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1、7.2 行波的折射与反射 7.2 Refraction & Reflection of Traveling Wave,当波沿传输线传播，遇到线路参数发生突变，即波阻抗发生突变的节点时，都会在波阻抗发生突变的节点上产生折射和反射。 While the wave is being propagated along the wire and the mutation of parameters occure suddenly, namely the node of mutation of wave impedance, the refraction and reflection will be pr
2、oduced at the node of mutation.,如图7-4，当无穷长直角波 uif =E 沿线路1达到A点后，在线路1上除 uf 、if 外又会产生新的行波 ub、ib ，总的电压和电流为: Just as shown in Figure 7-4, after an infinitely long rectangular wave (uif =E) propageted along the wire (1) to point A, new traveling waves (ub, ib) will be produced beside (uf, if). The total v
3、oltage and current are as followed:,（7-13）,图7-4 波通过节点的折反射 Fig.7-4 Refraction and reflection of wave while traveling through the node a）波通过节点前时 b）波通过节点后, 时 c）波通过节点后, 时 a ) before the wave traveling through the node b）after the wave traveling through node, while c）after the wave traveling through node
4、, while,设线路2为无限长，或线路2上未产生反射波前，线路2上只有前行波没有反行波，则线路2上的电压和电流为： Suppose wire 2 is infinitely long. Before the reflex is produced on wire 2, there is only the forward travleing wave on it. The voltage and current of the wire 2 are as followed.,，,，,（7-14）,然而节点 A 只能有一个电压电流，即,However, node A can only have a
5、voltage and current, i.e.,将下列式子代入（7-15） Substitut the following formulars into（7-15）,因此 Therefore,（7-15）, 折射系数 Refraction Coefficient 反射系数 Reflection Coefficient,（7-17）,（7-16）,7.2.1 线路末端的折射、反射 7.2.1 Refraction & Reflection at the End of Wire 7.2.2 集中参数等效电路 7.2.2 Equivalent Circuit of Lumped Paramete
6、rs 7.2.3 波的多次折射、反射 7.2.3 Multiple Refraction & Reflection of Wave,本节内容 Contents in this section,7.2.1 线路末端的折射、反射 7.2.1 Refraction & Reflection at the End of Wire,末端开路时的折射、反射 Refraction and reflection at an end of wire in open-circuit,末端开路， ，根据式（7-17） ，即末端电压 U2 = uf = 2E，反射电压 u1b = E，而末端电流 i2 = 0，反射电
7、流 ib = 。 While it is open-circuit at the end of the wire, According to (7-17), . The voltage at the end is U2 = uf = 2E and the reflective voltage is u1b = E. Similarly the current is i2 = 0 and the reflective current ib= .,图7-5 末端开路时波的折、反射 Fig.7-5 Refraction and reflection at an open-circuit end of
8、 wiret,图7-5中，由于末端的反射，在反射波所到之处电压提高1倍，而电流降为0。 In Figure 7-5, since the reflection occurred at the end, the voltage was increased by one fold and the current was reduced to zero in everywhere the reflective wave arrived.,2.末端短路时的折射、反射 Refraction and reflection at an short-circuit endof wire,短路 ，由计算公式（7
9、-17） ，即线路末端电压 U2 = u2f = 0，反射电压 u1b = -E，反射电流i1b= 。在反射波到达范围内导线上各点电流为 。 While it is short-circuit, . According to (7-17), . The voltage at the end is U2 = uf = 2E and the reflective voltage and current are respectively u1b = - E and i1b= . In the range of reflective wave, the current is .,图7-6 末端接地时波
10、的折、反射 Fig.7-6 Refraction and reflection at a grounded end of wiret,图7-6中，在反射波所到之处电流提高1倍，而电压降为0。 In Figure 7-6, the current was increased by one fold and the voltage was reduced to zero in everywhere the reflective wave arrived.,3.末端接集中负载时的折射、反射 Refraction and reflection at an end of wire connected w
11、ith lumped loads,当 时，来波将在集中负载上发生折反射。而当 R = Z1 时，没有反射电压波和反射电流波。 While , the refraction and reflection of incoming wave will be produced on centralized loads. However if R = Z1 , there will be no reflection waves of voltage and current.,图7-7 末端接集中负载 R =Z1 时的折、反射 Fig.7-7 Refraction and reflection at an
12、 end of wire connected with a centralized load R=Z1,由 Z1 传输过来的能量全部消耗在 R 上了，其结果如图7-7所示。 The energy transmitted from Z1 is all consumed by R and the result is shown in figure 7-7.,7.2.2 集中参数等效电路（彼得逊法则） 7.2.2 Equivalent Circuit of Lumped Parameters“Peterson Law“,在图7-8(a)中，任意波形的前行波u1 达到A点后，首先观察A点的电压波形变化
13、情况。Z2 可为长线路，也可是任意的集中阻抗。 In Fig.7-8(a), we can observe the changes of voltage wave at A point firstly after a forward traveling wave u1 with any waveform arrived A point. Z2 can be a long wire or any lumped impedance.,图7-8 计算折射波的值电路(电压源) Fig.7-8 Calculative circuit of the value of refractive wave(vol
14、tage source),代入（7-18）得 Substituted into (7-18),（7-18）,（7-19）,其中波阻抗 Z1 用数值相等的等效电阻来替代，把入射电压u1f 的2倍 2u1f 作为等值电压源，这就是计算节点电压u2的等值电路法则，也称为彼德逊法则。 Impedance Z1 can be replaced by equivalent resistance. Use 2u1f , double value of incidence voltage, as the equivalent voltage source. This is the law of calcula
15、ting the node voltage u2 .It is called Peterson Law.,计算A点电压时，可将分布参数等值电流转换成图7-9所示集中参数等效电路。 While calculating the voltage of A point, the equivalent current of distributed parameters can be transformed into equivalent circuit of lumped parameters shown in Fig.7-9.,图7-9 集中参数等值电路(电流源) Fig.7-9 Equivalent circuit of lumped parameters (current source),实际计算中，常遇到电流源的情况，如雷电流。此时采用图7-9所示的电流源等值电路较为方便。 In the practice of calculation, the current source such as the lightning current is often emerged. Here the equivalent circuit of current source shown as Fig.7-9 is for the convenience of calculation.,7.2.
