡) can be found:
𝛿1(𝑡) = 𝐴1𝐷𝑚(𝑡), (16)
where 𝐴1 = ∆𝑓𝑠𝑤/𝑓𝑠𝑤0.
In order to find 𝛿2(𝑡) to get zero LF ripples, < 𝑖𝑒 > of switching-frequency-modulated SMPC should
be constant and equal to < 𝑖𝑒 > for SMPC without SFM as follows:
𝐹
(𝐷 + 𝛿2(𝑡))2
𝑓𝑠𝑤0 + ∆𝑓𝑠𝑤𝑚(𝑡)
= 𝐹
𝐷2
𝑓𝑠𝑤0
(17)
From this follows that in order to get zero LF ripple, 𝛿2(𝑡) should be equal to 𝐴2𝐷𝑚(𝑡), where 𝐴2 =
∆𝑓𝑠𝑤/(2𝑓𝑠𝑤0).
It can be proved also that minimum peak current of magnetic components of switching-frequency-
modulated SMPC can be achieved if 𝛿(𝑡)equals 𝐴1𝐷𝑚(𝑡), because the peak current for unmodulated SMPC
is equal to 𝐸𝐷/𝑓𝑠𝑤0 (where 𝐸 = 𝑉𝑖𝑛/𝐿 for boost SMPC).
Based on the theoretical analysis shown above some conclusions can be drawn. Peak-to-peak output
voltage and peak currents of power magnetic and semiconductor components increased due to the use of
SFM can be reduced significantly using the hybrid modulation when switching frequency and duty ratio are
modulated simultaneously by the same periodic modulation signal m(t), because approximate 𝛿(𝑡) equals
𝐴𝐷𝑚(𝑡). Optimum value of the parameter A is somewhere between A1 and A2. This value can be calculated
by finding minimum of (1) analytically, numerically or using computer-simulation-based approach. If the
latter is used then it is necessary to make many simulations for different values of A in range between A2 and
A1 to find optimum A. If the LF ripples are much lower than the HF ripples, optimum A is equal to ∆𝑓𝑠𝑤/
𝑓𝑠𝑤0. If the LF ripples are much higher than the HF ripples, optimum A is equal to ∆𝑓𝑠𝑤/(2𝑓𝑠𝑤0). Note that
the conclusions are valid only when 𝑓𝑚 > 𝑓𝑐𝑟𝑜𝑠𝑠.
X A
+
-
+
-
Vref
Frequency
modulator
m(t)
generator
to MOSFET
driver
vea=VmD
Frequency modulated
triangular signal
0
Vm=1V
Comparator
from
output
voltage
divider
X +
+
Error
amplifier
AVmD
m(t)
AVmDm(t)

 ISSN: 2088-8694
1276
Figure 1. Switching-frequency-modulated SMPC control block with the proposed hybrid modulation
Block diagram of a switching-frequency-modulated SMPC control block with the proposed control
technique based on the hybrid modulation is shown in Figure 1. Amplitude of switching frequency variations
is equal to ∆𝑓𝑠𝑤, but amplitude of duty ratio variations should be equal to 𝐴.
In order to show usefulness of the proposed control technique based on the hybrid modulation, a
switching-frequency-modulated SMPC simulation model was created in PSIM software as shown in Figure
2. The model was initially simulated without SFM (when fsw0 =100 kHz; Vin=12 V; Rload=100 Ω; Vout=20 V).
Output voltage waveform, input current waveform and input current spectrum of unmodulated boost SMPC
operating in DCM are depicted in Figure 3 a, Figure 4 a and Figure 5 a. Then the model was simulated with
SFM enabled (fm = 10 kHz, Δfsw=30 kHz; m(t) is sine). The results of the simulations are shown in Figure 3 b,
Figure 4 b and Figure 5 b. As it can be seen SFM along with noticeable reduction of input current harmonic
amplitudes leads to significant increase in peak-to-peak output ripple voltage and peak inductor current. As
shown in Table 1 SFM leads to percentage increase in peak-to-peak output voltage as high as 42.4 % and
percentage increase in peak inductor current as high as 41 %. However after applying the proposed control
method based on hybrid modulation (with A=0.3), peak-to-peak output voltage and peak inductor current
decreased significantly as shown in Figure 3 c and Figure 4 c. Along with high reduction of peak-to-peak
output voltage and peak inductor current, reduction of input current harmonics amplitudes is almost the same
as in case when conventional control scheme (in which switching frequency is modulated only) is used (see
Figure 5 c). It should be noted that the technique proposed is less effective to reduce peak-to-peak output
voltage when output capacitor (e.g. ceramic cap.) with capacitive reactance much higher than ESR is used.
Triangular voltage
frequency modulator
modulation signal
m(t) generator
2πΔfsw
fsw0
Rload
Vin
A
s+500
4.3∙10-6
s2
+0.045s
H(s)=
Note each summers
input has adjustable
gain shown close to
each input
Note
1) for conventional boost SMPC without
SFM, m(t) generator peak amplitude
should be 0;
2) for boost SMPC with SFM only, m(t)
generator peak amplitude should be 1, but
A=0;

