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8/9/2019 Small and High Frequency Model Signal BJT
http://slidepdf.com/reader/full/small-and-high-frequency-model-signal-bjt 1/5
Discuss The BJT small-signal model
• The small signal model of the BJT amplifier is shown in figure . These models are
valid for both NPN and PNP transistors.For the same operating point, the BJT has
higher transconductance and higher output resistance that the MOF!T.
Figure small signal-models of the BJT
The BJT small"signal parameters ma# be summari$ed in Table %
Table BJT small signal parameters
&a' &b'
&c'&d'
8/9/2019 Small and High Frequency Model Signal BJT
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Symbol Parameter Value
gm
Transconductance
C m
T
I g
V =
(T is the thermal voltage ) *T+, whicheuals -m( at room temperature.
* is Bolt$man/s constantT is the absolute temperature in 0elvins
is the electron charge
rπ Base input resistanceT T
B C m
V V r
I I g π
β β
= = = ÷
1 is the common"emitter current gain
re !mitter input resistanceT T
e
E C m
V V
r I I g
α
α
= = = ÷ 2 is the common"base current gain
ro Output resistance
A ACE o
C C
V V V r
I I
+= ;
(3 is the earl# voltage.
Discuss The BJT high-frequency model
Figure The high-frequency hybrid- π model of the BJT
8/9/2019 Small and High Frequency Model Signal BJT
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• T#picall#, the base"emitter 4unction capacitance 56 is in the range of few pF to few
tens of pF, while the collector"base 4unction capacitance 5 μ is in the range of
fraction of pF to few pF The base resistor r 7 is added partl# to account for thecomparativel# long internal connection from the base e7ternal connection and the
actual internal base connection. Note that r 7 becomes the dominant input
resistance for freuencies so high that 56 effectivel# short"circuits r 6.• 3 second base"width modulation effect, characteri$ed b# a resistor connected
between the base and collector is omitted8 its influence is dominated b# thecollector 4unction reverse"bias capacitance 59.The emitter 4unction &diffusion'
capacitance 56 represents the charge store to support the current flow across the
base.
Discuss The BJT !utoff frequency
The freuenc# at which the current gain of the transistor becomes one. &i.e. nomore active element'. :t is calculated b# finding the short circuit collector current
in terms of the base current.;sing the high freuenc# model of BJT we can draw the circuit to estimate thecut"off freuenc# of the BJT as shown in Figure .
Figure !ircuit used to estimate the BJT cutoff frequency
3ppl#ing nodal anal#sis at the input and output nodes as we did earlier. <e can
estimate the cut"off freuenc# as follows=
b
V
I s C V s C V r
π
π π µ π π = + +
& 'b
V I s C C V
r
π π µ π
π
= + +
>& '
mc fe
b
g sC I h
I s C C
r
µ
π µ
π
−≡ =
+ +
8/9/2019 Small and High Frequency Model Signal BJT
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3ssuming m g sC µ >>'
> &
m fe
g r h
s C C r
π
π µ π
≅+ +
⇒
3ssuming> & '
mm fe
g r g sC h
s C C r
π µ
π µ π
>> ⇒ ≅+ +
>where& '
>
o fe p
p
h s C C r π µ π
β ω
ω
≅ = ++
;nit# gain bandwidth
'
&& '
mT o p
g
C C π µ
ω β ω = =
+
∴
>& '
assuming> & '
>where
& '>
;nit# gain bandwidth & '& '
mc fe
b
m fe m
o fe p
p
mT o p
g sC I h
I s C C
r g r
h g sC s C C r
h s C C r
g
C C
µ
π µ
π
π µ
π µ π
π µ π
π µ
β ω
ω
ω β ω
−
≡ =
+ +
≅ >>
+ +
≅ =
++
∴ = =
+
<e can observe from the last anal#sis that the common"emitter current gain &hfe'
freuenc# response is similar to a simple pole with ? p as the pole freuenc#. This
ma# be drawn as shown in Figure @
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Fig"@ in &AecC%(erC>.vsd'
Figure " Bode plot of #hfe#
• 3s we can see from the last euation. Digher ωT means higher gm and lower internal BJT capacitances which means better amplifier operation.
• T#picall#, f T is ranging from about >CCMD$ to Tens of ED$.