# 电气工程代写|数字电路代写digital circuit代考|EECS312

## 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

$$\left[V_{d c}\right] \text { full-wave }=\frac{1}{T} \int_0^T v_o(t) d t \quad=2[V d c] \text { half-wave }=\frac{2 V_m}{\pi} .$$

$$V \mathrm{rms}=\left[\frac{1}{T} \int_0^T v_o^2(t) d t\right]^{\frac{1}{2}}=\frac{V_m}{\sqrt{2}} .$$

$$\eta_{\text {full-wavc }}=\frac{P_{d c}}{P_{a c}}=\frac{\left(2 V_{m / \pi}\right)^2}{R_L} \frac{\left(V_m / \sqrt{2}\right)^2}{R_L}=\frac{8}{\pi^2}=2 \eta_{\text {half-wave }} \Rightarrow 81.2 \%$$

## 电气工程代写|数字电路代写digital circuit代考|ZENER DIODES AND APPLICATIONS

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