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Figure 2. Boost SMPC simulation model created in PSIM. Note: the model can be used to simulate the boost
SMPC without SFM, with SFM alone and with the proposed control technique based on hybrid modulation
0.1913 0.1914 0.1915
Time (s)
19.98
20
20.02
20.04
20.06
20.08
20.1
20.12
vout
0.1874 0.1875 0.1876 0.1877
Time (s)
19.98
20
20.02
20.04
20.06
20.08
20.1
20.12
vout
0.19068 0.19072 0.19076
Time (s)
19.98
20
20.02
20.04
20.06
20.08
20.1
20.12
vout
vout (V) vout (V) vout (V)
(a) (b) (c)
Figure 3. Simulated output voltage waveforms of boost SMPC in DCM: (a) for boost SMPC without SFM;
(b) for boost SMPC with SFM only; (c) for boost SMPC with the hybrid modulation
0.188 0.1881 0.1882 0.1883
Time (s)
0
0.5
1
1.5
2
I(L1)
0.1879 0.188 0.1881
Time (s)
0
0.5
1
1.5
2
I(L1)
0.18788 0.18792 0.18796
Time (s)
0
0.5
1
1.5
2
I(L1)
iL (A) iL (A) iL (A)
(a) (b) (c)
Figure 4. Simulated inductor current waveforms of boost SMPC in DCM: (a) for boost SMPC without SFM;
(b) for boost SMPC with SFM only; (c) for boost SMPC with the hybrid modulation
200 400 600 800 1000
Frequency (KHz)
0
0.05
0.1
0.15
0.2
0.25
0.3
I(L1)
amplitude (A)
(a)
200 400 600 800 1000
Frequency (KHz)
0
0.05
0.1
0.15
0.2
0.25
0.3
I(L1)
amplitude (A)
(b)
200 400 600 800 1000
Frequency (KHz)
0
0.05
0.1
0.15
0.2
0.25
0.3
I(L1)
amplitude (A)
(c)
Figure 5. Simulated input current spectra of boost SMPC in DCM: (a) for boost SMPC without SFM; (b) for
boost SMPC with SFM only; (c) for boost SMPC with the proposed control technique based on the hybrid

