BITS Pilani
presentation
BITS Pilani
Dubai Campus
Dr Jagadish Nayak
BITS Pilani
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 Cde
۞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 Qn ia represented by
Qn
W2
iC Where W
2 Dn
Dn
Eletron Diffusivity in Base
Base width
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BJT Internal Capacitances
We can write
W2
Qn
F iC Where
F
2 Dn
is called as Forward base transient time
F
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 Cde,
Cde
dQn
dvBE
F
diC
dvBE
F
gm
IC
F
VT
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BJT Internal Capacitances
The Base Emitter Junction Capacitance:
(depletion layer capacitance)
Approximate value
of Cje =2 Cje0
EBJ Built in voltage
(0.9)
C je
Value of Cje at zero
voltage
C je 0
VBE
1
V0 e
m
Grading coefficient of
EBJ (0.5)
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BJT Internal Capacitances
The Collector-Base Junction capacitance:
In active mode collector base junction is reverse biased and its
depletion capacitance
C
C
0
VCB
1
V0 c
CBJ Built in voltage
(0.75V)
Value of Cµ at zero
voltage
m
Grading coefficient of
EBJ (0.2 to 0.5)
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High frequency Hybrid-π
model
Emitter base capacitance
(Cde+Cje)pfarads
Collector base
capacitance
B
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)
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High frequency Hybrid-π
model
Emitter base capacitance
(Cde+Cje)pfarads
B
Collector base
capacitance
B’
(Few tens of Ωs)
Since rx <<< rπ , its
effect is negligible at
low frequencies , it
becomes apparent in
the high frequencies.
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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
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Cut off frequency
Collector is shorted to the emitter at Junction C
E
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Cut off frequency
Ib
sCµVπ
E
Ic=(gm-sCµ)Vπ
Ic
sC V
g mV
Ic
g mV
sC V
gm
sC V
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Cut off frequency
Ib
sCµVπ
Vπ = Ib x [Impedence sum
between B’ and E]
Ic=(gm-sCµ)Vπ
E
V
I b [r || C || C ]
Ib
1
sC
r
sC
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Cut off frequency
h fe (or )
Ic
Ib
gm
1
r
sC
s (C
C )
The model is valid for gm>>>wCµ , we can neglect wCµ in the numerator
h fe (or )
Ic
Ib
gmr
1 s (C C )r
Low frequency value of β
0
1 s (C
C )r
This has a single pole response with
3dB frequency at w=wβ
Where
w
(C
1
C )r
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Cut off frequency
We can observe from the above slope that frequency at which
|hfe| drops to unity is called as unity gain bandwidth wT and is
given by wT=β0wβ
wT
gm
; fT
(C C )
gm
2 (C
fT is some times specified in the
datashet or given as a function of
Ic and VCE
C )
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