BJT Internal Capacitances and High Frequency Model - BITS Pilani

BITS Pilani 

presentation 


Dubai Campus 

Dr Jagadish Nayak


Dubai Campus 

The BJT Internal Capacitances and 

High Frequency Model

BJT Internal Capacitances 

۞Transistor exhibit charge storage phenomenon that limit the 

speed and frequency of their operation 

۞These charge effects are accounted by adding capacitances 

to the hybrid π model. 

Base charging or diffusion capacitance C de 

۞When the transistor is operating in active or Saturation region 

mode, minority carrier charge is stored in the base region. 

۞When an npn transistor is operating in active mode, this 

charge Q n ia represented by 

Q 

n 

2 

W 

2D 

n 

i 

C 

Where 

W 

Basewidth 

D 

n 

Eletron Diffusivityin Base 

BITS Pilani, Dubai Campus


We can write 

Q 

F 

n 

is 

2 

W 

FiC 

Where 

F 

2Dn 

called as Forward base 

transient 

time 

Which is the average time a charge carrier (electron) spends in 

crossing the base (10ps to 100ps) 

۞For the small signals we can define the small signal diffusion 

capacitance C de , 

C 

de 

dQ 

dv 

n 

BE 

F 

di 

dv 

C 

BE 

F 

g 

m 

F 

I 

V 

C 

T 



The Base Emitter Junction Capacitance: 

(depletion layer capacitance) 

Value of C je at zero 

voltage 

Approximate value 

of C je =2 C je0 

EBJ Built in voltage 

(0.9) 

C 

je 

1 

C 

je0 

V 

V 

BE 

0e 

m 

Grading coefficient of 

EBJ (0.5) 



The Collector-Base Junction capacitance: 

In active mode collector base junction is reverse biased and its 

depletion capacitance 

CBJ Built in voltage 

(0.75V) 

C 

1 

C 

V 

V 

0 

CB 

0c 

m 

Value of C µ at zero 

voltage 

Grading coefficient of 

EBJ (0.2 to 0.5) 


High frequency Hybrid-π 

model 

Emitter base capacitance 

(C de +C je )pfarads 

B 

Collector base 

capacitance 

Model resistance of 

silicon material of 

the base region , 

between base B and 

a fictitious internal 

or intrinsic, base 

terminal B’ (right 

under the emitter 

region) 


High frequency Hybrid-π 

model 

Emitter base capacitance 

(C de +C je )pfarads 

B 

B’ 

Collector base 

capacitance 

(Few tens of Ωs) 

Since r x

Cut off frequency 

۞Value of Cπ is not given in the data sheet rather behavior 

of β (or hfe) versus frequency is normally given. 

۞To find Cπ and Cµ , derive an expression for hfe. i.e short 

circuit current gain as a function of frequency interms of 

hybrid π components. 

Consider following model 



Collector is shorted to the emitter at Junction C 

E 



E 

I 

c 

I b sC µ V π I c =(g m -sC µ )V π 

V 

sC V 

g 

m 

V 

I 

c 

g 

m 

V 

sC V 

g 

m 

sC 



I b sC µ V π I c =(g m -sC µ )V π 

V π = I b x [Impedence sum 

between B’ and E] 

E 

V 

1 

r 

I 

I 

b 

b 

[ r 

sC sC 

|| 

C 

|| 

C 

] 



The model is valid for g m >>>wC µ , we can neglect wC µ in the numerator 

h 

fe 

h 

fe 

( or 

I 

c 

gmr 

0 

( or ) 

I 1 s( 

C C ) r 1 s( 

C 

Low frequency value of β 

b 

) 

I 

I 

c 

b 

1 

r 

g 

m 

s( 

C 

sC 

w 

C 

) 

( C 

1 

C 

C 

) r 

) r 

This has a single pole response with 

3dB frequency at w=w β 

Where 



We can observe from the above slope that frequency at which 

|h fe | drops to unity is called as unity gain bandwidth w T and is 

given by w T =β 0 w β 

w 

T 

gm 

gm 

; fT 

( C C ) 2 ( C C 

) 

f T is some times specified in the 

datashet or given as a function of 

I c and V CE

BJT Internal Capacitances and High Frequency Model - BITS Pilani

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