Canavero, Flavio

Maio, Ivano Adolfo

Tarateeraseth, V.

English

PORTO Publications Open Repository TOrino

Assessment of Equivalent Noise Source Approach
for EMI Simulations of Boost Converter
Vuttipon Tarateeraseth
1, Ivan A. Maio
2, Flavio G. Canavero
3
Dipartimento di Elettronica, Politecnico di Torino
Corso Duca degli Abruzzi 24, 10129, Torino, Italy
1vuttipon.tarateeraseth@polito.it
2maio@polito.it
3flavio.canavero@polito.it
Abstract—This paper presents the analytical equations to
model the equivalent noise source for conducted EMI simulation
in the frequency domain. The continuous conduction mode boost
converter is modeled. By means of a test case, it is shown that
the equivalent noise source provides a reasonable estimate of the
switching waveform and a good estimate of the EMI noise.
I. INTRODUCTION
Nowadays, the use of power electronics is widespread,
because there are signiﬁcant beneﬁts in both reduction of
physical sizes and efﬁciency. However, power electronics in-
crease the conducted electromagnetic interference (EMI). The
conducted EMI is generated by the high frequencies inherent
in fast-transition voltage and current waveforms [1]. Prior re-
search has recommended several ways to predict the conducted
EMI [5] - [7]. They can be categorized into two approaches:
time domain and frequency domain approaches. The frequency
domain approach is preferable because it requires shorten
simulation time and has no convergence problem. However,
equivalent noise sources are demanded to replace the switching
elements of the circuits. In order to represent the switching
elements, the waveform of the equivalent noise source has to
be as similar as possible to the switching waveform. The error
depends on the waveshape and parameters of the equivalent
noise source.
In this paper, we apply the frequency domain method to
the analysis of a boost converter circuit. The equivalent noise
source required by the method is estimated by means of
analytic relations. The accuracy of the approach is veriﬁed by
comparison to time domain simulations and measurements.
II. DEFINITION OF THE TEST CASE
The layout of boost converter involved in the comparison of
this paper is shown in Fig. 1. This layout has been designed to
validate the modeling of the noise path. The converter operates
at f0 =4 0kHz with 45% duty cycle; its input voltage is
Vin =2 0Vdc and is applied through a Line Impedance
Stabilization Network (LISN). The converter is composed of:
load resistor (300 Ω), boost inductor (Lboost = 470 μH,
Rlp =1 .3Ωand Clp =2 7pF), output capacitor (Lcp =
25 nH,C o = 470 μF,ESR = 280 mΩ), diode (BYW77P-
220) and MOSFET (IRFP250N). The parasitic elements of
boost L
o C o R
Zpcb1 Zpcb2 Zpcb4
Zpcb3
REFERENCE PLANE
28 mm
Fig. 1. Layout of boost converter
the boost inductor and the output capacitor are extracted from
their datasheets.
III. MODELING OF THE NOISE PATH
The modeling of Switched Mode Power Supply (SMPS)
can be divided into three parts: the noise sources (switching
elements: MOSFET and diode), the noise path (PCB traces
and passive components) and the LISN. This section deals
with the modeling of the noise path and the LISN for the test
case.
The structure of the noise path is illustrated by the elemental
schematic of Fig. 2, which shows the interconnection of the
LISN model and of a switched mode circuit containing one
switch only. The impedances of the elemental schematic repre-
sent the impedances of the connections of the switch terminals
to the line terminal (L,ZL), to the neutral terminal (N,ZN)
and to the reference terminal (ZLc and ZNc; the laboratory
reference plane is deﬁned as a perfect conductor). These
impedances take into account all possible galvanic and para-
sitic connection between the switch and the LISN terminals. In
our case, ZL is composed of the parasitic resistance (Rpcb) and
inductance (Lpcb) of PCB and boost inductor (Lboost), with its
parasitic resistance (Rlp) and parasitic capacitance (Clp). ZN
is composed of the parasitic resistance and inductance of PCB.
According to the fact that Rlp  
 
Rpcb, Lboost  
 
Lpcb
and ZL   ZN, the Rpcb and Lpcb have a minor effect on
both differential mode (DM) and common mode (CM) noise
predictions and are ignored.
353
Proceedings, 20th Int. Zurich Symposium on EMC, Zurich 2009VL
VN
L
N
ZL
ZN
ZLc
ZNc
SW
I
Fig. 2. Elemental schematic describing the conversion of the switch current
into noise signal detected at the LISN
In contrast, ZLc and ZNc, which have a capacitive nature,
play an important role to determine the common mode noise.
The per-unit-length capacitance (pF/in) of straight traces over
a reference plane at distance (h) can be analytically estimated
by (1). The validity of this formula is 0.1 < w
h < 3.0 and
1 <  r < 15 [3].
Cpcb =
0.67( r +1 .41)
ln
 
