离线式反激转换器的反馈设计

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<div class="WordSection1"> <h1>离线式反激转换器的反馈设计</h1> Feedback Control Design of Off-line Flyback Converter <h2 id="__Bookmark__0">摘要</h2> 离线式反激转换器 (off-line flyback converter) 的反馈控制经常困扰着电源工程师，因为牵涉到连续导通模式 (continuous conduction mode, CCM) 与非连续导通模式(discontinuous conduction mode, DCM)的小信号模型、TL431与光耦合器(opto-coupler)的特殊反馈补偿模式，使得反馈参数的设计，还流于试误(cut and try)模式。本设计指南提供完整的理论设计，从功率级的转换函数到设计TL431与光耦补偿器，使得系统获得良好的相位裕度(phase margin)，达到瞬时稳定度的要求。本文将利用Mathcad 软件做理论计算，同时以Simplis 模拟做比较验证。此法可应用于立锜科技 RT773x 系列离线式反激控制IC的电路设计中。 <h2 id="__Bookmark__1">一、适用范围 : 次级稳压反激转换器</h2> 绝大部份反激转换器都采用次级稳压的峰值电流控制(peak current mode control)来完成调节输出电压的反馈方式，图一为其简图。次级输出电压经过光耦与TL431电路，在初级侧形成电压VCOMP，这个电压与初级峰值电流比较，决定开关晶体管Q的占空比，完成负反馈稳压的作用。其中，RS 为初级电流检测电阻，CTR 为光耦的电流传递比(current transfer ratio)，GFB为小信号增益 (在RT773x IC内部设计为1/3)，Se为消除次谐波振荡(sub-harmonic oscillation) 所外加的斜率补偿(slop compensation)。 为方便后续的推导与说明，电路做了基本的假设如下： 1.开关器件Q与次级二极管D为理想组件 2.变压器视为理想器件 3.TL431的开回路增益为无限大 (常规的开路增益约50 ~ 60dB) 4.光耦的电流传递比为一常数 其中，光耦的电流传递比是一个极非线性的数值，随着工作点(通过光耦二极管的电流)的变动，电流传递比也会随着变化。但为了方便说明与推导起见，姑且将其视为定值。在常规的应用中，流过光耦二极管的电流很低，可能低于1mA，导致电流传递比可能小于20%。 其他名詞與符號定義如下： <a class="fancybox" href="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image001_zh-cn.png"> <img id="圖片 9" alt="Technical Document Image Preview" height="381" src="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image001_zh-cn.png" width="426"></a> <a class="fancybox" href="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image002_zh-cn.png"> <img id="圖片 5" alt="Technical Document Image Preview" height="268" src="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image002_zh-cn.png" width="347"></a> 图一、利用TL431与光耦反馈的反激转换器 <h2 id="__Bookmark__2">二、功率电路的小信号模型</h2> 在许多不同的参考文献中可以找到不同的反激转换器小信号模型[1-3]，这些模型都是基于状态平均(state averaging)法推导的，可能是因为简化或假设条件不同而有些许差异。本文乃采用 Christophe Basso 的小信号模型作反馈补偿设计[1]。从实用的角度而言，所有小信号模型都将得到近似的结果。 连续导通模式(CCM)的转移函数(transfer function) <a class="fancybox" href="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image003_zh-cn.png"> <img id="圖片 10" alt="Technical Document Image Preview" height="369" src="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image003_zh-cn.png" width="365"></a> 这是一个一个极点(pole)、两个零点(zero)的系统，如图二所示。极点的位置与电路参数以及负载轻重有关，而第一个零点为输出电容与其等效串联电阻(ESR)所构成，为一固定不动的零点。另一个零点在s-平面的右半边，称为右半平面零点(RHP zero)，这个右半平面零点的位置与输入电压、负载电流的高低有关。在一个设计良好的系统里，交越频率 (cross-over frequency) 必须设计得远低于右半平面零点频率，才能有足够的相位裕量(phase margin)。所以在补偿电路设计时，这个高频的零点将忽略不计。 <a class="fancybox" href="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image004_zh-cn.png"> <img id="圖片 12" alt="Technical Document Image Preview" height="211" src="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image004_zh-cn.png" width="325"></a> 图二、CCM 1P2Z 的转移函数图 非连续导通模式 (DCM)的转移函数 <a class="fancybox" href="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image005_zh-cn.png"> <img id="圖片 11" alt="Technical Document Image Preview" height="437" src="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image005_zh-cn.png" width="364"></a> 将(2)式的转移函数绘制在波德图(Bode Plot)上，如图三。在DCM 模式下，功率电路小信号模型呈现两极点与两零点，不过其中有一个极点ωp2频率极高(远高于目标的交越频率)，在设计反馈时不需考虑。所以等效上，不论CCM 或是DCM，其功率级的转移函数，均可视为一极点、两零点(1P2Z)的形式，这非常有利于反馈组态电路的选定。从(1)与(2) 转移函数来看，这些极点与零点，有些是固定不变的，如输出电容等效串联电阻ESR造成的零点。大部份的极零点与直流增益都与工作点(operating point)有关，所谓工作点即指某一个输入电压与某个负载电流工作条件。接下来，就用数值来说明这些极零点的变化。 <a class="fancybox" href="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image006_zh-cn.png"> <img id="圖片 13" alt="Technical Document Image Preview" height="210" src="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image006_zh-cn.png" width="315"></a> 图三、DCM 2P2Z 的转移函数图 工作点与极零点变化 举一个常规的应用例子来说明：一个反激转换器，输入电压范围为90V 到360V，负载范为为0到3A，输出电压为12V。并有着下列的电路参数 : LP = 1.1mH, NP : NS = n = 7.7, CO = 1360μF, RESR = 30 mΩ, RS = 0.56Ω, fS = 65kHz, Se = 3.46 x 104 V/sec, GFB = 0.3333。