在之前的博客文章中，我们已经看到在无源元件（如电容器和电感器）中发现的寄生术语如何影响开关转换器的传递函数。
实际上，所有损耗，无论是来自无源元件（等效串联电阻[ESR]）还是来自有源部件（二极管正向压降，动态电阻，MOSFET rDS（on）等）都会影响转换器传输功能。
例如，在直流中，电感ESR，二极管正向压降和MOSFET rDS（on）会影响控制 - 输出传递函数：理想情况下，您可以计算给定工作点的占空比，但电路板上的实验显示不同
随温度而变化的价值。
交流传递函数也受各种损失机制的影响。
诸如电容器和电感器ESR之类的永久性损耗肯定会影响效率，但二极管反向恢复时间，磁损耗和MOSFET开关损耗会耗散能量并倾向于降低转换器品质因数。
理论指出了一个高峰响应，实验室实验表明曲线相当平缓。
我们之前在降压转换器上进行的计算可以扩展到其隔离版本的正向转换器。
这种转换器如图1所示。
图1：正向转换器的典型实现，这里带有去磁绕组。
导出包括损耗的这种正向转换器的直流传递函数的最简单和最快的方法是计算施加到输出电感器L1的导通和关闭伏秒。
该原理如图2所示。在稳态时，伏秒平衡法告诉我们电感两端的平均电压必须为零。
在数学上，这意味着图2中的区域（0轴上方和下方）必须相等。
现在，练习包括在开启和关闭时间内定义电感器电压，包括各种下降。
图2：电感中的磁通平衡意味着0以上和0以下的区域相等。
图3显示了电源开关打开时的各种路径。
在变压器中循环的初级侧电流是添加到磁化电流Imag的反射电感器电流IL。
平均电感电流是负载电阻Rload上的Vout。
因此，在变压器初级上施加的电压是Vin减去MOSFET rDS（on）引起的下降，其中可以添加感测电阻器值（1）。
忽视Imag，我们有：
图3：在导通期间，在电感左端施加的电压是由变压器按比例缩小的输入电压，并受到多个损耗的影响。
（1）
该电压按比例缩小变压器匝数比N，并经受二极管正向压降和电感器欧姆损耗带来的其他损耗。
观察到电感器右端子偏置到Vout，那么ton期间的电感器电压是
（2）
在关闭期间，必须更新草图，如图4所示。当电源开关打开时，漏极电压上升，退磁二极管D1导通。
图4：在关断期间，电感器复位电压取决于Vout减去几滴。
磁化电流现在循环到反方向并流回到源极。
在次级侧，电感器左端子下降到由续流二极管压降Vf3和电阻损耗rL施加的负电压：
（3）
现在通过将（2）乘以DTsw和（3）乘以（1-D）Tsw来计算伏特秒。
这两个方程的总和必须返回0以满足伏秒平衡定律：
（4）
解决输出电压和占空比导致
（5）
（6）
当忽略所有损失时，公式简化为
（7）
和
（8）
假设以下参数
使用（6）我们发现占空比为40.4％，而（8）中的简化计算将给出36.7％。
占空比的这种变化将影响传统正激转换器的工作点，但也可以在有源钳位版本中改变陷波。
因此，如果稍后进行交流分析，则以更高的精度计算它是一件好事。
________________________________________
注1：在这种情况下，术语rDS（on）变为rDS（on）+ Rsense。
以上来自于谷歌翻译
以下为原文
In a previous blog post, we have seen how parasitic terms found in passive components such as capacitors and inductors can affect the transfer function of a switching converter. Actually, all losses, whether they are coming from passive elements (equivalent series resistances [ESR]) or from active parts (diodes forward drops, dynamic resistances, MOSFET rDS(on) and so on) affect the converter transfer function. For instance, in dc, the inductor ESR, the diode forward drop and the MOSFET rDS(on) affect the control-to-output transfer function: you ideally calculate a duty ratio for a given operating point but experiments on the board show a different value that can potentially evolve with temperature. The ac transfer function is also affected by various loss mechanisms. Permanent losses such as capacitor and inductor ESR surely affect efficiency, but diode reverse recovery time, magnetic losses and MOSFET switching losses dissipate energy and tend to lower the converter quality factor. Theory points out a peaky response and laboratory experiments show a rather flat curve.
Calculations that we previously carried on the buck converter can be extended to its isolated version, the forward converter. Such a converter appears in Figure 1.
![]()
Figure 1: A forward converter typical implementation, here with a demagnetization winding.
The easiest and fastest way to derive the dc transfer function of such a forward converter including losses is to calculate the on and off volt-seconds applied to the output inductor L1. This principle is shown in Figure 2. At steady-state, the volt-second balance law tells us that the average voltage across the inductor must be zero. Mathematically, it means that areas in Figure 2 (above and below the 0-axis) must be equal. The exercise now consists of defining the inductor voltage during the on and off times, including the various drops.
![]()
Figure 2: Flux balance in the inductor implies that area above and below 0 are equal.
Figure 3 shows the various paths at play when the power switch turns on. The primary-side current circulating in the transformer is the reflected inductor current IL added to the magnetizing current Imag. The average inductor current is Vout over the load resistor Rload. The voltage applied at the transformer primary is thus Vin minus the drop incurred to the MOSFET rDS(on) to which a sense resistor value can be added (1). Neglecting Imag, we have:
![]()
Figure 3: During the on-time, the voltage applied at the inductor left terminal is the input voltage scaled down by the transformer and affected by several losses.
![]() (1)
This voltage is scaled down by the transformer turns ratio N and undergoes other losses brought by the diode forward drop and the inductor ohmic loss. Observing that the inductor right terminal is biased to Vout, then the inductor voltage during ton is
![]() (2)
During the off time, the sketch must be updated as shown in Figure 4. As the power switch opens, the drain voltage rises up and the demagnetization diode D1 conducts.
![]()
Figure 4: During the off-time, the inductor reset voltage depends on Vout minus several drops.
The magnetizing current now circulates into a reverse direction and flows back into the source. In the secondary side, the inductor left terminal drops to a negative voltage imposed by the freewheel diode drop Vf3 and the resistive loss rL:
![]() (3)
The volts-seconds are now calculated by multiplying (2) by DTsw and (3) by (1-D)Tsw. The sum of these two equations must return 0 to satisfy the volts-seconds balance law:
![]() (4)
Solving for the output voltage and the duty ratio leads to
![]() (5)
![]() (6)
When all losses are neglected, formulas simplify to
![]() (7)
and
![]() (8)
Assume the following parameters
![]()
Using (6) we find a duty ratio of 40.4% while the simplified calculation in (8) would give 36.7%. This change in duty ratio will affect the operating point for a classical forward converter but could also shift the notch in an active clamp version. Calculating it with greater precision is thus a good thing if ac analysis is carried later on.
________________________________________
Note 1: in this case, the term rDS(on) becomes rDS(on) + Rsense.
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