设计一款LLC谐振半桥式功率转换器 Topic_3_Huang_28pages

3-1 To pi c 3 Designing an LLC Resonant Half-Bridge Power Converter Hong Huang AbstrAct While half-bridge power stages have commonly been used for isolated, medium-power applications, converters with high-voltage inputs are often designed with resonant switching to achieve higher efficiency, an improvement that comes with added complexity but that nevertheless offers several performance benefits. This topic provides detailed information on designing a resonant half-bridge converter that uses two inductors (LL) and a capacitor (C), known as an LLC configuration. This topic also introduces a unique analysis tool called first harmonic approximation (FHA) for controlling frequency modulation. FHA is used to define circuit parameters and predict performance, which is then verified through comprehensive laboratory measurements. IntroductIon Higher efficiency, higher power density, and higher component density have become common in power-supply designs and their applications. Resonant power converters—especially those with an LLC half-bridge configuration—are receiving renewed interest because of this trend and the potential of these converters to achieve both higher switching frequencies and lower switching losses. However, designing such converters presents many challenges, among them the fact that the LLC resonant half-bridge converter performs power conversion with frequency modulation instead of pulse-width modulation, requiring a different design approach. This topic presents a design procedure for the LLC resonant half-bridge converter, beginning with a brief review of basic resonant-converter operation and a description of the energy-transfer function as an essential requirement for the design process. This energy-transfer function, presented as a voltage ratio or voltage-gain function, is used along with resonant-circuit parameters to describe the relationship between input voltage and output voltage. Next, a method for determining parameter values is explained. To demonstrate how a design is created, a step-by-step example is then presented for a converter with 300 W of output power, a 390- VDC input, and a 12-VDC output. The topic concludes with the results of bench-tested per- form ance measurements. A. Brief Review of Resonant Converters There are many resonant-converter topologies, and they all operate in essentially the same way: A square pulse of voltage or current generated by the power switches is applied to a resonant circuit. Energy circulates in the resonant circuit, and some or all of it is then tapped off to supply the output. More detailed descriptions and discussions can be found in this topic’s references. Among resonant converters, two basic types are the series resonant converter (SRC), shown in Fig. 1a, and the parallel resonant converter (PRC), shown in Fig. 1b. Both of these converters regulate their output voltage by changing the frequency of the driving voltage such that the impedance of the resonant circuit changes. The input voltage is split between this impedance and the load. Since the SRC works as a voltage divider between the input and the load, the DC gain of an SRC is always Fig. 1. Basic resonant-converter configurations. Lr LrCr CrRL RL a. Series resonant converter. b. Parallel resonant converter. 3-2 To pi c 3 lower than 1. Under light-load conditions, the impedance of the load is very large compared to the impedance of the resonant circuit; so it becomes difficult to regulate the output, since this requires the frequency to approach infinity as the load approaches zero. Even at nominal loads, wide frequency variation is required to regulate the output when there is a large input-voltage range. In the PRC shown in Fig. 1b, the load is connected in parallel with the resonant circuit, inevitability requiring large amounts of circulating current. This makes it difficult to apply parallel resonant topologies in applications with high power density or large load variations. B. LCC and LLC Resonant Converters To solve these limitations, a converter combining the series and parallel configurations, called a series-parallel resonant converter (SPRC), has been proposed. One version of this structure uses one inductor and two capacitors, or an LCC configuration, as shown in Fig. 2a. Although this combination overcomes the drawbacks of a simple SRC or PRC by embedding more resonant fre- quen cies, it requires two independent physical capacitors that are both large and expensive because of the high AC currents. To get similar characteristics without changing the physical com- ponent count, the SPRC can be altered to use two inductors and one capacitor, forming an LLC reso- nant converter (Fig. 2b). An advantage of the LLC over the LCC topology is that the two physical inductors can often be integrated into one physical