Planar electromagnetic interference (EMI) filters are widely used to restrain the conducted EMI of switching power supplies. Such filters are characterized by small size, low parasitic parameters, and better highfrequency performance than the passive discrete EMI filter. However, EMI filter performance cannot be exactly predicted by using existing methods. Therefore, this paper proposes a method to use scattering parameters (
S
parameters) for the measurement of EMI filter performance. A planar EMI filter sample is established. From this sample, the relationship between
S
parameters and insertion gain (
IG
) of EMI filter is derived. To determine the
IG
under different impedances, the EMI filter is theoretically calculated and practically measured. The differential structure of the nearfield coupling model is also deduced, and the
IG
is calculated under standard impedance conditions. The calculated results and actual measurements are compared to verify the feasibility of the theory.
I. INTRODUCTION
Electromagnetic interference (EMI) is a serious problem in the development of the switching power supply and affects the normal operation of the grid and surrounding equipment
[1]
. According to the different interference patterns, EMI can be classified into two forms: radiated and conducted emissions. The latter is the most serious concern in power electronic systems. To meet the EMC standard, an EMI filter is often used to attenuate the conducted EMI noise.
Fig. 1
shows a typical measurement setup.
Measurement setup.
Line impedance stabilization network (LISN) has been traditional used to determine the specified impedance over the working frequency range. In particular, noise can be measured when both source and load impedances are 50 Ω. An EMI filter is placed between LISN and the equipment under test (EUT), which is composed of the common mode (CM) and differential mode (DM) filters. In the EMI filter, the left DM capacitor
C
x bypasses most of the DM noise because of the low
C
x impedance. The remaining noise is blocked by the
L
_{DM}
, which is the leakage inductance of CM inductance. The right DM capacitor
C
x bypasses most of the remaining DM currents because of the high LISN impedance.
C
_{Y}
is the CM capacitor and
L
_{CM}
is CM inductance, which constitute the CM filter used to attenuate the CM noise.
A conventional EMI filter comprises up to onethird of converter volume and weight. . To reduce the size of passive components, an integration technology that implements multiple functions into one component is proposed. The development of integration technology has made integrated EMI filters an important means to reduce the volume and weight of the whole converter. Among these integrated EMI filters, the planar EMI filter is the focus of this study. Similar to the conventional EMI filter, the planar EMI filter is composed of the CM and DM parts
[2]

[4]
. The core component of the planar EMI filter is an annular
inductorcapacitor
unit. To analyze the performance of the planar EMI filter and EMI noise transmission,
S
parameters are employed
[5]
.
The performance of EMI filters is often evaluated on the basis of insertion gain (
IG
)
[6]
. However, matching state is difficult to achieve in both the source and load in practical implementations. Consequently, the EMI filter is also difficult to select on the basis of the
IG
curves given by manufacturers. Therefore, the selection of the source and load impedances is important. This selection significantly affects filter performance. Notably, failing to select the appropriate impedances will sometime magnify noise.
In the highfrequency range, the effect of nearfield coupling on the EMI filter is sometimes more severe than that of the parasitic parameters of components
[7]
. When the nearfield coupling effect of components is considered, parameter extraction becomes especially significant. Numerous extraction methods, such as the impedance and
S
parameter methods, can be selected. However, the impedance method cannot guarantee the ideal
shortcircuit
and
opencircuit
of the port, as well as the accuracy of branch and stray impedances, at high frequencies. Therefore, the Sparameter method is selected to extract the nearfield coupling parameters while avoiding the aforementioned problems
[8]
.
Several studies
[9]

[11]
have proposed methods to establish the highfrequency model on the basis of the impedance measurement method. However, ensuring that one end of the filter is a
short circuit
or
open circuit
is difficult under high frequency. In practice, model parameter accuracy is difficult to guarantee. More importantly, the existing models are unrelated, which causes problems attributed to the lack of coupling parameters. Compared with those of the filter composed of discrete components, the coupling parameters of a planar filter are more serious because all cells are integrated into a core. Therefore, the model established by using the impedance measurement method is insufficiently accurate when applied to a planar filter. For instance, literature
[12]
reveals that the actual insertion loss is obtained through the calculation of the minimum IL and coefficients. In fact, the IL proposed in
[12]
is the opposite of
IG
. However, numerous parameters are ignored in the calibration coefficient process, which causes low accuracy. Consequently, this approach has a certain application limitations.
