Mixed-Mode EMI Noise and Its Implications to Filter Design

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NLM与比率图像的多时相SAR图像去噪方法

为锐爲一吨,，求出噪声图像与各个时间序列的高斯加权欧式距离并进行算数平均值的计算，其临近像素块尺寸大小决定高斯的标准偏差a（a> 0）。权值g由式（1）定义。
Z（Z9』）
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（1）式中：z（i,j）是归一化常数；|lC-<,；!C,a是像
素点（诂）图像块和/时间序列像素点（耳仏）图像
块加权欧式距离的平方池为滤波参数，决定欧式加
BU Lijing,ZHAO Shuang,ZHANG Zhengpeng (School of Geomatics ,Liaoning Technical University ,Fu^cin,Liaoning 123000,China) Abstract: Aiming at the problem that the coherent speckle noise of synthetic aperture radar images has a great impact on image quality,a multi-temporal SAR image denoising method combining NLM and ratio images is proposed. The method firstly uses NLM filter to calculate the similarity weights between the SAR images of each scene, thereby obtaining the average image, and applies the MuLoG filter to perform denoising. Secondly,the noise image is divided by the filtered average image to obtain the ratio image and then filter the ratio image. Finally,the filtered average image and the ratio image are multiplied to obtain the denoised image. Experiments are carried out with different sequences of airborne SAR data. The experimental results show that compared with other similar algorithms, the method proposed in this paper can effectively suppress the coherent speckle noise in SAR images and improve the image quality. Key words: multi-temporal SAR image ； coherent speckle suppression ； non-local mean ； average image ； ratio image