component, including both the series resonant inductance, Lr, and the transformer’s magnetizing inductance, Lm. The LLC resonant converter has many addi- tional benefits over conventional resonant con- vert ers. For example, it can regulate the output over wide line and load variations with a relatively small variation of switching frequency, while main- taining excellent efficiency. It can also achieve zero- voltage switching (ZVS) over the entire operating range. Using the LLC resonant configuration in an isolated half-bridge topology will be described next, followed by the procedure for designing this topology. II. LLc resonAnt HALf-brIdge converter This section describes a typical isolated LLC resonant half-bridge converter; its operation; its circuit modeling with simplifications; and the relationship between the input and output voltages, called the voltage-gain function. This voltage-gain function forms the basis for the design procedure described in this topic. Fig. 2. Two types of SPRC. Lr LrCr1 Cr LmCr2 RL RL a. LCC configuration. b. LLC configuration. 3-3 To pi c 3A. ConfigurationFig. 3a shows a typical topology of an LLC resonant half-bridge converter. This circuit is very similar to that in Fig. 2b. For convenience, Fig. 2b is copied as Fig. 3b with the series elements interchanged, so that a side-by-side comparison with Fig. 3a can be made. The converter configuration in Fig. 3a has three main parts: 1. Power switches Q1 and Q2, which are usually MOSFETs, are configured to form a square- wave generator. This generator produces a unipolar square-wave voltage, Vsq, by driving switches Q1 and Q2, with alternating 50% duty cycles for each switch. A small dead time is needed between the consecutive transitions, both to prevent the possibility of cross- conduction and to allow time for ZVS to be achieved. 2. The resonant circuit, also called a resonant network, consists of the resonant capacitance, Cr, and two inductances—the series resonant inductance, Lr, and the transformer’s mag net- izing inductance, Lm. The transformer turns ratio is n. The resonant network circulates the electric current and, as a result, the energy is circulated and delivered to the load through the transformer. The transformer’s primary wind- ing receives a bipolar square-wave voltage, Vso. This voltage is transferred to the secondary side, with the transformer providing both electrical isolation and the turns ratio to deliver the required voltage level to the output. In Fig. 3b, the load R′L includes the load RL of Fig. 3a together with the losses from the transformer and output rectifiers. 3. On the converter’s secondary side, two diodes constitute a full-wave rectifier to convert AC input to DC output and supply the load RL. The output capacitor smooths the rectified voltage and current. The rectifier network can be implemented as a full-wave bridge or center- tapped configuration, with a capacitive output filter. The rectifiers can also be implemented with MOSFETs forming synchronous rectification to reduce conduction losses, especially beneficial in low-voltage and high- current applications. B. Operation This section provides a review of LLC resonant-converter operation, starting with series resonance. Resonant Frequencies in an SRC Fundamentally, the resonant network of an SRC presents a minimum impedance to the sinusoidal current at the resonant frequency, regardless of the frequency of the square-wave voltage applied at the input. This is sometimes called the resonant circuit’s selective property. Away from resonance, the circuit presents higher impedance levels. The amount of current, or associated energy, to be circulated and delivered to the load is then mainly dependent upon the value of the resonant circuit’s impedance at that frequency for a given load impedance. As the frequency of the square-wave generator is varied, a. Typical configuration. Fig. 3. LLC resonant half-bridge converter. Rectifiers for DC Output Square-Wave Generator Resonant Circuit Cr Lr LmVso + + – – Vsq Ir D2 Co Io RL Vo D1 Q1 Q2 Vin = VDC n:1:1 b. Simplified converter circuit. Ir Ios Lr + + Cr Vsq Vsq Vso Vso Lm Im RL´ 3-4 To pi c 3 the resonant circuit’s impedance varies to control that portion of energy delivered to the load. An SRC has only one resonance, the series resonant frequency, denoted as 0 r r 1f . 2 L C = π (1) The circuit’s frequency at peak resonance, fc0, is always equal to its f0. Because of this, an SRC requires a wide frequency variation in order to accommodate input and output variations. fc0 , f0 , and fp in an LLC Circuit However, the LLC circuit is different. After the second inductance (Lm) is added, the LLC circuit’s frequency at peak resonance (fc0) becomes a function of load, moving within the range of fp ≤ fc0 ≤ f0 as the load changes. f0 is still described by Equation (1), and the pole frequency is described by p r m r 1f . 