Optimization of Modulation Waveforms for Improved EMI Attenuation in Switching Frequency Modulated Power Converters

Electromagnetic interference (EMI) is one of the major problems of switching power converters. This paper is devoted to switching frequency modulation used for conducted EMI suppression in switching power converters. Comprehensive theoretical analysis of switching power converter conducted EMI spectrum and EMI attenuation due the use of traditional ramp and multislope ramp modulation waveforms is presented. Expressions to calculate EMI spectrum and attenuation are derived. Optimization procedure of the multislope ramp modulation waveform is proposed to get maximum benefits from switching frequency modulation for EMI reduction. Experimental verification is also performed to prove that the optimized multislope ramp modulation waveform is very useful solution for effective EMI reduction in switching power converters.


Introduction
Switching power converters (SPC) used in many electronic devices for electric power conversion are noticeable sources of electromagnetic interference (EMI) which can deteriorate normal operation of other electronic equipment.EMI both conducted and radiated must be reduced in order to meet international electromagnetic compatibility standards (e.g.CISPR 22) requirements.Traditional ways for conducted EMI re-duction usually are input EMI filters, proper design of printed circuit boards, soft-switching techniques, etc.
Recently two more novel conducted EMI reduction techniques have been proposed and used [1], [2], [3], [4], [5].The first one is active EMI filtering using digital signal processing [4] and the second one is spread spectrum technique [3].The spread spectrum technique which is usually based on switching frequency modulation (SFM) is very attractive technique mainly because it is simple to implement.By modulating the switching frequency peak conducted EMI levels can be easily suppressed using simple periodic modulation waveforms (such as sine, triangle, sawtooth, etc) as shown in Fig. 3.The main parameters of periodic SFM are switching frequency deviation ∆f sw , modulation frequency f m and modulating waveform m(t) with unitary amplitude.Of course, for modulating the switching frequency random and chaotic signals can be used, but the use of simple periodic modulation waveforms is more popular in practical SPC, mainly because negative effect of periodic SFM on peak-to-peak output voltage ripples is less visible and periodic SFM is simpler to implement than random or chaotic SFM [6], [7].
Benefits of periodic SFM for EMI reduction can be significantly reduced due to amplitude modulation of SPC currents caused by SFM [8].The amplitude modulation leads to EMI spectrum sidebands distortion and asymmetry with respect to central switching frequency f sw0 and consequently EMI attenuation is lower than expected for the given value of modulation index [8], [9].In order to increase effectiveness of SFM for EMI reduction in SPC (especially for higher values of ∆f sw ), multislope ramp modulating waveform (MRMW) was proposed by S. Johnson and R. Zane [8].Slopes of the MRMW are set by parameter t 0 (Fig. 5).
As it is stated in [8], electronic ballast output current spectral distortion and output EMI can be effectively reduced when t 0 = 0.35T m (where T m is modulation period).However as it will be proved in our paper, t 0 is the function of both ∆f sw and f m .Thus t 0 = 0.35T m can be optimal only for one set of ∆f sw and f m values (e.g. for ∆f sw = 5 kHz and f m = 500 Hz), but for the other set of values of the parameters, it can even worsen EMI attenuation and be less effective than traditional ramp modulating waveform.Therefore optimization of MRMW is necessary.Lack of the theoretical analysis in [8] does not give a possibility to calculate optimum values of t 0 to get maximum EMI attenuation.Thus the main aim of the paper is to make the theoretical analysis of EMI spectrum and its attenuation due to the use of MRMW and propose a procedure for optimum t 0 values calculation in order to get full benefits from the use of MRMW for EMI reduction in SFM SPC.
The paper is organized as follows.In the section 2 effect of SFM on conducted EMI of boost converter is theoretically analyzed in details.In the section 3 theoretical analysis of conducted EMI and attenuation due to the use of MRMW is presented, expressions to calculate EMI spectrum are derived and procedure to calculate optimum t 0 values is proposed.In the section 4 experimental verification of the theoretical results is performed.And finally, in the section 5 conclusions are given.