Common Phase Error due to Phase Noise in OFDM - Estimation and Suppression

COMMON PHASE ERROR DUE TO PHASE NOISE IN OFDM-ESTIMATION AND SUPPRESSIONDenis Petrovic,Wolfgang Rave and Gerhard FettweisV odafone Chair for Mobile Communications,Dresden University of Technology,Helmholtzstrasse18,Dresden,Germany{petrovic,rave,fettweis}@ifn.et.tu-dresden.deAbstract-Orthogonal frequency division multiplexing (OFDM)has already become a very attractive modulation scheme for many applications.Unfortunately OFDM is very sensitive to synchronization errors,one of them being phase noise,which is of great importance in modern WLAN systems which target high data rates and tend to use higher frequency bands because of the spectrum availability.In this paper we propose a linear Kalmanﬁlter as a means for tracking phase noise and its suppression.The algorithm is pilot based.The performance of the proposed method is investigated and compared with the performance of other known algorithms.Keywords-OFDM,Synchronization,Phase noise,WLANI.I NTRODUCTIONOFDM has been applied in a variety of digital commu-nications applications.It has been deployed in both wired systems(xDSL)and wireless LANs(IEEE802.11a).This is mainly due to the robustness to frequency selective fading. The basic principle of OFDM is to split a high data rate data stream into a number of lower rate streams which are transmitted simultaneously over a number of orthogonal subcarriers.However this most valuable feature,namely orthogonality between the carriers,is threatened by the presence of phase noise in oscillators.This is especially the case,if bandwidth efﬁcient higher order modulations need to be employed or if the spacing between the carriers is to be reduced.To compensate for phase noise several methods have been proposed.These can be divided into time domain[1][2]and frequency domain approaches[3][4][5].In this paper we propose an algorithm for tracking the average phase noise offset also known as the common phase error(CPE)[6]in the frequency domain using a linear Kalmanﬁlter.Note that CPE estimation should be considered as aﬁrst step within more sophisticated algorithms for phase noise suppression[5] which attempt to suppress also the intercarrier interference (ICI)due to phase noise.CPE compensation only,can however sufﬁce for some system design scenarios to suppress phase noise to a satisfactory level.For these two reasons we consider CPE estimation as an important step for phase noise suppression.II.S YSTEM M ODELAn OFDM transmission system in the presence of phase noise is shown in Fig. 1.Since all phase noise sources can be mapped to the receiver side[7]we assume,without loss of generality that phase noise is present only at the front end of the receiver.Assuming perfect frequency and timing synchronization the received OFDM signal samples, sampled at frequency f s,in the presence of phase noise can be expressed as r(n)=(x(n) h(n))e jφ(n)+ξ(n).Each OFDM symbol is assumed to consist of a cyclic preﬁx of length N CP samples and N samples corresponding to the useful signal.The variables x(n),h(n)andφ(n)denote the samples of the transmitted signal,the channel impulse response and the phase noise process at the output of the mixer,respectively.The symbol stands for convolution. The termξ(n)represents AWGN noise with varianceσ2n. The phase noise processφ(t)is modelled as a Wiener process[8],the details of which are given below,with a certain3dB bandwidth∆f3dB.,0,1,2...m lX l=,0,1,2...m lR l=Fig.1Block diagram of an OFDM transmission chain.At the receiver after removing the N CP samples cor-responding to the cyclic preﬁx and taking the discrete Fourier transform(DFT)on the remaining N samples,the demodulated carrier amplitude R m,lkat subcarrier l k(l k= 0,1,...N−1)of the m th OFDM symbol is given as[4]:R m,lk=X m,lkH m,lkI m(0)+ζm,lk+ηm,lk(1)where X m,lk,H m,lkandηm,lkrepresent the transmitted symbol on subcarrier l k,the channel transfer function andlinearly transformed AWGN with unchanged variance σ2n at subcarrier l k ,respectively.The term ζm,l k represents intercarrier interference (ICI)due to phase noise and was shown to be a gaussian distributed,zero mean,randomvariable with variance σ2ICI =πN ∆f 3dB s[7].The term I m (0)also stems from phase noise.It does not depend on the subcarrier index and modiﬁes all subcarriers of one OFDM symbol in the same manner.As its modulus is in addition very close to one [9],it can be seen as a symbol rotation in the complex plane.Thus it is referred to in the literature as the common phase error (CPE)[6].The constellation rotation due to CPE causes unaccept-able system performance [7].Acceptable performance can be achieved if one estimates I m (0)or its argument and compensates the effect of the CPE by derotating the received subcarrier symbols in the frequency domain (see Eq.(1)),which signiﬁcantly reduces the error rate as compared to the case where no compensation is used.The problem of esti-mating the CPE was addressed by several authors [3][4][10].In [3]the authors concentrated on estimating the argument of I m (0)using a simple averaging over pilots.In [10]the argument of I m (0)was estimated using an extended Kalman ﬁlter,while in [4]the coefﬁcient I m (0)itself was estimated using the LS algorithm.Here we introduce an alternative way for minimum mean square estimation (MMSE)[11]of I m (0)using a linear scalar Kalman ﬁlter.The algorithm is as [4]pilot based.III.P HASE N OISE M ODELFor our purposes we need to consider a discretized phase noise model φ(n )=φ(nT s )where n ∈N 0and T s =1/f s is the sampling period at the front end of the receiver.We adopt a Brownian motion model of the phase noise [8].The samples of the phase noise process are given as φ(n )=2πf c √cB (n )where f c is the carrier frequency,c =∆f 3dB /πf 2c [8]and B (n )represents the discretizied Brownian motion process,Using properties of the Brownian motion [12]the fol-lowing holds:B (0)=0and B (n +1)=B (n )+dB n ,n ∈N 0where each increment dB n is an independent random variable and dB n ∼√T s N (0,1).Noting that φ(n )=2πf c √cB (n )we can write the discrete time phase noise process equation asφ(n +1)=φ(n )+w (n )(2)where w (n )∼N (0,4π2f 2c cT s )is a gaussian randomvariable with zero mean and variance σ2w =4π2f 2c cT s .IV.CPE E STIMATION U SING A K ALMAN F ILTER Since all received subcarriers within one OFDM symbolare affected by the same factor,namely I m (0),the problem at hand can be seen as an example of estimating a constant from several noisy measurements given by Eq.(1)for which purpose a Kalman ﬁlter is well suited [11].For a Kalmanﬁlter to be used we need to deﬁne the state space model of the system.Deﬁne ﬁrst the set L ={l 1,l 2,l 3,...l P }as a subset of the subcarrier set {0,1,...N −1}.Using Eq.(1)one can writeR m,l k =A m,l k I m,l k (0)+εm,l k(3)where A m,l k =X m,l k H m,l k and I m,l k (0)=I m (0)for all k =1,2...,P .Additional indexing of the CPE terms is done here only for convenience of notation.On the other hand one can writeI m,l k +1(0)=I m,l k (0).(4)Equations (3)and (4)are the measurement and processequation of the system state space model,where A m,l k represents the measurement matrix,while the process matrix is equal to 1and I m,l k (0)corresponds to the state of the system.The measuring noise is given by εm,l k which combines the ICI and AWGN terms in Eq.