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Chapter 3

Lecture Homepage : http://signal.korea.ac.kr

Signal Processing Lab., http://signal.korea.ac.krDept. of Elec. and Info. Engr., Korea Univ.

2016년 6월 27일2 pages

3.3) Modeling The Diode Forward CharacteristicThe Exponential Model

Figure 3.10 A simple circuit used to illustrate the analysis of circuits in which the diode is forward conducting.

V / V (3.6)D TnD SI I e

V V (3.7)DD D

DIR

Kirchhoff loop equation, resulting in

Chapter 3




3.3) Modeling The Diode Forward CharacteristicGraphical Analysis Using the Exponential Model

Figure 3.11 Graphical analysis of the circuit in Fig. 3.10 using the exponential diode model.

Chapter 3




3.3) Modeling The Diode Forward CharacteristicThe Piecewise-Linear Model

Figure 3.12 Approximating the diode forward characteristic with two straight lines: the piecewise-linear model.

0

0 0

0, V( V ) / , V (3.8)

D D D

D D D D D D

ii r

VD0 is the intercept of line B on the voltageaxis and rD is the inverse of the slope ofline B.

Chapter 3





Figure 3.13 Piecewise-linear model of the diode forward characteristic and its equivalent circuit representation.

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Figure 3.10 A simple circuit used to illustrate the analysis

of circuits in which the diode is forward conducting.Figure 3.14 The circuit of Fig. 3.10 with the diode replaced with

its piecewise-linear model of Fig. 3.13.

Chapter 3




3.3) Modeling The Diode Forward CharacteristicThe Constant-Voltage-Drop Model

Figure 3.15 Development of the constant-voltage-drop model of the diode forward characteristics. A vertical straight line (B) is used to approximate the fast-rising exponential. Observe that this simple model predicts VD to within 0.1 V over the current range of 0.1 mA to 10 mA.

Chapter 3




3.3) Modeling The Diode Forward CharacteristicThe Constant-Voltage-Drop Model

Figure 3.16 The constant-voltage-drop model of the diode forward characteristics and its equivalent-circuit representation.

V 0.7

5 0.7 = 4.3 mA1

DDDI

R

Chapter 3




3.3) Modeling The Diode Forward CharacteristicThe Small-Signal Model

Figure 3.17 Development of the diode small-signal model. Note that the numerical values shown are for a diode with n = 2.

Chapter 3




3.3) Modeling The Diode Forward CharacteristicThe Small-Signal Model In the absence of the signal vd(t) the diode voltage is equal to VD, and

correspondingly, the diode will conduct a dc current ID given byV / V (3.9)D Tn

D SI I e

(t) V + (t) (3.10)D D d

/ V( ) (3.11)D TnD Si t I e

(V ) / V( ) D d TnD Si t I e

/ VV / V( ) d TD T nnD Si t I e e

When the signal vd(t) is applied, the total instantaneous diode voltagevd(t) will be given by

Correspondingly, the total instantaneous diode current iD(t) will be

Substituting for vD from Eq. (3.10) gives

which can be rewritten

Chapter 3




3.3) Modeling The Diode Forward CharacteristicThe Small-Signal Model

/ V( ) (3.12)d TnD Di t I e

Using Eq. (3.9) we obtain

if the amplitude of the signal vd(t) is kept sufficiently small such that

(3.13) 1T

d

nVv

then we may expand the exponential of Eq. (3.12) in a series and truncatethe series after the first two terms to obtain the approximate expression

(3.14) 1)(

T

dDD nV

vIti

• This is the small-signal approximation.

Chapter 3




3.3) Modeling The Diode Forward CharacteristicThe Small-Signal Model From Eq. (3.14) we have

( ) + (3.15)VD

D D dT

Ii t I

n

+ (3.16)D D di I i

(3.17)VD

d dT

Ii

n

V (3.18)T

dD

nr

I

superimposed on the dc current ID, we have a signal current component directly proportional to the signal voltage vd. That is,

the diode small-signal resistance, or incremental resistance, rd,

1 (3.19)D D

Dd

D i I

ir

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