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SquareWave Generator Resonant Circuit Rectifiers for DC Output Q1 n:1:1 D11 DC h 册 D a. Typical configuration 6. Simplified converter circuit Fig 3. LLC resonant halfbridge converter A. Configuration together with the losses from the transformer Fig 3a shows a typical topology of an LLC and output rectifiers resonant halfbridge converter. This circuit is very 3. On the converter's secondary side, two diodes similar to that in Fig 2b. For convenience, Fig 2b constitute a fullwave rectifier to convert Ac is copied as Fig. 3b with the series elements input to dC output and supply the load ri. The interchanged, so that a sidebyside comparison output capacitor smooths the rectified voltage with Fig. 3a can bc madc. Thc converter and current. The rectifier network can be configuration in Fig 3a has three main parts implemented as a fullwave bridge or center 1. Power switches QI and Q2, which are usually tapped configuration, with a capacitive output MOSFETS are configured to form a square filter. The rectifiers can also be implemented wave generator. This generator produces a with MOSFETs forming synchronous unipolar squarewave voltage, Vsa, by driving rectification to reduce conduction losses switches Ql and Q2, with alternating 50% especially beneficial in lowvoltage and high duty cycles for each switch. A small dead time current applications is needed between the consecutive transitions both to prevent the possibility of cross B Operation conduction and to allow time for zys to be This section provides a review of llC achicved resonantconverter operation, starting with series 2. The resonant circuit. also called a resonant resonance network, consists of the resonant capacitance Resonant frequencies in an SrC Cr and two inductancesthe series resonant Fundamentally, the resonant nctwork of an inductance, Lr, and the transformer's magnet SRC presents a minimum impedance to the izing inductance, Lm. The transformer turns sinusoidal current at the resonant frequency, ratio is n. The resonant network circulates the regardless of the frequency of the squarewave electric current and, as a result, the energy is voltage applied at the input. This is sometimes circulated and delivered to the load through the called the resonant circuit's selective propert transformer. The transformer's primary wind Away from resonance, the circuit presents higher ing receives a bipolar square wave voltage impedance levels. The amount of current, or so This voltago is transferred to the sccondary associated energy to be circulated and delivered side, with the transformer providing both to the load is then mainly dependent upon the electrical isolation and the turns ratio to deliver value of the resonant circuit's impedance at that the required voltage level to the output In Fig frequency for a given load impedance. As the 3b, the load ri includes the load RL of Fig 3a fro cqucncy of the squarcwavc generator is varied the resonant circuit's impedance varies to control It is apparent from Fig. 3b that fo as described that portion of energy delivered to the load by Equation (1) is always true regardless of the An SrC has only onc rcsonancc, the scrics load, but f described by equation(2)is truc only resonant frequency, denoted as at no load. Later it will be shown that most of the time an LlC converter is designed to operate in (1) the vicinity of fo. For this reason and others yet to 2 be explained, fo is a critical factor for the converter's The circuit's frequency at peak resonance, f opcration and dcsign is always equal to its fo. Because of this, an Sro Operation At, Below, and Above fo requires a wide frcqucncy variation in ordcr to The operation of an LLC resonant converter accommodate input and output variations may be characterized by the relationship of the fco, fo, and fn in an LLC Circuit switching frequency, denoted as fsw, to the series However the llc circuit is different. After the resonant frequency (fo). Fig. 4 illustrates the second inductance(Lm) is added, the LLC circuits ypical waveforms of an LLC resonant converter frequency at peak resonance(fco) becomes a function with the switching frequency at, below, or above of load, moving within the range of f≤fo≤foas the series resonant frequency. The graphs show the load changes. fo is still described by Equation from top to bottom, the Q1 gate (Vo ou, the Q2 (1), and the pole frequency is described by gate (V 8_Q2), the switchnode voltage (V resonant circuit's current (I), the magnetizing (2) current (Im), and the secondaryside diode current 2√Lx+Lm)T (s. Note that the primaryside current is the sum of the magnetizing current and the secondaryside At no load, fco=fp. As the load increases, feo current referred to the primary, but, since the moves towards fo. At a load short circuit, fco=fo magnetizing current flows only in the primary Hence, LLC impedance adjustment follows a side, it does not contribute to the power transferred family of curves with fp s fco s fo, unlike that in from the primaryside source to the secondary SRO, where a single curve defines fco= fo. This side load helps to reduce the frequency range required from an LLC resonant converter but complicates the circuit analysis sq 0 0 0 D1 D1 0 0 0 t1 t2 