EE130 Lecture 27, Slide 1 Spring 2007

Lecture #27

OUTLINE

• BJT small signal model

• BJT cutoff frequency

• BJT transient (switching) response

Reading: Finish Chapter 12

EE130 Lecture 27, Slide 2 Spring 2007

Transconductance:

vber gmvbe

C

E

B

E

C

+

Small-Signal ModelCommon-emitter configuration,forward-active mode:

kTqVFFC

EBeII /0

qkT

IeI

dV

dI

dV

dIg CkTqV

FFEB

C

EB

Cm

EB

//

0

“hybrid-pi” BJT small signal model:

EE130 Lecture 27, Slide 3 Spring 2007

Small-Signal Model (cont.)

, mFBE

CFBED

C

FF

gdV

IdC

I

Q

BE

F

dV

dQC BED,

m

dc

dc

m

BE

C

dcBE

B

gr

g

dV

dI

dV

dI

r

11

BEDBEDBEJ CCCC ,,,

BEdep

s

W

AC

,BEJ,

where QF is the magnitude of minority-carrier charge stored in the base and emitter regions

forward transit time

EE130 Lecture 27, Slide 4 Spring 2007

A BJT is biased at IC = 1 mA and VCE = 3 V. dc=90, F=5 ps, and T = 300 K. Find (a) gm , (b) r , (c) C .

Solution:

(a)

(b) r = dc / gm = 90/0.039 = 2.3 k

c)

Example: Small-Signal Model Parameters

siemens)(milliqkTIg Cm mS 39V

mA39

mV 26

mA 1)//(

ad)(femto fargC mF fF 19F109.1039.0105 1412

EE130 Lecture 27, Slide 5 Spring 2007

The cutoff frequency is defined to be the frequency (f = /2) at which the short-circuit a.c. current gain equals 1:

Cutoff Frequency, fT

CBEJFTac qIkTC

f/2

1at 1

,

CBEJFdc

BEJmFdcm

mm

b

c

bemc

bbbe

qIkTCj

Cgjg

g

Cjr

g

i

i

vgi

Cjr

iiv

//1

1

//1)(

/1admittanceinput

,

,

vber gmvbe

C

E

B

E

C

+

EE130 Lecture 27, Slide 6 Spring 2007

fT is commonly used as a metric for the speed of a BJT.

SiGe HBT by IBM

For the full BJT equivalent circuit: ceBCJCBCJBEJF

T rrCqIkTCCf

,,, /2

1

To maximize fT:

– increase IC

– minimize CJ,BE, CJ,BC

– minimize re, rc

– minimize F

EE130 Lecture 27, Slide 7 Spring 2007

• At very high current densities (>0.5mA/m2), base widening occurs, so QB increases.

F increases, fT decreases.

Top to bottom : VCE = 0.5V, 0.8V, 1.5V, 3V.

Base Widening at High IC: the Kirk Effect

Consider an npn BJT:At high current levels, the density of electrons (n IC/qAvsat) in the collector depletion region is significant, resulting in widening of the quasi-neutral base region.As W increases, the depletion width in the collector also increases, since the charge density decreases:

At very high current densities, the excess hole concentration in the collector is so high that it effectively extends the p-type base.

sat

CCCCdep Av

IqNqnqN ,

EE130 Lecture 27, Slide 8 Spring 2007

Summary: BJT Small Signal Model

vber gmvbe

C

E

B

E

C

+

Hybrid-pi model for the common-emitter configuration, forward-active mode:

m

dc

gr

mFBEJ gCC ,

qkT

Ig C

m /

EE130 Lecture 27, Slide 9 Spring 2007

BJT Switching - Qualitative

EE130 Lecture 27, Slide 10 Spring 2007

Turn-on transient• We know:

• The general solution is:

• Initial condition: QB(0)=0. since transistor is in cutoff

B

BBB

B QI

dt

dQ

BtBBBB AeItQ /)(

)1()( / BtBBBB eItQ

rL

CC

rt

tBBB

t

B

C

ttR

V

ttAeItQ

ti

B

0)(

)(

/

where IBB=VS/RS

BBB

LCCBr

IRV

t

/

1

1ln

EE130 Lecture 27, Slide 11 Spring 2007

Turn-off transient

• We know:

• The general solution is:

• Initial condition: QB(0)=IBBB

B

BBB

B QI

dt

dQ

BtBBBB AeItQ /)(

BtBBBB eItQ /1)(

sdt

eBBB

t

B

sdCC

C ttItQ

ttI

ti Bt

/1)(

0

)(

BBB

tCCBsd

II

t1

ln

EE130 Lecture 27, Slide 12 Spring 2007

Reducing B for Faster Turn-Off

• The speed at which a BJT is turned off is dependent on the amount of excess minority-carrier charge stored in the base, and also the recombination lifetime B

– By reducing B, the carrier removal rate is increased

Example: Add recombination centers (Au atoms) in the base

EE130 Lecture 27, Slide 13 Spring 2007

Schottky-Clamped BJT

• When the BJT enters the saturation mode, the Schottky diode begins to conduct and “clamps” the C-B junction voltage at a relatively low positive value. reduced stored charge in quasi-neutral base