* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download 全面认识开关型电源中的 BUCK-BOOST 应用报告 ZHCA041–1999年3月–2002年11月修订
Standby power wikipedia , lookup
Wireless power transfer wikipedia , lookup
Solar micro-inverter wikipedia , lookup
Mercury-arc valve wikipedia , lookup
Power factor wikipedia , lookup
Electrification wikipedia , lookup
Three-phase electric power wikipedia , lookup
Power over Ethernet wikipedia , lookup
Electric power system wikipedia , lookup
Electrical ballast wikipedia , lookup
Audio power wikipedia , lookup
Electrical substation wikipedia , lookup
Resistive opto-isolator wikipedia , lookup
Current source wikipedia , lookup
Variable-frequency drive wikipedia , lookup
Amtrak's 25 Hz traction power system wikipedia , lookup
Power inverter wikipedia , lookup
Stray voltage wikipedia , lookup
Surge protector wikipedia , lookup
History of electric power transmission wikipedia , lookup
Voltage regulator wikipedia , lookup
Power engineering wikipedia , lookup
Pulse-width modulation wikipedia , lookup
Voltage optimisation wikipedia , lookup
Distribution management system wikipedia , lookup
Power MOSFET wikipedia , lookup
Mains electricity wikipedia , lookup
Opto-isolator wikipedia , lookup
Alternating current wikipedia , lookup
应用报告 ZHCA041–1999年3月–2002年11月修订 全面认识开关型电源中的BUCK-BOOST功率级 Everett Rogers 系统能源 摘要 开关电源由功率级和控制电路组成,功率级完成从输入电压到输出电压的基本能量转换,它包括开关 和输出滤波器。这篇报告只介绍降压–升压(buck-boost)功率级,不包含控制电路。详细介绍了工 作在连续模式和非连续模式下buck-boost功率级的稳态和小信号分析,同时也介绍了标准buck-boost 功率级的不同变型,并讨论了功率级对组成部件的要求。 目录 1 简介 2 2 Buck-Boost级稳态分析 2.1 Buck-Boost 稳态连续导通模式分析 2.2 Buck-Boost 稳态非连续导通模式分析 2.3 Critical Inductance 3 3 7 11 3 Buck-Boost功率级小信号模型 3.1 Buck-Boost 连续导通模式小信号分析 3.2 Buck-Boost非连续导通模式小信号分析 12 13 16 4 Buck-Boost功率级的变型 4.1反向(Flayback)功率级 21 21 5 组件选择 24 5.1输出电容 5.2输出电感 5.3功率开关 5.4输出二极管 24 26 27 28 6 总结 29 7 参考文献 31 商标属于各自所有者持有。 ZHCA041–1999年3月–2002年11月修订 全面认识开关型电源中的BUCK-BOOST功率级 www.BDTIC.com/TI 1 www.ti.com.cn 简介 1 介绍 开关电源最常见的三种结构布局是降压(buck)、升压(boost)和降压–升压(buck-boost),这 三种布局都不是相互隔离的,也就是说,输入级电压和输出电压是共地的,但是也存在这种隔离拓 扑的变型 。电源布局主要是指这些开关、输出电感和输出电容怎么连接的。每种布局都有它独自的 特性,这些性能主要包括稳态电压转换比、输入输出电流的状态、输出电压的纹波特征,另一个主 要特性就是占空比–输出电压的传输函数的频率响应。 Buck-boost是一种流行的非隔离、逆功率级的拓扑,有时也称为升降功率级。电源设计者选用buckboost功率级是因为输出电压和输入电压是反向的,这种拓扑结构可以得到在幅度上,比输入电压更 高的输出电压(像升压(boost)功率级),或者更低的输出电压(像降压(buck)功率级),这就 是它名字的由来,但是输出电压在极性上跟输入电压是相反的。由于功率开关(Q1)的作用,buckboost的输入电流是非连续的或脉冲的,在每个开关周期内,脉冲电流从0变化到IL,输出电流也是 非连续或脉冲的,这是因为输出二极管只能在开关周期内的一部分时间内导通,输出电容提供开关 周期内其它时间的所有负载电流。这篇报告描述了在给定的理想波形下,连续模式和非连续模式中 buck-boost转换器的稳态工作过程。 在介绍了脉冲宽度调制(PWM)开关模型后,给出了占空比–输出电压的传输函数。图1显示了包括 驱动电路模块在内的buck-boost功率级的简单原理图,功率开关Q1是以一个n通道的金属氧化物半导 体场效应管(MOSFET),输出二极管是CR1。电感L和电容C组成了有效的输出滤波器。在分析过 程中,考虑了电容ESR(等效串联电阻),RC ,和电感DC的阻抗,R L 。电阻R ,代表了在功率输出端的 负载。 a CR1 Q1 p VO ia VI + Drive Circuit C c L IL = ic R RC RL 图1.buck-boost 功率级原理图 在buck-boost功率级的正常工作中,Q1在控制电路的开关时间内,重复的打开、关上。在Q1、CR1 和L的连结节点处,开关动作产生了一个脉冲序列。电感L跟输出电容C相连,只有在CR1导通时,一 个有效的L/C输出滤波器才形成,过滤脉冲序列,产生直流输出电压。 2 全面认识开关型电源中的BUCK-BOOST功率级 ZHCA041–1999年3月–2002年11月修订 www.BDTIC.com/TI 2 Buck-Boost Stage Steady-State Analysis A power stage can operate in continuous or discontinuous inductor current mode. Continuous inductor current mode is characterized by current flowing continuously in the www.ti.com.cn inductor during the entire switching cycle in steady-state operation. Discontinuous inductor 级稳态分析 Buck-Boost current mode is characterized by the inductor current being zero for a portion of the switching cycle. It starts at功率级稳态分析 zero, reaches a peak value, and returns to zero during each switching cycle. 2 Buck-Boost The two different modes are discussed in greater detail later and design guidelines for the 功率级可以在连续电感器电流和非连续电感器电流模式下工作 连续电感器电流模式在稳态工作 inductor value to maintain a chosen mode of operation as a, function of rated load are given. 时 整个开关周期内都有电流连续通过电感器 非连续电感器电流模式是开关周期内的一部分时间 It is,very desirable for a converter to stay;in one mode only over its expected operating 电感电流为because 达到一个峰值后 conditions the power stage frequency response changes significantly between the ,再回到 0,它在整个周期内从 0开始, 0. two different modes of operation. 这两种模式稍后再详细探讨,在给出额定负载情况下如何选择电感值,来保证工作在选定模式的设 For this analysis, an n-channel power MOSFET is used and a positive voltage, VGS(ON) , is 计指导书也会提供 因为 。对于转换器来说 ,在预期工作条件下只保持希望的工作模式是很理想的 applied from the Gate to the Source terminals of Q1 by the drive circuit to turn ON the,FET. 在两种不同工作模式下功率级的频率响应变化相差很大 。 RDS(on) but the drive circuit is more The advantage of using an n-channel FET is its lower complicated because a floating drive is required. For the same die size, a p-channel FET has a经过这些分析发现 higher RDS(on) , but usually does not require a floating drive circuit. 采用 (MOSFET),驱动电路打开 n通道的功率型金属氧化物半导体场效应管 场效应管 的栅极和漏极间加上正的电压 (FET) ,Q1 ,采用n通道场效应管的优势在于它的 VGS(ON) The transistor Q1时and diode CR1 are drawn inside a dashed-line box with terminals labeled 低导致电阻 但是驱动电路就更加复杂 因为需要浮动电极 而同样大小的 , , 。 R a, p, and c. This section. DS(on) is explained fully in the Buck-Boost Power Stage Modelingp通道场效应管有 较高的R DS(on) ,通常也不需要浮动电极回路。晶体管Q1和二极管CR1画在点划线方框里面,终端接 详细讲到 功率级模型部分 口标为a,p和c, 这些会在BUCK–BOOST 。 Buck-Boost Steady-State Continuous Conduction Mode Analysis 2.1 The following is a description of steady-state operation in continuous conduction mode. The 2.1 Buck-Boost main goal of稳态连续导通模式分析 this section is to provide a derivation of the voltage conversion relationship for the continuous conduction mode buck-boost power stage. This is important because it shows 紧接着介绍 的稳态连续导通模式分析 稳态 ,这部分主要目的就是给出一个 Buck-Boost Buck-Boost how the output voltage depends on duty cycle and input voltage or conversely, how the duty 连续导通模式下电压转换关系的推导。这是很重要的,因为它揭示了输出电压怎样由占空比和输入 cycle can be calculated based on input voltage and output voltage. Steady-state implies that 电压决定 , 或者相反 , 怎样基于输入电压和输出电压来计算占空比 。 稳态说明输入电压 、 输出电 the input voltage, output voltage, output load current, and duty-cycle are fixed and not 压、输出负载电流和占空比都是固定不变的,大写字母表示出了稳态下的变量名。 varying. Capital letters are generally given to variable names to indicate a steady-state quantity. 在连续导通模式,buck-boost转换器保证每个开关周期有两个功率态,当Q1是开、CR1是关时,就 In continuous conduction mode, the buck-boost converter assumes two states per switching 是开态 (ON);当Q1是关而CR1是开时,就是关态(OFF)。在每个状态中,当回路中的开关被 cycle. The ON State is when Q1 is ON and CR1 is OFF. The OFF State is when Q1 is OFF 等价回路所代替时,一个简单的线性回路可以用来表示这两种状态,两种状态的回路图表见图2. and CR1 is ON. A simple linear circuit can represent each of the two states where the switches in the circuit are replaced by their equivalent circuit during each state. The circuit diagram for each of the two states is shown in Figure 2. OFF State ON State p a ia VI + RDS(on) L c ia IO IL = ic C RC R Vd a VO VI p VO c + L IL = ic IO C RC R RL RL Figure 2. Buck-Boost Power Stage States 图2.buck-boost功率级状态图 ZHCA041–1999年3月–2002年11月修订 Understanding Buck-Boost Power Stages in Switch Mode Power Supplies 3 全面认识开关型电源中的BUCK-BOOST功率级 3 www.BDTIC.com/TI www.ti.com.cn 级稳态分析 Buck-Boost SLVA059A 开态的时间为 代表了开关在开态的时间占 ,其中isD为由控制回路设定的占空比 T S =ON TONstate The durationDof×the D × TS = TON where D is,the duty cycle, set by the control 关态的时间叫 整个开关周期 因为对于连续导通模式下在整个开关周期 circuit, expressed as的比值 a ratio the switch ON time to the time of one complete switching cycle, 。of (T S) TOFF , T中只有两个状态 theTOFF OFF state is called TOFF Since there are only two states per switching 等于 有时被成为 × TS , 数值.(1 所以 这些时间与波 s . The duration,of (1 – D) D ’, – D) cycle for continuous conduction mode, T is equal to (1−D) × T . The quantity (1−D) is OFF S 形一起显示在图3中。 sometimes called D’. These times are shown along with the waveforms in Figure 3. IQ1 ICR1 IL Solid IO Dashed ∆IL 0 Vc-p Solid VO Dashed 0 TON TOFF TS 图3. 连续模式下buck-boost 功率级波形图 Figure 3. Continuous Mode Buck-Boost Power Stage Waveforms Referring to ON Figure 2, 此时为低电阻 during the ON Q1 presents a low resistance, RDS(on) , from its 参考图2,在 态,Q1 ,Rstate, DS(ON) ,从漏极到源极,只有很小的电压降V DS=I L × drain to source and exhibits a small voltage drop of VDS =IL × RDS(on) . There is also a small R DS(on) 。同时电感器的直流电阻上的电压降也很小,等于I L×R L 。因此,输入电压V I ,减去损 voltage drop across the dc resistance of the inductor equal to IL × RL . Thus, the input voltage, 耗(V DS + IL × RL) ,就加载到电感器L两端。在这段时间CR1是关的,因为它是反向偏置的。 VI , minus losses, (VDS + IL × RL ), is applied across the inductor, L. CR1 is OFF during this 电感电流 ,经过Q1, 。在开 (ON) 态, IL ,从输入源 VI 流出biased. time because it is reverse The 到地 inductor current, IL ,加在电感器两端的电压为定 flows from the input source, VI , 值,等于Q1 电感上的电流会随着所加的电压 × RL 。通过改变图 中电流 V I –and VDS –toILground. I L 的极性 through During the2ON state, the , voltage applied across the inductor is constant and equal to V − V − I × R . Adopting the polarity convention for the Tcurrent IL 而增大。同时,由于加载的电压通常必须为定值 ,所以电感电流线性增加 。图3描述了在 I DS L L ON shown in Figure 2, the。inductor current increases as a result of the applied voltage. Also, since 时间内电感电流的增加 the applied voltage is essentially constant, the inductor current increases linearly. This increase in inductor current during TON is illustrated in Figure 3. 4 4 全面认识开关型电源中的BUCK-BOOST功率级 Understanding Buck-Boost Power Stages in Switch Mode Power Supplies ZHCA041–1999年3月–2002年11月修订 www.BDTIC.com/TI SLVA059A SLVA059A the SLVA059A SLVA059A The amount that the inductor current increases can be calculated by using a version of familiar relationship: The amount that the inductor current increases can be calculated by using a Buck-Boost version of 级稳态分析 the The amount that the inductor current increases can be calculated by using a version of the familiar relationship: di familiar relationship: 电感电流的增加量可以由类似关系式来求得 : v L � �T v L � L � di L � �I L � vL dt v L � L � di L � �I L � v L � �T v LL � L � dtLL � �I L � LLL � �T dt L www.ti.com.cn The inductor current increase during the ON state is given by: The inductor current increase during the ON state is given by: 在开态 (ON)时间内电感电流的增量由下式可得 :� V I � �during V DS �the IL � R Lstate The inductor current increase ON is given by: �I L(�) � V � �V � T ON � � I � R I L DS L L � � T ON �I L(�) � V � �V I DS L� I L � R L This quantity,�I ∆ILL(�) (+), � is referred to as the inductor � ripple T ON current. Also notice that during this L period, all of the load current supplied byripple the output capacitor, C. that during this This quantity, ∆ILoutput (+), is referred to asisthe inductor current. Also notice This quantity, ∆ILoutput (+), is referred to asisthe inductor current. Also notice period, all of the load current supplied byripple the output capacitor, C. that during this Referring to 2, when is OFF, it presents a high impedance from its drain to source. period, ofFigure the output loadQ1 current is supplied by the output capacitor, C. 量ΔIL(+)all 代表了电感的纹波电流 同时注意在此期间 所有的输出负载电流由输出电容 , , 。 C提供 Therefore,tosince the flowing inductor L cannot change instantaneously, the Referring Figure 2, current when Q1 is OFF,initthe presents a high impedance from its drain to source. Referring tosince Figure 2, current when Q1 is OFF, itthe presents a high impedance from its drain across to source. current shifts fromthe Q1 to CR1. Due to in the decreasing inductor current, the voltage Therefore, flowing inductor L cannot change instantaneously, the 参考图2,当Q1关时,它的漏极和源极间有很高的阻抗,所以,流过电感L的电流不能瞬时的变化, Therefore, since flowing inductor L cannot change instantaneously, the inductor reverses polarity until rectifier CR1 becomes forward biased and turnsacross ON. The current shifts fromthe Q1current to CR1. Due to in thethe decreasing inductor current, the voltage 从 转移到 随着电感电流的减小 电感两段的电压改变极性直到整流器 变为前向偏置 , , Q1 CR1。 CR1 current shifts from Q1 to CR1. Due to the decreasing inductor current, the voltage across the voltage applied across L becomes (VO −CR1 Vd −becomes IL × RL ) where thebiased quantity, Vd turns , is theON. forward inductor reverses polarity until rectifier forward and The 打开的时候 这时电感 两段的电压变为 是 的前向电压降 电感电 × 式中的 ,of CR1. 。 L L becomes CR1 and (VO−CR1 –VV ILL × Rflows RL) Vdbiased inductordrop reverses polarity until rectifier forward The The inductor current, fromthe the output capacitor and load voltage applied across (VO Inow where quantity, Vd turns , is theON. forward dIdL−–, becomes L) , voltage applied across L becomes (VO,to −经过 V − I × R ) where quantity, V , is the forward resistor combination through CR1 and ground. Notice that the orientation of CR1 and the drop of CR1. The inductor current, I , now flows from the output capacitor and load 流IL,这时从输出电容和负载电阻的组合 到地 。 CR1 dL L L d voltage drop of CR1. The inductor current, I , now flows from the output capacitor and load direction of current flow in the inductor means that the current flowing in the output capacitor resistor combination through CR1 and to ground. Notice that the orientation of CR1 and the L 注意 CR1 的方向和电感中电流的流向意味着输出电容和负载电阻中电流导致 VO 为负电压 。 在关态 resistor combination through CR1 and to ground. Notice that the orientation of CR1 and the and load resistor combination causes V to be a negative voltage. During the OFF state, direction of, current flow in the inductor means the current flowing in the output capacitor O(VO – Vdthat 电感两端的电压为定数 (OFF)时 ,且为 – IL × RL) ,为了保证同样极性的转换,这个加载 direction of current flowthe in the inductor the current inILthe output capacitor voltage across inductor is constant and equal to (Vflowing −V ×the R ). Maintaining and loadapplied resistor combination causes Vmeans a negative voltage. During state, the d− LOFF O to bethat 电压必须是负的(或者在开态(ON)时为极性相反的加载电压 因为输出电压为负的 ),O 。因此,电 and loadapplied resistor combination causes VO to be and a negative voltage. During the OFF state, our same polarity convention, this applied voltage isequal negative (or opposite in polarity from the voltage across the inductor is constant to (V − V − I × R ). Maintaining O d L L 时间内电 感电流在 态时是减小的 而且由于加载电压必须是常数 所以电感电流线性减小 ,voltage 。 T OFF OFF from voltage applied across the,ON inductor isbecause constant andis equal to (V − V − I × R ). Maintaining applied voltage during the time), the output V is negative. Hence, our same polarity convention, this applied voltage negative (or opposite in polarity the O Od L L 感电流的减小见图 3. our same polarity convention, this applied voltage is negative (or opposite in polarity from inductor current decreases during the OFF time. Also, since the applied voltage is essentially applied voltage during the ON time), because the output voltage VO is negative. Hence, the applied voltage during the ON time), theAlso, output voltage Vin is negative. the constant, the inductor current decreases Thissince decrease during inductor current decreases during thebecause OFFlinearly. time. the applied voltagecurrent is Hence, essentially O inductor inductor current decreases during the OFF time. Also, since the applied voltage is essentially T is illustrated in Figure 3. constant, the inductor current decreases linearly. This decrease in inductor current during OFF constant, the inductor current T in Figure 3. decreases linearly. This decrease in inductor current during OFF is illustrated The inductor current decrease 在关态 电感电流的减小可以由下式求得 (OFF) : state is given by: T is illustrated in Figure 3. during the OFF OFF The inductor current decrease during the OFF state is given by: The inductor current decrease during OFF � is given by: � �V O � V d �the IL � R Lstate �I L(�) � � �V � V � I � R � � T OFF dL L O L �I L(�) � � �V O � V d � I L � R � � T OFF L dL L O � T OFF This quantity,�I ∆ILLL(�) (−),� is also referred to as the inductor ripple current. L 量ΔIL(–) 也代表了电感的纹波电流。 