The ideal Diode

Diodes

Figure 3.1 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.

The ideal Diode

 Diode – nonlinear circuit element

Current-voltage characteristics

1) reverse bias → cut off 2) forward bias → turn on

 The external circuit limits the forward current and the reverse voltage.

- Forward current

- Reverse voltage

The ideal Diode

Figure 3.2 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).

10V /1k = 10mA

iD  

10 1k 0 = 10V

D   

Figure 3.3 (a) Rectifier circuit. (b) Input waveform. (c) Equivalent circuit when v_I  0. (d) Equivalent circuit when v_I < 0. (e) Output waveform.

The ideal Diode

Rectifier

1) +tive half cycle

→ forward bias (short) 2) -tive half cycle

→ reverse bias (open)

Ex 3.1

The diode conducts when _s > 12V. The conduction angle is 2q.

,

The peak value of the diode current

The maximum reverse voltage across the diode occurs when _s is at its negative peak.

_s= _D +12 , -_D =- _s +12=24+12=36V

Figure 3.4 Circuit and waveforms for Example 3.1.

24 cos = 12 q

24 12

0.12 A

d 100

I   

The ideal Diode

= 60o

q

The ideal Diode

Figure 3.5 Diode logic gates: (a) OR gate; (b) AND gate (in a positive-logic system).

Diode logic gates

The circuit in Fig. 3.5(a) → logic OR function

The circuit of Fig. 3.5(a) → logic AND function

Y = A + B + C

Y = A B C  

Figure 3.6 Circuits for Example 3.2.

Ex 3.2

1) For the circuit in Fig. 3.6(a), we shall assume that both diodes are conducting.

V_B= 0V , V= 0V

The current through D₂ I_D2= (10 - 0)/10= 1mA

Writing a node equation at B, I+1= (0 -(- 10))/5, I= 1mA

Thus D₁ is conducting as originally assumed.

2) For the circuit in Fig. 3.6(a),

i) if we assume that both diodes are conducting, V_B= 0V , V= 0V.

The current in D₂

I_D2= (10-0)/5= 2mA The node equation at B is

I+2= (0 -(- 10))/10. I = -1mA → incorrect assumption

ii) Assuming that D₁is off, D₂ is on, I_D2= (10 -(- 10))/15= 1.33mA V_B= - 10+10ⅹ1.33= 3.3V

Thus D₁is reverse biased as assumed, and the final result is I= 0mA and V= 3.3V.

The ideal Diode

Figure 3.7 The i–v characteristic of a silicon junction diode.

 Operational region of diodes

1) The forward-bias region : v > 0

2) The reverse-bias region : -V_ZK < v ≤ 0 3) The breakdown region : v < -V_ZK

Terminal Characteristics of Junction Diodes

The forward-bias region

I_S : (reverse) saturation current V_T : thermal voltage

k = Boltzmann’s constant = 1.38ⅹ10^-23 joules/kelvin

T = the absolute temperature in kelvins = 273+temperature in ^oC q = the magnitude of electron charge = 1.60ⅹ10^-19 coulomb

(

1) i  I e



Figure 3.8 The diode i–v relationship with some scales expanded and others compressed in order to reveal details.

At room temperature(20^oC), V_T = 25.8㎷ ≈ 25㎷.

The constant, n = 1~ 2.

Specially for the forward current, i ≫ I_s

or

υ/ Vn _T

i  I e

ln

S

v nV i

 I

Terminal Characteristics of Junction Diodes

V_T kT

 q

Let us consider the forward i-v relationship

,

In terms of logarithms,

1/ V

1

V n T

I  I es I₂ I e_s ^{V2/ Vn T}

2 1

( ) / V 2

1

V V n T

I e

I

 

2

2 1

1

V V V ln_T I

n I

 

2

2 1

1

V V 2.3 V log_T I

n I

 

The reverse-bias region

If |v| ≫ V_T

: reverse saturation current

The breakdown region

When v < -V_ZK (breakdown voltage), the reverse current increases rapidly,

with the associated increase in voltage drop being very small as shown in Fig. 3.8.

i  I

characteristic. At a constant current, the voltage drop decreases by approximately 2 mV for every 1C increase in temperature.

Temperature dependence of the diode characteristic

Terminal Characteristics of Junction Diodes

The Exponential Model

Assuming that V_DD ≥ 0.5 V,

By KVL, : load line

→ Two equations with two unknown quantities I_D and V_D. Figure 3.10 A simple circuit used to illustrate the analysis of circuits in which the diode is forward conducting.

V / V_D n _T

D S

I  I e

DD D

D

V V

I R

 

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

 Graphical analysis

The solution can be obtained as the coordinates of the point of intersection of two graphs. (operating point or quiescent point) Its coordinates give the values of I_D and V_D.

Modeling The Diode Forward Characteristic

 Iterative analysis

Ex 3.4

Assuming that V_D=0.7V,

By the diode equation,

For this case, 2.3V_T=0.6V.

