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电气工程代写|数字电路代写digital circuit代考|FULL-WAVE RECTIFIERS
To remove the ripple from the output of a half-wave rectifier may require a very large capacitance. In many instances, the capacitor required to reduce the ripple on the half-wave rectified output voltage to the desired design specification may be prohibitively large.
A full-wave rectifier circuit can be used as a more efficient way to reduce ripple on the output voltage. A center-tapped input transformer-coupled full-wave rectifier is shown in Figure 2.21. Each half of the transformer with the associated diode acts as a half-wave rectifier. The diode $\mathrm{D} 1$ conducts when the input $v_i>V_\gamma$ and $\mathrm{D} 2$ conducts when the input $v_i<V_\gamma$. Note that the secondary winding is capable of providing twice the voltage drop across the load resistor. Additionally, the input to the diodes and the output share a common ground between the load resistor and the center-tap.
An isolation transformer is not required to design a full-wave rectifier. If ground isolation is not required, only a center-tapped well coupled coil is required as shown in Figure 2.22.
An alternate configuration for a full-wave rectifier exists with an addition of two diodes. In thê alteernaté configuration, called thẻ bridge rectifier shown in Figure 2.23, thê sourcẻ and lơad do not share an essential common terminal. Additionally, the secondary transformer does not require a center tap and provides a voltage only slightly greater than half that of the secondary in Figure $2.21$.
In the bridge rectifier circuit, diodes $D_2$ and $D_4$ are $\mathrm{ON}$ for the positive half cycle of the voltage across the secondary of the transformer. Diodes $D_1$ and $D_3$ are off in the positive half cycle since their anode voltages are less than the cathode voltages. This is due to the voltage drop across the ON diodes and the load resistor. In the negative half cycle of the voltage across the secondary of the transformer, diodes $D_1$ and $D_3$ are $\mathrm{ON}$, with $D_2$ and $D_4 \mathrm{OFF}$. In both half cycles, the current through the load resistor is in the same direction. Therefore, each half cycle, the output voltage appears in the same polarity.
From Equation (2.13), the output DC voltage of a full wave rectificr circuit is twice that of the half-wave rectifier since its period is half that of the half-wave rectifier circuit,
$$
\begin{aligned}
{\left[V_{d c}\right]{\text {full-wave }} } &=\frac{1}{T} \int_0^T v_o(t) d t \ &=2\left[V{d c}\right]{\text {half-wave }} \ &=\frac{2 V_m}{\pi} . \end{aligned} $$ Similarly, the RMS output voltage of a full-wave rectifier is found by applying Equation $(2.16)$ $$ \begin{aligned} V{\text {rms }} &=\left[\frac{1}{T} \int_0^T v_o^2(t) d t\right]^{\frac{1}{2}} \
&=\frac{V_m}{\sqrt{2}} .
\end{aligned}
$$
The maximum possible efficiency of the full-wave rectifier is significantly greater than that of the half-wave rectifier since power from both positive and negative cycles are available to produce a DC voltage,
$$
\eta_{\text {full-wavc }}=\frac{P_{d c}}{P_{a c}}=\frac{\left(2 V_{m / \pi}\right)^2}{R_L} \frac{\left(V_m / \sqrt{2}\right)^2}{R_L}=\frac{8}{\pi^2}=2 \eta_{\text {half-wave }} \Rightarrow 81.2 \%
$$
电气工程代写|数字电路代写digital circuit代考|ZENER DIODES AND APPLICATIONS
Diodes that at designed with adequate power dissipation capabilities to operate in breakdown are called Zener diodes and are commonly used as voltage reference or constant voltage devices.
The two mechanisms responsible for the breakdown characteristics of a diode are avalanche breakdown and Zener breakdown. Avalanche breakdown occurs at high voltages ( $\geq 10 \mathrm{~V})$ where the charge carriers acquire enough energy to create secondary hole-electron pairs which act as secondary carriers. This chain reaction causes and avalanche breakdown of the diode junction and a rapid increase in current at the breakdown voltage. Zener breakdown occurs in the heavily doped $p$ – and $n$-regions on both sides of the diode junction and occurs when the externally applied potential is large enough to create a large electric field across the junction to force bound electrons from the $p$-type material to tunnel across to the $n$-type region. A sudden increase in current is observed when sufficient external potential is applied to produce the required ionization energy for tunneling.
