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Chapter1: Diodes 1

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sedr42021_0301a.jpg Figure 2.1 The ideal diode: (a) diode circuit symbol; (b) i–v characteristic; (c) equivalent circuit in the reverse direction; (d) equivalent circuit in the forward direction.

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**Electrostatics of PN Junction**

NA ND Max Electric Field Depletion width 3

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**Depletion region expands with reverse bias**

Diode Connections Reverse bias connection Depletion region expands with reverse bias

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Forward connection For silicon diodes, the typical forward voltage is 0.7 volts, For germanium diodes, the forward voltage is only 0.3 volts.

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**Typical I-V Characteristics**

Thermal Voltage VT=k*T/q

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**Figure 2.7 The i–v characteristic of a silicon junction diode.**

sedr42021_e0305.jpg Figure 2.7 The i–v characteristic of a silicon junction diode.

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**i=is (ev/nVT -1) (¤) v=n VT ln(i/iS)**

The forward-Bias Region: It is entered when the terminal voltage v is positive. In the forward region the i-v relationship is closely approximated by: i=is (ev/nVT -1) (¤) Where VT=KT/q k=Boltzmann’s constant= 1.38*10-23 joules/kelvin T=the absolute temperature in kelvins=273+temperature in °C q=The magnitude of electronic charge= 1.6*10-19 coulomb n has a value between 1 and 2 For appreciable current I in the forward direction, specially for i>>Is, (¤) can be approximated by the relationship i=is ev/nVT v=n VT ln(i/iS) Example: A silicon diode said to be a 1mA device displays a forward voltage of 0.7v at a current of 1mA. Evaluate the junction scaling constant IS in the event that n is either 1 or 2. Solution: Since i=Is ev/nVT Then Is=i e-v/nVT n=1: Is= 10-3e-700/25=6.9*10-16A N=2: Is= 10-3e-700/50=8.3*10-10A

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Figure A simple circuit used to illustrate the analysis of circuits in which the diode is forward conducting. Example: Determine the current ID and the diode voltage VD of the circuit with VDD=5V and R=1kΩ. Assume that the diode has a current of 1mA at a voltage of 0.7V and that its voltage drop changes by 0.1V for every decade change in current. Solution: we assume that VD=0.7V Then , by employing the equation and considering That 2.3nVT =0.1V, we obtain: V1=0.7V, I1=1mA and I2=4.3mA results in V2=0.763V. Thus results permit to us to get: and sedr42021_e0309.jpg

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Resistance Levels sedr42021_0312.jpg Figure Approximating the diode forward characteristic with two straight lines: the piecewise-linear model.

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**iD=(vD –VDD)/rD , vD >VDD**

Figure Piecewise-linear model of the diode forward characteristic and its equivalent circuit representation. sedr42021_0313a.jpg The straight-lines (or piecewise linear) model of the fig (a) can be described by: iD=0 , vD <VDD iD=(vD –VDD)/rD , vD >VDD

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Application: 1- In case of DC current, Determine the dc resistance levels for the diode at (a) ID=2 mA (b) ID= 20 mA (c) VD=-10 V

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sedr42021_0317a.jpg Figure Development of the diode small-signal model. Note that the numerical values shown are for a diode with n = 2.

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**Application 2: In case of AC current :**

(a) Determine the ac resistance at ID= 2 mA. (b) Determine the ac resistance at ID =25 mA. sedr42021_0314.jpg

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**Load Line Analysis From the circuit above,**

Figure Graphical analysis of the circuit in Fig using the exponential diode model. sedr42021_0311.jpg From the circuit above, If we consider the 2 equations, we obtain the Q point in the intersection with the curve of the diode response I=f(V)

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**Series of Diode configurations**

sedr42021_0302a.jpg Figure 2.2 The two modes of operation of ideal diodes and the use of an external circuit to limit the forward current (a) and the reverse voltage (b).

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sedr42021_0305a.jpg Figure 2.5 Diode logic gates: (a) OR gate; (b) NAND gate (in a positive-logic system).

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**Example: Find the values of I and V in the circuits shown in Fig E2.4**

sedr42021_e0304a.jpg Example: Find the values of I and V in the circuits shown in Fig E2.4

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Application: 1- Determine Vo, I1, ID1, and ID2 for the parallel diode configuration of the figure shown below 2- Determine I1, I2, and ID2 for the parallel diode configuration of the figure shown below sedr42021_0316a.jpg

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**Homework: Assuming the diodes to be ideal, find the values of I and V in the circuit**

sedr42021_0306a.jpg Figure 2.6 Circuits for Example 3.2.

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Zener Diode Figure Circuit symbol for a zener diode and its Model. sedr42021_0320.jpg Figure The diode i–v characteristic with the breakdown region shown in some detail.

