LCC环路反馈设计Feedback Loop Design of an LLC Resonant Power Converter.pdf

Application ReportSLUA582AOctober 2010Revised November 2010Feedback Loop Design of an LLC Resonant PowerConverterHong Huang.Power-Supply Control ProductsABSTRACTThis application note describes an approach to design feedback loop compensation for an LLC resonanthalf-bridge power converter.The approach described here is based on the measured Bode plots of themodulator generated by a network analyzer.As we know,as long as the modulator Bode plots areobtained,the frequency domain poles and zeros in the feedback loop compensation can be analyticallydetermined,then fine-tuned with a bench test.This measurement is necessary as part of feedback loopdesign because a practical small-signal model is not available for LLC resonant converters.This documentuses the Texas Instruments UCC25600 as the frequency controller.A detailed description of theUCC25600 and its associated example design fixture,the UCC25600EVM-341,can be found in theproduct data sheet and the evaluation module users guide,respectively;both additional documents areavailable for download at .Contents1Control Loop Description of an LLC Converter.22Loop Compensation Design Approach.43Methodology.54References.8List of Figures1Block Diagram of a Typical LLC Resonant Half-Bridge Converter.22Another Way to Define Gm(w)and Gc(w).33Initial Gm(w)Measurement.64Re-Measurement of Gm(w).75Design of Gc(w).76Feedback Loop Bode Plots After Final Values Set.81SLUA582AOctober 2010Revised November 2010Feedback Loop Design of an LLC Resonant Power ConverterSubmit Documentation Feedback 2010,Texas Instruments IncorporatedC1CrR1R3R4Q1D1D2LrLmQ2R5R2VSCRSCRXVrefVoutVrVinVSUCC25600GateDrivefControlSW-FrequencyModulatorT1n:1:1FBOFBRFBCCTRG(s)cG(s)mRTG(s)=lp=G(s)G(s)cmV(s)V(s)outrG()=lpw=G()G()cmw wV()V()outrwwControl Loop Description of an LLC C1Control Loop Description of an LLC ConverterNOTE:For complete details on the design of an LLC resonant power converter,the recommendedreference is SEM1900 Topic 3,Designing an LLC Resonant Half-Bridge Power Converter.This application note will not repeat the discussion of these details.Figure 1 shows a typical block diagram of an LLC resonant converter.Figure 1.Block Diagram of a Typical LLC Resonant Half-Bridge ConverterThis diagram consists of two blocks:the modulator and the compensator,expressed in the respectivetransfer functions of Gm(s)and Gc(s),or Gm(jw)and Gc(jw).In Figure 1,the red outline defines the Gm(s)transfer function,and the blue outline defines the Gc(s)transfer function.Gm(w)and Gc(w)can be used to express Gm(jw)and Gc(jw)respectively in shorthand,where j=1 canbe omitted without confusion.Then the loop gain transfer function Glp(s),or Glp(w),is expressed asEquation 1.(1)or as Equation 2:(2)2Feedback Loop Design of an LLC Resonant Power ConverterSLUA582AOctober 2010Revised November 2010Submit Documentation Feedback 2010,Texas Instruments IncorporatedG()=mwFBOFBCG()=cwFBCFBRG()=lpwFBOFBRC1CrR1R3R4Q1D1D2LrLmQ2R5R2VSCRSCRXVrefVoutVrVinVSUCC25600GateDrivefControlSW-FrequencyModulatorT1n:1:1FBOFBRFBCCTRG()cwG()mwRTControl Loop Description of an LLC ConverterBoth Gm(w)and Gc(w)can be measured with a frequency sweeping signal applied on resistor RSC,asthese equations show:(3)(4)The loop gain transfer function Glp(w)is measurable and obtained as Equation 5.(5)It is obvious that FBC can be assigned at different locations in the converter circuit.For example,it can bemoved to the optocoupler input as Figure 2 illustrates.Here,the red area and the blue area represent theGm(w)and Gc(w)functions,respectively,as they do in Figure 1.Figure 2.Another Way to Define Gm(w)and Gc(w)In this position,then,the measured Gm(w)and Gc(w)are different from those measured in Figure 1.Note that it is possible to define Gm(w)and Gc(w)in several different ways.But Glp(w)will be the same,regardless of how Gm(w)and Gc(w)are defined.In this document,we use the definition as shown inFigure 1 to avoid confusion.3SLUA582AOctober 2010Revised November 2010Feedback Loop Design of an LLC Resonant Power ConverterSubmit Documentation Feedback 2010,Texas Instruments IncorporatedG(s)=cswIswp_opto+1(+1s1R1 C1wI=RCTR4RRC321G(s)=cjwwIjwwp_opto+1(+1=jw11jwwIR1 C1with:R1=0wwp_optojwwIG()=cw=1=wwIjwwI|G()|=cwfiLoop Compensation Design A2Loop Compensation Design ApproachUnlike Gm(w),Gc(w)can be expressed analytically.As shown in Figure 1,if we use Type I compensation,then Gc(w)is expressed as Equation 6:(6)Where wp_optois the angular frequency of the optocoupler frequency-domain pole.This value can betypically considered to be approximately wp_opto=2p 10 kHz,although the value varies with the particularoptocoupler in the circuit as well as with the bias point.CTR is the optocoupler current transfer ratio;theangular frequency wIis the gain of the frequency domain pole at origin;and therefore,we arrive at:(7)The angular frequency wIis the 0-dB crossover of Gc(w)when we set R1=0 and ignore wp_optoat alow-frequency range.In