�� Application ReportSLVA636 arch2014 - PDF document

�� Application ReportSLVA636 arch2014 Practical Feedback Loop Analysis for CurrentMode Boost Converter SW LeePower ManagementABSTRACTCurrentmode control is the industry standard method of controlling switching power supplies. Righthalfplane (zero expression is exactly the same as that for voltagemode control ( SLVA633 ��SLVA636��2 Practical Feedback Loop Analysis for CurrentMode Boost Converter IntroductionVoltageode control, also called dutycycle control, contains a single loop and adjusts the duty cycle directly in response to output voltage changes. Currentmode control, also called currentprogrammed mode or currentinjected control, is a multipleloop controlmethod that contains two loops (an inner current loop and an outer voltage loop). There are several types of currentmode control method, and the most popular method is fixedfrequency peakcurrentmode control with fixedslope compensationramp. The technique is called currentmode control because the inductor current is directly controlled, whereas the output voltage is controlled only indirectly by the current loop. A control reference is used to regulate the peak current of the converterdirectly, simplifying the dynamics of the converter.Figure 1shows the schematic of the boost converter with currentmode control. As with the bucconverter, the current is usually sensed in the power switch. RL LDRDRSWRCCRLOADVOVg Compensation Ramp VrampControl VcdPWM Logic & Gate Drive Current Sensing Current Signal Slope: SnSlope: Se Figure 1.oost onverter with urrentode ontrolRather than using a sawtooth ramp to control the duty cycle of the converter, the simplest form of currentmode control regulates the peak of the inductor current (or switch current, depending on where the sensing is done) with a control signal, V. In some cases the compensation sawtooth ramp is retained to stabilize the current loop feedback, and increase noise immunity.e typically do not sense the inductor current directly, because it is inconvenient or inefficient. The power switch current is usually sensed to gather the information about the inductor current.Subharmonic OscillationWhen currentmode control was first introduced to the power electronics community in the early 1980s, it was immediatelyseized upon as a superior control scheme. This simple control scheme, however, had an inherent oscillation phenomenon. This is, of course, well known and documented. If you have been in power supplies for some time, you know that retaining the sawtooth compensating ramp in the control system eliminates the problem. �� SLVA636�� Practical Feedback Loop Analysis for CurrentMode Boost Converter Figure 2shows the nature of the current loop oscillation. This figure shows the control waveform regulating the peak current at greater than a 50% duty cycle. The steadystate waveform can exist withthe clock initiating the ontime of the switch, and the control voltage terminating the ontime. Control Vc Steady StatePerturbedClock Figure 2.Subharmonic scillation aveformsIn the red waveform, the inductor current is perturbed at the beginningof the cycle. This perturbation will reach the same peak current, but at the next clock cycle, the perturbation has become negative, and the amplitude has increased. After another switch cycle, the perturbation is positive again, but has increased even further.Figure 3shows the frequency response of currentmode boost converter without compensation ramp. Subharmonic oscillations appear as the duty cycle exceeds 50% with the following design parameters (V= 5 V, V= 18 V, I= 3 A, L = 20 H, F= 200 kHz). T Gain (dB)-50.00 -40.00 -30.00 -20.00 -10.00 0.00 10.00 Frequency (Hz) 100 1k 10k 100k 1M Phase [deg]-300.00 -200.00 -100.00 0.00 FSW/2 peaking due to subharmonic oscillations Figure 3.AC mall ignal esponse without CompensationRampThe stabilizing effect of the compensation ramp is explained using the current feedback signal illustrated inFigure 4. The PWM waveforms are analyzed, which shows the propagation of the perturbed inductor current (). In the enlarged illustration in Figure 4is the slope of the ontime inductor current and Sis the current slope of the offtime inductor current, while Sis the slope of the compensation ramp. The denotes the deviation in the ontime period due to the inductor current perturbation. ��SLVA636��4 Practical Feedback Loop Analysis for CurrentMode Boost Converter Vc-ramp Slope SeSnSf iLiLiL(iL( dTs SfdTs SedTs SndTs Figure 4.PWM aveforms with ompensation ampFrom the graphical construction, the initial distance between the original inductor current (i) and the perturbed inductor current (i) is given by (1)The distance between the two currents after one operational period is given by (2)For the successive decrease in the distance between iin the ensuing operational periods, the condition ()() = (3) is required, leading to the following condition for