5.98h
0.8w+t
  (1)
The traces of the PCB of the test case are 15 mm wide and
28 mm above the reference plane. The w
h ratio is 0.5; that is
in the validity range of Eq. (1). The passive components of
the test circuit are modeled by the HF equivalent circuits [1].
The self resonant frequency of boost inductor (frl) is used
to estimate the parallel parasitic capacitance which can be
expressed as Clp =1 /[Lboost(2πfrl)2]. The LISN is modeled
by its schematic (see Fig. 3). In order to implement this
schematic in SPICE, Rdum ≥ 100MΩ is added to prevent
ﬂoating nodes by providing dc paths to ground [4].
IV. FREQUENCY DOMAIN SIMULATION METHOD
In order to carry out a frequency domain analysis of an
SMPS the non-linear and time-varying elements (e.g. MOS-
FET and diode for a simple boost converter) of the circuit
must be somehow replaced by linear elements. If the voltage or
current waveforms of the unwanted elements are known, then
the substitution theorem can be applied [2], making the circuit
compatible with a frequency domain analysis. According to the
theorem, the branch of a switching element (e.g. MOSFET)
can be replaced by either one independent voltage or current
source impressing waveforms identical to the original branch
voltage and current, respectively. The problem is then how to
obtain a reasonable estimate of the switch waveforms without
carrying out measurement or a time-domain analysis. The
voltage waveform across the switch depends on the operation
mode of the converter. The waveforms of the discontinuous
conduction mode (DCM) case are complicated and are not
addressed in this paper. For the continuous conduction mode
(CCM) case, the voltage across MOSFET or current passing
though it is in the form of trapezoid. The choice between using
trapezoidal voltage or current source as a noise source depends
on the converter topology. For buck converters and three phase
inverters [6], the trapezoidal current source is applied when
analyzing the DM noise and the trapezoidal voltage source is
utilized for the CM noise. For boost converter type, the main
disturbance sources of CM and DM are represented by the
voltage across the MOSFET switch [7]. Moreover, to simplify
the analysis, the diode recovery effect is not taken into account.
In order to estimate the parameters of the noise source, we
exploit the analytic relations of [8] as discussed in the next
subsection.
A. Equivalent Noise Source
The one-sided spectrum of a trapezoidal periodic waveform
with tr  = tf is:
C
+
tra(s)=
2
T
(
Vsw
s2 )
 
1
tr
 
1 − e−str 
(2)
−
1
tf
 
e−s(toff+tr) − e−s(toff+tr+tf)
  
where
s = jnω0 {n =1 ,2,...}
tr = Time taken for the voltage to rise to its off-state
value during the turn-off transient [s]
tf = Time taken for the voltage to fall to its on-state
value during the turn-on transient [s]
toff = Off state of the switch [s]
T =
2π
ω0
= Switching period [s]
The parameter Vsw is the amplitude of the voltage waveform
across the MOSFET. Vsw depends on the type of converter. In
this paper,the CCM boost converter is investigated and Vsw is
given by Eq. (3).
Vsw = VDS =
Vin
1 − D
(3)
where
Vin = Input voltage [V]
D = Duty cycle
=[ toff + tr + tf]/T
According to [8], the tr, tf and toff of voltage across
MOSFET are estimated by using Eqs. (4) - (6), respectively.
tr =
Qgd d(Rg + Rg app)
Vgp
(4)
tf =
Qgd d(Rg + Rg app)
VGS app − Vgp
(5)
toff = tg off +( Rg + Rg app)(C
@Vds
iss ) (6)
·ln
⎛
⎝ Vgp
VGS(th)
 
