Scattering Parameter-based Measurement of Planar EMI filter

Abstract

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 high-frequency 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 near-field 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.

Fig. 1.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 Cx bypasses most of the DM noise because of the low Cx impedance. The remaining noise is blocked by the LDM, which is the leakage inductance of CM inductance. The right DM capacitor Cx bypasses most of the remaining DM currents because of the high LISN impedance. CY is the CM capacitor and LCM is CM inductance, which constitute the CM filter used to attenuate the CM noise.

A conventional EMI filter comprises up to one-third 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 inductor-capacitor 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 high-frequency range, the effect of near-field coupling on the EMI filter is sometimes more severe than that of the parasitic parameters of components [7]. When the near-field 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 short-circuit and open-circuit of the port, as well as the accuracy of branch and stray impedances, at high frequencies. Therefore, the S-parameter method is selected to extract the near-field coupling parameters while avoiding the aforementioned problems [8].

Several studies [9]-[11] have proposed methods to establish the high-frequency 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 high-frequency characteristics, S-parameters are used to measure and calculate the coupling parameters of the planar filter.

 

II. MEASUREMENT OF FILTER CHARACTERISTICS BY USING S-PARAMETER

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.

Fig. 2.Structure of planar EMI filter.

Fig. 3.Integrated unit of planar LC.

B. S-Parameters

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, ῡk+ and Ῑk+ are the normalized incident voltage and normalized incident current waves, respectively. Similarly, ῡk- and Ῑk- 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, Vk, Ik are the voltage and current of the port, respectively; Zk is the input impedance of the EMI filter; and Zk* is the output impedance of the filter.

Equations (1) and (2) can yield ῡk+,ῡk- 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. S-Parameters of EMI Filter

Characterizing an EMI filter as a linear passive is reasonable only under the condition of small-signal 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 small-signal excitation to the DC bias.

Fig. 4.Two-port microwave network model. VS: switch power supply noise signal ZS, ZL: noise source impedance and load impedance ῡ1+,ῡ2+ : normalized incident voltage wave ῡ1-,ῡ2- : normalized reflection voltage wave V1, V2: port voltage

Fig. 5.Scattering parameter signal flow of EMI filter.

Fig. 6.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 Z0 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, ῡ1- and ῡ2- will also be reflected to the opposite position because of mismatched impedances. The reflection coefficients, ГS at source side and ГL 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 ZS 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 ῡ1+ , ῡ1- , ῡ2+ , and ῡ2-. 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 load-side 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 S-Parameters

In an actual system, the IG under the condition of specific impedance should be accurately obtained. IG refers to the ratio of the voltage V2 (or power P2) and voltage V0 (or power P0) [16]. When the filter is connected between the load and power side, this voltage can be expressed in decibel form (DB). V2 is the load voltage when the EMI filter is placed between the load and source side, whereas V0 refers to the voltage without the filter.

According to Equations (11) and (12)

According to the Mason formula,

From (14) and (15), when the ГS and the ГL are equal to zero, the source and load impedances are in a matching state. Therefore, S21 in Equation (35) is the IG. However, when the impedances are mismatched, the reflection parameters ГS and ГL can be calculated to improve EMI filter design.

For switching power supply, determining the hardware circuit enables the noise impedance ZS of the loop to be obtained through analysis and testing. The load impedance ZL of the EMI filter is the input impedance of the former device or the standard impedance, which is provided by LISN. S11, S21, S12, and S22 can be measured by using an S-parameter 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 short-circuit and open-circuit, the S-parameter test values are more precise compared with the impedance test values of |Y| |Z| parameters in the high frequency.

 

III. TESTING S-PARAMETERS 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.

TABLE ISTRUCTURE 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 amplitude-frequency and phase-frequency curves of the S-parameters.

Fig. 7.Test curves of S parameters for DM filter.

Fig. 8.Comparison of IG with different impedances. 1 ZS=50Ω, ZL=50Ω 2 ZS=10kΩ, ZL=50Ω 3 ZS=10Ω, ZL=100Ω

Fig. 9.Calculated curve of IG for CM filter. 1—ZS=50Ω, ZL=50Ω 2—ZS=1nF, ZL=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 in-circuit 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.

TABLE IITEST IG FOR CM FILTER

 

IV. EXTRACTION OF NEAR-FIELD COUPLING PARAMETERS IN A PLANAR FILTER BY USING S-PARAMETER

A. Coupling Parameters of Near-Field for Planar EMI Filter Structure

The high-frequency parameters of a planar filter differ from that of discrete structures. The traditional model (high-frequency 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.

Fig. 10.Three kinds of connection for integrated LC units.

In Fig. 8, LP1, LP2 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 near-field coupling parameters can be used to express mutual inductance. Without considering the coupling parameters with negligible effect, the near-field coupling parameter model of the DM structure in the planar filter is as (Fig. 11).

Fig. 11 shows that LP1, LP2 are the input and output inductances of the wire loop, respectively; and LP3, LP4 are the inductances between the interior units of the planar filter. LP3, LP4 are significantly less than LP1, LP2. Moreover, the coupling effect can be disregarded because of the extreme closeness of the LC units in terms of space position. Meanwhile, M1, M2 are equal because of the symmetrical electrical and mechanical structures of the planar EMI filter.

Fig. 11.Near-field coupling model of DM structure.

B. Use of S-Parameter to Extract Mutual Inductance

To extract the M1, M2, a CM inductor and differential capacitor are removed from the core. Fig. 12 shows the equivalent two-port network model.

Fig. 12.Calculated M1 through equivalent capacitor branch.

According to Fig. 12, M1 is given by

where f is the resonant frequency of the capacitor branch.

For the extraction of M3, the CM inductance and retained LC unit constituted by DM capacitance should be removed. Fig. 13 shows the high-frequency 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 T-transmission network equivalent circuit.

According to microwave network theory, further extraction of mutual inductance parameters results in the conversion of the S-parameters into T-transmission network parameters. The relationships of the each branch impedance with the S-parameters of the T-network (Fig. 14) are given by

Fig. 13.Calculation of M3 through equivalent circuit.

Fig. 14.S-parameters of T-network.

C. Experiments

Table 1 shows the parameters of the planar filter. Fig. 11 shows the M1, M2, and M3 extracted by using Agilent 4395A. The near-field coupling model is created (Fig. 15). Fig. 16 shows the IG test values of the differential-mode structure and the model simulation.

Fig. 15.Parameters for the near-field coupling model.

Fig. 16.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 low-frequency band. However, in the high-frequency band after 2M, the calculation curve of IG with near-field coupling is closer to the measurement curve than to the curve of the traditional differential structure model. Therefore, the near-field coupling model is better than the traditional differential model. Meanwhile, the S-parameters M1, M2, and M3 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 near-field coupling parameters. Therefore, establishing an effective near-field parameter model is possible. Compared with the traditional model, which only considers parasitic parameters, the near-field coupling model can predict the characteristics of planar EMI filter more accurately.