 ISSN: 2088-8694
1278
modulation
Table 1. Comparison of the simulation results (fm=10 kHz, fsw0=100 kHz, Δfsw=30 kHz; m(t) is sine; Vin=12V)
boost SMPC without SFM
boost SMPC with SFM
boost SMPC with the proposed
control technique based on
hybrid modulation
peak-to-peak output voltage,
mV
91.3 130 97
percentage increase in peak-to-
peak output voltage (in
comparison to SMPC without
SFM)
--- 42.4 % 6.2 %
peak inductor current, A 1.39 1.96 1.42
percentage increase in peak
inductor current (in comparison
to SMPC without SFM)
--- 41 % 2.1 %
3. EXPERIMENTAL VALIDATION OF THE PROPOSED CONTROL TECHNIQUE
3.1. Experimental setup
Detailed schematic diagram of an experimental prototype used to verify the usefulness of the
proposed control technique is shown in Figure 6. The experimental boost SMPC can be tested without SFM,
with conventional SFM and with hybrid modulation. Specifications of the experimental boost SMPC are
shown in Table 2.
Function
generator
TTI TG120
vtri(t)
0
Vm=1V
X +
0.1V
TC4427A
Cout1
Vin
L
16.7 μH
Rload
C1
330 μF
1μF
FDPF51N25
DSEI 12
R1
IN
+
-
+5.6V 6
Vcc
3
GND
7
OUT
Cout2
1 μF
2
MAX942
+
-
1
4
GND
OUT
Main OUT
3
2
+5.6V
8
Function
generator
Instek GFG-
8215A
Vcc
Output
Sweep
in
R3
W
AD633
X1
+
-
Vref
LM358
4.7nF
10nF
GND
4
+5.6V
4.7k
4.7k
2
3
1
C2
100μF
+
1
Y1
3
+Vs -Vs
8 5
+10V -10V
X2
Y2
4 2
6
Z
7
MBR1060
Cout3
1 μF
100 nF
27 R2
R4
Sw1
+
Cin1
+
330 μF
Cin2
1 μF
C3 C4
Control block
Figure 6. Detailed schematic diagram of the experimental boost SMPC

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Table 2. Experimental prototype specifications
Input DC voltage 8 Vdc – 14 Vdc
Output DC voltage 20 Vdc
Nominal switching frequency, fsw0 100 kHz
Type of control Analog, voltage mode control
Output capacitors
2 ceramic capacitors (nominal capacitance of each capacitor is of 1 μF);
electrolytic capacitor (nominal capacitance 330 μF; ESR≈66 mΩ)
Inductor Ferrite E core with a non-magnetic gap; L=16.7 µH
Four integrated circuits (ICs) and two function generators are used in the control block. The function
generator Instek GFG-8215A is used as modulation signal generator. The function generator TTI TG120 is
used as triangular voltage generator. The generator also has voltage controlled oscillator input (“sweep in”)
for SFM. TC4427A is power MOSFET driver. Potentiometer R1 is used to slow down the power MOSFET
switching for the purpose to reduce the power MOSFET and output voltage spikes. Potentiometer R2 is used
to adjust desirable DC output voltage. Error amplifier is composed of IC LM358 and simple (Type 1)
compensation network R2C3C4. Low-pass filter R3C1 is used to reduce parasitic HF components in the
comparator (IC MAX942) non-inverting pin input voltage. R3 in our experiments was equal to 8.6 kΩ. C2 is
used to limit duty ratio at start. Resistor R4 is used to regulate Δfsw. IC AD633 is analog signal multiplier and
summer which is used to implement the hybrid modulation. Voltage Vref is a reference voltage. To disable
SFM, the generator Instek should be turned off. If single pole double throw switch (Sw1) is in “up” position,
then hybrid modulation is enabled, otherwise it is disabled (if Sw1 is in “down” position only switching
frequency is modulated). It should be noted that the proposed control technique can also be implemented
digitally using e.g. a microcontroller with suitable program code. This implementation is recommended.
3.2. Experimental results and discussion
Initially the boost SMPC was examined when SFM was disabled. Output voltage waveform, input
current waveform and conducted EMI levels of unmodulated boost SMPC (with Vin=12 V) operating in DCM
are depicted in Figure 7 a, Figure 8 a and Figure 9 a. Then the experimental boost SMPC with SFM enabled
was tested. The results (when fm = 9.5 kHz, fsw0 =100 kHz, Δfsw=30 kHz, m(t) is sine, Vin=12 V, Rload=100 Ω,
fcross is of several kHz) of the measurements are shown in Figure 7 b, Figure 8 b and Figure 9 a. As it can be
seen SFM along with noticeable reduction of conducted EMI levels leads to significant increase in peak-to-
peak output ripple voltage and peak inductor current. As shown in Table 3 SFM leads to percentage increase
in peak-to-peak output voltage as high as 70.1 % and percentage increase in peak inductor current as high as
42.1 %. However after applying the proposed control method based on hybrid modulation (with A≈0.3),
peak-to-peak output voltage and peak inductor current decreased significantly as shown in Figure 7 c and
Figure 8 c respectively. Along with high reduction of peak-to-peak output voltage and peak inductor current,
reduction of the most dominant harmonic in conducted EMI spectrum is almost the same as in case when
conventional control scheme (in which switching frequency is modulated only) is used (see Figure 9 b).
Table 3. Comparison of the experimental results (fm=9.5 kHz, fsw0 =100 kHz, Δfsw=30 kHz; m(t) is sine;
Vin=12 V; Rload=100 Ω; fcross is of several kHz)
boost SMPC without
SFM boost SMPC with SFM
boost SMPC with the
proposed control technique
based on hybrid modulation
peak-to-peak output
voltage, mV
percentage increase in
peak-to-peak output
voltage (in comparison to
SMPC without SFM)
peak inductor current, A
87
---
1.78
148
70.1 %
2.53
95
9.2 %
1.86
percentage increase in
peak inductor current (in
comparison to SMPC
without SFM)
--- 42.1 % 4.5 %