1 −
Vgp
VGS app
 
⎞
⎠
354
Proceedings, 20th Int. Zurich Symposium on EMC, Zurich 2009where
Vgp = Gate plateau voltage [V]
VGS(th) = Gate threshold voltage [V]
VGS app = Applying gate source voltage [V]
Qgd d = Gate drain charge speciﬁed in datasheet [C]
C
@Vds
iss = Input capacitance at appropriate Vds[F]
Rg = Gate resistance internal of MOSFET[Ω]
Rg app = Resistance applied to gate of MOSFET[Ω]
tg off = Off period of gate drive voltage [s]
The numerical data of these equations are retrieved from
MOSFET’s datasheet, thereby obtaining the equivalent noise
sources without measurement or simulation.
V. OUTPUT NOISE
The model of the test case that has been developed in section
III is shown in Fig. 3. In order to check the accuracy of this
model, the transient analysis is carried out by SPICE. The
noise spectra are computed via Fast Fourier Transform (FFT)
by using the following simulation settings. These settings
guarantee the correct evaluation of the spectra in the 50 kHz
bandwidth and 30 MHz sweep range.
According to the Nyquist criterion, the printing increment
is about Tstep ≤ 1/(2fmax) ≤ 16.66 ns to reach the upper
frequency of conducted EMI (30 MHz). The maximum time
step is about Tmax = Tstep/2 ∼ = 8.33 ns to prevent aliasing
problem. To obtain 50 kHz bandwidth, the difference between
Tstart and Tstop is about BW =1 /fBW =2 0μs [5].
Lboost 250 uH 50 uH
250 uH 50 uH
4 uF
10 Ω 5 50
10 5 50
8 uF 0.25 uF
4 uF 8 uF 0.25 uF
NOISE SOURCE/PATH LISN: CISPR 16-1
ESR
Lcp
Co
Ro
Clp
Rlp
Vin
Rdum
Rdum
Ω
Ω
Ω
Ω
Ω
GROUND PLANE
Cpcb1 Cpcb3 Cpcb2 Cpcb4
Fig. 3. Modeling for time domain simulation
The accuracy of the model is assessed by comparing its
responses to the measurements of the actual voltage across the
MOSFET and the voltages across LISN at line-ground (vLG)
and neutral-ground (vNG) terminals. The vLG and vNG are
measured by a digital oscilloscope with sampling rate fs =
250 MS/s and number of samples N = 5002; the bandwidth
of measurement settings is BW = fs/N =5 0kHz [9]. The
measured DM and CM noise voltages are calculated by Eqs.
(7) - (8); the Discrete Fourier Transforms (DFT) of DM and
CM noise voltages are computed off-line by using MATLAB.
Lboost 250 uH 50 uH
250 uH 50 uH
4 uF
10 Ω 5 50
10 5 50
8 uF 0.25 uF
4 uF 8 uF 0.25 uF
NOISE SOURCE/PATH LISN: CISPR 16-1
Clp
Rlp
Rdum
Rdum
Ω
Ω
Ω
Ω
Ω
GROUND PLANE
Cpcb1 Cpcb3 Cpcb2
toff
on off
tr
T t
tf
Amplitude
Vsw
() tra Cs
+
Fig. 4. Simpliﬁed equivalent circuit for frequency domain simulation
TABLE I
COMPARISON AMONG THE EXPERIMENT, SIMULATION AND ANALYTICAL
CALCULATION
Measured Result Simulated Result Analytical Prediction1
tr (ns) 76 76 81.6
tf (ns) 44 54 40.8
toff (μs) 12.86 12.91 12.89
1IRF250P datasheet: Qgd d@40Vds  30 nC, Ciss@40Vds  2200 pF,
VGS app =1 5V, Rg app =1 0Ω , Rg =3 .6Ω(from SPICE),
VGS(th) =4V, Vgp  5 V
vdm(t)=
vLG(t) − vNG(t)
2
(7)
vcm(t)=
vLG(t)+vNG(t)
2
(8)
The equivalent noise source deﬁned in section IV is veriﬁed
by comparing it to the measured and simulated waveforms
of the voltage across MOSFET terminals; i.e. time domain
simulation and analytical prediction of VDS are compared. As
shown in Table I and Fig. 5, the estimated equivalent source
is pretty close to the actual switch waveform. To validate the
model in terms of conducted EMI, the DM and CM noise pre-
dictions in the frequency range 150 kHz - 30 MHz computed
by time domain approach are compared to the measurement
as shown in Fig 6. The model provides a good agreement for
DM noise prediction, but not for CM noise prediction. For
CM noise, the difference may be caused by lack of dominant
common mode noise paths. Furthermore, the overestimation
of the parasitic parameter of passive components might affect
to the difference in high frequency of both DM and CM noise
spectrum [6].
In order to estimate the error introduced by the frequency
domain approach, the same model of the test case used in
time domain approach is applied. However, the MOSFET is
replaced by the equivalent noise source. As indicated by the
voltage shift theorem [2], some components (diode, output
capacitor, Cpcb4, load resistor) can be ignored as shown in Fig.
355
Proceedings, 20th Int. Zurich Symposium on EMC, Zurich 20092.1828 2.1828 2.1828 2.1829
x 10
−3
0
5
10
15
20
25
30
35
40
45
Comparison of rise time of Voltage across Drian−Source
V
D
S
 