2 (L L )C = π + (2) At no load, fc0 = fp. As the load increases, fc0 moves towards f0. At a load short circuit, fc0 = f0. Hence, LLC impedance adjustment follows a family of curves with fp ≤ fc0 ≤ f0, unlike that in SRC, where a single curve defines fc0 = f0. This helps to reduce the frequency range required from an LLC resonant converter but complicates the circuit analysis. It is apparent from Fig. 3b that f0 as described by Equation (1) is always true regardless of the load, but fp described by Equation (2) is true only at no load. Later it will be shown that most of the time an LLC converter is designed to operate in the vicinity of f0. For this reason and others yet to be explained, f0 is a critical factor for the converter’s operation and design. Operation At, Below, and Above f0 The operation of an LLC resonant converter may be characterized by the relationship of the switching frequency, denoted as fsw, to the series resonant frequency (f0). Fig. 4 illustrates the typical waveforms of an LLC resonant converter with the switching frequency at, below, or above the series resonant frequency. The graphs show, from top to bottom, the Q1 gate (Vg_Q1), the Q2 gate (Vg_Q2), the switch-node voltage (Vsq), the resonant circuit’s current (Ir), the magnetizing current (Im), and the secondary-side diode current (Is). Note that the primary-side current is the sum of the magnetizing current and the secondary-side current referred to the primary; but, since the magnetizing current flows only in the primary side, it does not contribute to the power transferred from the primary-side source to the secondary- side load. Fig. 4. Operation of LLC resonant converter. Vg_Q1 Vg_Q1 Vg_Q1 Vg_Q2 Vg_Q2 Vg_Q2 Ir Ir Ir Is Is Is D1 D1 D1D2 D2 D2 Im ImIm Vsq Vsq Vsq 0 0 0 0 0 0 0 0 0 t0t0t0 t1t1t1 t3t3t3 t2t2t2 time, t time, t time, t t4t4t4 a. At f0. b. Below f0. c. Above f0. 3-5 To pi c 3 Operation at Resonance (Fig. 4a) In this mode the switching frequency is the same as the series resonant frequency. When switch Q1 turns off, the resonant current falls to the value of the magnetizing current, and there is no further transfer of power to the secondary side. By delaying the turn-on time of switch Q2, the circuit achieves primary-side ZVS and obtains a soft commutation of the rectifier diodes on the secondary side. The design conditions for achieving ZVS will be discussed later. However, it is obvious that operation at series resonance produces only a single point of operation. To cover both input and output variations, the switching frequency will have to be adjusted away from resonance. Operation Below Resonance (Fig. 4b) Here the resonant current has fallen to the value of the magnetizing current before the end of the driving pulse width, causing the power transfer to cease even though the magnetizing current continues. Operation below the series resonant frequency can still achieve primary ZVS and obtain the soft commutation of the rectifier diodes on the secondary side. The secondary-side diodes are in discontinuous current mode and require more circulating current in the resonant circuit to deliver the same amount of energy to the load. This additional current results in higher conduction losses in both the primary and the secondary sides. However, one characteristic that should be noted is that the primary ZVS may be lost if the switching frequency becomes too low. This will result in high switching losses and several associated issues. This will be explained further later. Operation Above Resonance (Fig. 4c) In this mode the primary side presents a smaller circulating current in the resonant circuit. This reduces conduction loss because the resonant circuit’s current is in continuous-current mode, resulting in less RMS current for the same amount of load. The rectifier diodes are not softly commutated and reverse recovery losses exist, but operation above the resonant frequency can still achieve primary ZVS. Operation above the reso- nant frequency may cause significant frequency increases under light-load conditions. The foregoing discussion has shown that the converter can be designed by using either fsw ≥ f0 or fsw ≤ f0, or by varying fsw on either side around f0. Further discussion will show that the best operation exists in the vicinity of the series resonant frequency, where the benefits of the LLC converter are maximized. This will be the design goal. C. Modeling an LLC Half-Bridge Converter To design a converter for variable-energy transfer and output-voltage regulation, a voltage- transfer function is a must. This transfer function, which in this topic is also called the input-to- output voltage gain, is the mathematical relation- ship between the input and output voltages. This section will show how the gain formula is developed and what the characteristics of the gain are. Later the gain formula obtained will be used to describe the design procedure for the LLC resonant half-bridge converter. 