Introduction to Microelectronics1

DIODE CIRCUITS

1 DC and low-frequency diode models

2 The diode-resistance circuit

3 Peak and power detectors

4 Rectifiers

5 Thermal sensor

Introduction to Microelectronics2

A

C

A

C

"On"

C

A

"Off"

"Short" Circuit

"Open" Circuit

+

-E

10 kΩ

VDID

+

-10 V

R

D

D

E VI

R

−=

10k Ω

10VI D =

1mAID =

Ideal diode model

Introduction to Microelectronics3

iD

iD

(a) (b)

vD Von

I = 10 – 0.6

10 k ΩI = 0.94 mA

•••• Constant-voltage-drop model Constant-voltage-drop +

resistance model

What if the input voltage is 1 V? 0.1V?

+

-10 V

10 kΩ

ID

-

(c)

V = 0.6 Von

I = ID

+

Introduction to Microelectronics

Graphical analysis

65432100.000e+0

2.000e-4

4.000e-4

6.000e-4

8.000e-4

1.000e-3

1.200e-3

1.400e-3

1.600e-3

1.800e-3

2.000e-3

Diode Voltage (V)

Dio

de C

urr

en

t (A

)

Load Line

Q-Point

Diode i-v characteristic and load line

ID (A)

VD (Volt)

D

D

E VI

R

−=

4

+

-E

10 kΩ

VDID

+

-10 V

R

Introduction to Microelectronics5

+

- R

iD

D1

v = VP

sin ω t S

0.0200.0150.0100.0050.000-15

-10

-5

0

5

10

15

Time (sec)V

olt

age (

V)

InputVoltage

OutputVoltage

InputVoltage

OutputVoltage

Half VP = 10 V and Von = 0.7 V

Simplified analysis

VS ≤ Von → Diode is ON

VS > Von → Diode is OFF

VS

VOVO = VS

Von

Half-wave rectifier circuit:

resistive load

R

V

π

1i

p

D =

R

Vi

p

Dmax =

If Vp >> Von

PIV = Vp

( average value )

Introduction to Microelectronics

6

If you know I, it is simple to

calculate E

ln 1t

S

IE RI n

Iφ

= + +

I/IS E (mV)

0 0

1 50 ln2

9 50 ln10

103 10+50 ln103

106 104 + 50 ln106

-0.5 -50 ln2

-0.9 -50 ln10

-1 -∞

-9 ???????

Example:

R= 10 kΩΩΩΩ,

IS=1 nA, nφφφφt = 50 mV

As you can see, for this specific example

the resistor does not play an important

role for current less than 1 µA whereas the

diode voltage drop is small for currents

greater than, say, 1 mA.

+

-E

10 kΩ

VDID

+

-10 V

R

Introduction to Microelectronics

+ vD -

iD

1φ

= −

DD S

vi I exp

tn

φt = kT/q

0.10.0-0.1-0.2

0.0

Diode Voltage (V)

Dio

de C

urr

ent

(A)

IS

7

In an IC implementation, most diodes (or diode-connected MOSFETs)

can be represented by Shockley equation.

IS (saturation current)- design parameter.

25

1

mV @ 290 K

to 1.5

t

n

φ ≅

∼

Introduction to Microelectronics

Voltage rectifier: fundamentals

Steady-state analysis

Basic principle: charge conservation/

average current through diode = 0

/ 2

/2

10

T

D

T

I dtT

−

=∫ [ 1]

D

t

V

n

D SI I e

φ= −

0 /2

/2 0

1 1 0

P o P o

t t

V V V VT

n nS

T

Ie dt e dt

T

φ φ

− − −

−

− + − =

∫ ∫

Assumption: very low ripple (high C)

→ Vo ≅ constant

( )ln ln cosh2

P t P tV n V no

P tt

V e eV n

n

− + = =

φ φ

φφ

8

A simple case: square-wave input

Introduction to Microelectronics

Power/Peak Detector

A simple case: square-wave input

( )ln cosh φφ

= o

P tt

VV n

n

φ<<P tV n

2

1

2

o P

t t

V V

n nφ φ

≅

→

Power Detector

Peak Detector

φ>>P tV n ln 2φ≅ −L P t

V V n→

Why?Input

Diode “ON”

voltage drop

Results for sine input are similar.