[
V
]
Time [s]
Measured
Simulated
Predicted
(a) Comparison of tr of voltage across MOSFET
2.1956 2.1957 2.1957 2.1957 2.1958 2.1958 2.1959
x 10
−3
0
5
10
15
20
25
30
35
40
45
Comparison of fall time of Voltage across Drian−Source
V
D
S
 
[
V
]
Time [s]
Measured
Simulated
Predicted
(b) Comparison of tf of voltage across MOSFET
Fig. 5. Comparison of voltage across MOSFET (Drain-Source)
10
6
10
7 0
20
40
60
80
100
120
140
160
180
Differential mode noise comparison
D
M
 
n
o
i
s
e
 
[
d
B
u
V
]
Frequency [Hz]
Measurement
t−domain simulation
f−domain simulation
(a) Differential mode noise comparison
10
6
10
7 0
20
40
60
80
100
120
140
160
180
Commond mode noise comparison
C
M
 
n
o
i
s
e
 
[
d
B
u
V
]
Frequency [Hz]
Measurement
t−domain simulation
f−domain simulation
(b) Common mode noise comparison
Fig. 6. Conducted EMI comparison
4. For the SPICE implementation, the ac analysis in SPICE
(sweeping frequency from 150 kHz - 30 MHz) is applied. The
equivalent noise source is represented by a voltage-controlled
voltage source (Elaplace) in Laplace form, following Eq. (2).
Elaplace is excited by ac voltage source (1 Vac). As illustrated
in Fig. 6, it is clear that the time domain and frequency
domain simulations are in a good agreement. Nevertheless,
the frequency domain approach provides shorter simulation
times and eliminates the convergence problems.
VI. CONCLUSIONS
This paper has shown that the equivalent noise source
for conducted EMI simulation of a continuous conduction
mode boost converter can be achieved by using the simple
generic equations and MOSFET’s datasheet. The accuracy of
equivalent noise source is veriﬁed by comparing the analytical
prediction of voltage across MOSFET to the time domain
simulation and the measurements. The good approximation
by using analytical approach is demonstrated. For conducted
EMI prediction, it is shown that both simulation approaches
are in a good agreement, yet the frequency domain approach
offers shorter simulation times and is free from convergence
problems. The equivalent noise source has been proven to be
accurate and efﬁcient enough for the conducted EMI prediction
in single-switch DC-DC converters working in continuous
conduction mode.
REFERENCES
[1] Clayton R. Paul, Introduction to Electromagnetic Compatibility, John
Wiley & Sons, second edition, 2006.
[2] D.L. Skaar and W.L. Brown,“Emphasizing some little-used theorems
in introductory network analysis,” IEEE Trans. Educ., Vol. 39, N. 4,
Nov 1996, pp. 532–539.
[3] IPC, Design Guide for Electronic Packaging Utilizing High-Speed
Techniques, IPC-2251, 2001.
[4] Muhammad H. Rashid, SPICE for Power Electronics and Electric
Power, 2nd edition, CRC Press, 2005.
[5] Christophe P. Basso, Switch-Mode Power Supply SPICE Cookbook,
McGraw-Hill, 2001.
[6] Jih-Sheng Lai, Xudong Huang, Pepa, E., Shaotang Chen and Nehl,
T.W.,“Inverter EMI modeling and simulation methodologies,” IEEE
Trans. Ind. Electron., Vol. 53, N. 3, June 2006, pp. 736–744.
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study in boost derived PFC rectiﬁers,” 30th Annual IEEE Power Elec-
tronics Specialists Conference, Vol. 2, 1999, pp. 855–860.
[8] Jess Brown, “Modeling the Switching Performance of a MOSFET in
the High Side of a Non-Isolated Buck Converter,” IEEE Trans. Power
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[9] Yuang-Shung Lee, Yu-Lin Liang, and Ming-Wang Cheng, “Time Do-
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Proceedings, 20th Int. Zurich Symposium on EMC, Zurich 2009

A new method for EMI study in boost derived

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Shaotang Chen and Nehl, T.W.,“Inverter EMI modeling and simulation methodologies,”

SPICE for Power Electronics and Electric Power, 2nd edition,

Switch-Mode Power Supply SPICE Cookbook,

Time Domain Measurement System for Conducted

Assessment of Equivalent Noise Source Approach for EMI Simulations of Boost Converter

Tarateeraseth V.