(其中 Se 与GFB 必须由控制IC提供)根据反激转换器的工作原理[4]，在常规的设计里，高输入电压与轻载状态总是让转换器倾向于非连续导通模式；反之，低输入电压与重载的条件下，转换器会走向连续导通模式。其间存在着一条所谓 CCM与DCM 的边界曲线，如图四所示，在曲线上方为CCM 工作模式，曲线下方为DCM 工作模示。(3)式就是代表这条曲线的方程式。 <a class="fancybox" href="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image007_zh-cn.png"> <img id="圖片 14" alt="Technical Document Image Preview" height="209" src="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image007_zh-cn.png" width="325"></a> 图四、CCM 与DCM 边界曲线 <a class="fancybox" href="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image008_zh-cn.png"> <img id="圖片 15" alt="Technical Document Image Preview" height="53" src="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image008_zh-cn.png" width="337"></a> 不同工作点的零极点变化 表一为范例中的直流增益以及零极点位置的计算结果。图五为输入电压与负载电流变化的波德示意图。可以看出，当低输入电压与高负载时，增益曲线较低；反之，高输入电压与轻载时，增益曲线较高。这个事实关系到如何选择工作点作为反馈设计的基准，很显然，低输入电压与重载条件做为反馈设计点是比较恰当的。也就是说在这样的条件下，如果拥有足够的相位裕量，通常也能延伸到其他工作点有着更好的相对稳定裕量。 表一、不同工作点的直流增益与零极点位置 <div> <table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="width: 450.0pt; border-collapse: collapse; border: none" width="600"> <tr> <td style="width: 9.0pt; border: solid #009EB8 1.0pt; background: #009EB8; padding: .75pt .75pt .75pt .75pt" width="12"> VIN (V) </td> <td style="width: 8.25pt; border: solid #009EB8 1.0pt; border-left: none; background: #009EB8; padding: .75pt .75pt .75pt .75pt" width="11"> 90 </td> <td style="width: 8.25pt; border: solid #009EB8 1.0pt; border-left: none; background: #009EB8; padding: .75pt .75pt .75pt .75pt" width="11"> 180 </td> <td style="width: 8.25pt; border: solid #009EB8 1.0pt; border-left: none; background: #009EB8; padding: .75pt .75pt .75pt .75pt" width="11"> 270 </td> <td style="width: 8.25pt; border: solid #009EB8 1.0pt; border-left: none; background: #009EB8; padding: .75pt .75pt .75pt .75pt" width="11"> 360 </td> <td style="width: 8.25pt; border: solid #009EB8 1.0pt; border-left: none; background: #009EB8; padding: .75pt .75pt .75pt .75pt" width="11"> 90 </td> <td style="width: 8.25pt; border: solid #009EB8 1.0pt; border-left: none; background: #009EB8; padding: .75pt .75pt .75pt .75pt" width="11"> 90 </td> <td style="width: 8.25pt; border: solid #009EB8 1.0pt; border-left: none; background: #009EB8; padding: .75pt .75pt .75pt .75pt" width="11"> 90 </td> <td style="width: 8.25pt; border: solid #009EB8 1.0pt; border-left: none; background: #009EB8; padding: .75pt .75pt .75pt .75pt" width="11"> 360 </td> <td style="width: 8.25pt; border: solid #009EB8 1.0pt; border-left: none; background: #009EB8; padding: .75pt .75pt .75pt .75pt" width="11"> 360 </td> <td style="width: 8.25pt; border: solid #009EB8 1.0pt; border-left: none; background: #009EB8; padding: .75pt .75pt .75pt .75pt" width="11"> 360 </td> </tr> <tr> <td style="border: solid #009EB8 1.0pt; border-top: none; background: #009EB8; padding: .75pt .75pt .75pt .75pt"> IO (A) </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 3.0 </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 3.0 </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 3.0 </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 3.0 </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 3.0 </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 2.0 </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 1.0 </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 3.0 </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 2.0 </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 1.0 </td> </tr> <tr> <td style="border: solid #009EB8 1.0pt; border-top: none; background: #009EB8; padding: .75pt .75pt .75pt .75pt"> Mode </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> CCM </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> CCM </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> CCM </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> DCM </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> CCM </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> CCM </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> DCM </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> DCM </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> DCM </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> DCM </td> </tr> <tr> <td style="border: solid #009EB8 1.0pt; border-top: none; background: #009EB8; padding: .75pt .75pt .75pt .75pt"> G0 (dB) </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 13.1 </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 16.5 </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 17.0 </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 17.1 </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 13.1 </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 15.6 </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 17.0 </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 17.1 </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 18.8 </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 21.8 </td> </tr> <tr> <td style="border: solid #009EB8 1.0pt; border-top: none; background: #009EB8; padding: .75pt .75pt .75pt .75pt"> fP1 (Hz) </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 59.0 </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 53.0 </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 57.0 </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 58.5 </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 59.0 </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 44.0 </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 19.5 </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 58.5 </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 39.0 </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 19.5 </td> </tr> <tr> <td style="border: solid #009EB8 1.0pt; border-top: none; background: #009EB8; padding: .75pt .75pt .75pt .75pt"> fP2 (Hz) </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> NA </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> NA </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> NA </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 21.7k </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> NA </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> NA </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 25k </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 21.7k </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 32.6k </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 65k </td> </tr> <tr> <td style="border: solid #009EB8 1.0pt; border-top: none; background: #009EB8; padding: .75pt .75pt .75pt .75pt"> fZ1 (Hz) </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 3.9k </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 3.9k </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 3.9k </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 3.9k </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 3.9k </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 3.9k </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 3.9k </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 3.9k </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 3.9k </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 3.9k </td> </tr> <tr> <td style="border: solid #009EB8 1.0pt; border-top: none; background: #009EB8; padding: .75pt .75pt .75pt .75pt"> fZ2 (Hz) </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 16.5k </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 44.2k </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 75k </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 106k </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 16.5k </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 