This quantity, ∆IL (−), is also referred to as the inductor ripple current. duringcurrent. the ON time and the current In steady state∆Iconditions, currenttoincrease, ∆IL (+), ripple This quantity, referred as the inductor L (−), is alsothe decrease during the(ON) OFF time, ∆IL (−), must equal. Otherwise, inductor current would (+), during thethe ON time and current In steady state conditions, the current increase, ∆I 在稳态条件下 下的电流增加量 ΔIbe 和关态 下的电流减小量 Δ ,开态 (OFF) (+) I Lthe (–) 必须是相 L L (+), during the ON time and the current In steady state conditions, the current increase, ∆I have a net increase or decrease from cycle to cycle which would not be a steady state decrease during the OFF time, ∆I (−), must be equal. Otherwise, the inductor current would L 等的。否则,在一个周期到下一个周期 L ,电感电流就会有一个净的增加量或者减小量 ,这就不是一 decrease during the OFF time, must betobe equal. Otherwise, the not inductor would condition. Therefore, these two∆I equations can equated and solved forbeV a current to obtain the have a net increase or decrease from cycle cycle which would steady state L (−), 个稳态了 。所以 ,这两个方程必须相等 ,从而求出 VO ,得到连续导通下buck-boostO能量转换的关系 have a netTherefore, increase or decrease from cycle which would notforbeVOa to steady continuous conduction mode buck-boost voltage conversion relationship: condition. these two equations cantobecycle equated and solved obtainstate the 式: condition. equationsvoltage can beconversion equated and solved for VO to obtain the continuousTherefore, conductionthese modetwo buck-boost relationship: Solving for V continuous conduction mode buck-boost voltage conversion relationship: O: 求解出VOfor : VO : Solving Solving for VO : �T T T V O � � �V I � V DS� � T ON � V d � I L � R L � T ON � T OFF T ON T OFFOFF V O � � �V I � V DS� � TOFF � V d � I L � R L � T ON � T OFF T T OFF ON ON V O � � �V I � V DS� � OFF � V d � I L � R L � T OFF T OFF �� � ZHCA041–1999年3月–2002年11月修订 OFF OFF �� � Understanding Buck-Boost Power Stages in Switch Mode Power Supplies Understanding Buck-Boost Power Stages in Switch Mode Power Supplies Understanding Buck-Boost Buck-Boost Power Power Stages Stages in in Switch Switch Mode Mode Power Power Supplies Supplies Understanding 全面认识开关型电源中的BUCK-BOOST功率级 www.BDTIC.com/TI 5 5 5 5 5 And, substituting TS for TON + TOFF, and using D = TON /TS and (1−D) = TOFF /TS , the steady-state equation for VO is: D � V � IL � RL www.ti.com.cn d 1�D 1�D And, substituting TS for TON + TOFF, and using D = TON /TS and (1−D) = TOFF /TS , the steady-state equation for VO is: Notice in simplifying the TOFF is /assumed to be equal to: TS . This is true 用TON+Tthat TS ,并利有 D =above, TON / TS T和 (1 +– D) = TOFF TS ,VO 的稳态方程可变为 ON OFF 来替换 only for continuous conduction mode as we will see in the discontinuous conduction mode analysis. I � RL V O � � �V I � V DS� � D � V d � L 1�D 1�D An important observation should be made here: Setting the two values of ∆IL equal to each other is precisely equivalent to balancing the volt-seconds on the inductor. The volt-seconds Notice that in simplifying the above, TON + TOFF is assumed to be equal to TS . This is true applied to the inductor is the product ofTthe voltage applied and the time, that the voltage is 注意在上式的化简中 用到了 在我们以后分析到 ,这只是在连续导通模式下成立的 TON +T OFF 等于 only for continuous, conduction mode asSwe will see in the discontinuous conduction mode applied. This is the best way to calculate unknown values such as VO or D in terms of known 非连续导通模式下就可以看到。 analysis. circuit parameters, and this method will be applied repeatedly in this paper. Volt-second balance on the inductor is a physical necessity and should be comprehended at least as well 我们还发现 ,等同于电感上的电压 ,Δ I L 的两个值相互相等的假定 -秒曲线的平衡 –秒 An important observation should be made here: Setting the two values of 。 ∆I电感上的电压 as Ohms Law. L equal to each other is precisely equivalent to balancing the volt-seconds on the inductor. The volt-seconds 关系是由加载在电感上的电压和加载电压的时间来确定的 。这是用已知的电路参数来计算像 VO 和D等 applied to the inductor is the product of the voltage applied and the time that the voltage is 未知值的最好方法 电感上的电压 ,这种方法在本文中将经常用到 , In the above equations for ∆IL (+) and ∆IL (−), the。output voltage-秒关系平衡在物理上是必须的 was implicitly assumed to be applied. This is the best way to calculate unknown values such as VO or D in terms of known 而且就像欧姆定律一样容易理解 。 constant with no AC ripple voltage during the ON time and the OFF time. This is a common circuit parameters, and this method will be applied repeatedly in this paper. Volt-second simplification and involves two separate effects. First, the output capacitor is assumed to be balance on the inductor is a physical necessity and should be comprehended at least as well large enough itsΔvoltage change is negligible. Second, , the voltage due the capacitor 在上面关于 ΔI Lthat 在ON 时间和 ,输出电压默认为常数定值 (+) 和 I L(–) 的方程中 OFFto时间内没有交流 as Ohms Law. ESR is also assumed to be negligible. These assumptions are valid because the AC ripple 纹波电压。这是一个常用的简化,涉及到两方面的假设,首先,输出电容足够大,它上面的电压变 voltage is designed to be much less than the DC part of the output voltage. 化可以忽略 其次,由于电容等效串联电阻 造成的电压也可以忽略 ;equations (ESR) 。这些假设是合理的 , In the above for ∆IL (+) and ∆IL (−), the output voltage was implicitly assumed to be 因为设计的交流纹波电压是远小于输出电压的直流部分的 。and the OFF time. This is a common constant with no AC ripple voltage during the ON time The above voltage conversion relationship for VO illustrates the fact that VO can be adjusted simplification and involves two separate effects. First, the output capacitor is assumed to be by adjusting the duty cycle, D. This relationship approaches zero as D approaches zero and large that its voltage change is negligible. Second, Dthe voltage due 。 to这种关系在 the capacitor 上面Venough 来调节输出电压 ,就是可以通过调节电控比 O 的电压转换关系表明一个事实 increases without bound as D approaches 1. A common simplification is to assume VDS , D Vd接, ESR is also assumed to be negligible. These assumptions are valid because the AC ripple 近于R 足够小, 。一个常用的简化就是假定 0时也接近 0,在 D接近1时逐渐增加而没有限制 VDS , Vd 和RLequation and are small enough to ignore. Setting VDS , Vd , and RL to zero, the above L is voltage designed to be much less than the DC part of the output voltage. 可以忽略 假设 和 等于 上面的式子就可以简单地看作为 : simplifies。considerably VDS, Vd Rto: 0, L SLVA059A Buck-Boost级稳态分析 VO � � �� � � � V I � V DS� � The above voltage conversion relationship for VO illustrates the fact that VO can be adjusted D relationship approaches zero as D approaches zero and by adjusting theVduty � V I D. � This O �cycle, 1�D increases without bound as D approaches 1. A common simplification is to assume VDS , Vd , and RL are small enough Setting VDS ,operation Vd , and R zero, the above equation A simplified, qualitative waytotoignore. visualize the circuit isLtotoconsider the inductor as an 一个简单定性的想象电路工作的方法就是把电感看作是一个能量储存单元 打开时 simplifies considerably ,当Q1 energy storage element.to: When Q1 is on, energy is added to the inductor. When Q1,is能量加到 off, the 电感器上delivers 电感就把它储存的一部分能量输送到输出电容和负载上 ,当Q1关上时 。输出电压就通过 inductor some,of its energy to the output capacitor and load. The output voltage is controlled by setting the, on-time of Q1. For example, by increasing the on-time of Q1, the 设定Q1的开关时间来控制 例如,D 增大 ,输送到电感的能量就增加 ,在Q1关时有越多 Q1开的时间 V Odelivered � � VI � amount of energy to the inductor is increased. More energy is then delivered to the 1�D 的能量输出,输出电压就会增加。 output during the off-time of Q1 resulting in an increase in the output voltage. A simplified, qualitative way to visualize the circuit operation is to consider the inductor as an 不像降压 功率级, 电感电流的平均值并不等于输出电流 (buck) 。想知道电感电流和输出电流的关 energy storage element. When Q1 is on, energy is added to the inductor. When Q1 is off, the Unlike the buck power stage, the average of the inductor current is not equal。to the output 系,可以参考图 注意电感只有在能量级的关 态才向输出传送电流 这样在整个开 2和图 3,of inductor delivers some its energy to the output(OFF) capacitor and load. The output voltage is current. To relate the inductor current to the output current, referring to Figures 2 and 3, note controlled by setting the on-time of Q1. For example, by increasing the on-time of Q1, the 关周期内的电流平均值就等于输出电流 因为输出电容中的电流平均值必须等于 that the inductor delivers current to , the output only during the off state of0.the power stage. amount of energy delivered to the inductor is increased. More energy is then delivered to the This current averaged over a complete switching cycle is equal to the output current because output during the off-time of Q1 resulting in an increase in the output voltage. the average current in the output capacitor must be equal to zero. Unlike the buck power stage, the average of the inductor current is not equal to the output to Figures 2 and 3, note that the inductor delivers current to the output only during the off state of the power stage. This current averaged over a complete switching cycle is equal to the output current because the average current in the output capacitor must be equal to zero. 6 current. To relate the inductor current to theMode output current, referring Understanding Buck-Boost Power Stages in Switch Power Supplies 6 6 Understanding Buck-Boost Power Stages in Switch Mode Power Supplies 全面认识开关型电源中的BUCK-BOOST功率级 ZHCA041–1999年3月–2002年11月修订 www.BDTIC.com/TI www.ti.com.cn SLVA059A Buck-Boost级稳态分析 The relationship between the average inductor current and the output current for the 在buck-boost 功率级的连续导通模式中 电感电流的平均值和输出电流的关系有下式给出 : continuous mode buck-boost power,stage is given by: I L(Avg) � T OFF � I L(Avg) � (1 � D) � � I O TS 或者 or I L(Avg) � � IO (1 � D) Another important observation is that the average inductor current is proportional to the output current, and since the inductor ripple current, ∆IL , is independent of output load 另外一个重要的现象就是电感电流的平均值跟输出电流是成比例的 ,因为电感纹波电流 I L 是跟输 current, the minimum and the maximum values of the inductor current track theΔaverage 出负载电流无关的 ,电感电流的最大值和最小值精确的跟随电感电流的平均值变化 。例如 inductor current exactly. For example, if the average inductor current decreases by , 2 当电感 A due 电流的平均值由于负载电流降低而减小 时,电感电流的最大值和最小值也会随着减小 假定一 to a load current decrease, then the2A minimum and maximum values of the inductor 2A(current decrease by 2 A (assuming 直保持在连续导通模式下 )。 continuous conduction mode is maintained). The forgoing analysis was for the buck-boost power stage operation in continuous inductor 现在就停止对 能量级在连续导通模式下电感电流的分析了 在接下来的部分描述在非连 current mode.buck-boost The next section is a description of steady-state , operation in discontinuous 续模式下的稳态工作 主要任务是 能量级在非连续导通模式下电压转换关系的推导 , 。 for buck-boost conduction mode. The main result is a derivation of the voltage conversion relationship the discontinuous conduction mode buck-boost power stage. 2.2 Buck-Boost 稳态非连续导通模式分析 2.2 现在我们研究当导通模式从连续变为非连续 ,负载电流降低时会发生什么 ,回想连续导通模式 ,电 Buck-Boost Steady-State Discontinuous Conduction Mode Analysis 感平均电流跟随输出电流变化,也即是,如果输出电流减小,电感电流平均值也会减小。此外,电 We now investigate what happens when the load current is decreased and the conduction 感电流的最大值和最小值也会准确的随着电感电流平均值变化。 mode changes from continuous to discontinuous. Recall for continuous conduction mode, the average inductor current tracks the output current, i.e. if the output current decreases, 如果输出负载电流减小到临界电流水平以下 在开关周期的一部分时间内电感电流就会变为 0。从 then so does the average inductor current.,In addition, the minimum and maximum peaks of 图3inductor 的波形图中可以明显看出来这点 the current follow the average inductor current exactly. ,因为纹波电流的峰峰值幅度并不随着输出负载电流变化 。在 buck-boost 能量级 , 如果电感电流试图减低到 0 以下时 , 它会停在 0( 因为 CR1 只能有单向电流通 If过the output load current is reduced below the critical current level, the inductor current will ),并保持为0直到下一个开关周期的开始。这个工作模式就叫做非连续导通模式。一个工作在 be zero for a portion of the switching cycle. This should be evident from the waveforms shown 非连续导通模式下的功率级在一个开关周期内有三个状态,相比下连续导通模式只有两个状态。功 in Figure 3, since the peak to peak amplitude of the ripple current does not change with output 率级在连续模式和非连续模式的分界处电感电流的条件见图 这也是电感电流突然降到 0,而且在 load current. In a buck-boost power stage, if the inductor4, current attempts to fall below zero, 和IO(Crit) 的绝对值 。注意 ,图flow ,因为 0时并马上开始下个开关周期的地方 4中显示的是 IL it电流降到 just stops at zero (due to the unidirectional current in CR1)IOand remains there untilIO和 the 有相反的极性 beginning of。the next switching cycle. This operating mode is called discontinuous conduction mode. A power stage operating in discontinuous conduction mode has three unique states during each switching cycle as opposed to two states for continuous conduction mode. The inductor current condition where the power stage is at the boundary between continuous and discontinuous mode is shown in Figure 4. This is where the inductor current just falls to zero and the next switching cycle begins immediately after the current reaches zero. Note that the absolute values of IO and IO(Crit) are shown in Figure 4 because IO and IL have opposite polarities. ZHCA041–1999年3月–2002年11月修订 Understanding Buck-Boost 全面认识开关型电源中的BUCK-BOOST功率级 Power Stages in Switch Mode Power Supplies www.BDTIC.com/TI 7 7 www.ti.com.cn Buck-Boost SLVA059A 级稳态分析 IL Solid |IO| Dashed = |IO(Crit)| ∆IL(max) 0 TON TOFF TS Figure 4. Boundary Between Continuous and Discontinuous Mode 图4.连续模式和非连续模式的分界线 Further reduction in output load current puts the power stage into discontinuous conduction mode. This condition is illustrated in Figure 5. , The mode power stage 输出负载电流的继续下降把功率级变为非连续导通模式 在图discontinuous 。非连续导通模式的 5中说明这种情况 frequency response is quite different from the continuous mode frequency response and is 功率级频率响应跟在连续导通模式下的频率响应非常不一样 这会在 功率级模型部分给 , buck-boost given in the Buck-Boost Power Stage Modeling section. Also, the input to output relationship 出;而且,输入到输出的关系也非常不一样,会在下面的推导中看出来。 is quite different as shown in the following derivation. IL Solid |IO| Dashed ∆IL 0 DTs D3Ts D2Ts TS 图5.Discontinuous 非连续电流模式Current Mode Figure 5. To begin the derivation of the discontinuous conduction mode buck-boost power stage 在开始推导 buck-boost 功率级非连续导通模式下电压转换比之前 , 先回想一下在非连续导通模式 voltage conversion ratio, recall that there are three unique states that the converter assumes 下工作的转换器的三种状态 。 在 Q1 开 ,CR1 关时 , 是开态 (ON); 在 Q1 关 ,CR1 开时 , 是关态 during discontinuous conduction mode operation. The ON State is when Q1 is ON and CR1 前两种状态跟连续模式下的是一样的 (OFF); ,是空闲态 (IDLE)。 ,图Q1 Q1和State CR1都关时 2中 is OFF. The在OFF is when Q1 is OFF and CR1 is ON. The IDLE state is when both 显示的电路也适用 只是first ≠ (1– 开关周期的剩余时间就是空闲 态。case 此外, 输 (IDLE) TOFF two D) ×are TS 。 and CR1 are OFF.,The states identical to those of the continuous mode and the circuits of Figure 2 are applicable except that TOFF ≠ (1−D) × TS . The remainder of the 出电感的直流阻抗 开 、输出二极管的前向电压降和功率型金属氧化物半导体场效应管 (MOSFET) switching cycle is the IDLE state. In addition, the DC resistance of the output inductor, the 态下的电压降都足够小,可以忽略。 output diode forward voltage drop, and the power MOSFET ON-state voltage drop are all assumed to be small enough to omit. 开态(ON)的时间TON = D × TS ,D为占空比,由控制电路来设定,表征开关开态内的时间与开关 周期总时间TS的比值。关态(OFF)的时间T = D2 × TS ,空闲态(IDLE)的时间就是开关周期内 The duration of the ON state is TON = D OFF × TS where D is the duty cycle, set by the control × TS 。ON 的剩余时间 在图time ,即为Tas TONratio – TOFF D3switch 6中给出这三种时间和响应的波形 S –a circuit, expressed of =the to the time of one complete。 switching cycle, Ts . The duration of the OFF state is TOFF = D2 × TS . The IDLE time is the remainder of the 跟前面一样cycle switching and is given as T, − TON − TOFF = D3 × TS . These times are ,没有进行详细的解释 。 shown with the S 电感电流增加和减少的方程直接在下面给出 waveforms in Figure 6. Without going through the detailed explanation as before, the equations for the inductor current increase and decrease are given below. 