t3 t4 t1 t2 t3 t4 time, t time, t time, t aAt fo b. Below fo C.Above fo Fig. 4. Operation of llc resonant converter Operation at Resonance(Fig 4a) Operation Above Resonance(Fig. 4c In this mode the switching frequency is the In this mode the primary side presents a smaller samc as the scrics resonant frcqucncy. When circulating current in the resonant circuit. This switch Q1 turns off, the resonant current falls to reduces conduction loss because the resonant the value of the magnetizing current, and there is circuit,'s current is in continuouscurrent mode no further transfer of power to the secondary side. resulting in less RMs current for the same amount By delaying the turnon time of switch Q2, the of load. The rectifier diodes are not softly circuit achieves primarysidc Zvs and obtains a commutated and rcvcrsc recovery losscs exist, but soft commutation of the rectifier diodes on the operation above the resonant frequency can still secondary side. The design conditions for achieving achieve primary ZVS. Operation above the reso ZVS will be discussed later. However, it is obvious nant frequency may cause significant frequency that operation at series resonance produces only a increases under lightload conditions single point of operation. To cover both input and The foregoing discussion has shown that the output variations, the switching frequency will converter can be designed by using either fsw 2 have to be adjusted away from resonance or fsw s fo, or by varying fsw on either side around fo. Further discussion will show that the best Operation Below R esonance (flg operation exists in the vicinity of the series resonant Here the resonant current has fallen to the frequency, where the benefits of the LlC converter value of the magnetizing current before the end of are maximized. This will be the design goal the driving pulse width, causing the power transfer to cease even though the magnetizing current C Modeling an LLC HalfBridge Converter continues. Operation below the series resonant To design a converter for variableenergy frequency can still achieve primary Zvs and transfer and outputvoltage regulation, a voltage abtain the soft commutation of the rectifier diodes transfer function is a must. This transfer function on the secondary side. The secondaryside diodes which in this topic is also called the inputto are in discontinuous current mode and require output voltage gain, is the mathematical relation more circulating current in the resonant circuit to ship between the input and output voltages deliver the same amount of energy to the load. This section will show how the gain formula is This additional current results in higher conduction developed and what the characteristics of the losses in both thc primary and the sccondary sides. gain are. Later the gain formula obtained will be However, one characteristic that should be noted used to describe the design procedure for the LLC is that the primary ZVS may be lost if the switching resonant halfbridge converter frequency becomes too low. This will result in high switching losses and several associated issues This will be explained further later C so RL ResV a Nonlinear nonsinusoidal circuit 6. Linear sinusoidal circuit Fig 5 Model ofllC resonant halfbridge converter Traditional Modeling Methods Do Not Work Well Thc Fha mcthod can bc used to devclop the To develop a transfer function, all variables gain, or the inputtooutput voltagetransfer should be defined by equations governed by the function. The first steps in this process are as LLC converter topology shown in Fig 5a. These follows equations are then solved to get the transfer Represent the primaryinput unipolar square function, Conventional methods such as state wave voltage and current with their fundamental space averaging have been successfully used in components, ignoring all higherorder modeling pulsewidthmodulated switching harmonics converters, but from a practical viewpoint they Ignore the effect from the output capacitor and have proved unsuccessful with resonant converters, the transformer's secondarySide leakage forcing designers to seek different approaches Inductance Modeling with Approximations Refer the obtained secondarySide variables to As already mentioned, the llC converter is the primary side operated in the vicinity of series resonance. This Represent the referred secondary voltage, which means that the main composite of circulating is the bipolar squarcwave voltage(Vso), and the current in the resonant network is at or close to the referred secondary current with only their series resonant frequency. This provides a hint that fundamental components, again ignoring all the circulating current consists mainly of a single higherorder harmonics frequency and is a pure sinusoidal current With these steps accomplished, a circuit model Although this assumption is not completely of the LLC resonant halfbridge converter in Fig accurate, it is closeespecially when the square 5a can be obtained(Fig. 5b). In Fig. 5b, Vge is the wavc's switching cyclc corresponds to thc scrics fundamental component of Vsa, and Voe is the fun resonant frequency. But what about the errors? damental component of Vso. Thus, the nonlinear If the square wave is different from the series and nonsinusoidal