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Application: 1- (a) For the Zener diode network, determine VL, VR, IZ, and PZ. (b) Repeat part (a) with RL = 3 k. Homework: Ex 42 P130

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**Find V0 with no load and with V+ at its nominal value **

Figure (a) Circuit for Example 2.8. (b) The circuit with the zener diode replaced with its equivalent circuit model. The -6.8v zener diode in the circuit is specified to have Vz =6.8v at Iz=5.mA. rs=20, and Izk=20mA. The supply voltage V+ is nominally 10v but can vary by ±1v Find V0 with no load and with V+ at its nominal value Find the change in V0 resulting from the ±1 vchange in V+ . Note that (ΔV0/ΔV+), usually expressed in mV/V, is known line regulation Find the change in V0 resulting from connecting a load resistance RL that draws a current IL=1mA, and hence find the load regulation (ΔV0/ΔIL), in mV/mA. Find the change inV0 when RL=2kΩ Find the value of V0 when RL=0.5kΩ What is the minimum value of RL for which the diode still operates in the breakdown region sedr42021_0323a.jpg

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**Diodes in AC analysis with Ac source**

sedr42021_0303a.jpg Figure 2.3 (a) Rectifier circuit. (b) Input waveform. (c) Equivalent circuit when vI 0. (d) Equivalent circuit when vI 0. (e) Output waveform.

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Figure E2.1 sedr42021_e0301.jpg Figure E2.2

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**Figure 2.4 Circuit and waveforms for Example 3.1.**

Example: (a) shows a circuit for charging a -12v battery. If Vs is a sinusoid with 24v peak amplitude. Find the fraction of each cycle during which the diode conducts. Also, find the peak value of the diode current and the maximum reverse-bias voltage that appears across the diode Solution: The diode conducts when Vs exceeds 12v. As shown in Fig2.4 (b). The conduction angle is 2θ, where θ is given by: 24 cosθ= 12 Thus θ=60° and the conduction angle is 120°, or one-third of a cycle. The peak value of the diode current is given by The maximum reverse voltage across the diode occurs when Vs is at its negative peak and is equal to 24+12=36V sedr42021_0304a.jpg

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**Figure 2.24 Block diagram of a dc power supply.**

APPLICATIONS OF DIODES: Diodes are used in so many ways that we will not be able to discuss all of them. The major applications of the diodes that will be discussed are: Rectifiers Clippers or Limiters Clampers Voltage Multipliers sedr42021_0324.jpg Figure Block diagram of a dc power supply.

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Half-wave rectifier Conduction region ( T/2).

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**No conduction region (T/2 T).**

Half-wave rectified signal

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**Effect of VK on half-wave rectified signal.**

If we consider a network for the example

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**The resulting vo for the circuit**

If we consider the effect of VK on output of Figure

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**Full-wave bridge rectifier**

Network of this Figure for the period T/2 of the input voltage vi.

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**Conduction path for the positive region of vi.**

+

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That’s why if we consider the Input and output waveforms for a full-wave rectifier, we will obtain the following result Determining VOmax for silicon diodes in the bridge configuration.

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**Full-Wave Rectifier using a center-tapped secondary**

Network conditions for the positive region of vi.

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**Series clipper with a dc supply: if we consider the following figure**

Network conditions for the negative region of vi. Series clipper with a dc supply: if we consider the following figure

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sedr42021_0325a.jpg Figure (a) Half-wave rectifier. (b) Equivalent circuit of the half-wave rectifier with the diode replaced with its battery-plus-resistance model. (c) Transfer characteristic of the rectifier circuit. (d) Input and output waveforms, assuming that rD ! R.

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sedr42021_0326a.jpg Figure Full-wave rectifier utilizing a transformer with a center-tapped secondary winding: (a) circuit; (b) transfer characteristic assuming a constant-voltage-drop model for the diodes; (c) input and output waveforms.

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sedr42021_0327a.jpg Figure The bridge rectifier: (a) circuit; (b) input and output waveforms.

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sedr42021_0328a.jpg Figure (a) A simple circuit used to illustrate the effect of a filter capacitor. (b) Input and output waveforms assuming an ideal diode. Note that the circuit provides a dc voltage equal to the peak of the input sine wave. The circuit is therefore known as a peak rectifier or a peak detector.

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sedr42021_0329a.jpg Figure Voltage and current waveforms in the peak rectifier circuit with T. The diode is assumed ideal.

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**Figure 2.30 Waveforms in the full-wave peak rectifier.**

sedr42021_0330.jpg

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**Applications: Voltage doubler**

sedr42021_0338a.jpg Figure Voltage doubler: (a) circuit; (b) waveform of the voltage across D1.

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