24.7k </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 49.5k </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 106k </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 160k </td> <td style="border-top: none; border-left: none; border-bottom: solid #009EB8 1.0pt; border-right: solid #009EB8 1.0pt; padding: .75pt .75pt .75pt .75pt"> 319k </td> </tr> </table> </div> <a class="fancybox" href="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image009_zh-cn.png"> <img id="圖片 16" alt="Technical Document Image Preview" height="392" src="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image009_zh-cn.png" width="606"></a> 图五、改变工作点的增益曲线变化 <h2 id="__Bookmark__3">三、反馈补偿电路设计</h2> 从前面的分析得知，不同的操作点有着不同的零极点位置以及不同的低频直流增益，所以存在着许多设计补偿电路的方法。基本上一个Type II 的补偿器 (一个零频率的极点，随着一个低频零点以及一个极点) 最适合做此类的补偿。如果用一个低频零点来补偿功律电路的低频极点，同时利用高频极点来补偿ESR零点，这样将容易获得较好的相位裕量。利用补偿器的中频段增益来设定适当的交越频率，系统将有相当好的稳定度。 一种简单实用的方法便是先设定好一个“目标回路增益”(target loop gain)为： <a class="fancybox" href="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image010_zh-cn.png"> <img id="圖片 19" alt="Technical Document Image Preview" height="45" src="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image010_zh-cn.png" width="351"></a> 这样的回路增益在波德图上就是一条 -20dB/dec 斜率的直线，如图六，在低频直流部分有着极高(相当于补偿器的开路增益)的增益，所以整个电路的直流稳态电压调整率理论值可为零。同时，其交越频率fC为 <a class="fancybox" href="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image011_zh-cn.png"> <img id="圖片 18" alt="Technical Document Image Preview" height="38" src="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image011_zh-cn.png" width="320"></a> 因为斜率近似 -20dB/dec，所以在交越频率有着近90° 的相位裕量。对一个离线的反激转换器而言，交越频率设计在低压输入满载时工作点为800Hz到3kHz为最恰当 (以65kHz 开关频率而言)。 <a class="fancybox" href="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image012_zh-cn.png"> <img id="圖片 20" alt="Technical Document Image Preview" height="208" src="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image012_zh-cn.png" width="313"></a> 图六、功率电路转移函数曲线(红色)与目标回路增益(蓝色) 设计步骤 有了以上的了解与认知后，很自然的一般补偿器设计的方法就可以应用了，现将这些步骤整理如下: 1.选择低压输入与满载做为补偿电路设计基准的功率电路。如前所述，采用这个工作点设计的补偿器可以延伸涵盖到其他工作点，并且有更好的相位裕量。 2.设定交越频率 fC，其回路增益波德图为 -20dB/dec 斜率。越高的交越频率，虽然代表着更快的瞬时响应，但是别忘了反激转换器固有的右半平面零点问题，这个零点无法用传统的极点补偿，所以交越频率必须远低于这个零点位置。实务上，离线反激转换器的交越频率多半设计在3kHz以下。 3.定义一个两极点、一零点的补偿电路，并设定补偿电路的零点为功率电路的低频极点；设定补偿电路的高频极点为功率电路的ESR零点。利用一组Type II 的补偿电路，恰可以结合功率电路的转移函数，成为目标回路增益。 4.根据功率电路在fC 的增益，算出补偿器的中频增益。 5.同时，相位裕量可以先预估。 6.补偿电路的转换函数可以确定了： <a class="fancybox" href="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image013_zh-cn.png"> <img id="圖片 21" alt="Technical Document Image Preview" height="77" src="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image013_zh-cn.png" width="302"></a> 也就是说 (6) 式的 A、ωcp1 與 ωcz1 都可以计算出来了。 补偿电路的实现 1.选用最广泛使用的TL431与光耦合器架构，如图七。实现Type II 补偿器的电路结构有许多种，不在此讨论，仅提供最常用结合TL431与光耦的常规Type II电路计算与说明。 <a class="fancybox" href="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image014_zh-cn.png"> <img id="圖片 22" alt="Technical Document Image Preview" height="231" src="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image014_zh-cn.png" width="274"></a> 图七、实现反馈补偿的电路结构 2.图七补偿电路的小信号转换函数如下 [5] <a class="fancybox" href="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image015_zh-cn.png"> <img id="圖片 23" alt="Technical Document Image Preview" height="47" src="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image015_zh-cn.png" width="296"></a> 图八为相应的补偿器波德图。 <a class="fancybox" href="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image016_zh-cn.png"> <img id="圖片 24" alt="Technical Document Image Preview" height="203" src="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image016_zh-cn.png" width="322"></a> 图八、Type II 补偿器波德图 3.从(7)式看，共有Ra、Rb、Rc3、Rd、Ca、Cb 及 CTR 等七个参数待定。而已知的只有前面算出的三个关系式。 <a class="fancybox" href="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image017_zh-cn.png"> <img id="圖片 26" alt="Technical Document Image Preview" height="39" src="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image017_zh-cn.png" width="288"></a> <a class="fancybox" href="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image018_zh-cn.png"> <img id="圖片 27" alt="Technical Document Image Preview" height="36" src="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image018_zh-cn.png" width="291"></a> <a class="fancybox" href="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image019_zh-cn.png"> <img id="圖片 28" alt="Technical Document Image Preview" height="37" src="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image019_zh-cn.png" width="290"></a> 换句话说，有四个参数必须从其他条件获得。 4.首先为电阻Rd，大部份新型的控制IC都已设定好，设计者可以从IC供货商数据中获得。 5.其次，TL431 的参考电压也可从供货商数据中得取，常规约为2.5V。为让TL431正常运作，通过Rb 的电流(Ivd) 至少须125μA，一般加上余裕，可以设定成250μA。所以 Ra 与Rb 就可以很容易的计算出来。 <a class="fancybox" href="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image020_zh-cn.png"> <img id="圖片 29" alt="Technical Document Image Preview" height="36" src="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image020_zh-cn.png" width="294"></a> <a class="fancybox" href="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image021_zh-cn.png"> <img id="圖片 30" alt="Technical Document Image Preview" height="21" src="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image021_zh-cn.png" width="297"></a> 6.此外，光耦的电流传递比(CTR)可以从供货商数据里估计。事实上如前所述，CTR 为一非线性值，随通过光耦二极管电流大小而变。一般通过光耦二极管电流约为几百μA，CTR 约在0.1 到0.5之间，确实的数值必须透过精密量测而得。此例将假设CTR 为0.5。 7.如此一来，七个参数已经决定了四个，其余的三个参数可藉由(8)、(9)及(10)三个关系式算出唯一解。 8.算出RC3 的数值后必须要检讨一下。从TL431 运行原理，其阴极电压必须高于2.5V，同时流过阴极的电流必须大于1mA 才可以获得正确的稳压。通常会在光耦二极管上并联一个1kΩ 左右的电阻以提供足够的阴极电流。特别注意，这个并联电阻并不会改变系统小信号特性。所以可以得到下列关系式: <a class="fancybox" href="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image022_zh-cn.png"> <img id="圖片 31" alt="Technical Document Image Preview" height="20" src="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image022_zh-cn.png" width="300"></a> <a class="fancybox" href="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image023_zh-cn.png"> <img id="圖片 32" alt="Technical Document Image Preview" height="39" src="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image023_zh-cn.png" width="300"></a> 其中VF 为光耦二极管的顺向压降，常规约略为1.0V。RC3的最大值就可以估计出来了。 <a class="fancybox" href="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image024_zh-cn.png"> <img id="圖片 33" alt="Technical Document Image Preview" height="42" src="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image024_zh-cn.png" width="299"></a> 代入前面的例子，同时假定最大阴极电流为1.5mA，则RC3必须小于5.6kΩ。太高的RC3会降低补偿电路的中频增益。如果计算出来的RC3大于上限值就表示必须降低设定交越频率，或采用其他的补偿计算方法。 9.光耦合器在先天上存在一个并联于光耦三极管的等效电容，必须用电路量测的方法测得，常规约在2nF到5nF之间。补偿器计算出来的Cb值必须减去这个杂散电容，才是要外加的电容值。如果算出来的Cb值比杂散电容小，那就不需要外加电容了，不过因为不能完全补偿ESR零点(极点靠近低频)，所以相位裕量会变差一些。 設計工具與模擬驗證 为了让上述计算可以快速进行，特别制作两个Mathcad计算程序“Flyback CCM Type II Compensation” 与 “Flyback Loop Gain Analysis”，方便反馈的计算与分析。同时可藉由Simplis仿真来比较本文模型计算的误差。图九为Simplis仿真电路图，图十到图十二为本文提供的设计方法用Mathcad 分析计算与Simplis 模拟结果比较。图十为功率电路转移函数波德图，图十一为补偿器电路转移函数波德图，图十二为回路增益波德图。(a)为幅值，(b)为相位。图中红色实曲线为Mathcad依据小信号模型计算结果，蓝色虚曲线为用Simplis直接仿真的结果。可以看出从低频段到交越频率，小信号模型有很好的准确度。高频部份由于小信号模型的误差，有比较大的误差，不过因为回路增益已远小于1，对于实际瞬时响应影响不大。图十三为用Simplis仿真在输入电压为90V情况下阶梯负载变化(负载自1A瞬变到3A)的输出电压瞬时响应图，可以看出只有很小的过冲(overshoot)以及很快的回复时间(settling time)。 <a class="fancybox" href="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image025_zh-cn.png"> <img id="圖片 34" alt="Technical Document Image Preview" height="348" src="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image025_zh-cn.png" width="553"></a> 图九、Simplis 仿真电路图 <a class="fancybox" href="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image026_zh-cn.png"> <img id="圖片 35" alt="Technical Document Image Preview" height="174" src="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image026_zh-cn.png" width="584"></a> 图十、功率电路转移函数波德图 (a) 幅值, (b) 相位 <a class="fancybox" href="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image027_zh-cn.png"> <img id="圖片 36" alt="Technical Document Image Preview" height="175" src="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image027_zh-cn.png" width="600"></a> 图十一、补偿器电路转移函数波德图 (a) 幅值, (b) 相位 <a class="fancybox" href="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image028_zh-cn.png"> <img id="圖片 37" alt="Technical Document Image Preview" height="196" src="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image028_zh-cn.png" width="580"></a> 图十二、回路增益波德图 (a) 幅值, (b) 相位 <a class="fancybox" href="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image029_zh-cn.png"> <img id="圖片 38" alt="Technical Document Image Preview" height="214" src="/content/dam/richtek-eds/resources/application-notes/an017/html-images-zh-cn/image029_zh-cn.png" width="342"></a> 图十三、负载瞬变瞬态响应图 <h2 id="__Bookmark__4">參考文獻</h2> [1] Christophe P. Basso, “Switch-Mode Power Supplies Spice Simulations and Practical Designs”, McGraw_Hill, 2008. [2] W. Kleebchampee and C. Bunlaksananusorn, “Modeling and Control Design of a Current-Mode Controlled Flyback Converter with Optocoupler Feedback”, IEEE PEDS 2005. [3] Yuri Panov and Milan M. Jovanovic´, “Small-Signal Analysis and Control Design of Isolated Power Supplies with Optocoupler Feedback”, IEEE TRANSACTIONS ON POWER ELECTRONICS, JULY 2005. [4] 王信雄, “定频返驰式转换器设计指南”, RTAD1202TC, 立锜科技设计指南, 2012. [5] John Schönberger, ”Design of a TL431-Based Controller for a Flyback Converter”, Plexim GmbH. <div> <table border="1" cellpadding="0" cellspacing="0" class="3-51" style="width: 637.5pt; border-collapse: collapse; border: medium none;"> <tr style="height: 17pt;"> <td colspan="2" style="border-width: 1pt 1px 1px 1pt; border-style: solid; border-color: #009eb8; background-color: #009eb8; background-image: url(e); background-repeat: repeat; background-attachment: scroll; background-clip: border-box; background-origin: padding-box; background-size: auto auto; padding-right: 5pt; padding-left: 5pt; height: 17pt;"> 相关资源 </td> </tr> <tr> <td style="border-width: 1pt 1px 1px 1pt; border-style: solid; border-color: #009eb8; background-color: #ffffff; background-image: url(e); background-repeat: repeat; background-attachment: scroll; background-clip: border-box; background-origin: padding-box; background-size: auto auto; padding-right: 5pt; padding-left: 5pt; height: 17pt;"> 立锜科技电子报 </td> <td style="border-width: 1pt 1px 1px 1pt; border-style: solid; border-color: #009eb8; background-color: #ffffff; background-image: url(e); background-repeat: repeat; background-attachment: scroll; background-clip: border-box; background-origin: padding-box; background-size: auto auto; padding-right: 5pt; padding-left: 5pt; height: 17pt;"> <a class="link" href="http://www.richtek.com/My%20Richtek/Newsletters" target="_blank"> 订阅立锜科技电子报</a> </td> </tr> <tr> <td style="border-width: 1pt 1px 1px 1pt; border-style: solid; border-color: #009eb8; background-color: #ffffff; background-image: url(e); background-repeat: repeat; background-attachment: scroll; background-clip: border-box; background-origin: padding-box; background-size: auto auto; padding-right: 5pt; padding-left: 5pt; height: 17pt;"> 档案下载 </td> <td style="border-width: 1pt 1px 1px 1pt; border-style: solid; border-color: #009eb8; background-color: #ffffff; background-image: url(e); background-repeat: repeat; background-attachment: scroll; background-clip: border-box; background-origin: padding-box; background-size: auto auto; padding-right: 5pt; padding-left: 5pt; height: 17pt;"> <a class="link" href="http://www.richtek.com/Design%20Support/Technical%20Document/~/media/AN%20PDF/AN017_CN.ashx"> PDF 下载</a> </td> </tr> </table> </div> </div>

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