8 8 全面认识开关型电源中的BUCK-BOOST功率级 Understanding Buck-Boost Power Stages in Switch Mode Power Supplies ZHCA041–1999年3月–2002年11月修订 www.BDTIC.com/TI www.ti.com.cn SLVA059A Buck-Boost级稳态分析 SLVA059A SLVA059A SLVA059A 在开态 内电感电流的增加为 (ON)current : The inductor increase during the ON state is given by: The inductor current increase during the ON state is given by: The during The inductor inductor current current increase increase duringVthe the ON ON state state is is given given by: by: V �I L(�) � V I � T ON � V I � D � T S � I PK LI T � VLI � D � T � I �I L(�) � V VLII � ON � V S � I PK (�) � D � �I LII � � L� �T T ON �(+), � Dalso �T Tthe I PK �I LL(�)magnitude, S PK inductor current, I ON S �peak L The ripple current ∆I is L L L pk because in Δ 也是峰值电感电流 纹波电流幅度 因为在非连续模式下 每个周期内电流都是从 , , I (+) I 0开始的。 The ripple current magnitude, ∆I (+), is also the peak inductor current, I because in discontinuous mode, the current starts L pk at zero each cycle. L (+), The ripple current magnitude, ∆I is also the peak inductor current, IIpk because in L pk The ripple current magnitude, ∆I (+), is also the peak inductor current, because in L pk discontinuous mode, the current starts at zero each cycle. discontinuous mode, the current starts at zero each cycle. discontinuous mode, the current starts at zero each cycle. The inductor current decrease during the OFF state is given by: 在关态 内电感电流的减小为 (OFF) : The inductor current decrease during the OFF state is given by: The during the OFF state is given by: The inductor inductor current current decrease decrease � V O during the OFF � V Ostate is given by: �I L(�) � � V � T OFF � � V � D 2 � T S L O�T � �LV O �D �T �I L(�) � � �LV VO O � T OFF � �LV O O � D2 � TS (�) � �I (�) � � T � � D 22 �increase, T SS �I L OFF L L OFFcase, L As in the continuous conduction mode the current ∆IL (+), during the ON time L L As the current continuous conduction mode current increase, ∆IL (+), during the ON time andinthe decrease during the case, OFF the time, ∆IL (−), are equal. Therefore, these two As in the continuous conduction mode case, the current increase, ∆I (+), during the ON time L As in the continuous conduction mode case, the current increase, ∆I (+), during the ON time and the current decrease during the OFF time, ∆I (−), are equal. Therefore, these two L equations can be equated and solved for VO to obtain the first of two equations to be used L (−), and the current decrease during the OFF time, ∆I are equal. Therefore, these two 跟在连续导通模式下一样 开态 的电流增量 Δ Δ 是相 和关态 的电流减小 L and the current decrease during the OFF time, ∆I (−), are equal. Therefore, these two , (ON) , (OFF) I I (+) (–) L L L the first of two equations to be used equations equated and solved for VO to obtain to solve forcan thebe voltage conversion ratio: equations can be equated and solved for V to obtain the first of two equations to be used O equations can be equated and solved for V to obtain the first of two equations to be used 等的 从而由这两个方程中第一个来解出电压转换比 。所以这两个方程相等 ,解出VO ,ratio: : to solve for the voltage conversion O to ratio: to solve solve for for the the voltage voltage conversion conversion T ON ratio: � � VI � D VO � � VI � T ON T 2 � � V � DD VO � � VI � T TOFF ON D ON � � V I � D D2 � � V � V T � � V � � � V � VO I I OFF I I O D2 T T OFF Now we calculate the output current VO divided by the output load R). It 2 OFF (the outputDvoltage Now calculate theone output currentcycle (the of output voltage Vcurrent by the load R). It is thewe average over switching the inductor during theoutput time when CR1 O divided Now we calculate the output current (the output voltage V divided by the output load R). It 现在我们来计算输出电流 输出电压 除以负载电阻 它是在 导通时间内 × 整个 ( )。 (D2 ) O V R CR1 T Now we calculate the output current (the output voltage V divided by the output load R). It O S is the average over one switching cycle of the inductor current during the time when CR1 O conducts (D2 × TS). is the average over one switching cycle of the inductor current during the time when CR1 is the average over one switching cycle of the inductor current during the time when CR1 开关周期上的电感电流的平均值 。 conducts (D2 × TS). conducts ). conducts (D2 (D2 × ×T TS S). VO � I PK 1 VRO � I O � T1 � �2I PK � D 2 � T S V � I � 1S � � �D �T VRO �2II PK O � I O � T1 PK � D 2 � T S � � I � � � D2 � TS O S 2 O R T R relationship T SS for I 2 (∆I (+)2 ) intoS the above equation to obtain: Now, substitute the PK L Now, substitute the relationship for IPK (∆IL(+) ) into the above equation to obtain: 把 IPK substitute ,可以得到 (ΔIL(+) ) 的关系代入上式 : (∆I (+) Now, the for ) into the above equation to obtain: Now, substitute the relationship relationship for IIPK PK (∆IL L(+) ) into the above equation to obtain: VO 1 � ( � 1) � V I � D � T � D � T 1 2 VRO � I O � T1 � 1 S S VLI V S� 2 ( � 1) � V � I � � � D � T � D � T VRO V 1 I 1 2 O S S O � I � T1 � 2 I�D�T � � IO � TS � 1 � ((� �1 1)) � � L � D � T SS � �D D 22 � �T T SS 2 O R L 2 R L TS VO � V I �SD � D 2 � T S � VRO �LD 2 � T S � V I � 2D� V � D � � V � VRO � D �LD D 22 � �T T SS � V I I O� 2� � R 2 � L We now have two equations, the one for the output current (VO divided by R) just derived and R 2�L We now for have equations, theboth oneinforterms the output divided R) just derived and the one thetwo output voltage, of VI , current D, and (V D2O. We nowby solve each equation We now have two equations, the one for the output current (V divided by R) just derived and O We now have two equations, the one for the output current (V divided by R) just derived and O the one for the output voltage, both in terms of V , D, and D . We now solve each equation for D2 and set the , two equations equal to each other. Using the resulting an I , OD, 2 .一个就是用 现在我们有两个方程 一个就是刚得到的输出电流 除以 和D 2equation 来表示的 (V R), V I , each Dequation, the one for the output voltage, both in terms of V and D We now solve I 2 the one for the output voltage, both in terms of V , D, and D . We now solve each equation for D2 and for setthe theoutput two equations equal to each other. Using the resulting equation, an I 2 expression voltage, V , can be derived. O 输出电压 。 从每个方程中解出 , 再解这个方程就可以得到输出电压的表达式 D 2 , 然后令它们相等 for D and set the two equal to each other. Using the resulting equation, an for D2 setthe theoutput two equations equations to each other. Using the resulting equation, an 2 and for expression voltage, Vequal , can be derived. O expression for ,, can be derived. VO。 expression for the the output output voltage, voltage, V VO can be derived. O �� � �� � ZHCA041–1999年3月–2002年11月修订 �� � �� � �� � �� � Understanding Buck-Boost 全面认识开关型电源中的BUCK-BOOST功率级 Power Stages in Switch Mode Power Supplies Understanding Buck-Boost Power Stages in Switch Mode Power Supplies Understanding Understanding Buck-Boost Buck-Boost Power Power Stages Stages in in Switch Switch Mode Mode Power Power Supplies Supplies www.BDTIC.com/TI 9 9 9 9 9 www.ti.com.cn SLVA059A 级稳态分析 Buck-Boost The discontinuous conduction mode buck-boost voltage conversion relationship is given by: 非连续导通模式下 buck-boost功率级电压转换关系为: VO � � VI � D �K Where K is defined as 其中K定义为 K� 2�L R � TS The above relationship shows one of the major differences between the two conduction 从上面的关系式可以看出两种导通模式的主要不同 对于非连续导通模式 ,电压转换关系是输入电 modes. For discontinuous conduction mode, the,voltage conversion relationship is a function 压、 功率级电感 、开关频率和输出负载的方程 ;而对于连续导通模式 ,电压转换关系只是 of the占空比 input、voltage, duty cycle, power stage inductance, the switching frequency, and the output load resistance. For continuous conduction mode, the voltage conversion relationship 取决于输入电压和占空比。 is only dependent on the input voltage and duty cycle. IQ1 ICR1 IL Solid IO Dashed ∆IL VC-P Solid VO Dashed 0 D3×TS D × TS D2×TS TS Figure 图 6.6.Discontinuous Mode Buck-Boost Converter Waveforms 非连续导通模式下 转换器波形图。 buck-boost In typical applications, the功率级或者工作在连续导通模式 buck-boost power stage is,operated in either continuous 在典型的应用中 或者工作在非连续导通模式 ,buck-boost 。而对 conduction mode or discontinuous conduction mode. For a particular application, one 于一些特殊的应用,选定一个导通模式后,功率级就会维持在这种相同的模式工作 下一部分会给 。 conduction mode is chosen and the power stage is designed to maintain the same mode. The 出功率级的电感关系 ,在已知给定的输入电压、输出电压和输出负载电流的范围内,让它工作在一 next section gives inductance relationships for the power stage that allow it to operate in only 种导通模式。 one conduction mode, given ranges for input and output voltage and output load current. 10 10 Understanding Buck-Boost Power Stages in Switch Mode Power Supplies 全面认识开关型电源中的BUCK-BOOST功率级 ZHCA041–1999年3月–2002年11月修订 www.BDTIC.com/TI 2.3 2.3 2.3 SLVA059A SLVA059A Critical Inductance Critical Inductance Critical Inductance The previous analyses for the buck-boost converter have been for continuous and The previous discontinuous www.ti.com.cn analyses for the buck-boost converter haveThe been for continuous and conduction modes of steady-state operation. conduction mode of a The previous analyses for the buck-boost converter have been for continuous and 级稳态分析 Buck-Boost discontinuous conduction modes of steady-state operation. The conduction mode of a converter is a function of input voltage, output voltage, output current, and the value of the discontinuous conduction modes of steady-state operation. The conduction mode of a converterAisbuck-boost a function of input voltage, voltage, output current, and the value the inductor. converter can beoutput designed to operate in continuous mode forofload converter is a function of input voltage, output voltage, output current, and the value of the inductor. above A buck-boost can5% be to designed to operate in continuous load 2.3 关键电感 currents a certainconverter level, usually 10% of full load. Usually, the input mode voltagefor range, inductor. A buck-boost converter can be designed to operate in continuous mode for load currents above a certain level,current usuallyare 5%defined to 10% by of full Usually, the input voltage range, the output voltage, and load theload. converter specification. This。leaves 前面对 转换器的分析主要是在连续导通模式下和非连续导通模式下的稳态工作 转换器 buck-boost currents above a certain level, usually 5% to 10% of full load. Usually, the input voltage range, the output voltage, and load current are defined by the converter specification. This leaves inductor value as the design parameter to maintain continuous conduction mode. 的导通模式是输入电压 输出电流和电感值的函数 转换器设计时 一般都 the output voltage, and 输出电压 load current are defined by the converter specification. This,leaves 。Buck-boost the inductor value as 、 the design、 parameter to maintain continuous conduction mode. the inductor value as the design parameter to maintain continuous conduction mode. 设定工作在连续导通模式下 ,负载电流都高于某个一定的水平 ,这个水平通常是全负载电流的 5% The minimum value of inductor to maintain continuous conduction mode can be determined 到10%。 输入电压范围 输出电压和负载电阻通常都是由转换器规格来确定 ,这样电感值就成了让 The minimum value of、inductor to maintain continuous conduction mode can be determined by the following procedure. The minimum value of inductor to maintain continuous conduction mode can be determined by the following procedure. 转换器工作在连续导通模式的可设计参数 。让转换器工作在连续导通模式的电感的最小值可以由下 by the following procedure. First, define IO(Crit) 面的过程来确定 。 as the minimum output current to maintain continuous conduction mode, First, define I output current to maintain continuous mode, normally referred toasasthe theminimum critical current. This value is shown in Figureconduction 4. Since we are First, define IO(Crit) as the minimum output current to maintain continuous conduction mode, O(Crit) normallytoward referred to as the critical current. This value is shown in Figure 4.toSince we are working a minimum value for the inductor, it is more straightforward perform the normally referred to as the critical current. This value is Ishown in Figure 4. Since,we are 首先,定义保持转换器工作在连续导通模式下的最小输出电流 通常是一个临界电流 这个值 , O(Crit) working toward minimum value for the inductor, it isaverage more straightforward to perform the derivation usingathe inductor current. The minimum inductor current to maintain working toward。a因为我们要得到电感的最小值 minimum value for the inductor, it is more straightforward 。 to perform the 在图4中给出了 ,所以用电感电流的推导更加直接 derivation using the inductor current. The minimum average inductor current保持连续导通 to maintain continuous conduction mode is given by: derivation using the inductor current. The minimum average inductor current to maintain 模式的电感电流平均值的最小值由下式给出 continuous conduction mode is given by:: continuous conduction mode is given by: �I I L(min�avg) � �I L � I O(crit) 2L � I I L(min�avg) � �I I L(min�avg) � 2 L � I O(crit) O(crit) 2 above Second, calculate L such that the relationship is satisfied. To solve the above equation, Second, calculate L∆I such above is Lsatisfied. To solve the above equation, either relationship, (+)that or ∆Ithe (−) may relationship be used for ∆I . Note also that either relationship for L L Second, calculate L such that the above relationship is satisfied.ΔTo solve the above equation, 第二is,independent 计算满足上述关系的 为了解出上面的方程 关系式中的 Δ 都可以看作是 和either , L。 I I (+) (–) either relationship, ∆I (+) or ∆I (−) may be used for . Note also that relationship for ∆I of the output current level. Here, ∆I (+) is used. The worst case condition L L L L L L either relationship, ∆IL (+) or ∆IL (−) may be used for ∆IL . Note also that either relationship for ∆I independent of the output current level. Here, ∆I (+) is used. The worst case condition ΔLI Lis Δ 的两个关系式都跟输出电流水平无关 这里 采用 Δ 最差情况 给 (giving the largest L, ) is at maximum input voltage because this gives the maximum ∆I , , 。同时还要注意 。 ( I I (+) L L min L. ∆IL is independent of the output current level. Here, ∆IL The worst case condition L (+) is used. (giving the largest L ) is at maximum input voltage because this gives the maximum ∆I . ΔIL 。 出最大的 )就是在最大输入电压下 ,因为这时有最大的 Lminlargest (giving the Lmin ) is at maximum input voltage because this gives the maximum ∆IL . min L Now, substituting and solving for Lmin : Now, substituting and solving for Lmin : Now, substituting 现在代换并解出 : solving for Lmin : Lminand T ON(min) L min � 1 � �V I(max) � V DS � I L � R L� � T ON(min) 1 � �V O(crit) � V DS � I L � R L� � TION(min) L min � 2 2 � �V I(max) � V DS � I L � R L� � I O(crit) L min � 1 I(max) 2 I O(crit) The above equation can be simplified by ignoring minor parasitic resistances and diode 通过忽略小寄生电阻和二极管电压降 上面的方程可以化简为 : parasitic resistances and diode The above equation can be simplified by ignoring voltage drops, and rearranged for, ease of use to: minor The above equation can be simplified by ignoring minor parasitic resistances and diode voltage drops, and rearranged for ease of use to: voltage drops, and rearranged for ease of use to: V I (max) �V �T V I (max) L min � � V O � T S � V I (max) S 2� I O(crit) � T VO L min � � � L min � 2 �OI O(crit)S � V O � V I (max) 2 � I O(crit) V O � V I (max) V O � V I (max) Using the inductor value just calculated will guarantee continuous conduction mode 利用刚计算的电感值,就可以保证转换器工作在连续导通模式下,而且输出负载电流高于临界电流 Using thefor inductor value just calculated guarantee continuous operation output load currents above the will critical current level, IO(crit) .conduction mode Using the inductor value just calculated will guarantee continuous conduction mode 水平IO(crit) 。