Regardless of the mechanism for breakdown, the breakdown diodes are usually called Zener diodes. The symbol and characteristic curve of a low voltage (referring to the breakdown voltage) Zener diode are shown in Figure 2.33. The forward bias characteristic is similar to conventional $p-n$ junction diodes. The reverse bias region depicts the breakdown occurring at $V_Z$ which is nearly independent of diode current. A wide range of Zener diodes are commercially available over a wide range of breakdown voltages and power ratings to $100 \mathrm{~W}$.
Changes in temperature generally cause a shift in the breakdown voltage. The temperature coefficient is approximately $+2 \mathrm{mV} /{ }^{\circ} \mathrm{C}$ for Zener breakdown. For avalanche breakdown, the temperature coefficient is negative.
The simplified SPICE model of a Zener diode is identical to that of the conventional diode with the addition of the reverse breakdown “knee” voltage $B_V$ and the corresponding reverse hreakdown “knee” current $I_{B V}$. The relationship herween $R_V$ and $I_{B V}$ is shown in the reversebias portion of the Zener diode characteristic curve of the Zener diode in Figure 2.34. To obtain a steeper reverse breakdown characteristic, a higher breakdown current $I_{B V}$ may, in general, be used without incurring significant errors. The Zener diode model statement for Figure $2.34$ uses $B_V=5$ and $I_{B V}=10 \mathrm{~m}$ for a Zener voltage of $5 \mathrm{~V}$ at $10 \mathrm{~mA}$. Both $B_V$ and $I_{B V}$ are positive quantities. If $I_{B V}$ is large, the reverse breakdown curve is steeper.
The dynamic resistance of the Zener dióde in the reverse breakdown region, $r_Z$, is then slope of the diode curve at the operating reverse bias current. Since the reverse current increases rapidly with small changes in the diode voltage drop, $r_Z$ is small (typically 1 to $15 \Omega$ ). The Zener diode piece-wise linear model and its simplified version are shown in Figure $2.35$.

数字电路代考
电气工程代写|数字电路代写digital circuit代考|FULL-WAVE RECTIFIERS
要消除半波整流器输出的纹波,可能需要非常大的电容。在许多情况下,将半波整流输出电压上的纹波降 低到所需的设计规范所需的电容器可能非常大。
全波整流器电路可用作降低输出电压纹波的更有效方式。中心抽头输入变压器耦合全波整流器如图 $2.21$ 所 示。菷有相关二极管的变压器的每一半充当半波整流器。二极管D1当输入时进行 $v_i>V_\gamma$ 和D2当输入时进 行 $v_i<V_\gamma$. 请注意,次级绕组能够在负载电阻上提供两倍的电压降。此外,二极管的输入和输出在负载电 阻和中心抽头之间共用一个接地。
设计全波整流器不需要隔离变压器。如果不需要接地隔离,则只需要一个中心抽头的良好耦合线瞎,如图 $2.22$ 所示
全波整流器的另一种配置是增加了两个二极管。在如图 $2.23$ 所示的称为 thẻ 桥式整流器的交替配置中, thê sourcè 和 load 不共享必要的公共端子。此外,次级变压器不需要中心抽头,提供的电压仅略大于图 2 中次级的一半。 $2.21$.