Difference is a “form factor”

Introduction to Microelectronics

Voltage rectifier: fundamentals

10

IS

IS

A simple case: square-wave input

Waveforms for φ>>P tV n

Introduction to Microelectronics11

Steady-state analysis

Waveforms for φ>>P tV n

0 /2

/2 0

1 1

P o P o

t t

V V V VT

n nS

L

T

Ie dt e dt I

T

φ φ

− − −

−

− + − =

∫ ∫

( )coshln

1 /

φ

φ

=

+

P to

t L S

V nV

n I I

Assumption: very low ripple → Vo ≅ constant

Voltage rectifier: fundamentals

IL+IS IL+IS

IS

2IL+IS IL

Introduction to Microelectronics12

Output voltage ripple

C C

C L S

dQ dVI C I I

dt dt= = ≅ +

The discharge rate of the capacitor diode

during the negative half-cycle of the input is

0

/22 2

L S L S

C

T

I I I ITdV V

C fC−

+ += ∆ ≅ =∫

Voltage rectifier: fundamentals

IL+IS IL+IS

IS

2IL+IS

IL

Introduction to Microelectronics

Gaussian

function

Voltage rectifier: fundamentalsSine-wave input Steady-state analysis

Basic principle: charge conservation/ 2

/2

1T

D L

T

I dt IT

−

=∫ [ 1]

D

t

V

n

D SI I e

φ= −

cos cos0

0

1 12

A o A o

t t

V V V V

n nS

L

Ie d e d I

− − −

−

− + − = ∫ ∫

θ θπφ φ

π

θ θπ

Assumption: very low ripple (high C)

→ Vo ≅ constant

13

modified Bessel function of

the first kind of zero order

( )0Iln

1

A to

t L S

V nV

n I I

=

+

φ

φ

( ) cos

0

0

1I

π

θ θπ

= ∫zz e d

cosin AV V= θ

VA

= 4.5 V, f=120 Hz, IL=4µA. I

S=

4.4 nA, nφt= 50 mV, C=150 nF.

Introduction to Microelectronics14

Voltage doubler → Clamping circuit & peak detector

D1, C1, and Vin →half-wave rectifier.

VC1 stored in C1 is a dc voltage equal

to that of a half-wave rectifier. VX

=

Vin+VC1. The dc output voltage of the

doubler is equal to the value calculated

for the half-wave rectifier plus VC1.

12L CV V=

The voltage multiplier

Introduction to Microelectronics15

Voltage doubler

The voltage multiplier

= =+

load L L

in load loss

P V IPCE

P P P

max)2(

@ L L

t S

V IPCE PCE

N n I= =

Φ

N-stage voltage multiplierVoltage doubler

PCE: Power Conversion Efficiency

Introduction to Microelectronics16

Applications:

Generation of voltages higher than the supply voltage, for

EEPROMs, flash memories

Energy harvesting for RFID tag chips, for example

The voltage multiplier

N-stage voltage multiplier

Introduction to Microelectronics17

The voltage multiplier model

N-stage voltage multiplier

DC Average diode capacitance

2

2= A

in

in

VR

P

≃RET DC NC( ) ( )1 0

′=ap apI v I v

Introduction to Microelectronics

VD1 VD2

18

Temperature sensor

1 21 2

1 2 1

2

ln 1 ln 1

ln ln ln

o D D tS S

o t tS S

I IV V V n

I I

I I IV n n

I I I

φ

φ φ

= − = + − +

≅ − =

Introduction to Microelectronics 19

References– EEL 7061 Eletrônica Básica

http://www.lci.ufsc.br/electronics/index7061.htm

– Charles Sodini, “6.012 Microelectronic Devices and Circuits, ” OpenCourseWarehttp://ocw.mit.edu

– R. Jaeger, “Microelectronic Circuit Design,” McGraw-Hill, New York, 1997.

– A. J. Cardoso, L. G. de Carli, C. Galup-Montoro, and M. C. Schneider, “Analysis of the Rectifier Circuit Valid Down to Its Low-Voltage Limit,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 59, no. 1, pp. 106 - 112, .–January 2012.

– A. J. Cardoso, Modelagem e projeto de conversores ac/dc de ultrabaixa tensão de operação, Tese de doutorado, UFSC, 2012

– L. G. de Carli, Modelagem e projeto de retificadores de múltiplos estágios para ultrabaixa tensão de operação, Trabalho de conclusão de curso, UFSC, 2013.

– P. Curty, N. Joehl, F. Krummenacher, C. Dehollain, and M. Declercq, “A model for u-power rectifier analysis and design,”IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 52, no. 12, pp. 2771–2779, Dec. 2005.