for operation output load currents above the critical current level, IO(crit) . operation for output load currents above the critical current level, IO(crit) . � �� ZHCA041–1999年3月–2002年11月修订 � �� Understanding Buck-Boost Power Stages in Switch Mode Power Supplies Understanding Buck-Boost Power Stages in Switch Mode Power Supplies Understanding Buck-Boost Power Stages in Switch Mode Power Supplies 11 11 11 全面认识开关型电源中的BUCK-BOOST功率级 11 www.BDTIC.com/TI www.ti.com.cn 功率级小信号模型 Buck-Boost SLVA059A 3 Buck-Boost Power Stage Small Signal Modeling 功率级小信号模型 3 Buck-Boost We now switch gears, moving from a detailed circuit oriented analysis approach to more of 功率级的分析从面向细节电路的分析方法转向系统级别的分析研究 ,功率 a现在把我们对 system levelbuck-boost investigation of the buck-boost power stage. This section presents techniques to assist the power supply designer in accurately modeling the power stage as a component 级设计者在模型中把功率级作为 功率源控制环路的一部分 文章这部分主要提供了针对 , buck-boost of the control , loop of a buck-boost power supply. The three major components of 、 the power 这些设计者的 在精确模拟时的辅助技术 脉冲宽度 。功率源控制环路的三个主要部分 (即功率级 supply control loop (i.e., the power stage, the pulse width modulator, and the error amplifier) 调制器和误差放大器)见图7中表格所示。 are shown in block diagram form in Figure 7. VI Power Stage VO Duty Cycle d(t) Pulse-Width Modulator Error Amplifier Error Voltage VE Reference Voltage Vref Figure 7. Power Supply Control Loop Components 图7.功率源控制环路部件图 Modeling the power stage presents one of the main challenges to the power supply designer. ,在模型设计中常用的技术只有 A对功率源进行建模模型分析是那些功率源设计者面临的最大的挑战 popular technique involves modeling only the switching elements of the power stage. An 功率级的开关部分 ,称为脉冲宽度调制 (PWM) ,其中 equivalent circuit 。 for这部分相同的电路可以推导出来 these elements is derived and is called the PWM Switch开关模型 Model where PWM is the abbreviation for the pulse width modulated. This approach is presented here. 是脉冲宽度调制的缩写 现在介绍这种方法 , 。 PWM As shown in Figure 7, the power stage has two inputs: the input voltage and the duty cycle. 如图7所示,功率级有两个输入量:输入电压和占空比。占空比是控制输入,也就是说这个输入是用 The duty cycle is the control input, i.e., this input is a logic signal which controls the switching 来控制功率级的开关动作和输出电压的逻辑信号。大多数的功率级具有非线性的电压转换比和占空 action of the power stage and hence the output voltage. Most power stages have a nonlinear 比的关系conversion 功率级的电压转换比 。为了显示这种非线性 ,图duty 8给出了工作在连续导通模式下 voltage ratio versus cycle. To illustrate this buck-boost nonlinearity, a graph of the 与稳态占空比voltage 和CR1 的开关动作造成的 。非线性特征是由功率级中开关部件 ,可 D的函数关系图 steady-state conversion ratio for a buck-boost power Q1 stage operating in continuous conduction mode as a function of steady-state duty cycle, D, is shown in Figure 8. 。同样参 以参考文献【5】, 只有功率级中的非线性部分是开关部件 ,电路其它部分由线性元件组成 考文献【5】可以发现,对于只有非线性部分的线性模型可以在整个开关周期内通过平均跟非线性部 The nonlinear characteristics are a result of the switching action of the power stage switching 件相关的电压和电流来得到。在分析完整的功率级的时候,就可以用这个模型来代替原始的电路, components, Q1 and CR1. It was observed in reference [5] that the only nonlinear 这样就得到了开关器件的模型,称为脉冲宽度调制(PWM)开关 模型。 components in a power stage are the switching devices; the remainder of the circuit consists of linear elements. It was also shown in reference [5] that a linear model of only the nonlinear components could be derived by averaging the voltages and currents associated with these nonlinear components over one switching cycle. The model is then substituted into the original circuit for analysis of the complete power stage. Thus, a model of the switching devices is given and is called the PWM switch model. 12 12 全面认识开关型电源中的BUCK-BOOST功率级 Understanding Buck-Boost Power Stages in Switch Mode Power Supplies ZHCA041–1999年3月–2002年11月修订 www.BDTIC.com/TI www.ti.com.cn SLVA059A Buck-Boost功率级小信号模型 10 Buck-Boost Power Stage Gain 9 8 7 6 5 4 3 2 1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Duty Cycle 图8.功率级增益 -占空比图 Figure 8. Buck-Boost Power Stage Gain vs Duty Cycle The basic objective behind modeling power stages is to represent the non-linear behavior of 对功率级进行模型设计的基本目标就是像工作点的线性一样,来表征功率级的非线性行为。我们希 power stages as linear about an operating point. We want linearity so that we can apply the 望是线性的,这样就可以应用很多已经有的用在线性系统的分析工具。再次参考图8,如果我们选 many analysis tools available for linear systems. Referring again to Figure 8, if we choose 择工作点在 的地方画出一条原始曲线的切线 ,这就是工作点的线性性的描 D为 0.7 ,of就可以在 the operating point D = 0.7,D=0.7 a straight line can be constructed that is tangent to the original 述,这种技术可以用推导脉冲宽度调制开关模型 定性的,可以看到 ,如果占空比的变化量保持很 curve at the point where D = 0.7. This is an 。 illustration of linearization about an operating point, a technique used to derive the PWM switch model. Qualitatively, one can see that if 小,现在分析的功率级的非线性行为就可以用线性模型来精确表征。 the variations in duty cycle are kept small, a linear model accurately represents the nonlinear behavior of the power stage being analyzed. 即连续导通模式 由于功率级可以工作在两种不同的导通模式下 和非连续导通模式 , (CCM) (DCM),这样脉冲宽度调制开关模型就也有两种导通模型。非连续导通模式脉冲宽度调制开关模 Since a power stage can operate in one of two conduction modes, i.e., continuous conduction 型(DCM PWM)在这里推导。连续导通模式脉冲宽度调制(CCM PWM)开关模式的推导请参考 mode (CCM) or discontinuous conduction mode (DCM), there is a PWM switch model for the 应用报告 《buck功率级开关模式功率源的综合分析 》 ,TI文献号为 SLVA057。 two conduction modes. The DCM PWM switch model is derived here. The CCM PWM switch model is derived in the Application Report Understanding Buck Power Stages in Switchmode Power Supplies, TI Literature Number SLVA057. 连续导通模式小信号分析 3.1 Buck-Boost 为工作在连续导通模式下的 buck-boost 功率级建立模型 , 我们采用了应用报告《buck 功率级开关 3.1 SLVA057。) Buck-Boost Continuous Conduction Mode Small-Signal Analysis 模式功率源的综合分析》 (TI 文献号为 中推导的连续导通模式脉冲宽度调制 (CCM 开关模型 通过替换开关元件 把脉冲宽度调制开关模型加入到功率级电路中 。 , 。CCM PWM) To model the buck-boost power stage operation in CCM, we use the CCM PWM switch model PWM 开关模型见图9,这个模型在确定功率级的直流工作点和交流传输函数上很有用。 derived in the Application Report Understanding Buck Power Stages in Switchmode Power Supplies, TI Literature Number SLVA057. The PWM switch model is inserted into the power 功率晶体管 和二极管 都画在点画线盒子里。这些部件将要由脉冲宽度调 再次参考图 stage circuit1, by replacing Q1, the switching CR1, elements. The CCM PWM Switch model is shown in 制开关等效电路来代替 脉冲宽度调制开关模型中用到的终端编号分别为 。 a(a有源极 Figure 9. This model is useful for determining the dc operating point of power),p( stage 无源 and 极 和 公共极 ) )。 c( for finding ac transfer functions of a power stage. Referring again to Figure 1, the power transistor, Q1, and the catch diode, CR1, are drawn inside a dashed-line box. These are the components that will be replaced by the PWM switch equivalent circuit. Terminal labels a (active), p (passive), and c (common) are used for the PWM switch model. ZHCA041–1999年3月–2002年11月修订 Understanding Buck-Boost 全面认识开关型电源中的BUCK-BOOST功率级 Power Stages in Switch Mode Power Supplies www.BDTIC.com/TI 13 13 SLVA059A SLVA059A 功率级小信号模型 Buck-Boost Vap D a ia ∧ d www.ti.com.cn c − + Vap ∧ d D − ∧+ Ic d a ia D 1 D 1 ∧ Ic d c ic ic p Figure 9. DC and Small Signalp CCM PWM Switch Model The a terminal is the terminal connected to the active switch. The p terminal is the terminal of the passive switch. terminal is the terminal is common to both the active and 9.The DCc and Small Signal CCMthat PWM Switch Model 图Figure 直流和小信号的连续导通模式脉冲宽度调制开关模型 9. passive switches. The three commonly used power stage topologies all contain active and The a terminal is the terminal connected the activecan switch. The p the terminal passive switches, and the above terminaltodefinitions be used. Interminal addition,issubstituting the 终端 是有源开关和无源开关共有的端 ,pc是无源开关的端 ,c 。三种通常使用的 a是连接有源开关的端 of the passive switch. The terminal is the terminal that is common to both the anda PWM switch model (that we will derive) into other power stage topologies also active produces passive switches. Theparticular three commonly used power topologies contain activepower and 功率级拓扑布局都包含了有源开关和无源开关 此外 ,使用了上面相同的终端定义 。 ,in把脉冲宽度调 valid model for that power stage. To usestage the PWM switchall model other passive and the above terminal used. In addition, the 制开关模型 替代进其它的功率级拓扑也可以得到其它特殊功率级的正确模型 为 (我们将要推导 ) 。 stages,switches, just substitute the model showndefinitions in Figure 9can intobethe power stage insubstituting the appropriate PWM switch model (that we will derive) into other power stage topologies also produces a 了在其它的功率级中使用脉冲宽度调制开关模型 orientation. ,只需要把图9中显示的模型替换为特定应用的功率 valid model for that particular power stage. To use the PWM switch model in other power 级。 stages, just substitute the model shown in Figure 9 intooccurrences the power stage the appropriate In the PWM switch model of Figure 9 and subsequent of theinmodel, the capital orientation. letters indicate steady-state (or dc) quantities dependent on the operating point of the circuit 在图9中的PWM开关模型和替代模型中,大写字母显示的稳态(或直流)参量取决于需要研究的电 under study. The lowercase letters indicate time varying quantities and can indicate a quantity In the aPWM model 9,and subsequent occurrences theamodel, the capital 路的工作点 小写字母显示了时间变量 也显示了跟直流部分和交流部分有关的参量 头上有线的 ;switch with dc component andofanFigure ac component. The lowercase letters of with caret; (hat) indicate letters indicate steady-state (orparticular dc) quantities on the D operating point the circuit 小写字母显示了特定可变的小的交流变量 ;例如 ,dependent , 代表了占空比的小的交 D 代表了稳态的占空比 the small ac variations of that variable. For example, represents theofsteady-state under study. The lowercase letters indicate time varying quantities and can indicate a quantity 流变量,d 或者^d(t) 就代表了包括任何直流部分和交流部分的全部的占空比。 dutya cycle, d represents small ac variations of lowercase the duty cycle, and da orcaret d(t) represents the with dc component and an ac component. The letters with (hat) indicate complete duty cycle including any dc component and ac variations. the small ac variations of that particular variable. For example, D represents the steady-state ^ duty cycle, d represents small ac avariations of the duty cycle, and d or d(t) represents the complete duty cycle including any dc component and ac variations. ia ia + VI VI a Vap ∧ d D Vap ∧ d D ∧ Ic d − + 1 ∧ Ic d − + c 1 + c RL L VO D DIL = ic L p IL = ic p C RC C R VO R RC RL Small Signal AC Power Stage Model Figure 10. CCM Buck-Boost 图10.连续导通模式下buck-boost小信号交流功率级的模型 Figure 10. CCM Buck-Boost Small Signal AC Power Stage Model 14 14 14 Understanding Buck-Boost Power Stages in Switch Mode Power Supplies Understanding Buck-Boost Power Stages in Switch Mode Power Supplies 全面认识开关型电源中的BUCK-BOOST功率级 ZHCA041–1999年3月–2002年11月修订 www.BDTIC.com/TI SLVA059A SLVA059A An example dc analysis is given to illustrate how simple power stage analysis becomes with www.ti.com.cn ^ is an open.功率级小信号模型 Then by the PWM switch model. For dc analysis, d is zero, L is a short and C Buck-Boost An example dc analysis is given to illustrate how simple power stage analysis becomes with a simple loop equation we get: ^ 下面给出一个直流分析的例子来说明运用 开关模型以后分析功率级变得多么简单 。对于直流 PWM zero, L is a short and C is an open. Then by the PWM switch model. For dc analysis, d is a分析 simple loop we get: V 是断路的 是短路的,C , 为 。这时我们就可以得到一个简单的回路方程: 0,Lequation � V I � ac � V O � 0 D V ac � V I �relationships � VO � 0 By using the following D 利用下面的关系式 IO By using the following� relationships IL � 1�D � IO IL � 1V� D IO � O R VO I O �loop to solve for V , we get: and writing another CP R and another loop to solve for VCP, we R L get: 写出writing VCP的另一个回路,我们得到: V cp � � V O � 1 � R � (1 � D) RL V cp � � V O � 1 � ( R �them 1 � to D)get the steady-state voltage conversion Using the two loop equations, we solve relationship for the buck-boost power stage operating in CCM and taking the inductor dc 利用这两个回路方程 我们解得了工作在连续导通模式下 功率级的稳态电压转换关系 , Using the two equations, we solve them to getbuck-boost the steady-state voltage conversion resistance, RL,loop into , account: relationship for the buck-boost power stage operating in CCM and taking the inductor dc 这个过程中我们考虑了电感的直流电阻和负载电阻 RL: resistance, RL, into account: D 1 � VO � � VI � 1�D RL 1� D 1 2 � VO � � VI � R�(R 1�D) 1�D L 1� The above equation is usually expressed asR� a ratio of) 2the output voltage, VO , to the input (1�D voltage, VI , and is usually called M as shown below: The above equation is usually expressed as a ratio of the output voltage, V , to the input 上面的方程通常用来描述输出电压VO 对输入电压VI 的比值,就像下面说的通常称为MO: V voltage, VI , and is usually called M as shown below: 1 M� O�� D � 1�D VI R VO 1� 1 L D 2 M� �� � R��R 1�D� 1�D VI L 1� 2 �1�D � steady-state I/O transfer function Which, when RL = 0, as assumed earlier, is R� equal to the previously calculated. With the PWM switch parameters Vap and Ic determined from the dc Which, RLanalysis = 0, as can assumed earlier, isFor equal to the steady-state I/Otransfer transfer function 当RL为0when 时an 得到的 传递函数 有了由直流分析 analysis, ac performed. ac analysis, theI/O following functions (就像前面假定的 )be ,就等于之前计算的稳态下的 。 previously calculated. PWM switch parameters Vap and Ic determined from output the dc can bePWM calculated: open-loop line-to-output, open-loop input impedance, open-loop 决定的 开关参数 和I c ,the 就可以进行交流分析 。对于交流分析 ,可以计算得到下面几个传递函 VapWith analysis, an ac analysis can be performed. For ac analysis, the following transfer functions impedance, and open-loop control-to-output. The control-to-output, or duty-cycle-to-output, 数:开环的线-输出、开环的输入阻抗、开环的输出阻抗和开环的控制-输出。控制-输出,或者占空 can betransfer calculated: open-loop line-to-output, open-loop impedance, output is比the function most used for control loop analysis.input To determine thisopen-loop transfer function, 为了确定这个传递函数,首先利用直流分析得到 。 -输出是在控制环路分析中用到最多的传递函数 impedance, and open-loop control-to-output. The control-to-output, or duty-cycle-to-output, first use the results from the dc analysis for operating point information. This information 这些信息决定了相关源的参数值 , ;例如 ,sources; is工作点的信息 the transfer function mostvalues used for loop analysis. To determine this transfer function, determines the parameter of control the dependent for example, first use the results from the dc analysis for operating point information. This information determines the V parameter values sources; for example, (1–M) V �ofVthe �dependent ap � V � � � I and 和 and O � � I ( –V ) V ap � V I � V–I –M � V I OO� V I � 1–M O � � Ic � IL � 1�D R � (1 � D) R � (1 � D) –I O –V O –M � V I � � Ic � IL � 1�D R � (1 � D) R � (1 � D) ZHCA041–1999年3月–2002年11月修订 Understanding Buck-Boost Power Stages in Switch Mode Power Supplies 15 Understanding Buck-Boost Power Stages in Switch Mode Power Supplies 15 全面认识开关型电源中的BUCK-BOOST功率级 15 www.BDTIC.com/TI SLVA059A The above two equations are then used with loop equations to derive the duty-cycle-to-output voltage transfer function. Then set the input voltage equal to zero because we only want the ac component of the transfer function. Without going through all the details, it can bewww.ti.com.cn shown SLVA059A 功率级小信号模型 Buck-Boost that the transfer function can be put in the following form: The above two equations are then used with loop equations to derive the duty-cycle-to-output 利用上面的两个方程和环路方程 可以导出占空比-输出电压的传递函数,然后设定输入电压为0, voltage transfer function. Then, set the input voltage equal to zero because we only want the 因为我们只希望得到传递函数的交流部分 。在不需要细节的情况下 ,传递函数可以表示为下面的形 ac component of the transfer function.sWithout goingsthrough all the details, it can be shown 1 � � 1 � ^ � z2 式:the transfer v O function can be put�inz1the following that form: (s) � G do � ^ 2 d 1� s � s � o�Q � 2 o Where: 1 � �s � 1 � �s ^ V vO z1 z2 G do(s)�� G I � 2 ^ do 2 (1 � D ) d 1� s � s � o�Q � 2 o 1 这里Where: : s z1 � V R �C G do � C I 22 ((11 � �D D)) � R s z2 � 1D � L s z1 � R �C � o � 1C� D �L � C 2 (1 � D ) � R s z2 � D� (1 � D) �LR Q� L �o � 1 � D �L �C C � � � � � � � � � Q� 3.2 (1 � D) � R �L Buck-Boost Discontinuous Conduction Mode Small-Signal Analysis C We now continue our discussion of modeling the power stage when it is operating in discontinuous conduction mode (DCM). This mode is quite different from continuous conduction mode just covered. We begin with the derivation of the PWM switch model for 非连续导通模式小信号分析 3.2 3.2 Buck-Boost Buck-Boost Discontinuous Conduction Mode Small-Signal Analysis DCM for the buck-boost power stage. This derivation can also be found in [4]. The waveforms 现在我们继续讨论工作在非连续导通模式下(DCM)功率级的模型,这个模型非常不同于刚才讲到 that voltage across Q1, vacthe , thepower voltage across CR1,it vis , the current We are nowaveraged continue are ourthe discussion of modeling stage when in cp operating 的连续导通模式下的模型 从 功率级的 下的脉冲宽度调制开关模型的推导开始 。 ,这 buck-boost DCM in Q1, ia and the current in CR1, . The waveforms areisshown Figure 6.from continuous discontinuous conduction modeip(DCM). This mode quite indifferent 个也可以在【4】 两端的电压 两端的电压 。平均后的波形是 Q1with CR1上的电流 vac ,CR1of i a 和switch p。 conduction mode中找到 just covered. We begin the derivation the PWM model i for 波形如图 所示 。 DCM for 6the buck-boost power stage. This that derivation can also be foundThe in [4]. The waveforms We first state some basic relationships are used repeatedly. terminal currents that are averaged the voltage Q1, by: vac , the voltage across CR1, vcp , the current averaged over oneare switching cycleacross are given in Q1, ia and the current in CR1, ip . , The waveforms are shown in Figure 6. : 我们首先给出了这个重复用到的关系式 整个开关周期内的终端平均电流由下式给出 i pk We first state some that are used repeatedly. The terminal currents �i a� �basic �relationships d 2 averaged over one switching cycle are given by: i �ip� � i pk � d2 2 �i a� � pk � d 2 括号里的变量 代表了在整个开关周期内取均值的量 (像<i 。 where variables ina>) brackets (e.g., 〈ia〉) represent quantities that are averaged over one i pk switching cycle. �ip� � � d2 2 16 Understanding Buck-Boost Power Stages Mode Power Supplies where variables in brackets (e.g.,in〈iSwitch 〉) represent quantities switching cycle. 16 16 a Understanding Buck-Boost Power Stages in Switch Mode Power Supplies 全面认识开关型电源中的BUCK-BOOST功率级 that are averaged over one ZHCA041–1999年3月–2002年11月修订 www.BDTIC.com/TI SLVA059A SLVA059A www.ti.com.cn Buck-Boost功率级小信号模型 SLVA059A Since the average over one switching cycle of the voltage across the inductor is zero, the following relationships hold: Since theaverage averagevoltage over one switching cycle the voltage across the 因为在整个开关周期内 下面的电压均值关系成立 ,电感上的电压均值为 : inductor is zero, the 0,of following average voltage relationships hold: �v ac ac� � V II � �i cc � R LL� �v ac� � V I � �i c � R L� �v cp� � � V O � �i c � R L� L O �v cp� � � V O � �i c � R L� Since the value of icc RL L is small compared to VII and VO O , ignore these values for modeling the 由于 的值相比于 和 很小 所以在做模型时就忽略了这些值以便方程更容易处理 , 。在时d ×the i R V V power stage to make the formulae much easier to manipulate. Duringvalues the time period Tss L I O small compared to V and V , ignore these Sincec the value of ic R for modeling L is I O the current i starts at a value of zero and ends at the value of i . And since the voltage across 间d × stage 电流 ,停止于 ,且有 Ts 内, ia 从0值开始 ipk ,因为在这段时间内电感上的电压是常数 VI =d × Ts power make the formulae much easier to manipulate. period a to pk During the time the inductor during this time is constant and equal to V = 〈v 〉, the following holds: current i starts at a value of zero and ends at the value of i . And since the voltage across I ac 〈vac〉,所以有下式成立 : I ac a pk the inductor during this time is constant and equal to VI = 〈vac〉, the following holds: i pk i pk �i a pk pk � VI � L a � L � i � �v ac � L � ac i pk I �i pkT ss �ta d � d � T ss VI � L �L� � �v ac� � L � �t d � Ts d � Ts Similarly, during the time period d2 Tss , the current ip p starts at a value of ipk pk and ends at zero. Also since the voltage across the inductor is equal to −V = 〈v 〉, the following holds: 类似的,在时间 电流iad2 从ipk 同样因为在这段时间内电感上的电压是 ×time Similarly, duringd2the period Ts值开始 , the current ip0, starts of ipk and ends at zero.– ,停止于 Ts 内, Oat a value cp O cp Also since the voltage across the inductor is equal to −V = 〈v 〉, the following holds: 所以有下式成立 : VO = 〈vcp〉, O cp � i pk i pk �i pp pk pk �L� �i � �v cp VO � L cp� � L � i pk T s �i �tp d2 �pkT ss d2 � s �L� � �v cp� � L � VO � L �t d2 � T s d2 � T s With the above four equations, we begin with the derivation of the input side (vac ac side) of the PWM switch model. With the above four equations, we begin with the derivation of the input side (vac side) of the 有了上面的四个方程 PWM switch model.,我们从脉冲宽度调制开关模型的输入边(vac 边)开始推导。解方程(3)得 VI =就可以得到 〈vac〉, then We solve ipk and use 到ipk ,利用equation 然后代入方程 〉,for (1) : substitute into equation (1) to get: VI = 〈vac(3) We solve equation (3) for ipk and use VI = 〈vac〉, then substitute into equation (1) to get: d 2 � T SS �i aa� � V I � 2 d �T �i a� � V I � 2 � LS 2�L ZHCA041–1999年3月–2002年11月修订 Understanding Understanding Buck-Boost Buck-Boost Power Power Stages Stages in in Switch Switch Mode Mode Power Power Supplies Supplies 全面认识开关型电源中的BUCK-BOOST功率级 Understanding Buck-Boost Power Stages in Switch Mode Power Supplies www.BDTIC.com/TI 17 17 17 17 SLVA059A SLVA059A SLVA059A SLVA059A www.ti.com.cn We note We功率级小信号模型 note that that the the average average current current flowing flowing into into terminal terminal a a is is proportional proportional to to the the input input voltage, voltage, Buck-Boost V . We define an effective resistance as follows: We note that the average current flowing into terminal a is proportional to the input voltage, I VII . We define an effective resistance as follows: VI . We define an effective resistance as follows: 我们注意到流进终端a的电流均值与输入电压VI 成正比,有效阻抗定义如下: V 2� V II �L L R R eee � � �V I� � � d222 � i 2�T I� 2 LSS T d � a i Re � a � �i aa� d 2 � T SS Once Once the the input input looks looks like like an an equivalent equivalent resistance, resistance, we we can can also also talk talk about about an an apparent apparent input input 2 2 power of V /R which will be used next. Once the input likewill anbe equivalent resistance, we can also talk about an apparent input III2 /Rlooks e power of V which used next. 2 e e ,我们就可以得到将要在下一步用到的表征输入功率VI /Re。 当输入像等效阻抗时 power of VI2 /Re which will be used next. side), we start with equation (4), solve equation To begin the derivation of To begin the derivation of the the output output side side (v (vcp cp cp side), we start with equation (4), solve equation 边 的推导 我们从方程 开始 解得i pk ,(4), 为了开始输出边 再代回方程 (3) for i and substitute back into equation (4), we get: ) , (4) ,从方程 (3) ( (4), v side), start with equation solve equation To begin the derivation of the output side (v cp cp (4), (3) for ipk back into equation wewe get: pk pk and substitute (3) for ipk and 就可以得到 : substitute back into equation (4), we get: ��v ac�� � d v ac � d . � �vvcp � �v ac � � . cp cp �vcp� � acdd222� d . d2 and substitute into equation (2) and also iipk [from We next solve the above equation for d substitute into (3) equation and also use use(2), We next solve the above equation d2 2 pk 再解上面的方程得到d 2 ,代入到方程for 再利用 得到(2) 代回到方程 经 (2), ), i pk (由方程 2 and pk [from equation (3)] and substitute into equation we get after rearranging: substitute into equation (2) and also use ipk [from We next solve the above equation for d2 and(2), equation (3)] and substitute into equation (2), we get after rearranging: 过整理我们得到: equation (3)] and substitute into equation (2), we get after rearranging: 2 ��v ac�� 22 � d 222 � T s v ac ��iipp�� � ac 2 � d � T ss p � �v�ac� �� d 2 � T s ��2�L �ip� � �vvcp cp � 2 � L �vcp cp� � 2 � L Finally, 〉 = V Finally, we we use use 〈v 〈vac VIII and and substitute substitute in in the the above above equation equation to to get get the the output output side side ac ac〉 =代入上面的方程 得到输出边的关系 最后 我们用 , : , 〈v 〉 V = relationship: Finally, we use ac〈vac〉 =I VI and substitute in the above equation to get the output side relationship: relationship: 2 2 V 2 2 d T V II2 2� s 2 d � T s 2 ��iipp�� � ��vcp�� � s � V I2 . V2 � 2 � . � T p � v cp cp � V III2 � d 2 � L �ip� � �vcp� � V � 2 � L s � RRIeee . 2�L Re I This equation shows that the average output current the average output voltage is This equation shows that the average output current times times 这个方程显示输出电流均值乘以输出电压均值等于表征输入功率 。 the average output voltage is equal to the apparent input power. This equation shows that average output current times the average output voltage is equal to the apparent inputthe power. equal to the apparent input power. 现在我们可以把上面的输入和输出关系应用到等效的电路模型 Now we into 。这个模型在确定功率源的直流工作 Now we can can implement implement the the above above input input and and output output relationships relationships into an an equivalent equivalent circuit circuit model. This model is useful for determining the dc operating point of a power supply. The input Now we can implement the above input and output relationships into an 点很有用 输入端口可以简化模型为电阻 输出端口简化为一个从属的功率源 这个功率源输送 。 model is useful for determining , Re ,the dc operating point of a powerequivalent model. This supply. Thecircuit input port is simply modeled with a resistor, R . The output port is modeled as a dependent power model. This model is determining the dc operating point of a power supply. Thepower input 消耗的功率 所示 的功率等于输入电阻 。这个等效电路的构成见图 。 port is simply modeled with for a resistor, Re . The output port is modeled as a dependent 11 Reuseful e e source. This source power equal to dissipated by the resistor, R . port is simply modeled with delivers a resistor, Re. The output port is modeled dependent power source. This power power source delivers power equal to that that dissipated byas thea input input resistor, Re e e. The equivalent circuit can be constructed as shown in Figure 11. source. This power source delivers power equal to that dissipated by the input resistor, R e. The equivalent circuit can be constructed as shown in Figure 11. The equivalent circuit can be constructed as shown in Figure 11. a a a a p p p p p(t) p(t) p(t) p(t) R R e Re e Re c c c c 图11.非连续导通模式脉冲宽度调制开关模型 Figure Figure 11. 11. DCM DCM PWM PWM Switch Switch Model Model Figure 11. DCM PWM Switch Model 18 18 18 18 18 Understanding Understanding Buck-Boost Power Stages in Switch Mode Power Supplies Understanding Buck-Boost Buck-Boost Power Power Stages Stages in in Switch Switch Mode Mode Power Power Supplies Supplies Understanding Buck-Boost Power Stages in Switch Mode Power Supplies 全面认识开关型电源中的BUCK-BOOST功率级 ZHCA041–1999年3月–2002年11月修订 www.BDTIC.com/TI SLVA059A www.ti.com.cn SLVA059A Buck-Boost功率级小信号模型 To illustrate discontinuous conduction mode power supply steady-state analysis using this To illustrate discontinuous conduction mode power supply steady-state analysis using this 为了用这个模型来描述非连续导通模式下功率级的稳态分析 这 model, we examine the buck-boost converter. The analysis proceeds likebuck-boost the CCM转换器 case. The ,我们研究这种 model, we examine the buck-boost converter. The analysis proceeds like the CCM case. 。 The equivalent circuit is substituted into the original circuit. The inductor is treated as a short 个分析过程跟之前的连续导通模式 是一样的circuit. 电感看作是短路 ,等效电路带进原始电路 , equivalent circuit is substituted (CCM) into the original The inductor is , treated as a short circuit and the capacitor is treated as an open circuit. The DCM buck-boost converter model 电容看作是断路 非连续导通模式下的 转换器的原理图如图 所示 。 。 converter model 12 circuit and the capacitor is treated asbuck-boost an open circuit. The DCM buck-boost schematic is shown in the Figure 12. schematic is shown in the Figure 12. p p a a p(t) p(t) Re Re + + VI VI VO VO C C R R c c L L 图12.Figure 非连续导通模式下的 转换器原理图 12. DCM Buck-Boost Converter Model buck-boost Figure 12. DCM Buck-Boost Converter Model The apparent power dissipated in Re is determined as: The apparent power dissipated in Re is determined as: R 上消耗的表征功率由下式决定: e V2 V2 P Re � II . P Re � R e . Re The dependent power source delivers the above amount of power to the output load resistor, 这个从属功率源传送上面数量的功率到输出负载电阻 R,我们可以通过令下面两个功率相等来计算 The dependent power source delivers the above amount of power to the output load resistor, R. We can calculate gain as a function of D by equating the two powers as shown: 电压增益关于 : voltage D的函数the R. We can calculate the voltage gain as a function of D by equating the two powers as shown: V2 V2 V2 O I � V2 O I Re � R Re R VO V O �� V I �� VI � �RRRR (choose the negative root) e (choose the negative root) e R�T R � D R � T ss R � �RRRR �� �D2�L 2�L �T e e �D D2 �T D 2�T ss � � 22 �� LL 转换器的电压转换关系由下式给出 : buck-boost is given by: DCMvoltage buck-boost The conversion relationship for the DCM The voltage conversion relationship for the DCM buck-boost is given by: VO VO � � D VI � � D VI � �RR22����TTLL s s 回想前面的: Recall from earlier that: Recall from earlier that: �L K� 2 �L K � R2� T R � T ss and making the substitution in the above equation, the稳态非连续导通模式分析部分中利用平衡 result is identical to that obtained by 将这个式子代入上面的方程 ,得到的结果跟在 and making the substitution in the above equation, the result is identical to that obtained by buck-boost balancing the inductor volt-seconds in the buck-boost steady-state discontinuous conduction balancing inductor volt-seconds 电感电压 秒关系得到的结果一样 。 in the buck-boost steady-state discontinuous conduction –the mode analysis section. mode analysis section. ZHCA041–1999年3月–2002年11月修订 Understanding Buck-Boost 全面认识开关型电源中的BUCK-BOOST功率级 Power Stages in Switch Mode Power Supplies Understanding Buck-Boost Power Stages in Switch Mode Power Supplies www.BDTIC.com/TI 19 19 19 www.ti.com.cn SLVA059A SLVA059A 功率级小信号模型 Buck-Boost SLVA059A The The steady steady state state voltage voltage conversion conversion relationship relationship for for the the DCM DCM buck-boost buck-boost becomes: becomes: The steady state voltage conversion relationship for the DCM buck-boost becomes: 非连续导通模式下 buck-boost的稳态电压转换关系变为: V VO O�� D � � �D VV �K K VOII �� D � VI K Now, Now, to to derive derive the the small small signal signal model, model, the the circuit circuit of of Figure Figure 12 12 is is perturbed perturbed and and linearized linearized following the procedure similar to the one in the CCM derivation. To see the detail of following the procedure similar to the one in the CCM derivation. To see the detail of the the Now, to derive the small,signal model, the (CCM) circuit of 中的推导过程一样 Figure 12 is perturbed and linearized 现在为了推导小信号模型 跟在连续导通模式 中的电路 , 扰动图 , 12 derivation, the reader is directed to reference [4] for details. The resulting small signal model derivation, the reader is directed to reference [4] for details. The resulting small signal model following the procedure similar to the one in the CCM derivation. To see the detail of the 并线性化 中的细节 ,想了解推导的详细过程 ,读者可以参考 【4】 。这个工作在非连续导通模式下 for the power stage in is shown in Figure 13. for the buck-boost buck-boost power stage operating operating in DCM DCM isdetails. shownThe in the the Figuresmall 13. signal model derivation, the reader is directed to reference [4] for resulting buck-boost功率级的小信号模型如图13所示。 for the buck-boost power stage operating in DCM is shown in the Figure 13. ∧ ∧ v vII ∧ vI + + + R Re e 2 2 ⋅⋅ V VII Re D ⋅⋅ R D 2 ⋅ Ve I D ⋅ Re ∧ ∧ ∧ 0 vO 0 ⋅⋅ v O ∧ 0 ⋅ vO ⋅⋅ ∧dd ∧ ⋅d 2 2 ⋅⋅ ∧∧vvII M Re M ⋅⋅2 R e ∧ ⋅ vI M⋅R e 2 2 ⋅⋅ V VII ⋅⋅ M M ⋅⋅R R D D2 ⋅ VI ee D ⋅ M ⋅R e ∧ ⋅⋅ ∧dd ∧ ⋅d 2 M M2 ⋅⋅ R Re e M2 ⋅ Re Re ∧ ∧ v vO O ∧ vO C C R R C R Figure 13. DCM Power Figure 13. Small Small Signal Signal buck-boost DCM Buck-Boost Buck-Boost Power Stage Stage Model Model 图13. 