(1),the varianceof which for all l k equals σ2ε=(σ2ICI +σ2n ).The process noise equals zero.Note that the deﬁned state space model is valid only for one OFDM symbol.For the state space model to be fully deﬁned,knowledge of the A m,l k =X m,l k H m,l k is needed.Here we assume to have ideal knowledge of the channel.On the other hand we deﬁne the subset L to correspond to the pilot subcarrier locations within one OFDM symbol so that X m,q ,q ∈L are also known.We assume that at the beginning of each burst perfect timing and frequency synchronization is achieved,so that the phase error at the beginning of the burst equals zero.After the burst reception and demodulation,the demodulated symbols are one by one passed to the Kalman ﬁlter.For a Kalman ﬁlter initialization one needs for eachOFDM symbol an a priori value for ˆI m,l 1(0)and an a priori error variance K −m,1.At the beginning of the burst,when m =1,it is reasonable to adopt ˆI −1,l 1(0)=1.Within each OFDM symbol,say m th,the ﬁlter uses P received pilot subcarriers to recursively update the a priori value ˆI −1m,l 1(0).After all P pilot subcarriers are taken into account ˆI m,l P (0)is obtained,which is adopted as an estimate ofthe CPE within one OFDM symbol,denoted as ˆIm (0).The Kalman ﬁlter also provides an error variance of the estimateof I m,l P (0)as K m,P .ˆI m,l P(0)and K m,P are then used as a priori measures for the next OFDM symbol.The detailed structure of the algorithm is as follows.Step 1:InitializationˆI −m,l 1(0)=E {I −m,l 1(0)}=ˆI m −1(0)K −m,1=E {|I m (0)−ˆIm −1(0)|2}∼=E {|φm −ˆφm −1|2}=σ2CP E +K m −1,Pwhere σ2CP E =4π2N 2+13N +N CP ∆f 3dBf s(see [10]),K 0,P =0and φm =arg {I m (0)}.Repeat Step2and Step3for k=1,2,...,P Step2:a-posteriori estimation(update)G m,k=K−m,kH H m,lkH m,lkK−m,kH Hm,l k+(σ2ICI+σ2n)ˆIm,l k (0)=ˆI−m,l k(0)+G m,k[R m,lk−H m,l kˆI−m,l k(0)]K m,k=(1−G m,k H m,lk )K−m,kStep3:State and error variance propagationK−m,k+1=K m,k(5)ˆI−m,l k+1(0)=ˆI m,lk(0)Note that no matrix inversions are required,since the state space model is purely scalar.V.CPE C ORRECTIONThe easiest approach for CPE correction is to derotate all subcarriers l k of the received m th symbol R m,lkby φm=−arg{ˆI m(0)}.Unambiguity of the arg{·}function plays here no role since any unambiguity which is a multiple of2πrotates the constellation to its equivalent position in terms of its argument.The presented Kalmanﬁlter estimation algorithm is read-ily applicable for the decision feedback(DF)type of algo-rithm presented in[4].The idea there was to use the data symbols demodulated after theﬁrst CPE correction in a DFE manner to improve the quality of the estimate since that is increasing the number of observations of the quantity we want to estimate.In our case that would mean that after theﬁrst CPE correction the set L={l1,l2,l3,...l P}of the subcarriers used for CPE estimation,which previously corresponded to pilot subcarriers,is now extended to a larger set corresponding to all or some of the demodulated symbols. In this paper we have extended the set to all demodulated symbols.The Kalmanﬁlter estimation is then applied in an unchanged form for a larger set L.VI.N UMERICAL R ESULTSThe performance of the proposed algorithm is investigated and compared with the proposal of[4]which is shown to outperform other known approaches.The system model is according to the IEEE802.11a standard,where64-QAM modulation is used.We investigate the performance in AWGN channels and frequency selective channels using as an example the ETSI HiperLAN A-Channel(ETSI A). Transmission of10OFDM symbols per burst is assumed.A.Properties of an EstimatorThe quality of an estimation is investigated in terms of the mean square error(MSE)of the estimator for a range of phase noise bandwidths∆f3dB∈[10÷800]Hz.Table1 can be used to relate the phase noise bandwidth with other quantities.Figures2and3compare the MSE of the LS estimator from[4]and our approach for two channel types and both standard correction and using decision feedback. Note that SNRs are chosen such that the BER of a coded system after the Viterbi algorithm in case of phase noise free transmission is around1·10−4.Kalmanﬁlter shows better performance in all cases and seems to be more effective for small phase noise bandwidths. As expected when DF is used the MSE of an estimator is smaller because we are taking more measurements into account.Fig.2MSE of an estimator for AWGN channel.Fig.3MSE of an estimator for ETSI A channel.Table 1Useful relationsQuantitySymbolRelationTypical values for IEEE802.11aOscillator constant c [1radHz]8.2·10−19÷4.7·10−18Oscillator 3dB bandwidth ∆f 3dB [Hz]∆f 3dB =πf 2cc 70÷400Relative 3dB bandwidth ∆f 3dB ∆f car∆f 3dBfsN 2·10−4÷13·10−4Phase noise energy E PN [rad]E PN =4π∆f 3dB∆fcar0.0028÷0.016Subcarrier spacing∆f car∆f car =f s N312500HzB.Symbol Error Rate DegradationSymbol error rate (SER)degradation due to phase noise is investigated also for a range of phase noise bandwidths ∆f 3dB ∈[10÷800]Hz and compared for different correc-tion algorithms.Ideal CPE correction corresponds to the case when genie CPE values are available.In all cases simpleconstellation derotation with φ=−arg {ˆIm (0)}is used.Fig.4SER degradation for AWGN channel.In Figs.4and 5SER degradation for AWGN and ETSI A channels is plotted,respectively.It is interesting to note that as opposed to the ETSI A channel case in AWGN channel there is a gap between the ideal CPE and both correction approaches.This can be explained if we go back to Eq.(1)where we have seen that phase noise affects the constellation as additive noise.Estimation error of phase noise affects the constellation also in an additive manner.On the other hand the SER curve without phase noise in the AWGN case is much steeper than the corresponding one for the ETSI A channel.A small SNR degradation due to estimation errors will cause therefore large SER variations.This explains why the performance differs much less in the ETSI A channel case.Generally from this discussion a conclusion can be drawn that systems with large order of diversity are more sensitive to CPE estimation errors.Note that this ismeantFig.5SER degradation for ETSI A channel.not in terms of frequency diversity but the SER vs.SNR having closely exponential dependence.It can be seen that our approach shows slightly better performance than [4]especially for small phase noise bandwidths.What is also interesting to note is,that DF is not necessary in the case of ETSI A types of channels (small slope of SER vs.SNR)while in case of AWGN (large slope)it brings performance improvement.VII.C ONCLUSIONSWe investigated the application of a linear Kalman ﬁlter as a means for tracking phase noise and its suppression.The proposed algorithm is of low complexity and its performance was studied in terms of the mean square error (MSE)of an estimator and SER degradation.The performance of an algorithm is compared with other algorithms showing equivalent and in some cases better performance.R EFERENCES[1]R.A.Casas,S.Biracree,and A.Youtz,“Time DomainPhase Noise Correction for OFDM Signals,”IEEE Trans.on Broadcasting ,vol.48,no.3,2002.[2]M.S.El-Tanany,Y.Wu,and L.Hazy,“Analytical Mod-eling and Simulation of Phase Noise Interference in OFDM-based Digital Television Terrestial Broadcast-ing Systems,”IEEE Trans.on Broadcasting,vol.47, no.3,2001.[3]P.Robertson and S.Kaiser,“Analysis of the effects ofphase noise in OFDM systems,”in Proc.ICC,1995.[4]S.Wu and Y.Bar-Ness,“A Phase Noise SuppressionAlgorithm for OFDM-Based WLANs,”IEEE Commu-nications Letters,vol.44,May1998.[5]D.Petrovic,W.Rave,and G.Fettweis,“Phase NoiseSuppression in OFDM including Intercarrier Interfer-ence,”in Proc.Intl.OFDM Workshop(InOWo)03, pp.219–224,2003.[6]A.Armada,“Understanding the Effects of PhaseNoise in Orthogonal Frequency Division Multiplexing (OFDM),”IEEE Trans.on Broadcasting,vol.47,no.2, 2001.[7]E.Costa and S.Pupolin,“M-QAM-OFDM SystemPerformance in the Presence of a Nonlinear Ampliﬁer and Phase Noise,”IEEE mun.,vol.50, no.3,2002.[8]A.Demir,A.Mehrotra,and J.Roychowdhury,“PhaseNoise in Oscillators:A Unifying Theory and Numerical Methods for Characterisation,”IEEE Trans.Circuits Syst.I,vol.47,May2000.[9]S.Wu and Y.Bar-ness,“Performance Analysis of theEffect of Phase Noise in OFDM Systems,”in IEEE 7th ISSSTA,2002.[10]D.Petrovic,W.Rave,and G.Fettweis,“Phase NoiseSuppression in OFDM using a Kalman Filter,”in Proc.WPMC,2003.[11]S.M.Kay,Fundamentals of Statistical Signal Process-ing vol.1.Prentice-Hall,1998.[12]D.J.Higham,“An Algorithmic Introduction to Numer-ical Simulation of Stochastic Differential Equations,”SIAM Review,vol.43,no.3,pp.525–546,2001.。