the compensation ramp slope � (4) for the stabilizing effect. The exact value of the compensation ramp slope should be determined in consideration of the closedloop performance of the converter.Figure 5shows the frequency response of currentmode boost converter with compensation ramp. As it is shown in Figure 5, the peaking is properly damped. �� SLVA636�� Practical Feedback Loop Analysis for CurrentMode Boost Converter T Gain (dB)-20.00 -10.00 0.00 10.00 20.00 30.00 Frequency (Hz) 100 1k 10k 100k 1M Phase [deg]-300.00 -200.00 -100.00 0.00 Peaking is damped by compensation ramp Figure 5.AC Small Signal Response withompensationRampBoost Converter (CurrentMode) Transfer Function PlotsThe boost converter has an additional term in the controloutput transfer function, caused by the RHP zero of the converter: =× × (5) The dc gain of the converter is given by ���� (6) For the lowfrequency part, the dominant pole is located at ���� (7) The capacitorESR zero is at the same location as the boost converter in voltagemode, given by: =× (8) and the RHP zero is at ���� (9) To account for the observed oscillation in the currentmode system, the highfrequency correction term (f(s))added to the basic power stage ()= (10) ��SLVA636��6 Practical Feedback Loop Analysis for CurrentMode Boost Converter Figure 6shows the schematic of the smallsignal analysis using a simple voltagecontrolled voltage source as an error amplifier. On this smallsignal boost, the voltagecontrolled voltage source amplifies by about 89.5the difference between a portion of Vand the 2.5reference. In order to avoid running the circuit in a closedloop configuration, we can install an LC filter featuring an extremely low cutoff frequency.The error amplifier canbe a simple voltagevoltage amplification device, that is, the traditional mp. This type of requires local feedback (between its output and inputs) to make it stable. Under steady DC conditions, both the input terminals are virtually at the same voltageand this determines the output voltage setting. However, though both resistors of the voltage divider affect the DC level of the converters output, from the AC point of view, only the upper resistor enters the picture. So the lower (R) is considered just a DC biasing resistor, and therefore we usually ignore it in control loop (AC) analysis. RL LDRDRSWRCCRLOADVoutVg Compensating Ramp VrampControl VcdPWM Logic Gate Drive Current Current Signal SlopenSlopee R1Rb Vref=5204808 6 Fsw=150 930 Figure 6.ControlOutput Transfer Function with CurrentMode Boost Converter �� SLVA636�� Practical Feedback Loop Analysis for CurrentMode Boost Converter Figure 7shows a comparison of the controloutput for currentmode boost converter, and the controloutput for voltagemode boost converter. Note that the RHP zero is exactly the same as that for voltagemode control. Using currentmode does not move this at all. The currentmode boost converter is easier to compensate, though, since we do not need to deal with the additional double pole response of the LC filter that is present with voltagemodecontrol. More phase margin in current Figure 7.Comparisonsof CurrentMode and VoltageMode ControlOutput Transfer Functions ��SLVA636��8 Practical Feedback Loop Analysis for CurrentMode Boost Converter Boost Converter (CurrentMode) Feedback CompensationNow we are ready to design the feedback loop of currentmode boost converter understanding the control scheme. In order to control the boost converter, it is now necessary to design a feedback amplifier to compensate for the naturallyoccurring characteristicsof the power stage. Figure 8shows a Type II compensation amplifier. This compensation scheme adds an RC branch toflatten the gain, and improve the phase response in the midfrequency range. The increased phase is achieved by increasing the separation of the pole and zero of the compensation. Vref C3C1R2R1Rb VcVO R1,C1R2,C1R2,C3 fp0 fz1 fp1 Figure 8.Type II Compensator with Gain CurveNote that this type of compensator still always has a net negative phaseand it cannot be used to improve the phase of the power stage. For this reason, Type II compensators cannot be used for voltagemode boost converter where there is a large phase drop just after the resonant frequency, as shown inFigure 7. Type II compensators are usually reserved for currentmode control compensation, or for converters that always operate in the DCM region.Type II (an origin pole, plus a pole/zero pair) gives us one polezero (fp0) and one pole (fp1) and one zero (fz1). We always need a polezero in the compensation for achieving high DC gain, good DC regulation, and lowfrequency line injection. Note that four components (R) are involved in determining the poles and zero, and the locations of the poles and zero are =×× (11) =×× (12) =×× (13) nd the transfer function (H(s)) for the feedback block with Type II is ()=(××)(××)×(××) if C��C (14) We can find the required Cand once