非连续导通模式下 功率级的小信号模型 Figure 13. Small Signal DCM Buck-Boost Power Stage power Model The The duty-cycle-to-output duty-cycle-to-output transfer transfer function function for for the the buck-boost buck-boost power stage stage 工作在非连续导通模式下 功率级的占空比-输出传递函数由下式给出: buck-boost operating in DCM is given by operating in DCM is given by The duty-cycle-to-output transfer function for the buck-boost power stage operating in DCM is given by vv^^ O 1 O�G � 1 ^^ � G do � ss do v^d 1 � 1 � 1� dO � G � �p p ^ do 1 � �s 其中 Where d p Where V V Where G O � O G do do � VD DO G do � D � D D� �� �M M� � �K K � D��M� K V VO M M� � VO VV I M � OI VI 2� �L L K K� � R2� T ss R2� T 还有:and K� �L and R � Ts 2 and � � 2 �p p�R C R� � C �p � 2 R�C : Gdo 的表达式可以简化为下面形式 The can be simplified to the following: The expression expression for for G Gdo do can be simplified to the following: The expression for Gdo can be simplified to the following: R�T �� �V VI � � R � T ss G do � G I � do 2� � TL Ls R2 G do � � V I � 2�L � � 20 20 20 Understanding 全面认识开关型电源中的BUCK-BOOST功率级 Understanding Buck-Boost Buck-Boost Power Power Stages Stages in in Switch Switch Mode Mode Power Power Supplies Supplies 20 Understanding Buck-Boost Power Stages in Switch Mode Power Supplies ZHCA041–1999年3月–2002年11月修订 www.BDTIC.com/TI www.ti.com.cn Buck-Boost功率级的变型 4 Buck-Boost功率级的变型 4.1 反驰式(Flyback)功率级 传统buck-boost功率级的变压器耦合的变型是反驰式功率级。这种功率级像传统的buck-boost功率 级一样的工作,除了把单一的线圈电感替换为两个(或者更多)的线圈耦合电感。功率开关Q1,见 图14,把输入电压加载到耦合电感的主线圈上(LPRI),能量储存直到Q1关上。接着从耦合电感的 副线圈(LSEC)通过输出二极管将能量传送到输出电容和负载电阻的组合上。这种功率级提供了输 入电压和输出电压间的电隔离,除了之外,隔离变压器还可以对输入电压进行降压(或升压)。通 过设计变压器的变换比得到合适的占空比,从而得到几乎任何的输入电压/输出电压的组合,以避免 出现极大或极小的占空比值。 这种反向功率级还可以消除两种有时会让标准buck-boost功率级变得不理想的缺点,即输出电压与 输入电压的极性相反和功率开关需要浮动驱动。除了提供隔离,耦合电感副线圈相连还可以用来产 生正极性的或者负极性的输出电压。此外,功率开关跟耦合电感的主线圈串联,可以连接功率开关 让源极为参考地,而不是像标准的buck-boost功率级一样,把漏极连接到输入电压。 反驰式功率级在48V输入电信应用和输出功率高到大约50瓦的110V交流或220V交流的离线应用上非 常流行。反驰式功率级的精确额定功率是由输入电压/输出电压组合、工作环境和许多其它因素来决 定的。通过在增加输出二极管和输出电容的同时,简单增加耦合电感的另一个线圈就可以很容易地 产生额外的输出电压。用单一的功率级得到多个输出电压是反向功率级的另一个优势。 带有驱动电路模块的反向功率级的简单原理图如图14所示,图中,连接耦合电感的副线圈用来产生 一个正极性的输出电压。功率开关Q1是一个n通道的金属氧化物半导体场效应管(MOSFET)。二 极管 CR1 通常叫做输出二极管 。 副线圈的电感 LSEC和电容 C 组成了滤波器 。 电容 ESR( 等效串联电 阻)RC未包括。电阻R代表了功率源的输出负载。 ZHCA041–1999年3月–2002年11月修订 全面认识开关型电源中的BUCK-BOOST功率级 www.BDTIC.com/TI 21 www.ti.com.cn Buck-Boost功率级的变型 SLVA059A SLVA059A CR1 Vb VI VI + LPRI b LVSEC + LPRI Va LSEC Drive Circuit Drive Circuit VO CR1 VO Va Q1 C R C R Q1 Figure 14.图Flyback Power Stage Schematic 14. 反向功率级的原理图 Figure The important waveforms for14. theFlyback flyback Power power Stage stage Schematic operating in DCM are shown in 工作在非连续导通模式下反向功率级的重要波形图如图 所示。 Figure 15. The important waveforms for the flyback power 15 stage operating in DCM are shown in Figure 15. IQ1 IQ1 ICR1 Solid IO Dashed ICR1 Solid IO Dashed Vb Solid VO Dashed Vb Solid VO Dashed 0 0 Va Va 0 0 D3*TS D*TS D*TS D3*TS D2*TS D2*TS TS TS Figure 15. Discontinuous Mode Flyback Waveforms Figure 15. Discontinuous Mode Flyback Waveforms 图15. 非连续模式下飞驰功率级的波形图 22 22 全面认识开关型电源中的BUCK-BOOST功率级 Understanding Buck-Boost Power Stages in Switch Mode Power Supplies 22 Understanding Buck-Boost Power Stages in Switch Mode Power Supplies ZHCA041–1999年3月–2002年11月修订 www.BDTIC.com/TI www.ti.com.cn Buck-Boost功率级的变型 SLVA059A SLVA059A 工作在连续导通模式下 反向功率级的简化电压转换关系 忽略寄生效应 )由下式给出 :工作在连续 The simplified voltage(CCM) conversion relationship for the flyback( power stage operating in CCM The simplified voltage conversion relationship for the flyback power stage由下式给出 operating in CCM 导通模式下 反向飞驰式功率级的简化电压转换关系 忽略寄生效应 (CCM) is given by: ( ) : (ignoring parasitics) (ignoring parasitics) is given by: N V O � V I � N ss � D D VO � VI � Np � 1 � D Np 1 � D 工作在非连续导通模式下 The simplified voltage conversion relationship for the flyback power stage operating in DCM (DCM)反向功率级的简化电压转换关系 (忽略寄生效应 )由下式给出 : The simplified voltage conversion relationship for the flyback power stage operating in DCM (ignoring parasitics) is given by: (ignoring parasitics) is given by: N V O � V I � N ss � D V O � V I � N p � �DK N p �K Where K is defined as: 其中 K定义为 : Where K is defined as: 2�L K � 2 � L SEC K � R � SEC T R � T ss The simplified duty-cycle-to-output transfer function for the flyback power stage operating in The simplified duty-cycle-to-output transfer function for the flyback power stage operating in 工作在连续导通模式下 (CCM)反向功率级的简化占空比-输出传输函数由下式给出: CCM is given by: CCM is given by: �� 式中 : Where: Where: �� �� �� 1 � �ss � 1 � �ss 1 � � z1 � 1 � � z2 v^^ O NS v O (s) � G � N S � z1 z2 ^ (s) � G do � N � 2 s s do d^ 2 NP 1 � � s�Q � s d P 1 � � o�Q � � 2 2 o �o o VI VI G do � G do � 2 (1 � D ) 2 (1 � D ) 1 � z1 � � z1 � R 1� C RC C � C2 (1 � D ) 2 � R � z2 � (1 � D) � R � z2 � D � L D � L SEC SEC 1�D �o � 1 � D � o � �L �C �LSEC SEC � C (1 � D) � R Q � (1 � D) � R Q� L SEC L SEC C C � � The simplified duty-cycle-to-output transfer function for the flyback power stage operating in The simplified duty-cycle-to-output transfer function for the flyback power stage operating in DCM is given by: DCM is given by: 工作在非连续导通模式下(DCM)反向功率级的简化占空比-输出传输函数由下式给出: ZHCA041–1999年3月–2002年11月修订 全面认识开关型电源中的BUCK-BOOST功率级 Understanding Buck-Boost Power Stages in Switch Mode Power Supplies Understanding Buck-Boost Power Stages in Switch Mode Power Supplies www.BDTIC.com/TI 23 23 23 1�� d Where: 组件选择 and SLVA059A N G do � V I � S � NP p � R � TS 2 � L SEC www.ti.com.cn 2 R � C vO 1 � G � ^ do 1 � �s d �p � ^ 5 55 5.1 5.1 Component 式中: Where: p Selection � NS R�T ThisGsection presents a discussionSof the function of each of the main components of the � V � � do I 2� L SEC requirements and applied stresses are given for each buck-boost powerNstage. The electrical P 和: and power stage component. �p � 2 R �power C The completed supply, made up of a power stage and a control circuit, usually must meet a set of minimum performance requirements. This set of requirements is usually referred to as the power supply specification. Many times, the power supply specification determines individual component requirements. Component Selection 部件选择 This section presents a discussion of the function of each of the main components of the 这部分主要讨论 功率级每个主要组成部件的功能 。给出了功率级中每个部件的电子性能需求和压 buck-boost buck-boost power stage. The electrical requirements and applied stresses are given for each 力。 5.1 Output Capacitance power stage component. 一个完整的功率源 ,由一个功率级和一个控制电路组成,通常满足最小的性能要求。这些要求通常是参考 In switching power supply power stages, the output。capacitance stores energy in the electric 功率源的规格。很多时候 ,功率源的规格决定了每个部件的需求 The completed power supply, made up ofThus, a power stage andthe a control circuit, usually must field due to the voltage applied. qualitatively, function of a capacitor is to attempt meet a set of minimum performance to maintain a constant voltage.requirements. This set of requirements is usually 输出电容 to as the power supply specification. Many times, the power supply specification referred determines requirements. Theindividual value of component output capacitance of a buck-boost power stage is generally selected to limit 在开关功率源的功率级中 ,由于加载电压输出电容在电场储存能量 ,所以定性的说 ,电容的功能就是试图 output voltage 。 ripple to the level required by the specification. The series impedance of the 保持一个固定不变的电压 capacitor and the power stage output current determine the output voltage ripple. The three elements of the capacitor that contribute to its impedance (and output voltage ripple) are Output Capacitance 通常选取Buck-boost功率级的输出电容值使得把输出电压的纹波电压限制在规格要求的水平。电容的串联 equivalent series resistance (ESR), equivalent series inductance (ESL), and capacitance 阻抗和功率级的输出电流决定了输出电压的纹波 和输出电压纹波 。导致电容产生阻抗 ( )的三个元素是等 In switching supply power the for output capacitance energy in the electric (C).power The following gives stages, guidelines output capacitorstores selection. field due to the voltage applied. Thus, qualitatively, the function of a capacitor is to attempt 效串联电阻(ESR)、等效串联电感(ESL)和电容(C)。下面给出了选择输出电容的原则。 to maintain constant voltage. Foracontinuous inductor current mode operation, to determine the amount of capacitance needed as a function of,output load current, IO , switching frequency, fS , and 对于连续电感器电流模式下的工作 为了确定电容值 开关频率output ,需要知道它一个关于输出负载电流 I O 、desired fS、 The value of output capacitance of a buck-boost power stage is generally selected to limit voltage ripple, ∆V , the following equation is used assuming all the output voltage ripple 要求的输出纹波电压ΔVO 的函数 O ,在假定所有的输出电压纹波都是由电容器的电容产生的情况,使用下面 is output voltage ripple to the levelcapacitance. required by This the specification. The series impedance of thethe entire due to the capacitor’s is because the output capacitor supplies 的方程。这是因为在功率级开态(ON),输出电容器提供了所有的输出负载电流 。 capacitor and the power stage output current determine the output voltage ripple. The three output load current during the power stage ON state. elements of the capacitor that contribute to its impedance (and output voltage ripple) are equivalent series resistance (ESR), equivalent series inductance (ESL), and capacitance I O(Max) � D Max (C). The following gives guidelines for output capacitor selection. C� f S � �V O For continuous inductor current mode operation, to determine the amount of capacitance Where IO(Max) is the maximum output current and DMax is the maximum cycle. needed as a function of output load current, IO , switching frequency, fS , and desiredduty output voltage ripple, ∆VO , the following equation is used assuming all the output voltage ripple is due the是最大输出电流 capacitor’s capacitance. This is。 because the output capacitor supplies the entire 式中to ,DMax是最大占空比 IO(Max) 24 load Understanding Buck-Boost Power Stages Switch Mode Power Supplies output current during the power stage in ON state. C� I O(Max) � D Max f S � �V O Where IO(Max) is the maximum output current and DMax is the maximum duty cycle. 24 24 全面认识开关型电源中的BUCK-BOOST功率级 Understanding Buck-Boost Power Stages in Switch Mode Power Supplies ZHCA041–1999年3月–2002年11月修订 www.BDTIC.com/TI www.ti.com.cn SLVA059A 组件选择 SLVA059A SLVA059A For discontinuous inductor current mode operation, to determine the amount of capacitance For discontinuous inductor current , mode operation, to determine the amount of capacitance 对于非连续电感器电流模式下的工作 为了确定需要的电容值 ,在假定所有的输出电压纹波都是由电容器 needed, the following equation is used, assuming all the output voltage ripple due to the For discontinuous inductor current mode operation, to determine the amount of is capacitance needed, the following equation is used, assuming all the output voltage ripple is due to the 的电容产生的情况 ,使用下面的方程 。 capacitor’s capacitance. needed, the following equation is used, assuming all the output voltage ripple is due to the capacitor’s capacitance. capacitor’s capacitance. �� �� �� 2�L I O(Max) � 1 � 2�L I O(Max) � 1 � R�T 2�Ls I O(Max) � 1 � R�T R�T ss C� C� f S � �V O f S � �V O C� f S � �V O However, in many practical designs, to get the required ESR, a capacitor with much more However, in many practical designs, to get the required ESR, a通常都要选择比我们计算出来的电容 capacitor with much more 但是在很多实际的设计中 ,为了得到需要的等效串联电阻 (ESR), capacitance than ispractical needed designs, must be selected. However, in many to get the required ESR, a capacitor with much more capacitance than is needed must be selected. 值大的电容器than 。 is needed must be selected. capacitance For continuous inductor current mode operation and assuming there is enough capacitance For continuous inductor current mode operation and assuming there is enough capacitance such that the ripple due to the,capacitance can beand ignored, the ESR to limit the ripple For continuous inductor current mode operation assuming thereneeded is enough capacitance 对于连续电感器电流模式工作 假定有足够的电容使得电容导致的纹波可以忽略不计 用来把限制纹波在 , such that the ripple due to the capacitance can be ignored, the ESR needed to limit the ripple to ∆V V peak-to-peak is: such that the ripple due to theESR capacitance can be ignored, the ESR needed to limit the ripple Δ∆V 而需要的 为: VO O (V peak-to-peak) to V peak-to-peak is: to ∆VO O V peak-to-peak is: �V O �V O ESR � �V ESR � I ESR � IO(Max) O �I �I L I O(Max) � �I L � 2L 1�D O(Max) 1�D Max � 2 2 1�D Max Max For discontinuous inductor current mode operation and assuming there is enough For discontinuous inductor current mode operation and assuming there is enough capacitance such that the ripple due tomode the capacitance ignored, the ESRisneeded to For discontinuous inductor current operation can andbe there enough 对于非连续电感器电流模式工作 ,假定有足够的电容使得电容导致的纹波可以忽略不计 ,用来把限制纹波 capacitance such that the ripple due to the capacitance can beassuming ignored, the ESR needed to limit the ripple to ∆V V simply: capacitance such that thepeak-to-peak ripple due tois the capacitance can be ignored, the ESR needed to O 而需要的 limit the ripple to ∆V V peak-to-peak is simply: 在ΔV 为 ( V peak-to-peak) ESR : O limit the ripple to ∆VO O V peak-to-peak is simply: �V O ESR � �V O ESR � �V �I O ESR � �I L �I L L Ripple current flowing through a capacitor’s ESR causes power dissipation in the capacitor. Ripple current flowing through a capacitor’s ESR causes power dissipation in the capacitor. This power dissipation causesaacapacitor’s temperature increase the capacitor. Ripple current flowing through ESR causesinternal power to dissipation in theExcessive capacitor. This power dissipation causes a temperature increase internal to the capacitor. Excessive 纹波电流流过电容器的 造成在电容器上的功率损耗 ,这个功率损耗会导致电容器内部的温度升高 , ESR, temperature can seriously shorten the expected life of internal a capacitor. Capacitors have ripple This power dissipation causes a temperature increase to the capacitor. Excessive temperature can seriously shorten the expected life of a capacitor. Capacitors have ripple 过高的温度会严重缩短电容器的预计寿命 。 电容器有取决于周围温度的额定纹波电流 , 而且不能超过 。 current ratings that are dependent on ambient temperature and should not behave exceeded. temperature can seriously shorten the expected life of a capacitor. Capacitors ripple current ratings that are dependent on ambient temperature and should not be exceeded. 参考图 3, 输出电容器纹波电流等于电感器电流 流过输出电容器的纹波电流均方根值 I O。 I L减去输出电流 Referring to Figure thedependent output capacitor ripple current is the inductor current, IL,exceeded. minus the current ratings that 3, are on ambient should not be Referring to Figure 3, the output capacitor ripple temperature current is theand inductor current, IL, minus the 由下式给出 (RMS) (连续电感器电流模式 ): output current, IO. The value of the ripplecurrent current flowing in thecurrent, output capacitance Referring to Figure 3, theRMS output capacitor the inductor L, minus the output current, IO. The RMS value of theripple ripple currentisflowing in the output Icapacitance (continuous inductor current mode operation) is given by: output current, I . The RMS value of the ripple current flowing in the output capacitance O (continuous inductor current mode operation) is given by: (continuous inductor current mode operation) is given by: D I C RMS � I O � D I C RMS � I O � 1 � DD D I C RMS � I O � 1 � 1�D ESL can be a problem by causing ringing in the low megahertz region but can be controlled ESL can be a problem by causing ringing in the low megahertz region but can be controlled 等效串联电感 但是可以通过选择低 (ESL) (兆赫兹 )区产生阻尼振荡的问题 ESL的电容器 by choosing ESL 有在低频 capacitors, limiting lead length (PCB and,capacitor), one 、限 ESL can be alow problem by causing ringing in the low megahertz region butand can replacing be controlled by choosing low ESL capacitors, limiting lead length (PCB and capacitor), and replacing one large device with several smaller ones connected in parallel. by choosing low ESL capacitors, limiting lead length (PCB and capacitor), and replacing one 制引线长度 印刷电路板 和电容器 和并联更大的器件代替几个小器件等方法来控制这个问题 ( ) PCB large device with several smaller ones connected in parallel. large device with several smaller ones connected in parallel. �� �� � � � ZHCA041–1999年3月–2002年11月修订 Understanding Buck-Boost 全面认识开关型电源中的BUCK-BOOST功率级 Power Stages in Switch Mode Power Supplies Understanding Buck-Boost Power Stages in Switch Mode Power Supplies Understanding Buck-Boost Power Stages in Switch Mode Power Supplies www.BDTIC.com/TI 25 25 25 25 www.ti.com.cn 组件选择 制作电容器的三种技术:低阻抗铝、有机半导体和固态钽主要用于廉价的商业应用中。