Effect of SFM on Conducted EMI
In the analysis boost DC-DC converter operating in continuous conduction mode will be used (Fig. 1).Since for conducted EMI measurements line impedance stabilization network (LISN) is used, it will be taken into account.To simplify the analysis several assumptions will be considered: • conducted EMI dominates at lower frequencies, because fundamental switching frequency harmonic amplitude is more pronounced than others [5], [10], Fig. 2: Simple boost SPC model.For boost SPC: Note the model is modified version taken from [11].
• conducted EMI levels are the highest when duty ratio D of control signal is 50 % [3], • inductor, power switch and diode voltages are of rectangular shape.
Considering the assumptions described above, simple EMI model [11] can be used as shown in Fig. 2. The model can be used up to several MHz.For higher frequencies more complex models (taking into account other non-idealities) should be used.Using the model the transfer function between equivalent noise source V ens and V LISN can be derived [9]: where Z e = (25 + Z C5 /2)(5 C h is parasitic capacitance between MOSFET drain and grounded heatsink; Z Cin is real input capacitor complex impedance and Z L is real power inductor complex impedance. If f sw0 /f m is an integer number then period of SFM voltage or current equals modulation waveform period T m .In this case complex Fourier series coefficients for SFM V ens (Fig. 2) can be derived as follows: where an integer number N = 2f sw0 /f m ; time instants t k at which V ens crosses zero (Fig. 2) can be calculated by solving the equation [12]: where time-dependent phase angle [3]: By solving Eq. ( 3) simple expression to calculate t k can be derived.For example, for sawtooth SFM it is [9]: where minimum switching frequency In general f sw0 /f m is not an integer number.In this case period of SFM voltage or current does not equal T m but it equals KT m , where positive integer K can be calculated as follows: where F and K are least positive integers.Let us consider two examples: • if f sw0 = 80 kHz and f m = 3 kHz (T m = 1/3 ms), then K = 3, F = 80 and SFM signal period is 3T m = 1 ms.In general case (when f sw0 /f m is not an integer) complex Fourier series coefficients for SFM V ens can be calculated using the following expression: In order to calculate V LISN (conducted EMI) spectrum the following Eq.( 8) can be used where n = 1, 2, 3 . . .
As an example calculated V LISN spectra of boost SPC with and without SFM are shown in Fig. 3. SFM leads to EMI spectrum spreading and in its turn to EMI attenuation.The attenuation (A EM I ) which is the difference in dB between maximum amplitude of unmodulated and SFM conducted EMI spectra in the frequency range of interest can be calculated as follows [9], [13]: where S V LISN and S V LISN 1 are unmodulated and SFM V LISN spectra.As an example, calculated A EM I versus ∆f sw is shown in Fig. 4.

Improving EMI Attenuation Using Optimization of MRMW
Fundamental switching frequency sideband can become highly asymmetrical with respect to f sw0 (Fig. 3) due to parasitic amplitude modulation of SPC currents [8], [9].As it is proved in [8], [9] this leads to degradation of benefits of SFM because EMI attenuation is lower than it is expected for the given set of values of ∆f sw and f m .In order to increase effectiveness of the use of SFM for EMI reduction in SPC (especially for higher values of ∆f sw ), multislope ramp modulating waveform (MRMW) can be used [8].

