Microelectronic Circuits I Ch 3: Diodes

Microelectronic Circuits I Ch 3: Diodes

3.1 Ideal diode

3.2 Terminal characteristics of Junction diodes 3.3 Modeling the diode forward characteristics

Introduction

Resistor

Two-terminal

Linear i-v relationship V=iR

Diode

Two-terminal

Nonlinear i-v relationship Switch-like characteristics Similarity

Difference

- OP amp : linear amplifier

- Nonlinear circuit : ac-dc conversion, various waveform generation (sinusoidal, square wave, pulses, tec.)

- Simplest & most fundamental nonlinear circuit element : diode

Ideal Diode

Reverse-biased (cut off, off) Forward-biased (turned on, on)

• Diode symbol • i-v characteristics (piecewise linear)

open circuit short circuit

How to Limit Forward Current and Reverse Voltage

The forward current through a conducting diode & the reverse voltage across a cutoff diode are determined by an external circuit

Simple application : Rectifier

Input v_I

• bipolar

• <v_I>=0

v_I > 0 v_I < 0

Output v_O

• unipolar

• < v_O>=dc

• dc-ac converter

• rectifier

Forward biased àshort circuit reverse biased àopen circuit

Diode Logic Gates

Common cathode OR gate

Y = A + B + C

Common anode AND gate Y = A • B • C

0V : logic 0 5V : logic 1

Figure 3.6 Circuits for Example 3.2.

EXAMPLE 3.2

2

10 0 10 1 mA

ID -

= =

0 ( 10)

1 5

I - -

+ =

2

10 ( 10)

1.33 mA

D 15

I - -

= =

2

10 0 2 mA

D 5

I -

= =

0 ( 10)

2 10

I - -

+ =

I=1mA V=0V D₁, D₂ on

I=0 V=3.3V

D₁ off, D₂ on

(b) (a)

Terminal Characteristics of Junction Diodes

Reverse(v < 0) Breakdown (v < -V_ZK )

Cut-in voltage

Forward-bias (v > 0)

Forward-Bias Region ( v > 0 ): i-v Characteristics

(

^{- 1} )

= I

e

i

• I

: saturation current or scale current

- Proportional to the junction area - 10^-12~10^-15 A

-Temperature dependence: doubled / 5^oC

• V

(thermal voltage) = kT/q = 25 mV @ T = 20

C

- k (Boltzman’s constant) = 1.38 x 10^-23 [joules/kelvin]

- T = the absolute temperature in kelvins = 273 + temperature in ^oC - q = the magnitude of electronic charge = 1.60 × 10^-19 coulomb - n : 1 ~ 2 (normally 1) , depends on material & physical structure

( )

/

when ln /

v nVT

S S

T S

i I e i I

v nV i I

» >>

=

Forward-Bias Region

( )

1

2

2 1

/ 1

/ 2

/

2 1

2 1 2 1

2 1 2 1

/

ln /

or 2.3 log /

T

T

T

V nV S

V nV S

V V nV

T

T

I I e I I e

I I e

V V nV I I

V V nV I I

-

ì = ïí ï = î

® =

\ - =

- =

For a decade change in current, the voltage drop changes by 2.3nV_T

(60mV for n=1, 120mV for n=2 or 0.1V/decade, approximately) For a decade change in current, the voltage drop changes by 2.3nV_T

(60mV for n=1, 120mV for n=2 or 0.1V/decade, approximately)

V₁ V₂ I₂

I₁

v i

Cut-in voltage (0.5V)

where, ln 10 = 2.3

10 ln log₁₀ ln A

A =

Reverse-Bias and Breakdown Regions

l Reverse-bias region (v < 0 & v > 2~3 V

)

l Breakdown region (v < -V

)

– Z : Zener, K : Knee

( )

S

nV v S

I e I

i

-

=

-

=

1

i is reverse directed & constant à Saturation current

I_S doubles for every 5^oC rise in temperature

§ Reverse current increases rapidly, with the small increase in voltage drop

§ Not destructive

Exponential Model

R V I

V

-

=

T D nV V S

D

I e

I =

by KVL

by exponential model

V_D & I_D ? 1) graphical analysis 2) iterative analysis

§ Assume V_DD > 0.5V, I_D >> I_S

§ The most accurate but hard to use

Modeling the Diode Forward Characteristic

V_DD=5V, R=1kW : V_D = 0.738V

I_D =4.262mA

Constant-Voltage-Drop Model

V 0.7

5 0.7

= 4.3 mA

DD

ID

R

= -

- =

r_D = 0

V_D= 0.7V

V_D = 0.7V

simpler model for diode forward characteristics

à a forward-conducting diode exhibits a constant voltage drop V_D (=0.7V).

à most frequently employed in the initial phases of analysis & design

Constant-voltage-drop model for Ex. 3.5 V_D = 0.7V

Ideal Diode Model

Application voltage >> diode voltage drop (0.6V – 0.8V) à neglect the diode voltage drop V_D =0V

à most frequently employed in the initial phases of analysis & design

Constant-voltage-drop model for Ex. 3.5 V_DD = 5V, R=1kW

R mA V I V

V V

D DD

D D

1 5 0 5 0

- = - =

=

=

Diode Small-Signal Model

DC bias Small-signal

Application, where a small ac signal is superimposed on the dc quantities 1) determine the dc operating point (V_D & I_D) by using 0.7V drop model

2) diode is modeled by r_d, the inverse of the slope of the tangent to the exponential model at the dc bias point

Diode Small-Signal Model

( )

( ) /

( ) / / ( ) /

/

or

( ) ( )

( ) ( )

( ) 1 , when 1

, where 1 ,

Here 1/

D T

D d T D T d T

D T

D D

D D d

v t nV

D S

V v t nV V nV v t nV

D S S

d D d

D D D d

T T T

V nV D

D D d d d d D S

T d

T D

d

D D v V

v t V v t

i t I e

i t I e I e e

v I v

i t I I v

nV nV nV

i I i i I v v I I e

nV r

nV i

r I v

+

=

= +

¯ =

= =

æ ö

® » ç + ÷ = + <<

è ø

\ = + = = =

= = ¶

¶

D D

i =I

: Diode small-signal resistance, or incremental resistance

T D nV V S D I e

I = ^/ In the absence of the signal v_d(t),

dc current I_D w/ dc voltage V_D only (n=1) Total instantaneous diode voltage v_D(t)

Small-signal approximation (when v_d < 10mV for n=2, 5mV for n=1, V_T=25mV)

§ r_d is inversely proportional to the bias current I_D.

T d t nV v

De

I ^{( )/}

=

(a) Circuit for Example 3.6. (b) Circuit for calculating the dc operating point.

(c) Small-signal equivalent circuit.

EXAMPLE 3.5

10 0.7

0.93 mA

D 10

I -

= =

Power supply V⁺ : 10V dc + 1 V_peak, 60Hz sinusoid (power-supply ripple) R : 10 kW, diode : 0.7V at 1mA, n=1

dc voltage V_D & the amplitude of the sine-wave signal v_d ?

v_d < 5mV for n=1,

Small-signal model is

O.K

mV r

R V r

peak v

I r V

d d peak d

D T d

68 . 0269 2 .

0 10

0269 . 1 0 ) (

9 . 93 26

. 0

25

+ =

=

= +

W

=

=

=