we select Rwith the desired fand f =×× (15) =× (16) �� SLVA636�� Practical Feedback Loop Analysis for CurrentMode Boost Converter =××× (17) The boostconverter with currentmode control can operate successfully with just a Type II compensator and hasfour main characteristics. Thee area single pole at low frequency determined by the output capacitor & load resistor, an ESR zero and aRHP zero which moves with operating conditions. Also, there is a pair of double poles at half the switching frequency. Q is controlled with ramp addition.In selecting values for the Type II compensator, these characteristics are taken into consideration in the placement of poles and the zero. The following list contains the design rules for the currentmode boost converterThe first pole (f) of the compensator is placed at the origin from an integrator.The compensation zero (f) is placed at onefifth the selected crossover frequency.The second pole (f) of the compensator is placed coincident with the ESR zero or the RHP zero frequency, which is lower.The crossover frequency should be less than about onetenth the switching frequency.The crossover frequency should be less than about onefifth the RHP zero frequency.Based on these rules, Figure 9shows an example for the compensator which has an appropriate shape, and usually a good phase margin. T Gain (dB)-60.00 -50.00 -40.00 -30.00 -20.00 -10.00 0.00 10.00 Frequency (Hz) 100 1k 10k 100k 1M Phase [deg]90.00 110.00 130.00 150.00 170.00 R1,1R2,1R2,3 fp fz fp Figure 9.Appropriate Compensator Design Example ��SLVA636��10 Practical Feedback Loop Analysis for CurrentMode Boost Converter As with the buck converterloop gain, it starts with a slope of 1, changes to 2 up to the compensation zero, thenreverts to a 1 slope for the whole loop since this would compromise the low frequencygainCurrentMode Compensation SummaryFigure 10and Figure 11show the schematic and the loop gain of applying these rules to a boost converter examplewith the following design parameters (V= 5 V, V= 18 V, I= 3 A, L = 20 H, F= 200 kHz). The converter switches at 200 kHz. The crossover frequency is limited to about 0.6 kHzpassing it through with 1 gain slope, and the phase margin measured to be 75 degrees at this crossover frequency. RL LDRDRSWRCCRLOADVoutVg Control VcdPWM Logic & Gate Drive Current Sensing R1Rb Vref=2.5V5V20uH480uF8m 6 Fsw=200kHz150k 930k C3C1R20.1nF7.5nF215k Figure 10.chematic with the iven arametersFigure 11shows the resulting loop gain (in blue) with the compensation (in red) and the controloutput (in green) waveforms when these rules are applied. The selected crossover frequency is 0.6 kHz, or onefifth the RHP zero frequency (3.6 kHz). Note that in the design rules, there was no requirement to cross the loop over in excessof the resonant filter frequency. This characteristic has already been eliminated by the current feedback loop. This is a very important observation, especially for currentmode boost converter which has a lowfrequency RHP zero.With voltagemode controlit is sometimes impossible to control such a converter with a loop crossover above the resonant frequency, and performance is very poor. Currentmode control solves this problem, and low RHP zero systems are controllable with good performance. �� SLVA636�� Practical Feedback Loop Analysis for CurrentMode Boost Converter T Gain (dB)-80.00 -60.00 -40.00 -20.00 0.00 20.00 40.00 Frequency (Hz) 100 1k 10k 100k 1M Phase [deg]-300.00 -200.00 -100.00 0.00 100.00 200.00 Total LoopCompensationControl-to-Output Figure 11.ain arginConclusionCompensation for currentmode boost converter is much easier than voltagemode boost converter, even if the RHP zero is at a low frequency. The Type II compensation has simple design rules, and good stability is usually achieved on the first attempt. There is no minimum requirement for the crossover frequency, so you can always make the system stable regardless of the RHP zero frequency. The current loop eliminates the ringing frequency of the filter, good performance is achieved even with relatively low crossover frequency on the voltage feedback loop. The proper ramp must be added to the currentmode boost converter to damp the subharmonicoscillations as shown inFigure 4ReferencePractical Feedback Loop Analysis for VoltageMode Boost Converter SLVA633 ), SW Lee, Texas Instruments, January 2014. IMPORTANTNOTICE TexasInstrumentsIncorporatedanditssubsidiaries(TI)reservetherighttomakecorrections,enhancements,improvementsandother changestoitssemiconductorproductsandservicesperJESD46,latestissue,andtodiscontinueanyproductorserviceperJESD48,latest issue.Buyersshouldobtainthelatestrelevantinformationbeforeplacingordersandshouldverifythatsuchinformationiscurrentand complete.Allsemiconductorproducts(alsoreferredtohereinas“components”)aresoldsubjecttoTI’stermsandconditionsofsale suppliedatthetimeoforderacknowledgment. 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