低阻抗铝电解电容 器最便宜,可以在很小的体积提供很高的电容值,但是等效串联电阻(ESR)都比其它两种高。有机半导 体电解电容器,像三洋(Sanyo)OS-CON系列,在最近几年功率源工业中非常流行,他们是世界上最好的 电容器,在整个温度范围稳定的低ESR和小体积提供大电容,大部分OS-CON电容器都是采用引线安装的辐 射形封装,也提供表面贴装器件,但是牺牲了很多体积和性能的优势。固态钽片电容器对于那种只能选用 表面贴装器件的情况是最好的选择。像AVX TPS系列和Sqrague 593D系列的产品就主要开发来用在功率源 上的。这些产品有很多优点:在温度范围内相对稳定的ESR、高的纹波电流容限、低的ESL、浪涌电流测试 和很高的电容体积比。 5.2 输出电感 在开关功率源的功率级中,电感器的功能是储存能量,电流流过时能量会以磁场的方式储存下来,所以定 性的说,电感器的作用就是试图保持固定不变的电流值,或者等效的说是限制流过电感器电流的变化率。 选择Buck-boost功率级的输出电感器电感值主要是限制流过它的纹波电流的峰峰值。选择以后,功率级的 工作模式,连续或非连续,就确定下来了。电感器纹波电流跟加载的电压和加载电压的时间成正比,跟电 感值成反比,这些在前面已经详细解释了。 很多设计者喜欢自己设计电感器,但是这不是我们这篇报告的主题。下面我们讨论在选择合适电感器必须 考虑的事项。 除了电感值,在选择电感器时需要考虑的其它重要因素有最大直流或峰值电流和最大工作频率。让电感器 在它的额定直流电流内工作对确保电感器不出现过热或饱和很重要。电感器工作在低于最大额定频率可以 保证不会超过最大内部损耗,从而避免出现过热或饱和。 磁器件制造商可以提供很多类型适用于直流-直流转换器的直接就可以买来用的电感器,其中有些是表面贴 装器件。电感器有很多种类,最流行的内部材料是铁氧体和铁精粉。筒管状或杆状核心电感器很容易买到 而且也很便宜,但是使用这些电感器的时候要非常小心,因为比起其它形状的电感器,它们更容易产生噪 声问题。考虑到体积空间足够大的话,用户自己设计也是可行的。 26 全面认识开关型电源中的BUCK-BOOST功率级 ZHCA041–1999年3月–2002年11月修订 www.BDTIC.com/TI Current flowing through an inductor causes power dissipation due to the inductor’s dc SLVA059A resistance; this power dissipation is easily calculated. Power is also dissipated in the inductor’s core due to the flux swing caused by the ac voltage applied across it but this www.ti.com.cn Current flowing through angiven inductor causes power dissipation due to the the inductor’s dc information is rarely directly in manufacturer’s data sheets. Occasionally, inductor’s 组件选择 resistance; this power dissipation is easily calculated. Power is also dissipated in the maximum operating frequency and/or applied volt-seconds ratings give the designer some inductor’s regarding core due core to the fluxThe swing caused by the causes ac voltage applied across it but guidance loss. power dissipation a temperature increase in this the 由于电感器直流电阻 电流流过电感器时会有功率损耗 ,这个损耗可以很容易计算得 。功率也会因为加载 information is rarely, directly givencan in manufacturer’s data sheets. Occasionally, inductor’s inductor. Excessive temperature cause degradation in the insulation of thethe winding and maximum operating and/or applied volt-seconds ratings giveinductor’s the designer some 在电感器上的交流电压导致的流量振荡而损耗在电感器的内核上 不过这些信息很少会在制造商的数据说 cause increased corefrequency loss. Care should be exercised to insure all the maximum , guidance regarding core loss. The power dissipation causes a temperature increase in the ratings are not exceeded. 明书中直接给出 。 一般 , 电感器的最大工作频率和 ( 或 ) 加载的额定电压 - 秒曲线给了设计者关于内核损 inductor. Excessive temperature can cause degradation in the insulation of the winding and 耗的指导。 功率的损耗会导致电感器内部温度升高 ,过高的温度会降低线圈的绝缘性,导致更多的内核损 cause increased core loss. Careby: should be exercised to insure all the inductor’s maximum The loss in the inductor is given 耗。必须注意保证电感器所有的最大额定值都没有超过。 ratings are not exceeded. 2 P inductor � �I Lrms� � R Cu � P Core 电感器的损耗由下式给出 : is given by: The loss in the inductor where, RCu is the winding resistance. 2 P inductor � �I Lrms� � R Cu � P Core 5.3 5.3 5.3 where, winding resistance. Power Switch 式中RCuR 为线圈电阻 Cu is the 。 In switching power supply power stages, the function of the power switch is to control the flow of energy from the input power source to the output voltage. In a buck-boost power stage, Power Switch 功率开关 the power switch (Q1 in Figure 1) connects the input to the inductor when the switch is turned In switching power supply power stages, theThe function the power is to on and disconnects when the switch is off. powerofswitch mustswitch conduct thecontrol current inflow the 功率 在开关式功率源的功率级 ,功率开关的功能是控制从输入功率源到输出电压的能量流动 。在the buck-boost of energy from the input power source to the output voltage. In a buck-boost power stage, output inductor while on and block the difference between the input voltage and output 级,功率开关(图1中的Q1)当开关打开时连通输入到电感器,开关关上时断开连接。功率开关必须在开 the power switch in the Figure 1) connects the input to the inductor when is turned voltage when off.(Q1 Also, power switch must change from one state to the switch other quickly in 时在输出电感器传导电流 ,关时阻止输入电压和输出电压的差值。而且功率开关必须很快的完成一个状态 on andtodisconnects whenpower the switch is off. The power musttransition. conduct the current in the order avoid excessive dissipation during theswitch switching 到另一个状态的转换 ,从而避免在开关转换时间内的功率损耗 。 the input voltage and output output inductor while on and block the difference between voltage off. Also, the power switch must change from one state toOther the other quickly in The typewhen of power switch considered in this report is a power MOSFET. power devices 这篇报告中考虑的功率开关类型是功率型金属氧化物半导体场效应管 (MOSFET)。 order to avoidbut excessive dissipation during the switching transition. are available in mostpower instances, the MOSFET is the best choice in terms 其它的功率器件也可 of cost and performance (when the drive circuits are considered). The two types of MOSFET available 。可以 以用,但是在大多数情况下 是最好的选择 ,在考虑到费用和性能时 (考虑驱动电路时 ),MOSFET The type of power switch considered in this report is a power MOSFET. Other power devices for use are the n-channel and the p-channel. P-channel MOSFETs are popular for use in 使用的MOSFET有两种类型:n通道型和p通道型。P通道型MOSFET在buck-boost功率级中的使用更流行 , are available but in most because instances, the MOSFET issimpler the best choice in terms of cost and buck-boost power stages driving the gate is than the gate drive required for 因为驱动p通道的门比驱动n通道MOSFET中的门要简单。 performance the drive circuits are considered). The two types of MOSFET available an n-channel (when MOSFET. for use are the n-channel and the p-channel. P-channel MOSFETs are popular for use in 功率开关 消耗的功率由下式给出 Q1dissipated : driving buck-boost power stages because the gate is simpler The power by the power switch, Q1, is given by: than the gate drive required for an n-channel MOSFET. P D(Q1) � The power dissipated by the power switch, Q1, is given I O by: 2 �I Lrms� � RDS(on) � D � 1 � �V I � V O� � � �t r � t f� � f S � Q Gate � V GS � f S 2 1�D P D(Q1) � 其中: Where: I 2 t are the 1MOSFET turn-on � � andOturn-off �switching � times 的打开和关闭的转换时间 t�rI和 tf是� MOSFET r and �tR Lrms DS(on)f � D � 2 � V I � V。 O � 1 � D � t r � t f � f S � Q Gate � V GS � f S QGate总的门电荷 is the MOSFET total gate charge 。 QGate是MOSFET Where: Other than selecting or n-channel, other to consider tr and p-channel tf are the MOSFET turn-on andparameters turn-off switching timeswhile selecting the appropriateQMOSFET are the maximum drain-to-source breakdown voltage, V(BR)DSS is the MOSFET total gate charge Gate ,I 除了选择 时需要考虑的其它参数是漏极 ,在选择合适的 p通道或n通道以外 MOSFET -源极间击穿电压的最大 and the maximum drain current . D(Max) Other than selecting p-channel or n-channel, other parameters to consider while selecting 值V(BR)DSS 和最大漏极电流 , ID(Max)。 the appropriate MOSFET are the maximum drain-to-source breakdown voltage, V(BR)DSS and the maximum drain current, ID(Max). � � ZHCA041–1999年3月–2002年11月修订 � � Understanding Buck-Boost Power Stages in Switch Mode Power Supplies 27 Understanding Buck-Boost Power Stages in Switch Mode Power Supplies 27 全面认识开关型电源中的BUCK-BOOST功率级 27 www.BDTIC.com/TI The MOSFET selected should have a V(BR)DSS rating greater than the maximum difference between the input voltage and output voltage, and some margin should be added for The MOSFET should have aselected V(BR)DSS ratingalso greater than maximum difference transients and selected spikes. The MOSFET should have an Ithe D(Max) rating of at least SLVA059A between the input voltage and output voltage, and some margin should be this added for two times the maximum power stage inductor current. However, many times is not transients and spikes. The MOSFET selected should also have an I rating of at least D(Max) sufficient margin and the MOSFET junction temperature should be calculated to make sure www.ti.com.cn The MOSFET selected should have a V(BR)DSS greater than the maximum difference two maximum power stage inductor rating current. However, many times this is not 组件选择 that ittimes is notthe exceeded. The junction temperature can be estimated as follows: between margin the input and output voltage, and some margin should be addedsure for sufficient andvoltage the MOSFET junction temperature should be calculated to make transients and spikes. The MOSFET selected should also have an I rating of at least that it is not exceeded. temperature can be estimated D(Max) as 而且要为瞬变量和尖峰信号预 follows: TJ � T The � Pjunction R �JA ,V , MOSFET D �stage (BR)DSSA的额定值要大于输入电压和输出电压的最大差值 two times选取时 the maximum power inductor current. However, many times this is not 留一点的余量 时还要求额定 至少是功率级电感器最大电流的两倍 然而有很多时候这 。选择 MOSFET ID sufficient margin and the MOSFET junction temperature should be calculated to。make sure (Max) T J � T A � P D � R �JA Where: 还不是足够的余量 还要考虑到 结的温度 that it is not The or junction temperature can be estimated as follows: ,保证没有超过范围 。结温度由下式估算 : MOSFET TA exceeded. is the,ambient heatsink temperature Where: R ΘJA is the thermal resistance from the MOSFET chip to the ambient TJ � TA � P � R �JA temperature TAor is heatsink. the ambient orDheatsink air RΘJA is the thermal resistance from the MOSFET chip to the ambient 式中: Where: air or heatsink. TA is the ambient or heatsink temperature ; TA是周围空气或热沉的温度 5.4 Output Diode R is the thermal resistance from 。 the MOSFET chip to the ambient ΘJA RΘJA是 MOSFET片到周围空气或热沉的热阻抗 The output diode conducts when the power switch turns off and provides a path for the or heatsink. 5.4 Output air Diode inductor current. Important criteria for selecting the rectifier include: fast switching, 输出二极管 5.4 The output voltage, diode conducts when the power switch turns provides a path for the breakdown current rating, low-forward voltage dropofftoand minimize power dissipation, inductor current. Important criteria for selecting the rectifier include: fast switching, 5.4 and Output Diode packaging. Unless appropriate the application justifies the expense and complexity of :快速 输出二极管在功率开关关闭时导通 ,为电感器电流提供通路 。在选择整流器时要考虑的主要要素为 breakdown voltage, current rating, low-forward voltage outputs drop to is minimize dissipation, a开关 synchronous rectifier, the best solution for low-voltage usually 。 apower Schottky rectifier. 击穿电压 除非应用场合确实需要用 、 、额定电流 、为降低功率损耗的低正向电压下降和合适的封装 The output diode conducts when the power switch turns off and provides a path for the and appropriate packaging. Unless the application justifies the expense and complexity of The breakdown voltage must be greater than the maximum difference。between the input 到高费用和复杂的同步整流器 肖特基整流器通常是低压输出的最好解决方案 , inductor current. Important criteria for selecting the rectifier include: fast switching, a synchronous rectifier, the best solution for low-voltage outputs is usually a Schottky rectifier. voltage and output voltage, and some margin should be added for transients and spikes. The breakdown voltage, current rating,greater low-forward voltage drop todifference minimize between power dissipation, The breakdown voltage than the maximum input current rating should be atmust leastbe two times the maximum power stage output current. the Normally and appropriate packaging. Unless the application justifies the expense and complexity of 击穿电压必须大于输入电压和输出电压的最大差值 而且必须为瞬时值和尖峰预留一定的余量 额定电流 voltage and output voltage, and some margin should be added for transients and spikes. The , 。 the current rating will be much higher than the output current because power and junction a synchronous rectifier, the best solution for low-voltage outputs is usually a Schottky rectifier. current ratinglimitations should be dominate at least。two times the selection. maximum power stage output current. Normally 要至少是功率级最大电流的两倍 通常额定电流要远大于输出电流 ,因为功率和结温度的限制决定了器件 temperature the device The breakdown voltage must be greater than the maximum difference between input the current rating will be much higher than the output current because power andthe junction 的选择。 voltage and output voltage, and some margin should be added for transients and spikes. The temperature limitations selection. The voltage drop acrossdominate the diode the in adevice conducting state is primarily responsible for the losses current rating should be at least two times the maximum power stage output current. Normally in the diode. The power dissipated by the diode can be calculated as the product of the 二极管上的损耗主要由导通态二极管上的电压降造成的 ,二极管上的功率损耗可以由前向电压和输出负载 the current rating will bethe much higher than the output current because power and The voltage drop and across diode in a conducting state is primarily responsible thejunction losses forward voltage the output load current. The switching losses which for occur at the temperature limitations dominate the device selection. 电流的乘积来计算得 从导通态转化为非导通态时的转换损耗相比于传导损耗来说 非常小 通常忽略 。 , , in the diode. The power dissipated by the diode can calculated as the product of the 。 transitions from conducting to non-conducting states arebevery small compared to conduction forward voltage and the output load current. The switching losses which occur at the losses and are usually ignored. The voltagefrom dropconducting across the to diode in a conducting state primarily forconduction the losses transitions non-conducting states areisvery smallresponsible compared to 整流器上的功率损耗为 : in the diode. The power dissipated by the diode can be calculated as the product of the losses and dissipated are usuallyby ignored. The power the catch rectifier is given by: forward voltage and the output load current. The switching losses which occur at the transitions conducting non-conducting states are very small compared to conduction The power from dissipated by theto� catch (1 � Dis ) given by: P �V I O �rectifier D losses and are D(Diode) usually ignored. P D(Diode) � voltage V D � I Odrop � (1of�the D)catch rectifier. forward where VD is the The power dissipated by the catch rectifier is given by: 式中VD为整流器的前向电压降。 forward voltage of the as catch rectifier. where VD is the The junction temperature can bedrop estimated follows: P D(Diode) � V D � I O � (1 � D) 结温度估算公式为 The junction temperature as follows: P Dbe � estimated R �JA T:J � T A �can voltage drop of the catch rectifier. where VD is the forward T J � T A � P D � R �JA The junction temperature can be estimated as follows: T J � T A � P D � R �JA 28 Understanding Buck-Boost Power Stages in Switch Mode Power Supplies 28 Understanding Buck-Boost Power Stages in Switch Mode Power Supplies 28 Understanding Buck-Boost Power Stages in Switch Mode Power Supplies 28 全面认识开关型电源中的BUCK-BOOST功率级 ZHCA041–1999年3月–2002年11月修订 www.BDTIC.com/TI www.ti.com.cn 总结 SLVA059A 6 66 6 6 SLVA059A SLVA059A SLVA059A Summary Summary 总结application report described and analyzed the operation of the buck-boost power stage. This Summary Summary The two modes report of operation, continuous conduction mode of and conduction This application described and analyzed the 。 operation thediscontinuous buck-boost power stage. 这篇应用报告介绍分析了 功率级的工作过程 研究了连续导通模式和非连续导通模式两种工作模 buck-boost This application report described described and analyzed the operation operation of the the buck-boost power stage. stage. This application report and analyzed the of buck-boost power mode, were examined. Steady-state and small-signal were the two analyses performed on The two modes of operation, continuous conduction mode and discontinuous conduction 式。two 分析了 功率级的稳态模型和小信号模型 。还介绍了作为基本 buck-boost buck-boost功率级变型的反向功 The modes of operation, continuous conduction mode and discontinuous conduction The two modes of operation, continuous conduction andtwo discontinuous conduction the buck-boost power stage. The flyback power stagemode was the presented as a variation of the mode, were examined. Steady-state and small-signal were analyses performed on 率级。 