在桥式整流电路中,二极管 $D_2$ 和 $D_4$ 是 $\mathrm{ON}$ 变压器次级电压的正半周。二极管 $D_1$ 和 $D_3$ 因为它们的阳极电 压小于阴极电压,所以它们在正半周期内关闭。这是由于导通二极管和负载电阻上的电压降造成的。在变 压器次级两端电压的负半周,二极管 $D_1$ 和 $D_3$ 是 $\mathrm{ON}$ ,和 $D_2$ 和 $D_4 \mathrm{OFF}$. 在两个半周期中,通过负载电阻 的电流方向相同。因此,每半个周期,输出电压出现相同的极性。由公式 (2.13) 可知,全波整流电路的输出直流电压是半波整流电路的两倍,因为它的周期是半波整流电 路的一半,
$$
\left[V_{d c}\right] \text { full-wave }=\frac{1}{T} \int_0^T v_o(t) d t \quad=2[V d c] \text { half-wave }=\frac{2 V_m}{\pi} .
$$
类似地,通过应用等式找到全波整流器的 RMS 输出电压 $(2.16)$
$$
V \mathrm{rms}=\left[\frac{1}{T} \int_0^T v_o^2(t) d t\right]^{\frac{1}{2}}=\frac{V_m}{\sqrt{2}} .
$$
全波整流器的最大可能效率明显高于半波整流器,因为正负周期的功率都可用于产生直流电压,
$$
\eta_{\text {full-wavc }}=\frac{P_{d c}}{P_{a c}}=\frac{\left(2 V_{m / \pi}\right)^2}{R_L} \frac{\left(V_m / \sqrt{2}\right)^2}{R_L}=\frac{8}{\pi^2}=2 \eta_{\text {half-wave }} \Rightarrow 81.2 \%
$$
电气工程代写|数字电路代写digital circuit代考|ZENER DIODES AND APPLICATIONS
设计具有足够功率耗散能力以在击穿时工作的二极管称为齐纳二极管,通常用作电压基准或恒压器件。
造成二极管击穿特性的两种机制是雪崩击穿和齐纳击穿。雪崩击穿发生在高电压 $(\geq 10 \mathrm{~V})$ 其中电荷载流 子获得足够的能量来产生充当二次载流子的二次空穴-电子对。这种连锁反应导致二极管结的雪崩击穿和击 穿电压下电流的快速增加。齐纳击穿发生在重掺杂 $p$ – 和 $n$-二极管结两侧的区域,当外部施加的电势足够大 以在结上产生大电场以迫使束缚电子从 $p$ 型材料隧道穿过 $n$ 型区域。当施加足够的外部电势以产生隧穿所需 的电离能时,会观察到电流的突然增加。
无论击穿机制如何,击穿二极管通常称为齐纳二极管。低压 (指击穿电压) 稳压二极管的符号和特性曲线 如图2.33所示。正向偏置特性类似于传统的 $p-n$ 结二极管。反向偏置区域描绘了发生在 $V_Z$ 这几乎与二极 管电流无关。市售的齐纳二极管范围广泛,击穿电压和额定功率范围广泛,可用于 $100 \mathrm{~W}$.
温度的变化通常会导致击穿电压的变化。温度系数约为 $+2 \mathrm{mV} /{ }^{\circ} \mathrm{C}$ 用于齐纳击穿。对于雪崩击穿,温度系 数为负。
齐纳二极管的简化 SPICE 模型与传统二极管相同,但增加了反向击穿“拐点”电压 $B_V$ 和相应的反向击穿“拐 点”电流 $I_{B V}$. 之间的关系 $R_V$ 和 $I_{B V}$ 如图 $2.34$ 中齐纳二极管的齐纳二极管特性曲线的反向偏置部分所示。为 了获得更陡峭的反向击穿特性,需要更高的击穿电流 $I_{B V}$ 一般来说,可以使用而不会产生重大错误。图的 齐纳二极管模型声明 $2.34$ 用途 $B_V=5$ 和 $I_{B V}=10 \mathrm{~m}$ 对于齐纳电压 $5 \mathrm{~V}$ 在 $10 \mathrm{~mA}$. 两个都 $B_V$ 和 $I_{B V}$ 是正 数。如果 $I_{B V}$ 越大,反向击穿曲线越陡。
齐纳二极管在反向击穿区的动态电阻, $r_Z$ ,然后是二极管曲线在工作反向偏置电流下的斜率。由于反向电 流随着二极管压降的微小变化而迅速增加, $r_Z$ 很小 (通常为 1 到 $15 \Omega$ ) 。齐纳二极管分段线性模型及其简 化版如图所示 $2.35$.

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