3-6 To pi c 3 Traditional Modeling Methods Do Not Work Well To develop a transfer function, all variables should be defined by equations governed by the LLC converter topology shown in Fig. 5a. These equations are then solved to get the transfer function. Conventional methods such as state- space averaging have been successfully used in modeling pulse-width-modulated switching converters, but from a practical viewpoint they have proved unsuccessful with resonant converters, forcing designers to seek different approaches. Modeling with Approximations As already mentioned, the LLC converter is operated in the vicinity of series resonance. This means that the main composite of circulating current in the resonant network is at or close to the series resonant frequency. This provides a hint that the circulating current consists mainly of a single frequency and is a pure sinusoidal current. Although this assumption is not completely accurate, it is close—especially when the square wave’s switching cycle corresponds to the series resonant frequency. But what about the errors? If the square wave is different from the series resonance, then in reality more frequency components are included; but an approximation using the single fundamental harmonic of the square wave can be made while ignoring all higher- order harmonics and setting possible accuracy issues aside for the moment. This is the so-called first harmonic approximation (FHA) method, now widely used for resonant-converter design. This method produces acceptable design results as long as the converter operates at or close to the series resonance. The FHA method can be used to develop the gain, or the input-to-output voltage-transfer function. The first steps in this process are as follows: Represent the primary-input unipolar square- • wave voltage and current with their funda men tal components, ignoring all higher-order harmonics. Ignore the effect from the output capacitor and • the transformer’s secondary-side leakage inductance. Refer the obtained secondary-side variables to • the primary side. Represent the referred secondary voltage, which • is the bipolar square-wave voltage (Vso), and the referred secondary current with only their fundamental components, again ignoring all higher-order harmonics. With these steps accomplished, a circuit model of the LLC resonant half-bridge converter in Fig. 5a can be obtained (Fig. 5b). In Fig. 5b, Vge is the fun damental component of Vsq, and Voe is the fun- damental component of Vso. Thus, the non linear and nonsinusoidal circuit in Fig. 5a is approx i- mately transformed into the linear circuit of Fig. 5b, where the AC resonant circuit is excited by an effective sinusoidal input source and drives an equivalent resistive load. In this circuit model, both input voltage Vge and output voltage Voe are in sinusoidal form with the same single frequency— i.e., the fundamental component of the square- wave voltage (Vsq), generated by the switching operation of Q1 and Q2. This model is called the resonant converter’s FHA circuit model. It forms the basis for the Fig. 5. Model of LLC resonant half-bridge converter. Ir Lr + – + + – + Cr VoeLm Im Ioe Re Ir Ios Lr Cr Vsq Vge Vsq Vso Vso Lm Im RL´ a. Nonlinear nonsinusoidal circuit. b. Linear sinusoidal circuit. 3-7 To pi c 3 design example presented in this topic. The voltage-transfer function, or the voltage gain, is also derived from this model, and the next section will show how. Before that, however, the electrical variables and their relationships as used in Fig. 5b need to be obtained. Relationship of Electrical Variables On the input side, the fundamental voltage of the square-wave voltage (Vsq) is ge DC sw 2v (t) V sin(2 f t),= × × ππ (3) and its RMS value is ge DC 2V V .= ×π (4) On the output side, since Vso is approximated as a square wave, the fundamental voltage is oe o sw V 4v (t) n V sin(2 f t ),= × × × π − ϕπ (5) where φV is the phase angle between Voe and Vge, and the RMS output voltage is oe o 2 2V n V .= × ×π (6) The fundamental component of current cor re- sponding to Voe and Ioe is oe o sw i 1i (t) I sin(2 f t ), 2 n π= × × × π −ϕ (7) where φi is the phase angle between ioe and voe, and the RMS output current is oe o 1I I . n2 2 π= × × (8) Then the AC equivalent load resistance, Re, can be calculated as 2 2 oe o e L2 2 oe o V V8 n 8 nR R . I I × ×= = × = × π π (9) Since the circuit in Fig. 5b is a single-frequency, sinusoidal AC circuit, the calculations can be made in the same way as for all sinusoidal circuits. The angular frequency is sw sw2 f ,ω = π (10) which can be simplified as sw sw2 f .ω = ω = π (11) The capacitive and inductive reactances of Cr, Lr, and Lm, respectively, are r r