运放噪声全模型

for practical application,opening the path for widespread adoption of the clock-gating technique in low-power design of custom IC’s.R EFERENCES[1]M.Pedram,“Power minimization in IC design:Principles and appli-cations,”ACM Trans.Design Automation ,vol.1,no.1,pp.3–56,Jan.1996.[2]G.Friedman,“Clock distribution design in VLSI circuits:An overview,”in Proc.IEEE ISCAS ,San Jose,CA,May 1994,pp.1475–1478.[3] E.Tellez,A.Farrah,and M.Sarrafzadeh,“Activity-driven clock designfor low power circuits,”in Proc.IEEE ICCAD ,San Jose,CA,Nov.1995,pp.62–65.[4]M.Alidina and J.Monteiro et al.,“Precomputation-based sequentiallogic optimization for low power,”IEEE Trans.VLSI Syst.,vol.2,pp.426–436,Dec.1994.[5]L.Benini and G.De Micheli,“Symbolic techniques of clock-gatinglogic for power optimization of control-oriented synchronous net-works,”in Proc.European Design Test Conf.,Paris,France,1997,pp.514–520.A Complete Operational Amplifier Noise Model:Analysisand Measurement of Correlation CoefficientJiansheng Xu,Yisong Dai,and Derek AbbottAbstract—In contrast to the general operational amplifier (op amp)noise model widely used,we propose a more complete and applicable noise model,which considers the correlation between equivalent input voltagenoisesourceand current noisesource .Based on the super-posi-tion theorem and equivalent circuit noise theory,our formulae for the equivalent input noise spectrum density of an op amp noise are applied to both the inverting and noninverting input terminals.By measurement,we demonstrate that the new expressions are significantly more accurate.In addition,details of the measurement method for our noise model parameters are given.A commercial operational amplifier (Burr–Brown OPA37A)is measured by means of a low-frequency noise power spectrum measuring system and the measured results of its noise model parameters,including the spectral correlation coefficient (SCC),are finally given.Index Terms—Noise models,operational amplifiers,spectral correlation coefficient.I.I NTRODUCTIONRecently,integrated operational amplifiers (op amps)have been used in more and more practical applications.With the continual improve-ment of their noise characteristics,they have been commonly found in the design of preamplifier circuits.For this reason,the calculation of the circuit noise of an op amp and its low-noise design are paid more attention than ever.At present,the noise models [1]–[3]of the over-whelming majority of op amps are illustrated as in Fig.1(a)and (b).The commonly accepted two-port noise model is in Fig.1(a).The op amp is considered noiseless and the equivalent voltage noise source e nManuscript received June 1,1998;revised May 20,1999.This work was supported in part by the China Natural Science Foundation under Contract 69672023.This paper was recommended by Associate Editor K.Halonen.J.Xu and Y .Dai are with the School of Information Science and Engineering,Jilin University of Technology,Changchun,China 130025.D.Abbott is with the Centre for Biomedical Engineering (CBME),Electrical and Electronic Engineering Department,the University of Adelaide,Adelaide,SA5005,Australia.Publisher Item Identifier S 1057-7122(00)02323-0.and current noise source i n are referred back to the input terminals.Fig.1(b)is commonly adopted when the positive terminal is grounded.To simplify calculation,in some models only e n is adopted and i n is ne-glected [4],[5].The advantage of these equivalent circuits is simplicity and convenience.However,in the area of small-signal detection,the re-quirements of noise specifications in the course of calculation and de-sign of a low-noise circuit become higher.The shortcoming of Fig.1(a)and (b)is obvious:the correlation between voltage noise source e n and current noise source i n is not considered,giving rise to inaccuracy.At present,methods for measuring e n and i n [6],[7]use a small value of source resistance to measure an equivalent input voltage noise e n and use a very large source resistance to measure an equivalent input current noise i n .Because the correlation is not considered in this method,the measuring method is only an approximate solution.In fact,it can be calculated that the neglect of the correlation item can lead to,at most,a 40%measurement error [7].Thus,it is commonly believed that the method can give only an approximate solution,and cannot give an accurate solution.To solve this problem,a more complete op amp noise model is pre-sented in this paper,based on Fig.1(c),which considers the correla-tion between e n and i n for each input terminal and then the formula of equivalent input noise power spectrum density for the inverting and noninverting input terminals can be derived.With different source re-sistors,the noise model parameters of an op amp have been measured by means of a low-frequency noise measuring system and the noise model parameters,including the spectral correlation coefficient,are presented.II.A C OMPLETE N OISE M ODEL AND ITS E QUIV ALENT I NPUT N OISEP OWER S PECTRUM In order to improve precision of the noise model,based on Fig.1(a)and (b),we use one equivalent voltage noise source and one equiva-lent current noise source at each op amp input terminal in our model.Second,it should be pointed out that the correlation between e n and i n at each input terminal should be considered for completeness.Let = 1+j 2be the spectral correlation coefficient (SCC),given by =S ei (f )=(a)(b)(c)Fig.1.Equivalent noise models for an opamp.(a)(b)Fig.2.(a)Inverting input op amp circuit.(b)The equivalent noise circuit of the inverting input op amp.spectrum.Therefore,from Fig.2(b),the contribution of inverting input terminal noise sources to the output noise can be expressed asS 00(f )=e 21Z fZ 12+f e 2n 1+(i 2n 1+i 2f )j Z 1==Z f j2+2e n 1i n 1Re[ (Z 1==Z f )3]g 1+Z fZ 12:(1)The contribution of noninverting input terminal noise sources to the output noise could be expressed asS 0+(f )=f e 2n 2+i 2n 2j Z 2j 2+e 22+2e n 2i n 2Re[ 0Z 32]g11+Z fZ 12:(2)Therefore,the total output noises contributed by the two input ter-minals areS 0(f )=S 00(f )+S 0+(f ):(3)The expressions of total output noise referred to inverting input ter-minal and noninverting input terminal can be expressed as follows.The equivalent noise power spectrum of inverting input terminal isS 0(f )=S 0(f )Z f Z 12=e 21+f e 2n 1+(i 2n 1+i 2f )j Z 1==Z f j2+2e n 1i n 1Re[ (Z 1==Z f )3]g 1+Z 1Z f2+f e 2n 2+i 2n 2j Z 2j2+e 22+2e n 2i n 2Re[Z 32]g1+Z 1Z f2:(4)The equivalent noise power spectrum of noninverting input terminal isS +(f )=S 0(f )1+Z f Z 12=e 211+Z 1Z f2+f e 2n 1+(i 2n 1+i 2f )j Z 1==Z f j2+2e n 1i n 1Re[ (Z 1==Z f )3]g+f e 2n 2+i 2n 2j Z 2j 2+e 22+2e n 2i n 2Re[ 0Z 32]g :(5)Now let us discuss (4)and (5).If the correlation between e n 1andi n 1,e n 2,and i n 2is neglected,then (4)can be simplified asS 0(f )=e 21+f e 2n 1+e 2n 2+e 22)1+Z 1Z f2+(i 2n 1+i 2f )j Z 1j2+i 2n 2j Z 2j 21+Z 1Z f2:(6)When Z 1=R 1,Z 2=R 2,Z f =R f ,(6)is equal to [7,p.59,(3-17)],which means that (4)is more general.Under the same condi-tions,(5)can be simplified asS +(f )=e 211+Z 1Z f2+f e 2n 1+e 2n 2+e 22+i 2n 2j Z 2j 2+(i 2n 1+i 2f )j Z 1==Z f j 2g :(7)According to the same conditions,(7)is equal to [7,p.60,(3-18)],which means that (5)is also more general.In addition,from (4)and (5)it can be theoretically concluded that the equivalent voltage noise sources e n 1and e n 2cannot be calculatedFig.3.The