Based on the above analysis,
S
parameters are used to measure the characteristics of the EMI filter in this study. Combining the reflection coefficients of the noise source with the load port enables the calculation of the filter
IG
. To establish a model with enhanced highfrequency characteristics,
S
parameters are used to measure and calculate the coupling parameters of the planar filter.
II. MEASUREMENT OF FILTER CHARACTERISTICS BY USING SPARAMETER
 A. Planar EMI Filter Structure
Applying the planar magnetic integration technology to the EMI filter and using a planar LC as a basic cell can realize the miniaturization of planar EMI filter. The basic principles of a planar EMI filter are similar to those of the discrete EMI filter (
Fig. 2
), both which contain the CM and DM parts. The CM module (
Fig. 3
) is formed by the LC unit composed of integrated inductance and capacitance. The planar LC unit uses a high dielectric constant ceramic as the substrate. Either side of the substrate is covered with one or more turns. The DM module is composed of DM capacitance and DM inductance. When the common mode choke is not wounded tightly, it will produce leakage inductance, that is DM mode inductors.
Structure of planar EMI filter.
Integrated unit of planar LC.
 B. SParameters
According to transmission line theory
[13]
, the normalized equivalent voltage and equivalent current at any
k
port reference surface for an
n
port network are as follows:
For port
k
,
ῡ
_{k}
^{+}
and
Ῑ
_{k}
^{+}
are the normalized incident voltage and normalized incident current waves, respectively. Similarly,
ῡ
_{k}
^{}
and
Ῑ
_{k}
^{}
are the normalized reflection voltage and normalized reflection current waves, respectively.
For a network characterized by
S
parameters
[14]
, the port impedance meets the requirements of conjugate matching. The normalized incident and reflection voltages are derived as
In the equation,
V
_{k}
,
I
_{k}
are the voltage and current of the port, respectively;
Z
_{k}
is the input impedance of the EMI filter; and
Z
_{k}
^{*}
is the output impedance of the filter.
Equations (1) and (2) can yield
ῡ
_{k}
^{+}
,
ῡ
_{k}
^{}
as follows:
Transforming the
k
port characteristics on all ports enables the derivation matrices of the incident and reflected waves of the normalized equivalent voltage. The matrix expression is given by
When the network is linear, substituting
into Equation (7) yields
In the equation,
E
is the unity matrix. Establishing the matrix
S
,
The expansion form of Equation (6) is
where
S
is known as the
S
parameter or parameter
S
.
 C. SParameters of EMI Filter
Characterizing an EMI filter as a linear passive is reasonable only under the condition of smallsignal excitation.
Fig. 4
shows the test setup for an EMI filter, which is characterized in terms of waves. Moreover, nonlinear characteristics can be simulated by adding smallsignal excitation to the DC bias.
Twoport microwave network model. V_{S}: switch power supply noise signal Z_{S}, Z_{L}: noise source impedance and load impedance ῡ_{1}^{+},ῡ_{2}^{+} : normalized incident voltage wave ῡ_{1}^{},ῡ_{2}^{} : normalized reflection voltage wave V_{1}, V_{2}: port voltage
Scattering parameter signal flow of EMI filter.
Single port model of EMI filter.
From the normalized port voltage definition and Equations (1) and (2), the port voltages and currents of two port networks can be derived as
where
Z
_{0}
is a positive real number that represents the reference impedance of the ports. According to
S
parameter theory and Equation (10), we derive
When reflected to the noise source or load side,
ῡ
_{1}
^{}
and
ῡ
_{2}
^{}
will also be reflected to the opposite position because of mismatched impedances. The reflection coefficients, Г
_{S}
at source side and Г
_{L}
at load side, are given by
[15]
The current of the circuit in
Fig. 4
is characterized by the signal flow graph shown in
Fig. 5
.
Figs. 5
and
6
show that
represents the normalized voltage wave, which is emitted by the noise source.
and
are the normalized incident and normalized reflection voltage waves of the source port. For the EMI filter, when the impedance
Z
_{S}
of noise source is determined, the normalized voltage wave is given by
According to Equation (1),
After measuring the
S
parameter, the Mason formula and signal flow diagram can be used to deduce
ῡ
_{1}
^{+}
,
ῡ
_{1}
^{}
,
ῡ
_{2}
^{+}
, and
ῡ
_{2}
^{}
. According to Equations (9) and (10), the port voltage and current are further calculated.