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(a)
(b)
(c)
Figure 7. Experimental output voltage waveforms of boost SMPC in DCM: (a) for boost SMPC without
SFM; (b) for boost SMPC with SFM only; (c) for boost SMPC with the hybrid-modulation-based technique.
(Scale: 20mV/div; 20μs/div)

1281
(a)
(b)
(c)
Figure 8. Experimental inductor current waveforms of boost SMPC in DCM: (a) for boost SMPC without
SFM; (b) for boost SMPC with SFM only; (c) for boost SMPC with the hybrid-modulation-based technique.
(Scale: 1.11A/div; 20μs/div)

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(a) (b)
Figure 9. Experimental conducted EMI spectra of boost SMPC in DCM. Parameters: fm=9.5 kHz, fsw0 =100 kHz,
Δfsw=30 kHz; m(t) is sine; Vin=12 V. Note that the spectra were measured using a spectrum analyzer Agilent E4402B with
RBW=9 kHz and self-made line impedance stabilization network (see Figure 10) in frequency range 180 kHz – 30 MHz
Llisn
100 μH
Clisn
2.2 μF
to DC
voltage
source
to a spectrum analyzer
with 50 Ω input impedance
to DC/DC
converter
under test
Figure 10. Self-made line impedance stabilization network (LISN) schematic diagram used in the
experiments. Note: 1) the self-made LISN is not standard specific device; 2) the spectrum analyzer used in
the measurements was connected to the LISN via coaxial cable with length of 9.5 cm and parasitic
capacitance of 10.8 pF
Measurements of peak-to-peak output voltage, peak inductor current and conducted emissions levels
for other values of Δfsw, input voltages (8 V – 14 V) and output loads showed that the proposed control
technique based on the hybrid modulation is very effective too. Measurements of efficiency of the boost
SMPC showed that there is no any noticeable deteriorations of the efficiency when the proposed control
technique is used. A comparison of the performance characteristics of SMPC with different control
techniques is shown in Table 4.
Table 4. Comparison of the performance characteristics of SMPC with different control techniques
Conventional SMPC
without SFM SMPC with SFM
SMPC with the proposed
control technique based on
hybrid modulation
Peak-to-peak output voltage
Conducted emissions levels
Peak power components
currents
+
(the smallest)
-
(the highest)
+
(the smallest)
-
(the highest)
+
(appreciably lower than for
conventional SMPC without
SFM)
-
(the highest)
+
(slightly higher than for
conventional SMPC without SFM)
+
(appreciably lower than for
+
(slightly higher than for
0.00E+00
1.00E+01
2.00E+01
3.00E+01
4.00E+01
5.00E+01
6.00E+01
7.00E+01
8.00E+01
9.00E+01
1.80E+05 1.80E+06 1.80E+07
frequency (Hz)
conducted
EMI
level
(dBμV)
SMPC without SFM
SFM SMPC with conventional
control technique
0.00E+00
1.00E+01
2.00E+01
3.00E+01
4.00E+01
5.00E+01
6.00E+01
7.00E+01
8.00E+01
9.00E+01
1.80E+05 1.80E+06 1.80E+07
conducted
EMI
level
(dBμV)
frequency (Hz)
SMPC without SFM
SFM SMPC with proposed
control technique