measurement system block diagram.separately.Therefore,for calculation convenience,it is supposed thate n 1is equal in magnitude to e n 2.Hence,let e 2n =e 2n 1+e 2n 2.Then (4)and (5)can be changed toS 0(f )=e 21+f e 2n +(i 2n 1+i 2f )j Z 1==Z f j2+p2e n i n 1Re[ (Z 1==Z f )3]+i 2n 2j Z 2j 2+e 22+p 2e n i n 2Re[ 0Z 32]g 1+Z 1Z f2(8)S +(f )=e 212+e 2n +(i 2n 1+i 2f )j Z 1==Z f j2+p2e n i n 1Re[ (Z 1==Z f )3]+i 2n 2j Z 2j 2+e 22+p 2e n i n 2Re[ 0Z 32]:(9)It should be noted that S +(f )and S 0(f )are different because thetwo input terminal voltage gains are different.III.M EASUREMENT S YSTEM AND M EASUREMENT M ETHOD Fig.3is the measurement system block diagram.In order to refer the measured output noise to the input terminals,it is necessary to have measured the frequency response A (f )of the op amp and measuring system.Therefore switch S is at A first.Then the switch S is at B to measure the output noise power spectrum of an op amp.We measure the output noise power spectrum S o (f )by means of an FFT spectrum analyzer (model:CF-920),then the equivalent input noise power spectrum is given byS i (f )=S o (f )A 2(f )where A (f )is the gain of measurement system,including the gain A 1(f )of amplifier measured and the measuring system gain A 2(f ),namely,A (f )=A 1(f )A 2(f ).In this system the cross-spectrum es-timation method is used to reduce preamplifier noise contribution be-cause the noise of the two preamplifiers are uncorrelated (powered by different batteries)and their cross-spectrum value is very small and,as a consequence,a small noise value (nV =p Hz )can be measured.The cross-spectrum estimation is measured in the frequency range of 1Hz–100kHz.The measuring process and data processing are auto-mated by computer.The measurement software is chiefly made up of two parts:1)the IEEE-488interface to control the CF-920and 2)the data processing parameter calculation from the measured results and display programs.In order to accurately measure equivalent input noise spectrum,A (f )is obtained by measuring the swept sine wave response.TABLE IT HEV ALUES OF R ANDTHES PECTRAL DENSITYTABLE II T HE V ALUES OF R,R1+R 1Rf1+R 1RfS 1(f )R 20S 2(f )R 1R 10R 20S 2(f )R 30S 3(f )R 2R 20R 3i 2n 1R 1R 20S 1(f )R 20S 2(f )R 1R 10R2Fig.4.The measured results of an op amp.(a)Equivalent input voltage noise eand versus frequency.(d)Imaginary part of SCC1+1K1+1K:(13)2)Let X 2=X f =R 2=0,R f =2k ,C 1=4 F,R 1=100 ,the corresponding equivalent input noise power can be measured and the expression is obtained asS 0(f )=4 T R 1+[X 21+(R 1+R f )2]R 2f1e 2n +(i 2n 1+i 2f )(R 21+X 21)+p 2e n i n 11[R 1(R 1+R f )+X 21]R 2f+p2e n i n 1 2X 1:(14)Then, 2can be calculated as 2=1+R 1Rf1+R 1Rf2:(16)LetS (f )=S 0(f )0e 21e 2n20(i 2n 1+i 2f )R 210p2e n i n 1R 11:(17)When source resistance R 2varies with Table II,the equivalent input noise power spectra can be measured,respectively,and then we can obtaini 2n 2=S 4(f )R 50S 5(f )R4S 4(f):(19)4)For the case of X 1=X f =0,then we haveS 0(f )=e 21+e 2n2+(i 2n 1+i 2f )1R 21+p2e n i n 1R 11+[i 2n 2(R 2+X 2)+4 T R +p 2e n i n 21(R 01+X 02]2(20)TABLE IVC OMPARISONS B ETWEEN O UR M EASURED V ALUE AND T YPICAL D ATASHEET V ALUES AT T HREE S POTF REQUENCIES (pA=pHz)where R 1=100 ;R f =2k ;R 2=100 ;C 2=4 F ;R =R 21+!2R 22C 22X =!R 22C 21+!R 22C 22.According to the noise power spectrum of the measured equivalent input S 0(f ),then we can have02=1p2e n i n2X11+R1R f1+R 1R f2:(21)In this way,all the noise model parameters (e n ,i n 1, = 1+j 2,i n 2,and 0= 01+j 02)of an op amp can be obtained by means of measuring the equivalent input noise power spectrum with varying source resistance.B.Noninverting Input TerminalIn the same way,for the case of the noninverting input terminal,all the noise model parameters can be also calculated with varying source impedance.For brevity,the formulae are not given here.IV .T HE M EASURED R ESULTSBy use of the method and the measuring system above,a commercial op amp (OPA37A)has been measured and the results are shown in Fig.4.From Fig.4(a)and (b)it can be seen that when the correlations be-tween e n 1and i n 1,e n 2,and i n 2are neglected,then the measured re-sults of both e n and i n are larger than the values when the correlation are considered.Thus,an overestimate results when the widely used method to measure e n and i n is carried out,where correlation is ne-glected and only noise contributions of a small source resistance and a large source resistance are considered in the course of noise model parameter calculation.Our measured results also show that the corre-lation between e n 1and i n 1,e n 2,and i n 2do exist,especially in low frequency.When 1=f noise dominates,the correlation coefficients be-tween e n 1and i n 1,e n 2,and i n 2become bigger.From Table III and IV (typical values can be found in the Burr–Brown datasheet)it can be seen that in low-frequency region the errors are bigger than those in the high-frequency region,which in another way demonstrates that the correlation does exist in the low frequency region and is strongerthan that of high-frequency region.If the correlation is neglected,then the errors in the low-frequency region become bigger.In addition,the results also show that the noise model and measurement method pro-posed in this paper can improve measurement and calculation precision in low-noise circuit design.V .C ONCULSIONAccording to the analysis and measured results,the following con-clusions can be reached.1)In contrast to the noise model commonly used at present,a com-plete noise model and its measurement method for an op amp are proposed in the paper.Because contributions of all noise sources to output noise and the correlation between e n 1and i n 1,e n 2,and i n 2are considered adequately,the noise model parameters can be obtained accurately through this way.2)The formulae of complete equivalent noise power spectra for inverting input and noninverting input terminals are derived,in which the contributions of all noise sources to output terminal and correlative coefficients between them are included.3)The main advantage of this method is that all internal parameters of an op amp do not need to be known in advance for noise model parameter calculations.And the experimental results are in good agreement with theoretical analysis.A CKNOWLEDGMENTThe authors wish to thank the associated editor and reviewers for a number of suggestions.R EFERENCES[1] D.F.Stout,Handbook of Operational Amplifier Circuit Design .NewYork:McGraw-Hill,1976,pp.45–51.[2]J.R.Hufault,Operational Amplifiers Network Design .New York:Wiley,1986,pp.36–48.[3]G.B.Clayton and B.W.G.Newby,Operational Amplifiers ,B.H.Newnes,Ed.,1992,ch.2–3.[4]G.Espinosa et al.,“Noise performance of OTA-C circuits,”in Proc.IEEE/ISCAS ,San Jose,CA,1988,pp.2173–2176.[5]P.Bowron and K.A.Mezher,“Noise analysis of second-order analogactive filters,”Proc.Inst.Elect.Eng.,vol.141,no.5,pp.350–356,Oct.1994.[6]J.G.Graeme et al.,Operational Amplifiers:Design and Applica-tions .New York:McGraw-Hill,1971,pp.492–493.[7] C.D.Motchenbacher and J.A.Connely,Low Noise Electronic SystemDesign .New Y ork:Wiley,1993.[8]J.Xu,Y .Dai,and Y .Li,“The study of the relation between R noisemodel and E noise model of an amplifier,”IEEE Trans.Circuits Syst.I ,vol.45,pp.154–156,Feb.1998.[9]Y .Dai,“Performance analysis of cross-spectral density estimation andits application,”Int.J.Electron.,vol.71,no.1,pp.45–53,1991.。

