4/18/2011 section 5_8 BJT Internal Capacitances 1/2
5.8 BJT Internal Capacitances
Reading Assignment: 485-490
BJT’s exhibit capacitance between each of its terminals (i.e., base, emitter, collector). These capacitances ultimately limit amplifier bandwidth.
Q: Yikes! Who put these capacitors in the BJT? Why did they put them there? Why don’t we just remove them?
A: These capacitances are parasitic capacitances. Since the terminals are made of conducting materials (e.g., metal), there will always be some capacitance associated with any two terminals.
BJT designers and manufacturers work hard to minimize these capacitances—and indeed they are very small—but we cannot eliminate them entirely.
If the signal frequency gets high enough, these capacitances can affect amplifier performance.
HO: BJT INTERNAL CAPACITANCES
Now that we are aware of these internal capacitances, we must modify our small-signal circuit models.
Jim Stiles The Univ. of Kansas Dept. of EECS 4/18/2011 section 5_8 BJT Internal Capacitances 2/2
HO: THE HIGH-FREQUENCY HYBRID PI MODEL
The significance of the internal capacitances are typically specified in terms of a frequency-dependent BJT parameter called
hfe ()ω . This parameter is often referred to as the “short-circuit current gain” of the BJT.
From this function hfe ()ω we can extract a BJT parameter called the unity-gain bandwidth—a result very analogous to op-amps!
HO: THE SHORT-CIRCUIT CURRENT GAIN
Jim Stiles The Univ. of Kansas Dept. of EECS
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Jim Stiles The Univ. of Kansas Dept. of EECS of Dept. ofKansas Univ. The Jim Stiles BJTInternalCa 4/18/2011
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.
v
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urn anlcue 1/8 Current Gain lecture
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g
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r
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But we knowthat: Therefore: Jim Stiles The Univ. of Kansas Dept. of EECS of Dept. ofKansas Univ. The Jim Stiles In this casewefind: 4/18/2011 The Short Circuit Just as we
expected
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! Idon’talreadyknow
gr
m
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π () () ω
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m 2/8 Current Gain lecture
T
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==
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- +
v
B
i
()
ω
i b
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collector ω
i
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i c
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be current is:
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urn anlcue 3/8 Current Gain lecture
π ( v
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()
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g
ω
m
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π μ
)
- v +
base
ce
model:
current is: r
i o
c
C ()
ω
Typically, we findthat and againwe know: current is:
Therefore: Jim Stiles The Univ. of Kansas Dept. of EECS of Dept. ofKansas Univ. The Jim Stiles Therefore, the 4/18/2011 The Short Circuit Here’s somethingyoudidnotknow ratio
ofsmall-signalcollectorcu
g m
i i i i i i
ω b b b c c c
rg () () () () () ()
ω ω ω ω ω C ω π μ
, sothat wefind: m ≈ ≈ = =
1 1 1
rg II VI II
++ ++ ++ π
BB TB
CC
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urn anlcue 4/8 Current Gain lecture
T
rg
CC rC CC rC CC rC −
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== β j
() () ()
ω
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rC πμ
rrent tosmall-signalbase β
frequency h Note this functionisa
Jim Stiles The Univ. of Kansas Dept. of EECS of Dept. ofKansas Univ. The Jim Stiles We 4/18/2011 The Short Circuit
Therefore: fe
() ω define :
Your BJTisfrequencydependent! as: thisratioasthe
low-pass
h fe
()
ω h
small-signal BJT(short-circuit)currentgain fe
()
ω
i
function,were wecan define a3dB i ω
b c
() ()
β
ω ω
i
i =
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++ ≈
1 j
+ ω
+
CC rC
j
μπ πμ
β β ωω ()
β
break
,
h We seethatfor frequencies Jim Stiles The Univ. of Kansas Dept. of EECS of Dept. ofKansas Univ. The Jim Stiles Plotting themagnitudeof 4/18/2011 The Short Circuit fe
() ω
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0 dB β 2
h fe
() ω
2 h
(dB)
fe
h ()
ω fe less
() βωω ωβ (i.e., beta thanthe3dBbreak frequency,thevalueof
≈< ω
β
:
h fe
urn anlcue 6/8 Current Gain lecture
() ω 2 ) wefindthat:
20 dB/decade
β
ω T
log ω
Jim Stiles The Univ. of Kansas Dept. of EECS of Dept. ofKansas Univ. The Jim Stiles Note thenforfrequenciesgreat 4/18/2011 The Short Circuit
We can thusdefinethis frequencyas so that: Note then that
This shouldSOremindyouofop-amps
h fe
)1 () ω =
when
h fe
()
ω
h ωβω
er thanthisbreakfrequency: eT fe ≈> =
()1.0
=
ωω ωβω
j 1
T +
βω
== ω ω j
T β
β
urn anlcue 7/8 ω Current Gain lecture
β
. , the
ω
β β
unity-gain ωω
β
frequency:
Jim Stiles The Univ. of Kansas Dept. of EECS of Dept. ofKansas Univ. The Jim Stiles We canthereforestatethat: 4/18/2011 The Short Circuit and also that:
Déjà vu;alloveragain
h fe
()
ωωω
h fe
()
=> ≈=
βωω ωβ
β
ωω ω
≈< β
urn anlcue 8/8 Current Gain lecture
ω
T β
β