1283
4. CONCLUSION
The proposed control technique based on hybrid modulation scheme in which both switching
frequency and duty ratio are simultaneously modulated by the same modulation signal is effective technique
which can be applied to single-switch switch-mode power converters with classical topologies to reduce
peak-to-peak output voltage and peak currents increased due to the use of conventional control scheme in
which only switching frequency is modulated. Both computer simulations and experiments show that
switching-frequency-modulated switch-mode power converter with the proposed control technique in
comparison to that without switching frequency modulation has appreciably lower conducted
electromagnetic interference levels, at the cost of slightly increased peak-to-peak output voltage and peak
currents.
The proposed control technique based on the hybrid modulation has some limitations. Firstly, it is
very useful to reduce peak-to-peak output voltage and peak currents significantly only when modulation
frequency is higher than the open loop gain crossover frequency. For modulation frequencies lower than the
crossover frequency this technique is much less effective. Secondly, it is very useful to reduce peak-to-peak
output voltage significantly only when output capacitor with capacitive reactance much lower than equivalent
series resistance is used (as in case of output electrolytic capacitor).The technique proposed is less effective
to reduce peak-to-peak output voltage when output capacitor with capacitive reactance much higher than
equivalent series resistance is used (as in case of output ceramic capacitor). However, peak currents can be
reduced as effectively as in case when electrolytic capacitors are used at output of SMPC.
ACKNOWLEDGEMENTS
Support for this work was provided by the Riga Technical University through the Scientific
Research Project Competition for Young Researchers No. ZP-2017/6.
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BIOGRAPHIES OF AUTHORS
Deniss Stepins received the B.Sc., M.Sc. (with honors) and Dr.Sc.ing degrees in electronics from
Riga Technical University, Riga, Latvia, in 2004, 2006 and 2011 respectively. He is currently a
senior researcher and assistant professor in the Department of Electronics and
Telecommunications, Riga Technical University. He is an author or co-author of more than 40
research papers. His research interests include EMI reduction techniques applied to switching
power converters, control of switch-mode power supplies and power factor correction. He is
currently IEEE member.
Jin Huang received the B.Sc. degree from Shanghai Jiaotong University, Shanghai, China, in
1992, and the M.Sc. and Ph.D. degrees from the Huazhong University of Science and
Technology, Wuhan, China, in 2003 and 2009, respectively. In 2000, he joined Huazhong
University of Science and Technology as a Lecturer. He is currently an Associate Professor in
the School of Electrical and Electronic Engineering. His research interests include the control
technique, EMC and reliability of power electronics devices.
Janis Audze received the B.Sc. and M.Sc. degrees in electronics from Riga Technical University,
Riga, Latvia, in 2008 and 2010 respectively. He is currently pursuing a PhD degree in the
Department of Electronics and Telecommunications, Riga Technical University, Latvia. His PhD
thesis is devoted to wireless power transfer technology and is supervised by Dr. D. Stepins. His
research interests include wireless power transfer, resonant converters and novel PCB design
techniques.

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