circuit in Fig. 5a is approxi resonance, then in reality more frequency matcly transformed into thc lincar circuit of Fig components are included; but an approximation 5b, where the AC resonant circuit is excited by an using the single fundamental harmonic of the effective sinusoidal input source and drives an square wave can be made while ignoring all higher equivalent resistive load. In this circuit model order harmonics and setting possible accuracy both input voltage Vge and output voltage Voe are issues aside for the moment. This is the socalled in sinusoidal form with the same single frequency first harmonic approximation(FHA) method, now i. e,, the fundamental component of the square widely used for resonantconverter design. This wave voltage (Vsa), generated by the switching method produces acceptable design results as long operation of Q1 and Q2 the converter operates at or close to the series This model is called the resonant converter's resonance fha circuit model, it forms the basis for the 36 design example presented in this topic. The which can be simplified as voltagetransfer function, or the voltage gain, is O 2f also derived from this model and the next scction (11) will show how. Before that, however, the electrical The capacitive and inductive reactances of Cr, Lrs variables and their relationships as used in Fig 5b and Lm, respectively, are need to be obtained X =OL and X (12) Relationship of Electrical variables C On the input side, the fundamental voltage of the squarewave voltage(Vsa) is The rms magnetizing current i e sin(2rfewt) (3) T and its rms value is The circulating current in the series resonant circuit is (4) 2 oe (14) On the output side, since Vso is approximated as With the relationships of the electrical variables square wave, the fundamental voltage Is established, the next step is to develop the voltage voe(t)=×n× V.xsin(2 nf.tqy),(5) gain function D. VoltageGain Function where (y is the phase angle between Voe and v Naturally, the relationship between the input and the rms output voltage is voltage and output voltage can be described by 2 their ratio or gain ×n× (6) 8DCn×Vo n×V (15) The fundamental component of current corre n DC sponding to Voe and loe is As described earlier. the dc input voltage and 0(1)=方×× Io xsin(2dswt01),(7) output voltage are converted into switching mode, and then equation (15)can bc approximated as the where (i is the phase angle between ioe and voe ratio of the bipolar squarewave voltage (vso)to and the rms output current is the unipolar squarewave voltage(Vsa) 一× gDC≈M g SW Then the AC equivalent load resistance, Re, can be The AC voltage ratio, M gAC, can be approx calculated as imated by using the fundamental components, V and Voe, to respectively replace Vsa and R 08×n2、V8×n ×R L 9 Equation(16) n Since the circuit in Fig 5b is a singlefrequency g /2 sinusoidal ac circuit. the calculations can be (17) Imade in the same way as for all sinusoidal circuits The angular frequency is NsoMg_AC Vge Osw=2Tfsw (10) 37 To simplify notation, Mo will be used here in Further to combine two inductances into one, an place of Mg ac. From Fig. 5b, the relationship inductance ratio can be defined as electrical parameter ge can bc cxprcsscd with the bctwccn V and v Lr Lms Cr, and re. Then the inputtooutput voltagegain or voltagetransfer function becomes The quality factor of the series resonant circuit is jXL‖R。 defined as (XL。‖Re)+j(X1 C (18) GalMa Notice that fn, Ln, and Qe are nounit variables With the help of these definitions, the voltage (joLm) Retour jo Cr gain function can then be normalized and expressed as where=v1 Equation(18)depicts a connection from the 23) input voltage (Vin) to the output voltage (Vo) (Ln+1)×f21]+j(f21)xfn×Q established in relation to M with LLCcircuit parameters. Although this expression is only The relationship between input and output voltages approximately correct, in practice it is close can also be obtained from Equation(23) enough to the vicinity of series resonance V=Mgx一 In Accepting the approximation as accurate allows Ma(fnLn,Q)×一 n 2 ,(24) Equation(19)to be written where V=V DC (19) Behavior of the voltageGain Function In other words, output voltage can be determined The voltagegain function expressed by equation after M.n. and Vi are known 23)and the circuit model in Fig 5b form the basis for the design method described in this topic Normalized Format of voltageGain Function herefore it is necessary to understand how M The voltagegain function described by behaves as a function of the three factors fn, Ln Equation (18) is expressed in a format with and Qe. In the gain function, frcqucncy fn is the absolute values. It is difficult to give a general control variable. Ln and Qe are dummy variables description of design issues with such a format. It since they are fixed after their physical parameters would be better to express it in a normalized are determined. Mo is adjusted by fn after a design format. To do this, the series resonant frequency is complete. As such, a good way to explain how (fo) can be selected as the base for normalization. the gain function behaves is to plot Mg with Then the normalized frequency is expressed as respect to fn at given conditions from a family of values for Ln and Q SW (20) 1.8 Q Q 1.8 Q=0 Q。