BI POLAR JUNCTION TRANSISTOR

Bipolar transistor of junction (TBJ)

Theory

Polarizing to the bases-emitter diode in direct and collector-bases on inverse, we have the

model approximated for continuous. The static gains of current in common emitter and common

bases are defined respectively

b = h21E = hFE = IC / IB ~ h21e = hfe (>> 1 para TBJ comunes)

a = h21B = hFB = IC / IE ~ h21b = hfb (~< 1 para TBJ comunes)

La corriente entre collector y base ICB es de fuga, y sigue aproximadamente la ley

The current between collector and bases ICB it is of loss, and it follows approximately the law

ICB   = ICB0 (1 - eVCB/VT) ~ ICB0

where

VT = 0,000172 . ( T + 273 )

ICB   = ICB0(25ºC) . 2 DT/10

with DT the temperature jump respect to the atmosphere 25 [ºC]. From this it is then

DT   = T - 25

¶ICB / ¶T = ¶ICB / ¶DT ~ 0,07. ICB0(25ºC) . 2 DT/10

On the other hand, the dependency of the bases-emitter voltage respect to the temperature, to

current of constant bases, we know that it is

¶VBE / ¶T ~ - 0,002 [V/ºC]

The existing relation between the previous current of collector and gains will be determined now

IC   = ICE   + ICB   = a IE + ICB

IC   = ICE   + ICB   = b IBE + ICB   = b ( IBE + ICB ) + ICB ~ b ( IBE + ICB )

b   = a / ( 1 - a )

a   = b / ( 1 + b )

Next let us study the behavior of the collector current respect to the temperature and the

voltages

DIC   = (¶IC/¶ICB) DICB  + (¶IC/¶VBE) DVBE  + (¶IC/¶VCC) DVCC  +

+ (¶IC/¶VBB) DVBB  + (¶IC/¶VEE) DVEE

of where they are deduced of the previous expressions

DICB   = 0,07. ICB0(25ºC) . 2 DT/10 DT

DVBE   = - 0,002 DT

VBB  - VEE   = IB (RBB + REE) + VBE  + IC REE

IC   = [ VBB  - VEE - VBE  + IB (RBB + REE) ] / [ RE + (RBB + REE) b-1 ]

SI = (¶IC/¶ICB) ~ (RBB + REE) / [ REE + RBB b-1 ]

SV = (¶IC/¶VBE) = (¶IC/¶VEE) = - (¶IC/¶VBB) = - 1 / ( RE + RBB b-1 )

(¶IC/¶VCC) = 0

being

DIC   = [ 0,07. 2 DT/10 (RBB + REE) ( REE + RBB b-1 )-1 ICB0(25ºC) +

+ 0,002 ( REE + RBB b-1 )-1 ] DT + ( RE + RBB b-1 )-1 (DVBB  - DVEE)

Design

Be the data

IC   = ... VCE   = ... DT = ... ICmax   = ... RC = ...

From manual or the experimentation according to the graphs they are obtained

b   = ... ICB0(25ºC)   = ... VBE = ... ( ~ 0,6 [V] para TBJ de baja potencia)

and they are determined analyzing this circuit

RBB   = RB // RS

VBB   = VCC  . RS (RB+RS)-1   = VCC  . RBB / RB

DVBB   = DVCC  . RBB / RS   = 0

DVEE   = 0

REE   = RE

RCC   = RC

and if to simplify calculations we do

RE   >> RBB / b

us it gives

SI = 1 + RBB / RE

SV = - 1 / RE

DICmax   = ( SI . 0,07. 2 DT/10 ICB0(25ºC) - SV . 0,002 ) . DT

and if now we suppose by simplicity

DICmax   >> SV . 0,002 . DT

are

RE = ... >> 0,002 . DT / DICmax

RE [ ( DICmax / 0,07. 2 DT/10 ICB0(25ºC) . DT ) - 1 ] = ... > RBB  = ... << b RE = ...

being able to take a DIC smaller than DICmax if it is desired.

Next, as it is understood that

VBB = IB RBB  + VBE  + IE RE ~ [ ( IC b-1 - ICB0(25ºC) ) RBB  + VBE  + IE RE = ...

VCC = IC RC  + VCE  + IE RE ~ IC ( RC + RE ) + VCE = ...

they are finally

RB = RBB VCC / VBB = ...

RS = RB RBB / RB - RBB = ...

Fast design

This design is based on which the variation of the IC depends solely on the variation of the

ICB. For this reason one will be to prevent it circulates to the base of the transistor and is amplified.

Two criteria exist here: to diminish RS or to enlarge the RE. Therefore, we will make reasons both;

that is to say, that we will do that IS >> IB and that VRE > 1 [V] —since for IC of the order of

miliamperes are resistance RE > 500 [W] that they are generally sufficient in all thermal stabilization.

Be the data

IC   = ... VCE   = ... RC = ...

From manual or the experimentation they are obtained

b   = ...

what will allow to adopt with it

IS   = ... >> IC b-1

VRE = ... > 1 [V]

and to calculate

VCC = IC RC  + VCE  + VRE = ...

RE = VRE / IC   = ...

RS = ( 0,6 + VRE ) / IS   = ...

RB = ( VCC - 0,6 - VRE ) / IS   = ...