The ultimate goal of the EMI filter is to control the noise energy transmitted to the load side under a certain standard. Extracting the loadside power is important. According to
S
parameter theory, the normalized power of the load side is
[14]
By using the Mason formula to analyze
Fig. 5
, we determine that
where
is the normalized power of source port
The EMI filter network energy transmission gain is given by
From Equation (26), the energy transmission characteristics of the filter network can be extracted by using the
S
parameter. Thereafter, the operating characteristics of the network can be expressed. However,
IG
should be further studied because of the differences in the characteristics of transmission gain and
IG
.
 D. IG Calculated by SParameters
In an actual system, the
IG
under the condition of specific impedance should be accurately obtained.
IG
refers to the ratio of the voltage
V
_{2}
(or power
P
_{2}
) and voltage
V
_{0}
(or power
P
_{0}
)
[16]
. When the filter is connected between the load and power side, this voltage can be expressed in decibel form (DB).
V
_{2}
is the load voltage when the EMI filter is placed between the load and source side, whereas
V
_{0}
refers to the voltage without the filter.
According to Equations (11) and (12)
According to the Mason formula,
From (14) and (15), when the Г
_{S}
and the Г
_{L}
are equal to zero, the source and load impedances are in a matching state. Therefore,
S
_{21}
in Equation (35) is the
IG
. However, when the impedances are mismatched, the reflection parameters Г
_{S}
and Г
_{L}
can be calculated to improve EMI filter design.
For switching power supply, determining the hardware circuit enables the noise impedance Z
_{S}
of the loop to be obtained through analysis and testing. The load impedance Z
_{L}
of the EMI filter is the input impedance of the former device or the standard impedance, which is provided by LISN.
S
_{11}
,
S
_{21}
,
S
_{12}
, and
S
_{22}
can be measured by using an Sparameter tester (Agilent 87511A). The
S
parameter tester has a calibration function, and its attenuation can be isolated from the noise and energy of the measuring line. Without shortcircuit and opencircuit, the
S
parameter test values are more precise compared with the impedance test values of 
Y
 
Z
 parameters in the high frequency.
III. TESTING SPARAMETERS AND INSERTION GAIN OF EMI FILTER
This study uses a typical planar EMI filter structure composed of the integrated capacitance of differential mode, leakage inductance layer, integrated LC unit, and magnetic core.
Fig. 1
shows the electrical configuration.
Table I
presents the parameters of the basic cell structure.
STRUCTURE PARAMETERS OF PLANAR EMI FILTER
STRUCTURE PARAMETERS OF PLANAR EMI FILTER
The test apparatus uses the Agilent 4395A and Agilent 87511A network analyzer to test the
S
parameters of the DM and CM structures in the planar filter, respectively. Taking the DM structure as an example,
Fig. 7
shows the amplitudefrequency and phasefrequency curves of the
S
parameters.
Test curves of S parameters for DM filter.
Comparison of IG with different impedances. 1 Z_{S}=50Ω, Z_{L}=50Ω 2 Z_{S}=10kΩ, Z_{L}=50Ω 3 Z_{S}=10Ω, Z_{L}=100Ω
Calculated curve of IG for CM filter. 1—Z_{S}=50Ω, Z_{L}=50Ω 2—Z_{S}=1nF, Z_{L}=10Ω
Fig. 8
clearly shows that when noise source and load impedances are changed, the influence of the different impedance characteristics of
IG
must be considered to optimize the planar EMI filter design.
To calculate the
IG
, the Agilent 4395A Impedance Analyzer is used to test the
S
parameters of the CM structure.
Fig. 9
shows the calculated curve. Subsequently, the signal generator, voltmeter, LISN, EMI filter, and EUT are used to establish the test circuit. The voltages before or after adding the EMI filter are determined by using the voltmeter. The real incircuit attenuation of several frequency points are then derived (
Table II
).
A comparison of the
IG
values of curve 2 in
Fig. 9
and in
Table II
reveals that the actual test value coincides with that calculated in the multiple frequency point. In Equation (35), the noise source impedance uses the ideal capacitor impedance curves. Thus, the calculated results are not fully consistent with the test results. Several errors can be assumed between the measured and calculated values.