MAIO, Ivano Adolfo

CANAVERO, Flavio

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

30 November 2022POLITECNICO DI TORINORepository ISTITUZIONALEAssessment of Equivalent Noise Source Approach for EMI Simulations of Boost Converter / Tarateeraseth, V.; Maio,Ivano Adolfo; Canavero, Flavio. - STAMPA. - (2009), pp. 353-356. ((Intervento presentato al convegno 20th InternationalZurich Symposium on Electromagnetic Compatibility tenutosi a Zurich (Switzerland) nel Jan. 12-16, 2009[10.1109/EMCZUR.2009.4783463].OriginalAssessment of Equivalent Noise Source Approach for EMI Simulations of Boost ConverterPublisher:PublishedDOI:10.1109/EMCZUR.2009.4783463Terms of use:openAccessPublisher copyright(Article begins on next page)This article is made available under terms and conditions as specified in the  corresponding bibliographic description inthe repositoryAvailability:This version is available at: 11583/1899600 since:IEEEAssessment of Equivalent Noise Source Approachfor EMI Simulations of Boost ConverterVuttipon Tarateeraseth 1, Ivan A. Maio 2, Flavio G. Canavero 3Dipartimento di Elettronica, Politecnico di TorinoCorso Duca degli Abruzzi 24, 10129, Torino, Italy1vuttipon.tarateeraseth@polito.it2maio@polito.it3flavio.canavero@polito.itAbstract—This paper presents the analytical equations tomodel the equivalent noise source for conducted EMI simulationin the frequency domain. The continuous conduction mode boostconverter is modeled. By means of a test case, it is shown thatthe equivalent noise source provides a reasonable estimate of theswitching waveform and a good estimate of the EMI noise.I. INTRODUCTIONNowadays, the use of power electronics is widespread,because there are significant benefits in both reduction ofphysical sizes and efficiency. However, power electronics in-crease the conducted electromagnetic interference (EMI). Theconducted EMI is generated by the high frequencies inherentin fast-transition voltage and current waveforms [1]. Prior re-search has recommended several ways to predict the conductedEMI [5] - [7]. They can be categorized into two approaches:time domain and frequency domain approaches. The frequencydomain approach is preferable because it requires shortensimulation time and has no convergence problem. However,equivalent noise sources are demanded to replace the switchingelements of the circuits. In order to represent the switchingelements, the waveform of the equivalent noise source has tobe as similar as possible to the switching waveform. The errordepends on the waveshape and parameters of the equivalentnoise source.In this paper, we apply the frequency domain method tothe analysis of a boost converter circuit. The equivalent noisesource required by the method is estimated by means ofanalytic relations. The accuracy of the approach is verified bycomparison to time domain simulations and measurements.II. DEFINITION OF THE TEST CASEThe layout of boost converter involved in the comparison ofthis paper is shown in Fig. 1. This layout has been designed tovalidate the modeling of the noise path. The converter operatesat f0 = 40 kHz with 45% duty cycle; its input voltage isVin = 20 Vdc and is applied through a Line ImpedanceStabilization Network (LISN). The converter is composed of:load resistor (300 Ω), boost inductor (Lboost = 470 μH,Rlp = 1.3 Ω and Clp = 27 pF), output capacitor (Lcp =25 nH, Co = 470 μF, ESR = 280 mΩ), diode (BYW77P-220) and MOSFET (IRFP250N). The parasitic elements ofboostLoC oRZpcb1 Zpcb2 Zpcb4Zpcb3REFERENCE PLANE28 mmFig. 1. Layout of boost converterthe boost inductor and the output capacitor are extracted fromtheir datasheets.III. MODELING OF THE NOISE PATHThe modeling of Switched Mode Power Supply (SMPS)can be divided into three parts: the noise sources (switchingelements: MOSFET and diode), the noise path (PCB tracesand passive components) and the LISN. This section dealswith the modeling of the noise path and the LISN for the testcase.The structure of the noise path is illustrated by the elementalschematic of Fig. 2, which shows the interconnection of theLISN model and of a switched mode circuit containing oneswitch only. The impedances of the