were mode, examined. Steady-state and small-signal were the two analyses performed on mode, were examined. Steady-state and small-signal were the two analyses performed on basic buck-boost power stage. the buck-boost power stage. The flyback power stage was presented as a variation of the the buck-boost power stage. The flyback power stage was presented as a variation of the the buck-boost power stage. The flyback power stage was presented as a variation of the basic buck-boost power stage. basic buck-boost power stage. basic buck-boost power stage. 稳态分析的主要结果总结如下 。 The main results of the steady-state analyses are summarized below. The main results of the steady-state analyses are summarized below. The main of analyses are The main results results of the the steady-state steady-state analyses are summarized summarized below. below. voltage conversion relationship for CCM is: 连续导通模式下的电压转换关系为 : The voltage conversion relationship for CCM is: The The voltage voltage conversion conversion relationship relationship for for CCM CCM is: is: I �R V O � � �V I � V DS� � D � V d � I L � R L 1�D 1� � DL V O � � ��V I � V DS�� � D � V d � II L �R RL L D L D V � � V � V � � V � 1 � D 1 DL VO d� 1� O � � �V II � V DS DS� � 1 � D � V d � or a slightly simpler version: 1�D 1�D D 或者稍微简单些的关系式为 : D 1 or a slightly simpler version: VO � � VI � � or or a a slightly slightly simpler simpler version: version: 1�D 1 RL VO � � VI � D �1� D 1 DD� 1R VO � �� �V VI � �1� � V L �2 I 1 � D O 1�D 1 � D 1 � R��R R L 2 L 1 1� � R��1�D �22 which can be simplified to: � � R� 1�D R��1�D� which can :be simplified to: 还可化简为 D which can be simplified to: V Oto:� � V I � which can be simplified 1�D VO � � VI � D D DD � � V V 1� I� � � V � VO I The relationship between the average current and the output current for the 1 � D O 1 � inductor D continuous mode between buck-boost stageinductor is givencurrent by: The relationship thepower average and the output current for the The relationship relationship between the the average average inductor inductor current and and the the output output current current for for the the The continuous mode between buck-boost power stage is givencurrent by: 连续导通模式 功率级的电感器平均电流和输出电流的关系为 continuous mode buck-boost power stage is given by: buck-boost : continuous mode buck-boost stage is given by: � power I I L(Avg) � � I O (1 �I OD) I L(Avg) � � � IO II L(Avg) � (1 �OD) � (1 � �mode D) buck-boost voltage conversion relationship is given by: L(Avg) The discontinuous conduction (1 D) �� � �� � The discontinuous conduction mode buck-boost voltage conversion relationship is given by: The discontinuous conduction mode voltage The discontinuous conduction mode buck-boost voltage conversion conversion relationship relationship is is given given by: by: Dbuck-boost 非连续导通模式 电压转换关系为 : buck-boost VO � �V � I �DK VO � � VI � D V � � V I � �DK VO O � � VI � � where K is defined as: �K K where K is defined as: where K 其中K定义为 : where K is is defined defined as:2 � L K �as: R� �TLs K� 2 2 � 2 �TL Ls K� �R� K R � T The major results of the small-signal analyses are summarized below. R� T ss The major results of the small-signal analyses are summarized below. The results the summarized The major major results of of the small-signal small-signal analyses analyses are summarized below. small-signal duty-cycle-to-output transferare function for thebelow. buck-boost power stage operating in CCM duty-cycle-to-output is given by: 。 The small-signal transfer function for the buck-boost power stage 小信号分析的主要结果总结在下面 The small-signal duty-cycle-to-output duty-cycle-to-output transfer function function for for the the buck-boost buck-boost power power stage stage The small-signal transfer operating in CCM is given by: operating in CCM is given by: operating in CCM is given by: 连续导通模式下buck-boost功率级的小信号占空比-输出电压传输函数有下式给出: ZHCA041–1999年3月–2002年11月修订 全面认识开关型电源中的BUCK-BOOST功率级 Understanding Buck-Boost Power Stages in Switch Mode Power Supplies 29 29 Understanding Buck-Boost Power Stages in Switch Mode Power Supplies Understanding Buck-Boost Buck-Boost Power Power Stages Stages in in Switch Switch Mode Mode Power Power Supplies Supplies Understanding 29 29 29 www.BDTIC.com/TI www.ti.com.cn 总结 SLVA059A SLVA059A v^ O ^ d (s) � G do � 式中: Where: G do � s z1 � s z2 � �1 � �sz1� � �1 � �sz2� 2 1 � � s�Q � s o �2 o VI 2 (1 � D ) 2 1 RC � C 2 (1 � D ) 2 � R D�L �o � 1 � D �L � C Q� (1 � D) � R L C � The small-signal duty-cycle-to-output transfer function for the buck-boost power stage 非连续导通模式下 功率级的小信号占空比-输出电压传输函数由下式给出: operating in DCMbuck-boost is given by: v^ O ^ d � G do � 1 1 � �s p 式中: Where: 和: and V V G do � O � – I D �K �p � 2 R�C Also presented were requirements for the buck-boost power stage components based on voltage and current stresses applied during the operation of the buck-boost power stage. 功率级工作过程中加载的电压和电流的压力,以及基于这些压力的buck-boost功率级组成部件的各种要求。 For further study, several references are given. 为了方便读者更深入的研究,这里给出了一些参考文献。 30 30 全面认识开关型电源中的BUCK-BOOST功率级 Understanding Buck-Boost Power Stages in Switch Mode Power Supplies ZHCA041–1999年3月–2002年11月修订 www.BDTIC.com/TI www.ti.com.cn 7 参考文献 参考文献 1. 应用报告TL5001脉冲宽度调制控制器设计, TI 文献号SLVA034A. 2. 应用报告 利用TPS5210设计快速响应的同步buck整流器, TI 文献号 SLVA044 3. V. Vorperian, R. Tymerski, and F. C. Lee,谐振腔和脉冲宽度调制开关的等效电路模型, IEEE功率电子学学 报, Vol. 4, No. 2, pp. 205-214, April 1989. 4. R. W. Erickson, 功率电子学基础 New York: Chapman and Hall, 1997. 5. V. Vorperian, 利用脉冲宽度调制开关模型来简单分析脉冲宽度调制转换器: Parts I and II, IEEE 航天和电 子系统学报, Vol. AES-26, pp. 490-505, May 1990. 6. E. van Dijk, et al., 直流-直流转换器的脉冲宽度调制开关模型, IEEE 功率电子学学报, Vol. 10, No. 6, pp. 659-665, November 1995. 7. G. W. Wester and R. D. Middlebrook, 开关式直流-直流转换器的低频特性, IEEE航天和电子系统学报, Vol. AES-9, pp. 376-385, May 1973. 8. R. D. Middlebrook and S. Cuk,一种设计开关式转换器功率级模型的通用一体化方法, 电子学国际期刊, Vol. 42, No. 6, pp. 521-550, June 1977. 9. E. Rogers, 开关式功率源的控制回路模型, Proceedings of EETimes模拟和混合信号应用会议, July 13-14, 1998, San Jose, CA. ZHCA041–1999年3月–2002年11月修订 全面认识开关型电源中的BUCK-BOOST功率级 www.BDTIC.com/TI 31 样片及品质信息 免费样片索取 品质保证 您是否正没日没夜的忙于工作而又急需一块免费的 TI 产品 样片?那就请立刻登录 TI 样片中心,马上申请吧! 持续不断的专注于品质及可靠性是 TI 对 客户承诺的一部分。 1995 年, TI 的半导 体群品质系统计划开始实施。该全面的品 质系统的使用可满足并超越全球客户及业 界的需求。 数千种器件,极短的递送时间,高效的反馈速度: • 8000多种器件及各种封装类型任君选择 • 一周 7*24 小时网上随时申请 • 两个工作日内得到反馈 立即注册my.TI会员,申请免费样片,只需短短几天,样片 将直接寄到您所指定的地址。 http://www.ti.com.cn/freesample TI 深愔促进业界标准的重要性,并一直致力于美国 (U.S) 及国际性自发标准的调整。作为活跃于诸多全球性的业界 协会的一员,以及 TI 对环境保护负有强烈的使命感, TI 引 领其无铅 (lead[Pb]-free) 计划,并逐渐成为了该方向的领 导者。该计划始于上世纪 80 年代,旨在寻求产品的可替代 原料,时至今日,绝大多数的 TI 产品均可提供无铅及绿色 (Green)的封装。 电话支持——如果您需要帮助如何选择样片器件,敬请致 电中国产品信息中心 800-820-8682 或访问 如果您对“无铅”抱有任何疑问,敬请访问: • 已经有成千上万的客户通过申请样片,优质高效地完成 了产品设计。 www.ti.com.cn/support www.ti.com.cn/quality Safe Harbor Statement: This publication may contain forward-looking statements that involve a number of risks and uncertainties. These “forwardlooking statements” are intended to qualify for the safe harbor from liability established by the Private Securities Litigation Reform Act of 1995. These forward-looking statements generally can be identified by phrases such as TI or its management “believes,” “expects,” “anticipates,” “foresees,” “forecasts,” “estimates” or other words or phrases of similar import. Similarly, such statements herein that describe the company’s products, business strategy, outlook, objectives, plans, intentions or goals also are forward-looking statements. All such forward-looking statements are subject to certain risks and uncertainties that could cause actual results to differ materially from those in forward-looking statements. Please refer to TI’ s most recent Form 10-K for more information on the risks and uncertainties that could materially affect future results of operations. We disclaim any intention or obligation to update any forward-looking statements as a result of developments occurring after the date of this publication. Trademarks: The platform bar is a trademark of Texas Instruments. All other trademarks are the property of their respective owners. Real World Signal Processing, the balck/red banner, C2000, C24x, C28x, Code Composer Studio, Excalibur, Just Plug It In graphic, MicroStar BGA, MicroStar Junior, OHCI-Lynx, Power+ Logic, PowerPAD, SWIFT, TMS320, TMS320C2000, TMS320C24x, TMS320C28x, TMS320C6000, TPS40K, XDS510 and XDS560 are trademarks of Texas Instruments. All other trademarks are the property of their respective owners. IMPORTANT NOTICE Texas Instruments Incorporated and its subsidiaries (TI) reserve the right to make corrections, modifications, enhancements, improvements, and other changes to its products and services at any time and to discontinue any product or service without notice. Customers should obtain the latest relevant information before placing orders and should verify that such information is current and complete. All products are sold subject to TI’s terms and conditions of sale supplied at the time of order acknowledgment. TI warrants performance of its hardware products to the specifications applicable at the time of sale in accordance with TI’s standard warranty. Testing and other quality control techniques are used to the extent TI deems necessary to support this warranty. Except where mandated by government requirements, testing of all parameters of each product is not necessarily performed. TI assumes no liability for applications assistance or customer product design. Customers are responsible for their products and applications using TI components. To minimize the risks associated with customer products and applications, customers should provide adequate design and operating safeguards. TI does not warrant or represent that any license, either express or implied, is granted under any TI patent right, copyright, mask work right, or other TI intellectual property right relating to any combination, machine, or process in which TI products or services are used. Information published by TI regarding third-party products or services does not constitute a license from TI to use such products or services or a warranty or endorsement thereof. Use of such information may require a license from a third party under the patents or other intellectual property of the third party, or a license from TI under the patents or other intellectual property of TI. Reproduction of TI information in TI data books or data sheets is permissible only if reproduction is without alteration and is accompanied by all associated warranties, conditions, limitations, and notices. Reproduction of this information with alteration is an unfair and deceptive business practice. TI is not responsible or liable for such altered documentation. Information of third parties may be subject to additional restrictions. Resale of TI products or services with statements different from or beyond the parameters stated by TI for that product or service voids all express and any implied warranties for the associated TI product or service and is an unfair and deceptive business practice. TI is not responsible or liable for any such statements. TI products are not authorized for use in safety-critical applications (such as life support) where a failure of the TI product would reasonably be expected to cause severe personal injury or death, unless officers of the parties have executed an agreement specifically governing such use. Buyers represent that they have all necessary expertise in the safety and regulatory ramifications of their applications, and acknowledge and agree that they are solely responsible for all legal, regulatory and safety-related requirements concerning their products and any use of TI products in such safety-critical applications, notwithstanding any applications-related information or support that may be provided by TI. Further, Buyers must fully indemnify TI and its representatives against any damages arising out of the use of TI products in such safety-critical applications. TI products are neither designed nor intended for use in military/aerospace applications or environments unless the TI products are specifically designated by TI as military-grade or "enhanced plastic." Only products designated by TI as military-grade meet military specifications. Buyers acknowledge and agree that any such use of TI products which TI has not designated as military-grade is solely at the Buyer's risk, and that they are solely responsible for compliance with all legal and regulatory requirements in connection with such use. TI products are neither designed nor intended for use in automotive applications or environments unless the specific TI products are designated by TI as compliant with ISO/TS 16949 requirements. Buyers acknowledge and agree that, if they use any non-designated products in automotive applications, TI will not be responsible for any failure to meet such requirements. Following are URLs where you can obtain information on other Texas Instruments products and application solutions: 相关产品链接: • DSP - 数字信号处理器 http://www.ti.com.cn/dsp • 电源管理 http://www.ti.com.cn/power • 放大器和线性器件 http://www.ti.com.cn/amplifiers • 接口 http://www.ti.com.cn/interface • 模拟开关和多路复用器 http://www.ti.com.cn/analogswitches • 逻辑 http://www.ti.com.cn/logic • RF/IF 和 ZigBee® 解决方案 www.ti.com.cn/radiofre • RFID 系统 http://www.ti.com.cn/rfidsys • 数据转换器 http://www.ti.com.cn/dataconverters • 时钟和计时器 http://www.ti.com.cn/clockandtimers • 标准线性器件 http://www.ti.com.cn/standardlinearde • 温度传感器和监控器 http://www.ti.com.cn/temperaturesensors • 微控制器 (MCU) http://www.ti.com.cn/microcontrollers 相关应用链接: • 安防应用 http://www.ti.com.cn/security • 工业应用 http://www.ti.com.cn/industrial • 计算机及周边 http://www.ti.com.cn/computer • 宽带网络 http://www.ti.com.cn/broadband • 汽车电子 http://www.ti.com.cn/automotive • 视频和影像 http://www.ti.com.cn/video • 数字音频 http://www.ti.com.cn/audio • 通信与电信 http://www.ti.com.cn/telecom • 无线通信 http://www.ti.com.cn/wireless • 消费电子 http://www.ti.com.cn/consumer • 医疗电子 http://www.ti.com.cn/medical www.BDTIC.com/TI ZHCA041 重要声明 德州仪器 (TI) 及其下属子公司有权在不事先通知的情况下,随时对所提供的产品和服务进行更正、修改、增强、改进或其它更改, 并有权随时中止提供任何产品和服务。 客户在下订单前应获取最新的相关信息,并验证这些信息是否完整且是最新的。 所有产品的 销售都遵循在订单确认时所提供的 TI 销售条款与条件。 TI 保证其所销售的硬件产品的性能符合 TI 标准保修的适用规范。 仅在 TI 保修的范围内,且 TI 认为有必要时才会使用测试或其它质 量控制技术。 除非政府做出了硬性规定,否则没有必要对每种产品的所有参数进行测试。 TI 对应用帮助或客户产品设计不承担任何义务。 客户应对其使用 TI 组件的产品和应用自行负责。 为尽量减小与客户产品和应用相关 的风险,客户应提供充分的设计与操作安全措施。 TI 不对任何 TI 专利权、版权、屏蔽作品权或其它与使用了 TI 产品或服务的组合设备、机器、流程相关的 TI 知识产权中授予的直接 或隐含权限作出任何保证或解释。 TI 所发布的与第三方产品或服务有关的信息,不能构成从 TI 获得使用这些产品或服务的许可、授 权、或认可。 使用此类信息可能需要获得第三方的专利权或其它知识产权方面的许可,或是 TI 的专利权或其它知识产权方面的许 可。 对于 TI 的数据手册或数据表,仅在没有对内容进行任何篡改且带有相关授权、条件、限制和声明的情况下才允许进行复制。 在复制 信息的过程中对内容的篡改属于非法的、欺诈性商业行为。 TI 对此类篡改过的文件不承担任何责任。 在转售 TI 产品或服务时,如果存在对产品或服务参数的虚假陈述,则会失去相关 TI 产品或服务的明示或暗示授权,且这是非法的、 欺诈性商业行为。 TI 对此类虚假陈述不承担任何责任。 可访问以下 URL 地址以获取有关其它 TI 产品和应用解决方案的信息: 产品 放大器 http://www.ti.com.cn/amplifiers 数据转换器 http://www.ti.com.cn/dataconverters DSP http://www.ti.com.cn/dsp 接口 http://www.ti.com.cn/interface 逻辑 http://www.ti.com.cn/logic 电源管理 http://www.ti.com.cn/power 微控制器 http://www.ti.com.cn/microcontrollers 应用 音频 http://www.ti.com.cn/audio 汽车 http://www.ti.com.cn/automotive 宽带 http://www.ti.com.cn/broadband 数字控制 http://www.ti.com.cn/control 光纤网络 http://www.ti.com.cn/opticalnetwork 安全 http://www.ti.com.cn/security 电话 http://www.ti.com.cn/telecom 视频与成像 http://www.ti.com.cn/video 无线 http://www.ti.com.cn/wireless 邮寄地址:Texas Instruments, Post Office Box 655303, Dallas, Texas 75265 Copyright © 2006, Texas Instruments Incorporated www.BDTIC.com/TI