Chapter1: Diodes

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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

Reverse bias connection

Depletion region expands with reverse bias

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Diode Connections

Forward connection

For silicon diodes, the typical forward voltage is 0.7 volts, For germanium diodes, the

forward voltage is only 0.3 volts. 5

Typical I-V Characteristics

VT=k*T/q

Thermal Voltage

Figure 2.7 The i–v characteristic of a silicon junction diode.7

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/kelvinT=the absolute temperature in kelvins=273+temperature in °Cq=The magnitude of electronic charge= 1.6*10-19 coulomb

n has a value between 1 and 2For 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*10-16AN=2: Is= 10-3e-700/50=8.3*10-10A

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Figure 2.10 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

mAR

VVI DDD

D 3.41

7.05

1

212 log3.2

I

InVVV T

1

212 log3.2

I

InVVV T

mAID 237.41

763.05

VV 762.0

3.4

237.4log1.0763.02

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Figure 2.12 Approximating the diode forward characteristic with two straight lines: the piecewise-linear model.

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Resistance Levels

Figure 2.13 Piecewise-linear model of the diode forward characteristic and its equivalent circuit representation.

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

Figure 2.17 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.

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Figure 2.11 Graphical analysis of the circuit in Fig. 3.10 using the exponential diode model.

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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Load Line Analysis

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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Series of Diode configurations

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

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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

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Figure 2.6 Circuits for Example 3.2.

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

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Figure 2.20 Circuit symbol for a zener diode and its Model.

Zener Diode

Figure 2.21 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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Figure 2.23 (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

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

b)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

c)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.

d)Find the change inV0 when RL=2kΩ

e)Find the value of V0 when RL=0.5kΩ

f)What is the minimum value of RL for which the diode still operates in the breakdown region23

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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Diodes in AC analysis with Ac source

Figure E2.1

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= 12Thus 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

AR

VVI S

d 12,0100

12240max

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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

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Half-wave rectifier

Conduction region (0 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 0 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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Network conditions for the negative region of vi.

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

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Figure 2.25 (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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Figure 2.26 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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Figure 2.27 The bridge rectifier: (a) circuit; (b) input and output waveforms.

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Figure 2.28 (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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Figure 2.29 Voltage and current waveforms in the peak rectifier circuit with CR @ T. The diode is assumed ideal.

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Figure 2.30 Waveforms in the full-wave peak rectifier.

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Figure 2.38 Voltage doubler: (a) circuit; (b) waveform of the voltage across D1.

Applications: Voltage doubler

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