fact:(8)If we let|Gc(w)|=1,then:(9)To compensate the LLC converter feedback loop,Gm(w)must first be obtained by measurement.To makeGm(w)measurable,the feedback loop must be stable,which is our design goal yet to be achieved.So weare now in a circle that we must break in order to achieve our design goal.To break this circle,onecommon technique is to use a large-value capacitor for C1in Figure 1 to push the loop bandwidth(that is,the gain crossover frequency)low enough in the expectation that the loop can be stable enough for initialmeasurement.This idea is workable and allows us to obtain initial Gm(w)value.Sometimes,though,wemay be confused about how large a capacitor is adequate for a specific application in order to make astable Gm(w)measurement.If an estimated C1value is not sufficient,we have a potential risk that theresulting loop may not be stable to measure Gm(w),and potential circuit damage can occur.To avoid these issues,we propose a more reliable approach that combines with the practice of using aninitial low bandwidth measurement from a large value C1.As we know,to maintain output voltageregulation in an LLC resonant converter,the input voltage must be great enough to achieve the desiredoutput voltage.If the input voltage is not sufficient,the output voltage regulation cannot be achievedbecause the maximum gain has already reached its limit.However,even if output regulation is notachieved,the converter is stable,and this stability is not related to the feedback loop parameters.Duringsuch an operation,bench tests show a Gm(w)can continue to be measured in the usual way.Although themeasured Gm(w)is not exactly the same as that obtained from an operation when the output comes intoregulation,it is sufficient to give us an idea of how large the value of C1must be and how wIshould bedesigned.Then,we will be able to complete the remaining design and avoid the risks noted earlier.4Feedback Loop Design of an LLC Resonant Power ConverterSLUA582AOctober 2010Revised November 2010Submit Documentation Feedback 2010,Texas Instruments IncorporatedwI=RCTR4RRCMethodology3MethodologyTo implement this approach,we first must make sure that all other segments of the converter workproperly,especially the associated power stage.This operation is usually called an open-loop test,whichmust be passed to assure full functionality.Then we can close the feedback loop and measure Gc(w)inthis way:We first increase the input voltage slowly from zero and observe the output voltage.Because the input voltage is low,the controller in the feedback loop will generate the maximum gain toraise the output voltage as much to the point of regulation as it can.We then continue to increase the input voltage until the output voltage is close to the regulation(within10%).At that point,we stop increasing the input voltage.The converter should now be stable and quite independent of the feedback loop compensationparameters.Then,we apply a frequency sweeping signal to RSCand measure the Bode plots between FBO andFBC.This measurement gives us the initial Gm(w)value.We can make several more measurements by further increasing the input voltage in 1%increments ifGm(w)does not show good measurement results.However,do not risk increasing the voltage to bring theoutput voltage into regulation yet.Here,we offer an example to show how to make this type of initial Gm(w)measurement,then how todesign the subsequent feedback loop once the measurement is complete.We use theUCC25600EVM-341 as our example with the corresponding circuit diagram shown in Figure 1.Completeschematics for this device are found in the UCC25600EVM-341 User Guide.This converter has these electrical specifications:Input voltage:375 VDCto 405 VDCOutput power(rated):300 WOutput voltage:12 VDCOutput current(rated):25 AOutput voltage line regulation(with IO=1.0 A):1%Output voltage load regulation(at VIN=390 V):1%Output voltage peak-to-peak ripple(at VIN=390 V and IO=25 A):120 mVEfficiency(at VIN=390 V and IO=25 A):90%Switching frequency:70 kHz to 150 kHz in normal operationConverter topology:LLC resonant half-bridge converter3.1Procedure and ResultsStep 1.Gm(w)measurement;C1initial value.In the expression:(10)C1is only the parameter we must determine initially for a stable Gm(w)measurement.The remainingparameters are determined by other design factors and generally have a limited adjustable range.Forexample,CTR is fixed after an optocoupler is selected.Additionally,R3and R4are determined by therequirements of the frequency range and the optocoupler configuration.The value of C1is not critical from our proposed approach.For example,an initial C1value can bebetween 0.1 mF and 1 mF;this range is given only to show some commonly-used values.If C1isoutside these values,the process should work.In this example,we use C1=1.0 mF(note that it doesnot make much difference to use C1=0.1 mF).Step 2.Gm(w)measurement with output voltage not in regulation.As shown in Step 1,the output voltage regulation is 12 V with minimum input voltage 