elemental schematic repre-sent the impedances of the connections of the switch terminalsto the line terminal (L,ZL), to the neutral terminal (N, ZN )and to the reference terminal (ZLc and ZNc; the laboratoryreference plane is defined as a perfect conductor). Theseimpedances take into account all possible galvanic and para-sitic connection between the switch and the LISN terminals. Inour case, ZL is composed of the parasitic resistance (Rpcb) andinductance (Lpcb) of PCB and boost inductor (Lboost), with itsparasitic resistance (Rlp) and parasitic capacitance (Clp). ZNis composed of the parasitic resistance and inductance of PCB.According to the fact that Rlp ∑Rpcb, Lboost ∑Lpcband ZL  ZN , the Rpcb and Lpcb have a minor effect onboth differential mode (DM) and common mode (CM) noisepredictions and are ignored.353Proceedings, 20th Int. Zurich Symposium on EMC, Zurich 2009VLVNLNZLZNZLcZNcSWIFig. 2. Elemental schematic describing the conversion of the switch currentinto noise signal detected at the LISNIn contrast, ZLc and ZNc, which have a capacitive nature,play an important role to determine the common mode noise.The per-unit-length capacitance (pF/in) of straight traces overa reference plane at distance (h) can be analytically estimatedby (1). The validity of this formula is 0.1 < wh < 3.0 and1 < εr < 15 [3].Cpcb =0.67(εr + 1.41)ln(5.98h0.8w+t) (1)The traces of the PCB of the test case are 15 mm wide and28 mm above the reference plane. The wh ratio is 0.5; that isin the validity range of Eq. (1). The passive components ofthe test circuit are modeled by the HF equivalent circuits [1].The self resonant frequency of boost inductor (frl) is usedto estimate the parallel parasitic capacitance which can beexpressed as Clp = 1/[Lboost(2πfrl)2]. The LISN is modeledby its schematic (see Fig. 3). In order to implement thisschematic in SPICE, Rdum ≥ 100MΩ is added to preventfloating nodes by providing dc paths to ground [4].IV. FREQUENCY DOMAIN SIMULATION METHODIn order to carry out a frequency domain analysis of anSMPS the non-linear and time-varying elements (e.g. MOS-FET and diode for a simple boost converter) of the circuitmust be somehow replaced by linear elements. If the voltage orcurrent waveforms of the unwanted elements are known, thenthe substitution theorem can be applied [2], making the circuitcompatible with a frequency domain analysis. According to thetheorem, the branch of a switching element (e.g. MOSFET)can be replaced by either one independent voltage or currentsource impressing waveforms identical to the original branchvoltage and current, respectively. The problem is then how toobtain a reasonable estimate of the switch waveforms withoutcarrying out measurement or a time-domain analysis. Thevoltage waveform across the switch depends on the operationmode of the converter. The waveforms of the discontinuousconduction mode (DCM) case are complicated and are notaddressed in this paper. For the continuous conduction mode(CCM) case, the voltage across MOSFET or current passingthough it is in the form of trapezoid. The choice between usingtrapezoidal voltage or current source as a noise source dependson the converter topology. For buck converters and three phaseinverters [6], the trapezoidal current source is applied whenanalyzing the DM noise and the trapezoidal voltage source isutilized for the CM noise. For boost converter type, the maindisturbance sources of CM and DM are represented by thevoltage across the MOSFET switch [7]. Moreover, to simplifythe analysis, the diode recovery effect is not taken into account.In order to estimate the parameters of the noise source, weexploit the analytic relations of [8] as discussed in the nextsubsection.A. Equivalent Noise SourceThe one-sided spectrum of a trapezoidal periodic waveformwith tr = tf is:C+tra(s) =2T(Vsws2)[1tr(1 − e−str) (2)− 1tf(e−s(toff +tr) − e−s(toff+tr+tf ))]wheres = jnω0 {n = 1, 2, . . .