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4/18/2011 The Short Circuit Current Gain lecture 1/8
Jim Stiles The Univ. of Kansas Dept. of EECS
The Short-Circuit Current Gain hfe
Consider the common emitter low-frequency small-signal model
with its output short-circuited.
+ vbe -
r m beg v
( )bi
C
or
( )ci
+ vce -
( )iv
B
+ -
E
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4/18/2011 The Short Circuit Current Gain lecture 2/8
Jim Stiles The Univ. of Kansas Dept. of EECS
Boring! Tell me something I dont already know
In this case we find:
( ) ( )( )
c m be
m b
i g v g r i
==
But we know that:
C CTm
T B B
I IVg r V I I
= = =
Therefore: ( )( )
c
b
i
i =
Just as we expected!
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4/18/2011 The Short Circuit Current Gain lecture 3/8
Jim Stiles The Univ. of Kansas Dept. of EECS
When the input signal is changing rapidly Now, contrast this
with the results using the high frequency model: Evaluating this
circuit, it is evident that the small-signal base current is:
( )1( ) ( )b
i v j C Cr
= + +
While the small-signal collector current is: ( )( ) ( )c m i v g
jC=
+ vbe -
r mg v
B C
or + vce -
C
C
( )bi ( )ci
+ -
( )iv
E
- vce +
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4/18/2011 The Short Circuit Current Gain lecture 4/8
Jim Stiles The Univ. of Kansas Dept. of EECS
Heres something you did not know Therefore, the ratio of
small-signal collector current to small-signal base current is:
( )( )( ) 1
m c
b
r g j r Ci i j r C C
= + +
Typically, we find that m g C , so that we find:
( )( )( ) 1
mc
b
r gi i j r C C
+ +
and again we know:
C CT m
T B B
I IVr g V I I
= = = Therefore:
( )( )( ) 1
c
b
i i j r C C
+ +
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4/18/2011 The Short Circuit Current Gain lecture 5/8
Jim Stiles The Univ. of Kansas Dept. of EECS
Your BJT is frequency dependent! We define this ratio as the
small-signal BJT (short-circuit) current gain,
( )feh :
( )( )
( )( ) 1
cfe
b
i h i j r C C
+ +
Note this function is a low-pass function, were we can define a
3dB break frequency as:
( )1
r C C
= +
Therefore: ( )
( )( ) 1
cfe
b
i h i j
+
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4/18/2011 The Short Circuit Current Gain lecture 6/8
Jim Stiles The Univ. of Kansas Dept. of EECS
This is how we define BJT bandwidth Plotting the magnitude of (
)feh (i.e.,
2( )feh ) we find that:
We see that for frequencies less than the 3 dB break frequency,
the value of
( )feh is approximately equal to beta:
( )fe h <
log
2(dB)( )hfe
2log
T 0 dB
20 dB/decade
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4/18/2011 The Short Circuit Current Gain lecture 7/8
Jim Stiles The Univ. of Kansas Dept. of EECS
This should SO remind you of op-amps
Note then for frequencies greater than this break frequency:
( )1fe
h j
j
=+
>
Note then that ( ) 1feh = when = . We can thus define this
frequency as T , the unity-gain frequency:
T
so that: ( ) 1.0fe Th = =
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4/18/2011 The Short Circuit Current Gain lecture 8/8
Jim Stiles The Univ. of Kansas Dept. of EECS
Dj vu; all over again We can therefore state that:
( ) Tfe h
= >
and also that:
( )fe h <