开关电源变换器传导干扰分析及建模方法_孟进

第25卷第5期中国电机工程学报V ol.25 No.5 Mar. 20052005年3月Proceedings of the CSEE ©2005 Chin.Soc.for Elec.Eng. 文章编号：0258-8013（2005）05-0049-06 中图分类号：TM461；TN03 文献标识码：A 学科分类号：470·40开关电源变换器传导干扰分析及建模方法孟进，马伟明，张磊，赵治华（海军工程大学电力电子技术研究所，湖北省武汉市 430033）METHOD FOR ANALYSIS AND MODELING OF CONDUCTED EMI IN SWITCHINGPOWER CONVERTERSMENG Jin, MA Wei-ming, ZHANG Lei, ZHAO Zhi-hua（Research Institute of Power Electronic Technology, Navy University of Engineering, Wuhan 430033, HubeiProvince, China）ABSTRACT: Electromagnetic interference (EMI) problems are usually complicated by the presence of modeling of noise source and noise coupling paths. The effective EMI prediction often relies on the engineers’ experience or extensive numerical simulation models. This paper proposes an analysis and modeling approach for describing the conducted EMI in switching power converter. The mechanisms and coupling paths associated with three dominant modes of EMI noise are analyzed and investigated based on time domain measured waveforms. A noise model which includes the measured and calculated component values is given to evaluate the EMI level for each mode of noise. Comparison with experimental results and predicted EMI verify the proposed method.KEY WORDS: Power electronics; Electromagnetic compati- bility; Conducted EMI; Coupling paths; Switching power converter摘要：电磁干扰的复杂性在于缺乏干扰源和干扰耦合通道的精确描述，实施干扰预测常常依赖于设计者的经验或庞大的数值仿真模型。

改善eemd的混沌去噪方法

改善EEMD的混沌去噪方法位秀雷1林瑞霖1 刘树勇1陈燕2（1.海军工程大学动力工程学院，湖北武汉，430033；2.61062部队，北京，100091）摘要：为了提高EEMD在混沌信号去噪中的时效性，提出一种改善EEMD的混沌去噪方法。

该算法将小波包分析作为EEMD的预滤波单元，剔除了部分噪声干扰，大大减少了高斯白噪声的叠加次数，并结合EEMD抑制模式混叠的特性，可以有效地提高EEMD去噪的时效性。

利用两自由度非线性系统详述了混合滤波算法的实施过程，结果表明该方法切实可行，具有非常好的应用价值。

关键词：混沌信号；小波变换；去噪；EEMDSTUDY ON CHAOTIC DE-NOISING METHOD BASED ON IMPROVED EEMDWei Xiulei1Lin Ruilin1Liu Shuyong1Chen Yan2(1.College of Power Engineering，Naval University of Engineering，Wuhan 430033，China;2.Army 61062，Bei Jing，100091）Abstract:For the purpose of improving the timeliness performance of chaotic signals de-noising based on ensemble empirical mode decomposition(EEMD), An improved EEMD method was proposed. The wavelet packet method is taken as the pre-filter of EEMD, thus some white noise was removed and the superposition times of Gauss white noise were reduced greatly, and then it is combined with the characteristics restraining mode mixing of EEMD to extract the chaotic signal from complex strong disturbances fleetly. The process of the proposed method was discussed in detail with two-degree-freedom chaotic vibration signals, and the results show that the contaminated noise can be filtered normally.Key words:chaotic signal; wavelet transform; de-noising; EEMDHuang等[1]提出了处理非线性非平稳信号的新方法—经验模态分解（Empirical Mode Decomposition, EMD），与小波变换方法相比，EMD无需信号的先验知识，其分解完全依赖信号本身，数据分解真实可靠。

非均匀噪声背景下混合信号DOA估计算法

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电磁兼容EMC的基础知识：模式噪声和共模噪声

电磁兼容EMC的基础知识：模式噪声和共模噪声电磁干扰EMI可以大致分为“传导发射”和“辐射发射”两种类型，其中，根据传导的类型，传导发射可以进一步分为两种类型，“差分（正常）模式噪声”和“共模噪声”。

在本节中，我们将解释后两种类型的噪声。

差分（正常）模式噪声和共模噪声传导发射可分为两种类型，一种是“差模噪声”，也称为“正常模式噪声”。

这些名称有时会根据适用的条件有选择地使用，但在这里我们假设它们是相同的，另一种类型是“共模噪声”。

使用下图解释这些。

这里的讨论基于电源，因此这些图是带有电路的印刷电路板（PCB）容纳在外壳内，外部供电的示例。

在差模噪声中，噪声源出现在电源线上并与电源线串联，并且噪声电流以与电源电流相同的方向流动，它被称为“差分模式”，因为输出和返回电流是相反方向的。

共模噪声是这样的噪声，其中通过杂散电容等泄漏的噪声电流通过地并返回到电源线。

它被称为“共模”噪声，因为电源正（+）和负（- ）侧的噪声电流方向具有相同的方向。

电源线上不会出现噪声电压。

如上所述，这些类型的噪声是传导发射，然而，噪声电流在电源线中流动，因此噪声被辐射。

由差模噪声引起的辐射的电场强度Ed可以使用下面的等式表示，Id是差分模式下的噪声电流，r是到观察点的距离，f是噪声频率，差模噪声会产生噪声电流环路，因此环路区域S成为一个重要因素，如图和等式所示，如果其他元素是恒定的，则对于更大的环区域，电场强度更高。

由共模噪声引起的辐射的电场强度Ec可以由右下方的等式表示，如图和方程所示，电缆长度L是一个重要因素。

这里，为了确认由于不同类型的噪声引起的辐射特性，我们将插入实际数值来计算电场强度，每种情况下的条件完全相同，观察到的电场强度由蓝点表示。

在这些计算结果中重要的是，对于相同的噪声电流值，由共模噪声引起的辐射要大得多（在该示例中，大约大100倍），在任何情况下，如果构成电磁干扰EMI的这些类型的传导发射和辐射发射中的任何一种超过允许的范围，则噪声对策变得必要。