Theoretical Analysis of MRMW
In this subsection comprehensive theoretical analysis of MRMW for conducted EMI reduction in boost SPC will be done.
As it can be seen from Fig. 5 slopes of the MRMW are set by parameter t 0 .V LISN spectrum can be calculated using Eq. ( 7) and Eq. ( 8).However it should be noted that in the case of MRMW (when t 0 = 0.5T m ) central switching frequency is: Time instants t K at which V ens crosses zero (Fig. 2) can be calculated by solving the following Eq.( 11): where time dependent phase angle can be derived using Eq. ( 4) as follows: where a = 0.5 − t 0 /T m ; b = T m (p − 1); p is modulation period number(p = 1, 2, 3 . . .K).
Following the derivations given in App.A, time instants t k can be derived as follows ( 12) where b 1 = f sw01 −∆f sw (1+a+b/t 0 ); a 1 = ∆f sw /(2t 0 ); + aT m (p − 1) − 1 2 t 0 .V LISN spectra and EMI attenuation due to the use of MRMW can be calculated using Eq. ( 7), Eq. ( 8), Eq. ( 9), Eq. ( 10), Eq. ( 11), Eq. ( 12), Eq. ( 13).For all the calculations Matlab software is used.As an example A EM I as a function of both t 0 /T m and ∆f sw for f m = 1 kHz is shown in Fig. 6.But in Fig. 7 A EM I as a function of t 0 /T m for different values of f m is also shown.Presented results clearly show that optimum t 0 for which EMI attenuation is maximum is function of both ∆f sw and f m .That is why for a given set of ∆f sw and f m values optimum t 0 value should be found.For example, if f m = 1 kHz and ∆f sw = 40 kHz, then (according to Fig. 7) optimum value of t 0 is 0.23 and maximum A EM I is 16.8 dB; if f m = 10 kHz and ∆f sw = 40 kHz, then (according to Fig. 7) optimum value of t 0 is 0.34 and maximum A EM I is 7.5 dB.

MRMW Optimization Procedure
In order to get full benefits from the use of MRMW for EMI reduction procedure for optimum t 0 value calculations is to be proposed.The optimization procedure can be used not only for boost converter with different specifications but also for other power converter topologies.Since f m and ∆f sw can affect not only EMI attenuation, but also other SPC parameters, such as peak-to-peak output voltage ripples, then recommendations for the choice of f m and ∆f sw values proposed in [8], [14] will be taken into account in the procedure.
The MRMW optimization procedure is as follows: • choose f m slightly higher than RBW (resolution bandwidth) of a spectrum or EMI analyzer [8], • choose ∆f sw lower than ∆f swcr at which peak-topeak output voltage ripples are equal to maximally allowable values [14], • derive conducted EMI equivalent circuit model (with LISN), • derive analytic expression for complex transfer function K EM I (f ) between equivalent noise source V ens and V LISN , • calculate values of B 1 and B 2 for V ens , • change t 0 with a small step (e.g.0.01), and using Eq. ( 7), Eq. ( 8), Eq. ( 9), Eq. ( 10), Eq. ( 11), calculate V LISN spectrum and A EM I for each value of t 0 in the range 0.1 − 0.9, • find global maximum for all A EM I values calculated in the previous step and find optimum t 0 for which A EM I is maximum, • end.
For determining optimized t 0 value Matlab software algorithm has been implemented.Matlab code for the optimization procedure is shown in App.B.
In order to show usefulness of the optimization procedure proposed, let us consider one example.Let us assume that we have boost converter with the following specifications: V in = 4 . . .

1) 1 st
Step: Choice of f m Since CISPR16 in Band A requires conducted EMI measurements to be done with RBW = 200 Hz and f m should be higher than RBW, let us choose f m = 1 kHz.

2) 2 nd
Step: Choice of ∆f sw According to the procedure ∆f sw should be lower than ∆f swcr at which V pp max are equal to maximally allowable values.In order to calculate ∆f swcr expression for the V pp max calculation should be derived.The expression for the boost converter is as follows [15] V pp max = If f sw is modulated then f sw min = f sw0 − ∆f swcr should be substituted in Eq. ( 14) instead of f sw .It can be derived that From Eq. ( 15) it can be obtained that ∆f swcr = 40.4kHz.So ∆f sw is chosen to be 40 kHz.

3) 3 rd
Step Boost converter conducted EMI equivalent circuit model (with LISN) is derived as shown in Fig. 2.
c 2015 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING Fig. 8: V LISN spectra before and after the use of SFM with optimized MRMW (t 0 = 0.23Tm).Other modulation and circuit parameters: the same as in Fig. 3. Note: V LISN spectrum when non-optimized ramp modulation waveform is used is shown in Fig. 3.