The 1^st iteration results are I_D=4.3mA and V_D=0.738V.

The 2nd iteration proceeds in a similar manner:

V V 5 0.7

4.3 mA 1

DD D

ID

R

 

  

2

2 1

1

V V 2.3 V log_T I

n I

 

5 0.763

4.237 mA

D 1

I   

0.7V 0.738V 4.3mA

4.262mA

1mA

5mA

5V

Modeling The Diode Forward Characteristic

The constant voltage-drop model

From Ex 3.4 ,

The ideal-diode model

From Ex 3.4 ,

V

0.7 V V 0.7 5 0.7

= 4.3 mA

1

DD

ID

R

 

 

V

0 V 5 0

1 5 mA

Modeling The Diode Forward Characteristic

Figure 3.12 Development of the diode constant-voltage-drop model: (a) the exponential characteristic; (b) approximating the exponential characteristic by a constant voltage, usually about 0.7 V_i; (c) the resulting model of the forward–

conducting diodes.

The small-signal model

v_D(t) = V_D (v_d=0),

v_D(t) = V_D +v_d(t),

Thus,

If ,

: small-signal approximation

* It is valid for signals whose amplitudes are smaller than about 5㎷ for n=1.

Figure 3.13 Development of the diode small-signal model. Note that the numerical values shown are for a diode with n = 2.

V / V_D n _T

D S

I  I e

(V υ ) / V υ / V

υ / V V / V

( )

d T

D T

n n

D S S

n n

S

i t I e I e

I e e

 



υ / V

( )

D D

i t I e

υ_d nV_T

( ) (1+ ) V

d

D D

T

i t I

n



2 3

1 2! 3!

1

x x x

e x

x

    

 , |x| « 1 일때

Modeling The Diode Forward Characteristic

Figure 1.15 Symbol convention employed throughout the book.

Symbol Convention

 Symbol convention

i

= dc + ac I

= dc i

= ac

I

= the magnitude of ac

) ( )

( t I i t

i





t I

t

i

( ) 

sin w

The small-signal model

v_D(t) = V_D (v_d=0),

v_D(t) = V_D +v_d(t),

Thus,

If ,

: small-signal approximation

* It is valid for signals whose amplitudes are smaller than about 5㎷ for n=1.

Figure 3.13 Development of the diode small-signal model. Note that the numerical values shown are for a diode with n = 2.

V / V_D n _T

D S

I  I e

(V υ ) / V υ / V

υ / V V / V

( )

d T

D T

n n

D S S

n n

S

i t I e I e

I e e

 



υ / V

( )

D D

i t I e

υ_d nV_T

( ) (1+ ) V

d

D D

T

i t I

n



2 3

1 2! 3!

1

x x x

e x

x

    

 , |x| « 1 일때

Modeling The Diode Forward Characteristic

* Analysis of diode or transistor circuits → dc bias analysis + ac small-signal analysis Signal current directly proportional to the signal voltage v_d

Diode small signal resistance

The slope of the tangent to the i-v curve at the Q-point is equal to the small-signal conductance.

* The small-signal analysis can be performed separately from the dc dc bias analysis.

υ

V

d

d D

r n

i I

 

1

D D

D d

D i I

r i

 _

  

  

( ) + +

V

D

D D d D d

T

i t I I I i

n 

 

V υ

D

d d

T

i I

 n

Modeling The Diode Forward Characteristic

Ex 3.5

Diode incremental resistance

Peak amplitude of the diode small-signal voltage

Figure 3.14 (a) Circuit for Example 3.5. (b) Circuit for calculating the dc operating point. (c) Small-signal equivalent circuit.

10 0.7

0.93 mA

D 10

I   

V 2 25

53.8 0.93

T d

D

r n I

    

s

0.0538

(peak) V 1 5.35 mA

10 0.0538

d d

d

r R r

  ^  

 

Modeling The Diode Forward Characteristic

Use of the diode forward drop in voltage regulation

Ex 3.6

With no load, we assume V_D=0.7V.

Assuming n=1,

The three diodes in series will have a total incremental resistance of

The ripple in output voltage

→ ±0.5%

(b) connection of a 1㏀ load resistance

The load current is about 2.1mA, and the diode current decreases by 2.1mA.

→ decrease in diode voltage

Figure 3.19 Circuit for Example 3.6.

10 2.1

7.9 mA I  1 

V 2 25 7.9 6.3

T d

r n

I

    

3 _d 18.9

r  r  

0.0189

2 2 37.1 mV

0.0189 1

O

r r R



   

 

2.1 2.1 18.9 39.7 mV

O r



        

Modeling The Diode Forward Characteristic

Modeling The Diode Forward Characteristic

* Analysis of diode circuits

1) dc bias analysis → Q-point( I_D , V_D )

small-signal equivalent circuit

2) ac small-signal analysis → small-signal voltage and current ( i_d, v_d )

Modeling The Diode Forward Characteristic