Common Mode Filter Design Guide

Common M ode F ilter D esign G uideIntroductionThe selection of component values for common mode filters need not be a difficult and confusing process. The use of standard filter alignments can be utilized to achieve a relatively simple and straightforward design process, though such alignments may readily be modified to utilize pre-defined component values.GeneralLine filters prevent excessive noise from being conducted between electronic equipment and the AC line; generally, the emphasis is on protecting the AC line. Figure 1 shows the use of a common mode filter between the AC line (via impedance matching circuitry) and a (noisy) power con-verter. The direction of common mode noise (noise on both lines occurring simultaneously referred to earth ground) is from the load and into the filter, where the noise common to both lines becomes sufficiently attenuated. The result-ing common mode output of the filter onto the AC line (via impedance matching circuitry) is then negligible.Figure 1.Generalized line filteringThe design of a common mode filter is essentially the design of two identical differential filters, one for each of the two polarity lines with the inductors of each side coupled by a single core:L2Figure 2.The common mode inductorFor a differential input current ( (A) to (B) through L1 and (B) to (A) through L2), the net magnetic flux which is coupled between the two inductors is zero.Any inductance encountered by the differential signal is then the result of imperfect coupling of the two chokes; they perform as independent components with their leak-age inductances responding to the differential signal: the leakage inductances attenuate the differential signal. When the inductors, L1 and L2, encounter an identical signal of the same polarity referred to ground (common mode signal), they each contribute a net, non-zero flux in the shared core; the inductors thus perform as indepen-dent components with their mutual inductance respond-ing to the common signal: the mutual inductance then attenuates this common signal.The First Order FilterThe simplest and least expensive filter to design is a first order filter; this type of filter uses a single reactive component to store certain bands of a spectral energy without passing this energy to the load. In the case of a low pass common mode filter, a common mode choke is the reactive element employed.The value of inductance required of the choke is simply the load in Ohms divided by the radian frequency at and above which the signal is to be attenuated. For example, attenu-ation at and above 4000 Hz into a 50⏲ load would require a 1.99 mH (50/(2π x 4000)) inductor. The resulting common mode filter configuration would be as follows:50Ω1.99 mHFigure 3.A first order (single pole) common mode filter The attenuation at 4000 Hz would be 3 dB, increasing at 6 dB per octave. Because of the predominant inductor dependence of a first order filter, the variations of actual choke inductance must be considered. For example, a ±20% variation of rated inductance means that the nominal 3 dB frequency of 4000 Hz could actually be anywhere in the range from 3332 Hz to 4999 Hz. It is typical for the inductance value of a common mode choketo be specified as a minimum requirement, thus insuring that the crossover frequency not be shifted too high.However, some care should be observed in choosing a choke for a first order low pass filter because a much higher than typical or minimum value of inductance may limit the choke’s useful band of attenuation.Second Order FiltersA second order filter uses two reactive components and has two advantages over the first order filter: 1) ideally, a second order filter provides 12 dB per octave attenuation (four times that of a first order filter) after the cutoff point,and 2) it provides greater attenuation at frequencies above inductor self-resonance (See Figure 4).One of the critical factors involved in the operation of higher order filters is the attenuating character at the corner frequency. Assuming tight coupling of the filter components and reasonable coupling of the choke itself (conditions we would expect to achieve), the gain near the cutoff point may be very large (several dB); moreover, the time response would be slow and oscillatory. On the other hand, the gain at the crossover point may also be less than the presumed -3 dB (3 dB attenuation), providing a good transient response, but frequency response near and below the corner frequency could be less than optimally flat.In the design of a second order filter, the damping factor (usually signified by the Greek letter zeta (ζ )) describes both the gain at the corner frequency and the time response of the filter. Figure (5) shows normalized plots of the gain versus frequency for various values of zeta.Figure 4.Analysis of a second order (two pole) common modelow pass filterThe design of a second order filter requires more care and analysis than a first order filter to obtain a suitable response near the cutoff point, but there is less concern needed at higher frequencies as previously mentioned.A ≡ ζ = 0.1;B ≡ ζ = 0.5;C ≡ ζ = 0.707;D ≡ ζ = 1.0;E ≡ ζ = 4.0Figure 5.Second order frequency response for variousdamping f actors (ζ)As the damping factor becomes smaller, the gain at the corner frequency becomes larger; the ideal limit for zero damping would be infinite gain. The inherent parasitics of real components reduce the gain expected from ideal components, but tailoring the frequency response within the few octaves of critical cutoff point is still effectively a function of ideal filter parameters (i.e., frequency, capaci-tance, inductance, resistance).L0.1W n1W n 10W nRadian Frequency,WG a i n (d B )V s V s LR s LCs LC j L R j LC LR LCCMout CMin L L n n n L ()()=++=−+⎛⎝⎜⎞⎠⎟=+−⎛⎝⎜⎞⎠⎟≡≡≡≡111111212222ωωζωωωωωωζradian frequencyR the noise load resistance LFor some types of filters, the design and damping char-acteristics may need to be maintained to meet specific performance requirements. For many actual line filters,however, a damping factor of approximately 1 or greater and a cutoff frequency within about an octave of the calculated ideal should provide suitable filtering.The following is an example of a second order low pass filter design:1)Identify the required cutoff frequency:For this example, suppose we have a switching power supply (for use in equipment covered by UL478) that is actually 24 dB noisier at 60 KH z than permissible for the intended application. For a second order filter (12dB/octave roll off) the desired corner frequency would be 15 KHz.2)Identify the load resistance at the cutoff frequency:Assume R L = 50 Ω3)Choose the desired damping factor:Choose a minimum of 0.707 which will provide 3 dB attenuation at the corner frequency while providing favorable control over filter ringing.4)Calculate required component values:Note:Damping factors much greater than 1 may causeunacceptably high attenuation of lower frequen-cies whereas a damping factor much less than 0.707 may cause undesired ringing and the filter may itself produce noise.Third Order FiltersA third order filter ideally yields an attenuation of 18 dB per octave above the cutoff point (or cutoff points if the three corner frequencies are not simultaneous); this is the prominently positive aspect of this higher order filter. The primary disadvantage is cost since three reactive compo-nents are now required. H igher than third order filters are generally cost-prohibitive.Figure 6.Analysis of a third order (three pole) low pass filter where ω1, ω2 and ω4 occur at the same -3dB frequency of ω05)Choose available components:C = 0.05 µF (Largest standard capacitor value that will meet leakage current requirements for UL478/CSA C22.2 No. 1: a 300% decrease from design)L = 2.1 mH (Approx. 300% larger than design to compensate for reduction or capacitance: Coilcraft standard part #E3493-A)6)Calculate actual frequency, damping factor, and at-tenuation for components chosen:ζ = 2.05 (a damping factor of about 1 or more is acceptible)Attenuation = (12 dB/octave) x 2 octaves = 24 dB 7)The resulting filter is that of figure (4) with:L = 2.1 mH; C = 0.05 µF; R L = 50 ΩL 1L 2VCMout s VCMin s R R L s R L s sC R L s sC R L s L L s L s sC L L R s L Cs L L C R s L L L L L L L()()()()=+⎛⎝⎜⎞⎠⎟+++++⎛⎝⎜⎜⎜⎜⎞⎠⎟⎟⎟⎟=++++222121*********11Butterworth →+++112212233s s s n n n ωωω()()L L R R L L L n n L 12111222+==+ωω;()L L C n 1n2C =2;ωω2211414=.L L L L n n n 12L n3n2L2n2L2C R =1;R R ωωωωωω33224422===ωπωζωμn n n Lf C L L R L =====294248070727502rad /sec =1Hn .1215532πLC=Hz (very nearly 15KHz)The design of a generic filter is readily accomplished by using standard alignments such as the Butterworth (“maxi-mally flat”) alignments. Figure (6) shows the general analysis and component relationships to the Butterworth alignments for a third order low pass filter. Butterworth alignments provide an inherent ζ of 0.707 and a -3 dB point at the crossover frequency. The Butterworth alignments for the first three orders of low pass filters are shown in Figure (7).The design of a line filter need not obey the Butterworth alignments precisely (although such alignments do pro-vide a good basis for design); moreover, because of leakage current limits placed upon electronic equipment (thus limiting the amount of filter capacitance to ground),adjustments to the alignments are usually required, but they can be executed very simply as follows:1)First design a second order low pass with ζ ≥ 0.52)Add a third pole (which has the desired corner fre-quency) by cascading a second inductor between the second order filter and the noise load:L = R/ (2 π f c )Where f c is the desired corner frequency.Design ProcedureThe following example determines the required compo-nent values for a third order filter (for the same require-ments as the previous second order design example).1)List the desired crossover frequency, load resistance:Choose f c = 15000 Hz Choose R L = 50 Ω2)Design a second order filter with ζ = 0.5 (see second order example above):3)Design the third pole:R L /(2πf c ) = L 250/(2π15000) = 0.531 mH4)Choose available components and check the resulting cutoff frequency and attenuation:L2 = 0.508 mH (Coilcraft #E3506-A)f n= R/(2πL 1 )= 15665 HzAttenuation at 60 KHZ: 24 dB (second order filter) +2.9 octave × 6 = 41.4 dB5)The resulting filter configuration is that of figure (6)with:L 1 = 2.1 mH L 2 = 0.508 mH R L = 50 ΩConclusionsSpecific filter alignments may be calculated by manipu-lating the transfer function coefficients (component val-ues) of a filter to achieve a specific damping factor.A step-by-step design procedure may utilize standard filter alignments, eliminating the need to calculate the damping factor directly for critical filtering. Line filters,with their unique requirements, yet non-critical character-istics, are easily designed using a minimum allowable damping factor.Standard filter alignments assume ideal filter compo-nents; this does not necessarily hold true, especially at higher frequencies. For a discussion of the non-ideal character of common mode filter inductors refer to the application note “Common Mode Filter Inductor Analysis,”available from Coilcraft.Figure 7.The first three order low pass filters and their Butterworth alignmentse i +–e O +–R LL 2Ce i +–e O +–R LL 1Ce i +–e O +–R LL 1L 2Filter SchematicFilter Transfer FunctionButterworthAlignmentFirst OrderSecond OrderThird Ordere e Ls R o iL =+11e e LCs Ls R oi L=++112e e L L R s L Cs L L s R o iLL =++++111231212()e e s o in=+11ωe e LCs Ls R oiL =++112e e s s so i n n n =+++122133221ωωω。