4) 4 th
Step Analytic expression for complex transfer function K EM I (f ) between equivalent noise source V ens and V LISN is derived according to Eq. (1).

6) Final step
Using Matlab code shown in App.B optimum t 0 is calculated to be 0.23.
V LISN spectrum after the optimization of MRMW is shown in Fig. 8.As it can be seen from Fig. 3, Fig. 8 and Fig. 13d the use of optimized MRMW gives  3.5 dB better A EM I than the use of conventional ramp modulation waveform (when t 0 = 0.5T m ) and 1.7 dB better A EM I than the use of MRMW proposed in [8] (when t 0 = 0.35T m ).Comparison of A EM I versus ∆f sw for conventional ramp modulation waveform and optimized MRMW is depicted in Fig. 9.The results clearly show that optimized MRMW is more useful for higher ∆f sw .

Experimental Setup
For the experimental verifications a low power SFM boost SPC is used (Fig. 11).The converter operates in open-loop continuous conduction mode.Duty ratio D and input voltage of the converter can be varied.However in the experiments duty ratio of 50 % is chosen because from conducted EMI point of view it is the worst situation [3].Input DC voltage of the converter can be changed from 2 V to 8 V. Nominal switching frequency is 80 kHz.Nominal output power is 20 W. In the experiments power MOSFET is used with grounded external heatsink.Measured parasitic capacitance C h between MOSFET drain and ground is of about 10 pF.Arbitrary waveform generator (AWG) Agilent 33220A controls the power MOSFET via MOS-FET driver ICL7667.The control signal of the power MOSFET can be both unmodulated and switching frequency modulated.All the necessary SFM parameters (including t 0 ) can be set using the AWG which has built-in frequency modulator and waveform editor.MRMW with custom t 0 can be obtained using the waveform editor.Figure 12 depicts the photo of the AWG Agilent 33220A front panel and display.

Experimental Results
Conducted EMI (V LISN spectrum) is measured using Agilent E4402B spectrum analyzer with RBW=200 Hz and peak detector.Experiments have been done for different V in and output power values.Comparison of the experimental and the theoretical V LISN spectra when V in = 4 V and D = 50 % is presented in Fig. 13.Experiments revealed that changing input voltage and output load does not have any noticeable influence on EMI attenuation and optimized t 0 value.Experimental results confirm theoretical predictions that the use of optimized MRMW can noticeably increase EMI attenuation: the use of optimized MRMW gives 3.8 dB better A EM I than the use of conventional ramp modulation waveform (when t 0 = 0.5T m ) and 2 dB better A EM I than the use of MRMW proposed in [8] (when t 0 = 0.35T m ).Experimental and theoretical results are in a good agreement: when ∆f sw was increased to 40 kHz, experimental EMI attenuation increased to 16.9 dB, but theoretical one to 16.8 dB.

Conclusion
Comprehensive theoretical analysis of SPC conducted EMI spectrum and attenuation presented in the paper shows that the use of multislope ramp modulation waveform can noticeably improve EMI reduction in switching-frequency-modulated switching power converters.However in order to get full benefits from the use of MRMW, optimum value of the parameter t 0 which controls the slopes of the waveform should be found.For this purpose the optimization procedure has been proposed and usefulness of the procedure has been verified experimentally using boost SPC.The procedure is based on the analytic expressions derived for conducted EMI spectrum and attenuation calculation.

Fig. 1 :
Fig. 1: Typical conducted EMI measurement setup (top) and boost SPC schematic diagram with LISN (bottom) used in the analysis.
8 V, D max = 50 %, c 2015 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING

Fig. 7 :
Fig. 7: Theoretically calculated A EM I as a function of t 0 /Tm for different fm Parameters: ∆fsw = 40 kHz and f sw0 = 80 kHz.

Fig. 9 :
Fig. 9: Calculated A EM I (when t 0 = 0.5Tm) and A EM I1(when optimum t 0 is used) as a function of ∆fsw for fm = 1 kHz and f sw0 = 80 kHz.