375 V.If we usea voltage much lower than 375 V,the output voltage is not able to enter regulation.A good rule ofthumb is to use an input voltage low enough to keep the output voltage out of regulation,but close to5SLUA582AOctober 2010Revised November 2010Feedback Loop Design of an LLC Resonant Power ConverterSubmit Documentation Feedback 2010,Texas Instruments Incorporated6040200204060-Gain(dB)101001 k10 k100 k1 M18012060060120180-Phase(degrees)UCC25600EVM MODULATOR PLOT(285 V,1 A)Frequency(Hz)GainPhasewpI=102100(Hz)=25.0 rad/s-2820wI=RCTR4RRC321Mthe regulation voltage;say,within 10%.This technique generally should give an acceptablemeasurement.If it does not,a value closer to regulation may be tested,using a 1%increment eachtime until a good measurement is obtained.In this example,when we slowly increase VINto 285 V withIO=1 A,the output voltage showed to be approximately 11 V,which is 8.3%below 12 V.Then wemeasured Gm(w)with an acceptable result.A 25-mV frequency sweeping signal was used during thistest.The Gm(w)measurement is shown in Figure 3.Figure 3.Initial Gm(w)MeasurementStep 3.Determine initial Gc(w)based on Gm(w)measurement.Now we need to design a proper Gc(w)to allow the converter output to enter into regulation.Theminimum switching frequency of the converter is specified at 70 kHz.As a rule of thumb,the gaincrossover frequency should be below one-fifth of its minimum switching frequency.If we use one-tenthof its minimum switching frequency,that allows approximately 7 kHz to cover the entire operatingrange.Keep in mind,though,that we are only at the beginning stages and our primary purpose is toestablish an initial operating point.The Gm(w)obtained so far is also a very preliminary value.As such,we may want to make the target crossover frequency very conservative.Based on the measurementjust obtained,it appears acceptable to set the crossover frequency somewhere around 100 Hz.Oneadvantage to selecting 100 Hz is that it has a flat phase angle close to 0;this response helps toachieve the desired stability as a 90 phase margin can be expected at 100 Hz.Notice,again,thistarget is only an initial design;the final desired value can be adjusted further.At 100 Hz,|Gm(w)|=28 dB.Therefore,we would need to design|Gc(w)|to have:20log(|Gc(w)|)w=2p 100Hz=28 dBBecause the crossover frequency of 100 Hz is a rough number to be used initially,we can simply do aquick design with only wIwhile leaving out the zero of R1-C1by making R1=0,such that the zero ofR1-C1is pushed beyond its effect to the 100-Hz crossover.(11)(12)If C1=0.22 mF,we can obtain a wI=25.0 rad/s,or I=3.98 Hz,with a given CTR=120%,R4=510,R2=110 k,and R3=1.00 k.6Feedback Loop Design of an LLC Resonant Power ConverterSLUA582AOctober 2010Revised November 2010Submit Documentation Feedback 2010,Texas Instruments Incorporated6040200204060-Gain(dB)101001 k10 k100 k1 M18012060060120180-Phase(degrees)UCC25600EVM MODULATOR PLOT(TEST)Frequency(Hz)GainPhase4032241680816243240-Gain(dB)101001 k10 k100 k1 MPhase(degrees)GAIN OF TYPE I COMPENSATORFrequency(Hz)1801000100180-GainPMethodologyStep 4.Re-measurement of Gm(w).Now we are confident enough to increase the input voltage so the output is in regulation,and thenmake a stable measurement of Gm(w).The measured Gm(w)is shown in Figure 4,at 390-V input.Figure 4.Re-Measurement of Gm(w)Certainly,one can make additional measurements between 280 V and 390 V,say in 20-V increments,to gain confidence in what has already been obtained.An important note for test manipulation here isthat the input voltage increase should progress slowly until the feedback loop compensation iscomplete.A slow increase of the input voltage can allow time for the designer to decide to stop if thereis any sign that the feedback loop may become unstable.Step 5.Design Gc(w)based on measured Gm(w).To achieve the crossover frequency of 7 kHz with a minimum 45 phase margin,Gc(w)would need tobe designed to achieve the Bode plot responses shown in Figure 5.This result can be easilyaccomplished by arranging the pole and the zero shown in Equation 6.Below is one possible set ofparameters to achieve the illustrated Bode plots:R1=5.1 kR2=19.7 kR3=1.0 kR4=510 C1=0.22 mFCTR=120%Figure 5.Design of Gc(w)7SLUA582AOctober 2010Revised November 2010Feedback Loop Design of an LLC Resonant Power ConverterSubmit Documentation Feedback 2010,Texas Instruments Incorporated6040200204060-Gain(dB)101001 k10 k100 k1 M18012060060120180-Phase(degrees)UCC25600EVM LOOP PLOT(TEST)Frequency(Hz)GainPhaseRStep 6.Bench testing and fine tuning.The last step is to plug in the obtained parameter values to perform a bench test.Usually,fine tuning isnecessary to cover all operating conditions and to adapt to the parameters not modeled in the Gc(w)forexample parasitic variables.The compensation values are finalized as R1=17.8 k,R2=19.7 k,R3=1.0 k,R4=0.51 k,andC1=47 nF.Figure 6 shows the control loop Bode plots at VIN=390 V,Vo=12 V,and a 25-A load.Figure 6.Feedback Loop Bode Plots After Final Values Set4Referen