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0-7803-5867-8/00/$10.00 (c) 2000 IEEE
dotted lines in the figure. CM noise is, in general, voltage dependent. Both DM and CM can be measured using a noise separator [2] in which DM is the difference, and CM is the average of the two voltages Vx and Vy.
Mixed-Mode EMI Noise and Its Implications to Filter Design in Offline Switching Power Supplies †
Song Qu‡
Dan Y. Chen
Center for Power Electronic Systems
2.2 Mixed-Mode (MM) Phenomenon
DM noise current coupling path as indicated in Fig.1 passes through the input rectifier diodes (D1 to D4). The measured EMI noise envelop fluctuates with time because of rectifier diode “on” and “off”. Obviously, the worst EMI has to pass the specification. One question is asked: “Is the noise larger when diodes are ‘on’ or when diodes are ‘off’?” One would think that the noise magnitude should be larger when diodes are “on” because the noise current can couple to R1 and R2 with less impedance in the path. However, the measurement indicates otherwise, as reported in [1]. Further exploration of this fact leads to the discovery of this new mode of noise coupling.
Virginia Polytechnic Institute & State University
Blacksburg, VA 24061
Abstract- Analysis of the newly discovered MixedMode EMI noises provides a better understanding of the filter attenuation mechanism. Many practical design issues are investigated from this point of view. Hopefully, the results given in the paper reduce the mystery and the cut-and-try process in filter design in offline power supplies.
0.15MHz
Frequency (MHz)
30MHz
(a) Typical DM Noise Spectrum The Envelop is Fluctuating with Time due to Rectifier Diodes “on”
and “off”
Without cap
With X cap
II. REVIEW OF MIXED-MODE (MM) NOISES
2.1 Conventional Theory of Noise Coupling
Fig.1 shows the circuit diagram for conducted EMI measurement for an offline Flyback converter. A standard Line Impedance Stabilizing Network (LISN) is used for the measurement. In the LISN,
I. INTRODUCTION
Electromagnetic Interference (EMI) problems in switching power supplies have been traditionally treated with cut-and-try approaches. In recent years, advancement has been made to better understand the problems and minimize the cut-and-try design process. However, there are still phenomena difficult to explain in many practical design situations. Often, the problems may be solved by luck but many puzzles remain unresolved and are very likely to come back to haunt the designers.
According to the conventional theory, there are two modes of conducted EMI noise: the DifferentialMode (DM) noise and the Common-Mode (CM) noise. Recently, a new noise-coupling mode in an offline power supply, called Non-Intrinsic Differential-Mode (NIDM) noise, has been uncovered [1]. The generation mechanism of this mode of noise is similar to that of CM noise, but the noise can be suppressed by using DM capacitor (sometimes called X cap) [1]. For this reason, NIDM noise is for the first time called “Mixed-Mode” noise in this paper. The focus of the paper is to investigate the Mixed-Mode (MM) phenomenon and its implications to practical EMI filter design issues.
DM Noise Path CM Noise Path
In the paper, Mixed-Mode noise will be first reviewed. An understanding of this phenomenon is crucial to the understanding of the remaining of the present paper. Then many filter design issues pertinent to MM noise will be investigated. It turns out that many puzzles encountered in filter design can be explained with this Mixed-Mode noise.
there are inductors, capacitors and two 50Ω resistors R1 and R2. For noise frequency the two inductors
present high impedance and the two 0.1µF capacitors present small impedance. The noise voltage coupled through the two resistors R1 and R2 are counted as the conducted EMI. Vx is the line-side EMI and Vy is the neutral-side EMI. Both have to pass the EMI specifications.
Fig.1 Conducted Noise Emission Model
DM noise is coupled to R1 and R2 because of pulsating switching current. The dash-and-dot lines in the figure indicate DM coupling path. And DM noise is, in general, load current dependent. CM noise is coupled through R1 and R2 by MOSFET parasitic capacitance Cp because of the switching of MOSFET. CM coupling path is indicated by the
† This work made use of ERC Shared Facility supported by the National Science Foundation under award number EEC-9731677. ‡ The author is with Cherry Semiconductor, East Greenwich, RI 02818. Phone: 401-886-3850, Email: saq@.