Bjt Notes

npn Transistor: Complete Transport Model Equations     

    

 v v   BE i  I exp   exp  BC C S V   V T  T 

    

    

 v v   i  I exp BE   exp  BC  V E S V  T T  

    

      

      

v S  exp  BC  V  R  T I

      

v S  exp  BE  V  F  T I

   v  I v     BC S S BE i  exp   1   exp B  V      V T    F R  T

I

    

    

    1     

    1          1     

pnp Transistor: Complete Transport Model Equations     

    

 v v   C EB   exp  CB i  I exp  V C S V  T  T 

    

    

 v v   i  I exp EB   exp  CB  V E S V  T T  

      

      

      

v S  exp  CB  V  R  T I

      

v S  exp  EB  V  F  T I

   v  I v     CB S S EB   1  i  exp  exp B  V      V T     F R  T

I

    

    

    1     

    1          1     

Complete Transport Models npn

pnp

    

v   i  I exp BE  1 F S V   T       

    

v   i  I exp BC  1 R S V   T       

    

     

v   i  I exp EB  1 F S V   T       

    

v   i  I exp CB  1 R S V   T  

Simplified Transport Equations by Region of Operation* i

E

 i  i B C

V

and

 V

CE

Region

in all regions

BC

npn V I C  I S exp BE  Vth

Forward Active

Reverse Active

i

 VCE 1  VA  

v    I exp  BC  V E S T 

i

i

Cut off Cut-off

v

E

 V  V  I C  I S exp EB 1  EC  VA   Vth   V  i  i ;  F   FO 1  EC  F B C VA  

  



; i C

F

V

VA 

    

; i

T

i

B

ln



            





i

R

     

    

v i   I exp CB E S V T

i

 S

1  1

 i E R B

;

i

 S

CESAT

pnp

;  F   FO 1  VCE 

i  i F B C

Saturation

 V

BE

i

E



i (

R

i

C  1)i

1 C  i F B

B

           

v

F

            

i

B



F

* Simplifications valid when junction voltages are > 4VT or

E

1 

1  V ln T ECSAT  R

C



; i

 i R B

i ; i  S C  R

 S

R

    

< -4VT

i

C



F

     

i (

C  1)i

R B i 1 C  i F B

           

npn Transistor Regions Base-collector junction Base-emitter junction

v 0 BE v 0 BE

Reference Diagram

v 0 BC

v 0 BC

Forward active region

Saturation region

Cutoff region

Reverse-active region

pnp Transistor Regions

Emitter-base junction

v CB

Collector-base junction v 0 0 CB

v 0 EB

Forward active region

Saturation region

v 0 EB

Cutoff region

Reverse-active region

Reference Diagram

Simplified npn Models by Region of Operation* Forward-Active

Saturation

i i  C B  F

Cut-Off

Reverse-Active

Simplified pnp Models by Region of Operation* Forward-Active

Saturation E

E IE 0.75 V IB 0.7 V IB

+ -

0.7 V

B

IC

VEB SAT

+

VCB SAT

i i  C B  F

IC

C

C

Reverse-Active

Cut-Off

C

E

-IC = (βR+1)IB

IE

0 IB B

+ -

B

I=βF IB

VEB

IE

0.7 V

0

IB 0

IC C

+ -

I=βR IB

VCB

B

-IE E

i-v Characteristics C Common-Emitter i Output O Ch Characteristics i i

iC F  iB Int the Forward-Active Region

For this transistor

1.00mA F   25 40 A

DC and AC Analysis •

•

DC analysis: – Find dc equivalent circuit by replacing all capacitors by open circuits and inductors by short circuits. – Find Q Q-point p from dc equivalent q circuit by y using g appropriate pp p largeg signal transistor model. AC analysis: – Find ac equivalent circuit by replacing all capacitors by short circuits, circuits inductors by open circuits, dc voltage sources by ground connections and dc current sources by open circuits. – Replace transistor by small small-signal signal model – Use small-signal ac equivalent to analyze ac characteristics of amplifier. – Combine end results of dc and ac analysis to yield total voltages and currents in the network. network

Hybrid-Pi Hybrid Pi Model of BJT (npn and pnp) Transconductance: I gm  C  40I C V T Input resistance:  oV o T r   I gm C

Applies A li when: h v  0.005Volts be

S



Output resistance: V V V A CE  A ro  I I C C Amplification Factor: 

f 

g mro

