Small and High Frequency Model Signal BJT

8/9/2019 Small and High Frequency Model Signal BJT

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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'



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



• 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

−≡ =

+ +



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 @



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$.

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Small and High Frequency Model Signal BJT