TEST IG FOR CM FILTER
IV. EXTRACTION OF NEARFIELD COUPLING PARAMETERS IN A PLANAR FILTER BY USING SPARAMETER
 A. Coupling Parameters of NearField for Planar EMI Filter Structure
The highfrequency parameters of a planar filter differ from that of discrete structures. The traditional model (highfrequency parasitic mutual inductance) is no longer applicable. Under certain conditions, the planar filter units can be regarded as an integrated LC structure. Therefore, the use of different connecting methods will affect the equivalent series inductance (ESL) of the integrated capacitor, as shown in
Fig. 10
.
Three kinds of connection for integrated LC units.
In
Fig. 8
,
L
_{P1}
,
L
_{P2}
are the line inductances, whereas
L
is the planar LC unit inductance.
To reduce the integrated capacitor ESL and to form a complete EMI filter, the integrated LC unit uses the connection method shown in
Fig. 10
(c). In the EMI filter frequency, the nearfield coupling parameters can be used to express mutual inductance. Without considering the coupling parameters with negligible effect, the nearfield coupling parameter model of the DM structure in the planar filter is as (
Fig. 11
).
Fig. 11
shows that
L
_{P1}
,
L
_{P2}
are the input and output inductances of the wire loop, respectively; and
L
_{P3}
,
L
_{P4}
are the inductances between the interior units of the planar filter.
L
_{P3}
,
L
_{P4}
are significantly less than
L
_{P1}
,
L
_{P2}
. Moreover, the coupling effect can be disregarded because of the extreme closeness of the LC units in terms of space position. Meanwhile,
M
_{1}
,
M
_{2}
are equal because of the symmetrical electrical and mechanical structures of the planar EMI filter.
Nearfield coupling model of DM structure.
 B. Use of SParameter to Extract Mutual Inductance
To extract the
M
_{1}
,
M
_{2}
, a CM inductor and differential capacitor are removed from the core.
Fig. 12
shows the equivalent twoport network model.
Calculated M_{1} through equivalent capacitor branch.
According to
Fig. 12
,
M
_{1}
is given by
where
f
is the resonant frequency of the capacitor branch.
For the extraction of
M
_{3}
, the CM inductance and retained LC unit constituted by DM capacitance should be removed.
Fig. 13
shows the highfrequency model.
Figs. 12
and
13
shows that for any value of mutual inductance, the functional relationship is shown in
Fig. 14
after extracting amplitude and phase of the impedance of each branch in corresponding Ttransmission network equivalent circuit.
According to microwave network theory, further extraction of mutual inductance parameters results in the conversion of the
S
parameters into Ttransmission network parameters. The relationships of the each branch impedance with the
S
parameters of the Tnetwork (
Fig. 14
) are given by
Calculation of M3 through equivalent circuit.
Sparameters of Tnetwork.
 C. Experiments
Table 1
shows the parameters of the planar filter.
Fig. 11
shows the
M
_{1}
,
M
_{2}
, and
M
_{3}
extracted by using Agilent 4395A. The nearfield coupling model is created (
Fig. 15
).
Fig. 16
shows the
IG
test values of the differentialmode structure and the model simulation.
Parameters for the nearfield coupling model.
IG for planar EMI filter.
Fig. 16
shows that curve 1 represents the
IG
of the differential structure in the planar filter. Curve 2 is the calculation curve of the traditional differential structure, which only considers its own parasitic parameters. Curve 3 represents the
IG
of high frequency model when the near field coupling effect is considered. A comparison of the three curves reveal that the calculation values of the two models are extremely close to their test values in the lowfrequency band. However, in the highfrequency band after 2M, the calculation curve of
IG
with nearfield coupling is closer to the measurement curve than to the curve of the traditional differential structure model. Therefore, the nearfield coupling model is better than the traditional differential model. Meanwhile, the
S
parameters
M
_{1}
,
M
_{2}
, and
M
_{3}
are more suitable for the planar EMI filter.
V. CONCLUSIONS
A method using
S
parameters to characterize EMI filters is discussed. A simplified EMI filter model is proposed to help understand the transmission characteristics of the ports. Meanwhile, the
IG
is developed to predict the filter performance.
The
S
parameter can be used to extract the nearfield coupling parameters. Therefore, establishing an effective nearfield parameter model is possible. Compared with the traditional model, which only considers parasitic parameters, the nearfield coupling model can predict the characteristics of planar EMI filter more accurately.
Acknowledgements
This study is supported by the Power Electronics Science and Education Development Program of Delta Environmental & Educational Foundation; National Natural Science Foundation of China; Jiangsu Province University Outstanding Science and Technology Innovation Team Project.