}tr = Time taken for the voltage to rise to its off-statevalue during the turn-off transient [s]tf = Time taken for the voltage to fall to its on-statevalue during the turn-on transient [s]toff = Off state of the switch [s]T =2πω0= Switching period [s]The parameter Vsw is the amplitude of the voltage waveformacross the MOSFET. Vsw depends on the type of converter. Inthis paper,the CCM boost converter is investigated and Vsw isgiven by Eq. (3).Vsw = VDS =Vin1 − D (3)whereVin = Input voltage [V]D = Duty cycle= [toff + tr + tf ]/TAccording to [8], the tr, tf and toff of voltage acrossMOSFET are estimated by using Eqs. (4) - (6), respectively.tr =Qgd d(Rg + Rg app)Vgp(4)tf =Qgd d(Rg + Rg app)VGS app − Vgp (5)toff = tg off + (Rg + Rg app)(C@Vdsiss ) (6)· ln⎛⎝ VgpVGS(th)[1 − VgpVGS app]⎞⎠354Proceedings, 20th Int. Zurich Symposium on EMC, Zurich 2009whereVgp = Gate plateau voltage [V]VGS(th) = Gate threshold voltage [V]VGS app = Applying gate source voltage [V]Qgd d = Gate drain charge specified in datasheet [C]C@Vdsiss = Input capacitance at appropriate Vds[F]Rg = Gate resistance internal of MOSFET[Ω]Rg app = Resistance applied to gate of MOSFET[Ω]tg off = Off period of gate drive voltage [s]The numerical data of these equations are retrieved fromMOSFET’s datasheet, thereby obtaining the equivalent noisesources without measurement or simulation.V. OUTPUT NOISEThe model of the test case that has been developed in sectionIII is shown in Fig. 3. In order to check the accuracy of thismodel, the transient analysis is carried out by SPICE. Thenoise spectra are computed via Fast Fourier Transform (FFT)by using the following simulation settings. These settingsguarantee the correct evaluation of the spectra in the 50 kHzbandwidth and 30 MHz sweep range.According to the Nyquist criterion, the printing incrementis about Tstep ≤ 1/(2fmax) ≤ 16.66 ns to reach the upperfrequency of conducted EMI (30 MHz). The maximum timestep is about Tmax = Tstep/2 ∼= 8.33 ns to prevent aliasingproblem. To obtain 50 kHz bandwidth, the difference betweenTstart and Tstop is about BW = 1/fBW = 20 μs [5].Lboost250 uH 50 uH250 uH 50 uH4 uF10 Ω 5 5010 5 508 uF 0.25 uF4 uF 8 uF 0.25 uFNOISE SOURCE/PATHLISN: CISPR 16-1ESRLcpCoRoClpRlpVinRdumRdumΩΩΩΩΩGROUND PLANECpcb1 Cpcb3 Cpcb2 Cpcb4Fig. 3. Modeling for time domain simulationThe accuracy of the model is assessed by comparing itsresponses to the measurements of the actual voltage across theMOSFET and the voltages across LISN at line-ground (vLG)and neutral-ground (vNG) terminals. The vLG and vNG aremeasured by a digital oscilloscope with sampling rate fs =250 MS/s and number of samples N = 5002; the bandwidthof measurement settings is BW = fs/N = 50 kHz [9]. Themeasured DM and CM noise voltages are calculated by Eqs.(7) - (8); the Discrete Fourier Transforms (DFT) of DM andCM noise voltages are computed off-line by using MATLAB.Lboost250 uH 50 uH250 uH 50 uH4 uF10 Ω 5 5010 5 508 uF 0.25 uF4 uF 8 uF 0.25 uFNOISE SOURCE/PATHLISN: CISPR 16-1ClpRlpRdumRdumΩΩΩΩΩGROUND PLANECpcb1 Cpcb3 Cpcb2toffonofftrT ttfAmplitudeVsw( )traC s+Fig. 4. Simplified equivalent circuit for frequency domain simulationTABLE ICOMPARISON AMONG THE EXPERIMENT, SIMULATION AND ANALYTICALCALCULATIONMeasured Result Simulated Result Analytical Prediction1tr (ns) 76 76 81.6tf (ns) 44 54 40.8toff (μs) 12.86 12.91 12.891IRF250P datasheet: Qgd d@40Vds  30 nC, Ciss@40Vds  2200 pF,VGS app = 15 V, Rg app = 10 Ω, Rg = 3.6 Ω (from SPICE),VGS(th) = 4 V, Vgp  5 Vvdm(t) =vLG(t) − vNG(t)2(7)vcm(t) =vLG(t) + vNG(t)2(8)The equivalent noise source defined in section IV is verifiedby comparing it to the measured and simulated waveformsof the voltage across MOSFET terminals; i.e. time domainsimulation and analytical prediction of VDS are compared. Asshown in Table I and Fig. 5, the estimated equivalent sourceis pretty close to the actual switch waveform. To validate themodel in terms of conducted EMI, the DM and CM noise pre-dictions in the frequency range 150 kHz - 30 MHz computedby time domain approach are compared to the measurementas shown in Fig 6. The model provides a good agreement forDM noise prediction, but not for CM noise prediction. ForCM noise, the difference may be caused by lack of dominantcommon mode noise paths. Furthermore, the overestimationof the parasitic parameter of passive components might affectto the difference in high frequency of both DM and CM noisespectrum [6].In order to estimate the error introduced by the frequencydomain approach, the same model of the test case used intime domain approach is applied. However, the MOSFET isreplaced by the equivalent noise source. As indicated by thevoltage shift theorem [2], some components (diode, outputcapacitor, Cpcb4, load resistor) can be ignored as shown in Fig.355Proceedings, 20th Int. Zurich Symposium on EMC, Zurich 20092.1828 2.1828 2.1828 2.1829x 10−3051015202530354045Comparison of rise time of Voltage across Drian−SourceVDS [V]Time [s]MeasuredSimulatedPredicted(a) Comparison of tr of voltage across MOSFET2.1956 2.1957 2.1957 2.1957 2.1958 2.1958 2.1959x 10−3051015202530354045Comparison of fall time of Voltage across Drian−SourceVDS [V]Time [s]MeasuredSimulatedPredicted(b) Comparison of tf of voltage across MOSFETFig. 5. Comparison of voltage across MOSFET (Drain-Source)106 107020406080100120140160180Differential mode noise comparisonDM noise [dBuV]Frequency [Hz]Measurementt−domain simulationf−domain simulation(a) Differential mode noise comparison106 107020406080100120140160180Commond mode noise comparisonCM noise [dBuV]Frequency [Hz]Measurementt−domain simulationf−domain simulation(b) Common mode noise comparisonFig. 6. Conducted EMI comparison4. For the SPICE implementation, the ac analysis in SPICE(sweeping frequency from 150 kHz - 30 MHz) is applied. Theequivalent noise source is represented by a voltage-controlledvoltage source (Elaplace) in Laplace form, following Eq. (2).Elaplace is excited by ac voltage source (1 Vac). As illustratedin Fig. 6, it is clear that the time domain and frequencydomain simulations are in a good agreement. Nevertheless,the frequency domain approach provides shorter simulationtimes and eliminates the convergence problems.VI. CONCLUSIONSThis paper has shown that the equivalent noise sourcefor conducted EMI simulation of a continuous conductionmode boost converter can be achieved by using the simplegeneric equations and MOSFET’s datasheet. The accuracy ofequivalent noise source is verified by comparing the analyticalprediction of voltage across MOSFET to the time domainsimulation and the measurements. The good approximationby using analytical approach is demonstrated. For conductedEMI prediction, it is shown that both simulation approachesare in a good agreement, yet the frequency domain approachoffers shorter simulation times and is free from convergenceproblems. The equivalent noise source has been proven to beaccurate and efficient enough for the conducted EMI predictionin single-switch DC-DC converters working in continuousconduction mode.REFERENCES[1] Clayton R. Paul, Introduction to Electromagnetic Compatibility, JohnWiley & Sons, second edition, 2006.[2] D.L. Skaar and W.L. Brown,“Emphasizing some little-used theoremsin introductory network analysis,” IEEE Trans. Educ., Vol. 39, N. 4,Nov 1996, pp. 532–539.[3] IPC, Design Guide for Electronic Packaging Utilizing High-SpeedTechniques, IPC-2251, 2001.[4] Muhammad H. Rashid, SPICE for Power Electronics and ElectricPower, 2nd edition, CRC Press, 2005.[5] Christophe P. Basso, Switch-Mode Power Supply SPICE Cookbook,McGraw-Hill, 2001.[6] Jih-Sheng Lai, Xudong Huang, Pepa, E., Shaotang Chen and Nehl,T.W.,“Inverter EMI modeling and simulation methodologies,” IEEETrans. Ind. Electron., Vol. 53, N. 3, June 2006, pp. 736–744.[7] J.C. Crebier, M. Brunello and J.P. Ferrieux, “A new method for EMIstudy in boost derived PFC rectifiers,” 30th Annual IEEE Power Elec-tronics Specialists Conference, Vol. 2, 1999, pp. 855–860.[8] Jess Brown, “Modeling the Switching Performance of a MOSFET inthe High Side of a Non-Isolated Buck Converter,” IEEE Trans. PowerElectron., Vol. 21, N. 1, Jan 2006, pp. 3–10.[9] Yuang-Shung Lee, Yu-Lin Liang, and Ming-Wang Cheng, “Time Do-main Measurement System for Conducted EMI and CM/DM NoiseSignal Separation,” International Conference on Power Electronics andDrives System, Vol. 2, 2005, pp. 1640–1645.356Proceedings, 20th Int. Zurich Symposium on EMC, Zurich 2009

Assessment of Equivalent Noise Source Approach for EMI Simulations of Boost Converter

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