= 000 125 1.6 Qe=0.8 1.6 1258 Q Q。=1 1.4 Q 1.4 QQQ Q e 5810 1.2 Qe=0.5 e 0 Q 25810 10 p2= 0.8 0.8 0.6 0.1 0.6 Q。=0.1 0.4 0.4 000 2 0.2 Q。=0.5 0 1Qe=10 10 0.1 10 Normalized Frequency, fn Normalized Frequency, fn bL Qa=0.1 Q。= 1.8 Qa=02 1.8 Q。= 00 12 Q=0.1 Qa=0.5 Q。=0.1 Qe=0.5 1.6 Qe=0.8 0125 1.6 Q=0.8 Q=1 14 Q.= 2 1,4 Q。=2 Q。=5 Q=5 1.2 Q= 8 258 1.2 Qa=10 Q。=10 Qa=0.5 2 0 Qa=0.5 0.8 0.8 Q=0.1 Q。=0.1 0.6 0.6 0.4 0.4 Q。=0.5 Q。=0.5 0.2 0.2 0.1 1Qe=10 10 0.1 10 10 Normalized Frequency, f Normalized Frequency, f Ln=10 ig. 6. Plots of voltagegain function(Mo) with different values ofln Figs. 6a to 6d illustrate several possible represent both magnitude and phase angle, but relationships. Each plot is defined by a fixed value only the magnitude is useful in this case for Ln (Ln=1, 5,10, or 20)and shows a family of Within a given Ln and Qe, Mg presents a curves with ninc valucs, from 0. 1 to 10, for the convex curve shape in the vicinity of the circuit's variable Qe. From these plots, several observations resonant frequency. This is a typical curve that can be made shows the shape of the gain from a resonant The value of Mg is not less than zero. This is converter. The normalized frequency correspond obvious since Mg is from the modulus operator, ing to the resonant peak (f n co, or which depicts a complex expression containing moving with respect to a change in load and thus both real and imaginary numbers. These numbers to a change in Qe for a given Ln Changing Ln and Qe will reshape the Mg curve effect of Lm and shift fco towards fo. As a simple and make it different with respect to fn. As Qc is a illustration, it is helpful to examine two extremes function of load describcd by Equations(9)and 1. If ri is open, then Qe=0, and fco=fpas 22), Mg presents a family of curves relating described by Equation(2). fco sits to the far left frequency modulation to variations in load of fo, and the corresponding gain peak is very Regardless of which combination of Ln and Qe igh and can be infinite in theory is used, all curves converge and go through the 2. If Rl is shorted, then Qe = oc and Lm is com point of(n, Mg)=(l,I). This point is fsw=fo from Equation(20). By definition of series pletely bypassed or shorted, making the effect Xc=0 at fo. In other words, the of lm on the gain disappear. The corresponding resonance, ALr peak gain value from the Lm effect then voltage drop across Lr and Cr is zero, so that the becomes zero, and fo moves all the way to the input voltage is applied directly to the output load, resulting in a unity voltage gain of M,=1 right, overlapping fo Notice that the operating point(fn, Mo=(1, 1) Therefore, if Ri changes from infinite to zero is independent of the load; i.e., as long as the gain the resonant peak gain changes from infinite to (Mg) can be kept as unity, the switching frequency unity, and the corresponding frequency at peak will be at the series resonant frequency (fo) no resonance (fco) moves from fp to the series matter what the load current is. In other words. in resonant frequency (fo) a design whose operating point is at(fn, Mg) For a fixed Qe, a decrease in Ln shrinks the (l, 1)or its vicinity, the frequency variation is curve; the whole curve is squeezed, and fco moves narrowed down to minimal. At (fn, Mg=(1, 1), towards fo. This results in a bctter frcqucncy the impedance of the series resonant circuit is control band with a higher peak gain. There are zero, assuming there are no parasitic power losses two reasons for this. first, as Ln decreases due to The entire input voltage is then applied to the the decrease in Lm, Ip gets closer to fo, which output load no matter how much the load current squeezes the curves from fn to fo. Second ,a varies. However, away from (fn, Mg)=(, 1), the decreased Ln increases Lr, resulting in a higher Q impedance of the series resonant circuit becomes A higher Qe shrinks the curve as just described nonzero, the voltage gain changes with different At first glance, it appears that any combination load impedances, and the corresponding operation of Ln and Qe would work for a converter design becomes loaddependent and that the design could be made with fn operating For a fixed Ln: increasing Qe shrinks the curve, on either side of fn =1. However, as explained in resulting in a narrower frequencycontrol band, the following section, there are many more which is expected since Qe is the quality factor of considerat the series resonant circuit. In addition. as the whole curve shifts lower, the corresponding peak II. DESIGN CONSIDERATIONS value of ma becomes smaller and the f corresponding to that value moves towards the As discussed earlier, fn is the control variable in frequency modulation. Therefore the output right and closer to fn=l. This frequency shift with increasing Qe is due to an increased load. It voltage can be regulated by mg through controlling fn, as indicated by Fig. 6 and Equation(24), which apparent from reviewing Equations(9) and(22 that an increase in Qe may come from a reduction can be rearranged as in Ri, as both Lm and Lr are fixed For the same series resonant frequency, Cr is fixed as well. RL is V=M2(fn,Ln2Q)×一 (25) 2 in parallel with Lm, so reducing Ri will reduce the 310所需积分/C币：8 上传时间：20180419 资源大小：1.21MB