BIO
Shishan Wang was born in Shaanxi Province, China, in 1967. He received his Ph. D in Electrical Engineering in 2003 from Xi’an Jiaotong University, China. He is currently working at Nanjing University of Aeronautics and Astronautics in the Department of Electrical Engineering. His research interests include the electromagnetic compatibility of power electronic system, electromagnetic numerical calculation, and its application in electrical devices.
Min Gong was born in China in 1989. She received her B.S. in Electrical Engineering degree from Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2012. At present, she is pursuing an M.S. degree in Electrical Engineering at the same university. Her main research interests include the electromagnetic compatibility of power electronic system.
Chenchen Xu received her B.S. degree in Electrical Engineering and automation from the Anhui University of Technology, Anhui, China, in 2011. At present, she is working to complete her M.S. degree in Electrical Engineering at Nanjing University of Aeronautics and Astronautics, Nanging, China. Her main research interests include electromagnetic compatibility of power electronics, as well as the design and development of a new type electromagnetic interference filter.
Ozenbaugh R. L.
2001
EMI Filter Design
2nd ed.
Taylor & Francis
Wang S.
,
Xu Chenchen
2013
“Design theory and implementation of planar EMI filter based on annular integrated inductorcapacitor unit”
IEEE Trans. Power Electron.
28
(3)
1167 
1175
DOI : 10.1109/TPEL.2012.2207968
Hsieh H.
,
Li J.
,
Chen D.
2008
“Effects of X capacitors on EMI filter effectiveness”
IEEE Trans. Ind. Electron.
55
(2)
949 
955
DOI : 10.1109/TIE.2007.896258
Huang H.
,
Deng L.
2012
“Improving the highfrequency performance of integrated EMI filter with multiple ground layers”
AsiaPacific Symposium on Electromagnetic Compatibility
249 
252
Drinovsky J.
,
Svacina J.
,
Bednar P.
2007
“Operation amplifiers in EMI filter insertion loss measurement setup”
Radioelektronika, 17th International Conferences
1 
3
Wang S.
,
Lee F. C.
,
Odendaal W. G.
2005
“Characterization and parasitic extraction of EMI filters using scattering parameters”
IEEE Trans. Power Electron.
20
(2)
502 
510
DOI : 10.1109/TPEL.2004.842949
Chen W.
,
Feng L.
,
Chen H.
,
Qian Z.
2006
“Near field coupling effects on conducted EMI in power converter”
in 37th IEEE Power Electronics Specialists Conference, PESC '06
252 
259
Wang S.
,
Lee F. C.
2004
“Using scattering parameters to characterize EMI filter”
in 35th IEEE Annual Conference on Power Electronics Specialists Conference
297 
303
Tarateeraseth V.
,
See K. Y.
,
Canavero F. G.
,
Chang R. W.
2010
“Systematic electromagnetic interference filter design based on information from incircuit impedance measurements”
IEEE Trans. Electromagn. Compat.
52
(3)
588 
598
DOI : 10.1109/TEMC.2010.2046419
Espina J.
,
Balcells J.
,
Arias A.
,
Ortega C.
,
Berbel N.
2010
“EMI model of an AC/AC power converter”
Vehicle Power and Propulsion Conference ( VPPC)
1 
6
Pleite J.
,
Pietro R.
,
Asensi R.
,
Cobos J. A.
,
Olias E.
1999
“Obtaining a frequencydependent and distributedeffects model of magnetic components from actual measurements”
IEEE Trans. Magn.
35
(6)
4490 
4502
DOI : 10.1109/20.809142
Drinovsky J.
,
Svacina J.
,
Zamazal M.
,
Urbanec T.
,
Lacik J.
2005
“Variable impedance in measuring EMI filter’s insertion loss”
Communications, AsiaPacific Conference on
24 
27
Pozar D. M.
1998
Microwave Engineering
John Wiley & Sons, Inc
Besser L.
,
Gilmore R.
2006
Practical RF Circuit Design for Modern Wireless Communication Systems
Artech House Publishers
31 
49
Wang S.
,
Lee F. C.
,
Odendaal W. G.
2005
“Characterization and parasitic extraction of EMI filters using scattering parameters”
IEEE Trans. Power Electron.
20
(2)
502 
510
DOI : 10.1109/TPEL.2004.842949
Zhang D.
,
Chen D. Y.
,
Sable D.
1998
“A new method to Characterize EMI Filter,”
Applied Power Electronics Conference and Exposition
2
929 
933