EEE 51: Second Semester 2014 - 2015 Lecture 2
Transistor Models
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Today
Transistor Models Large Signal Small Signal
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From Transistors to Transistor Circuits
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transistors
[wikipedia]
transistor circuits
?
Transistor Models
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transistor operaGon
device characterizaGon
IC = IS eVBEVT 1( ) 1+VCEVA
"
#$
%
&' IB =
1IC
[wikipedia]
device models
I-V models (large signal approximaGon)
large signal terminal behavior (I-V curves)
transistor circuits
?
EEE 41
EEE 41 EEE 51
Large Signal Models
V and I over dierent transistor opera:ng regions BJT: Forward-acGve, saturaGon, cut-o MOSFET: SaturaGon, linear (ohmic), subthreshold (cut-o)
Large signal model reference largest gain topology Transfer CharacterisGc Output CharacterisGc Input CharacterisGc Unilateral Low frequency
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gain input output
How many ways can you congure a 3-terminal device?
C
E
B
BJT Transfer CharacterisGcs (IC vs. VBE)
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Common-Emi^er topology
IC = IS eVBEVT 1( ) 1+VCEVA
"
#$
%
&'
IS eVBEVT
MOSFET Transfer CharacterisGcs (ID vs. VGS)
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Common-Source topology
ID = k VGS VTH( )2 1+ VDS( )
k VGS VTH( )2
Output CharacterisGcs
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2N2222A
ZVN3306A
IB =10A
IB = 50A VGS = 9V
VGS =1V
IC = IS eVBEVT 1( ) 1+VCEVA
"
#$
%
&'
ID = k VGS VTH( )2 1+ VDS( )
(forward acGve)
(saturaGon)
ID = 2k VGS VTH( )VDS 12VDS2#$ %&(linear/ohmic)
Input CharacterisGcs
BJT MOSFET
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IB =IC
1IS e
VBEVT IG = 0
Two Ways to Bridge the Gap
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IC = IS eVBEVT 1( ) 1+VCEVA
"
#$
%
&'
IB =1IC
I-V models (large signal transfer, input and output characterisGcs)
transistor circuits
EEE 51 way ( aka the fun way J ) Allows us to use our EEE 31, 33 skills Allows us to break up large circuits into smaller ones Gives us more intuiGon in terms of circuit operaGon
direct applicaGon of KCL and KVL
linearizaGon + two-port network
reducGon
The complex, non-intuiGve, non-extendable way
LinearizaGon (1)
Consider an amplier with large gain:
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gain input output
5V
voltage gain = 1,000
input voltage levels?
In most amplier applicaGons, we are interested in the transistor behavior when we apply small signals
LinearizaGon (2) Consider a BJT in the forward acGve region:
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IC = IS eVBEVT
A is known as the quiescent DC operaGng point
LinearizaGon (3)
So what if the signals are small? Recall: Taylor Series expansion
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f x( ) = f a( )+f ' a( )1! x a( )+
f '' a( )2! x a( )
2+f ''' a( )3! x a( )
3+
ex = e0 + e0
1! x +e02! x
2 +e03! x
3 +
=1+ x + x2
2! +x33! +
Example:
Linearizing the BJT Transfer CharacterisGc (1)
Expanding the transfer characterisGc
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iC = IC,Q + ic = IS eVBE ,Q+vbe
VT
IC,Q + ic = IS eVBE ,QVT e
vbeVT = IC,Q e
vbeVT
= IC,Q 1+vbeVT
+v2be2V 2T
+v3be6V 3T
+"
#$
%
&'
IC,Q + ic = IC,Q + IC,QvbeVT
+IC,Q2
vbeVT
"
#$
%
&'
2
+IC,Q6
vbeVT
"
#$
%
&'
3
+
ic = IC,QvbeVT
+IC,Q2
vbeVT
"
#$
%
&'
2
+IC,Q6
vbeVT
"
#$
%
&'
3
+
(VBE,Q, IC,Q )
vbe
ic
vBE =VBE,Q + vbeiC = IC,Q + ic nonlinear!
Linearizing the BJT Transfer CharacterisGc (2)
If vbe is small
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ic = IC,QvbeVT
+IC,Q2
vbeVT
!
"#
$
%&
2
+IC,Q6
vbeVT
!
"#
$
%&
3
+
IC,QvbeVT
(VBE,Q, IC,Q )
vbe
ic
vBE =VBE,Q + vbeiC = IC,Q + ic
linear!
small means vbeVT
Linearizing the BJT Transfer CharacterisGc (3)
Another way to think about linearizaGon
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(VBE,Q, IC,Q )
vbe
ic
vBE =VBE,Q + vbeiC = IC,Q + ic
If we make vbe 0
m = limvbe0
iC VBE,Q + vbe( ) iC VBE,Q( )VBE,Q + vbe VBE,Q
=ICVBE VBE=VBE ,Q
We can make the approximaGon:
ic =m vbe =ICVBE VBE=VBE ,Q
vbe
Linearizing the BJT Transfer CharacterisGc (4)
Transconductance
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(VBE,Q, IC,Q )
vbe
ic
vBE =VBE,Q + vbeiC = IC,Q + ic
Dene transconductance as
ic = gm vbe
gm =ICVBE VBE=VBE ,Q
For small signals
Linearizing the BJT Transfer CharacterisGc (5)
BJT transconductance
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(VBE,Q, IC,Q )
vbe
ic
vBE =VBE,Q + vbeiC = IC,Q + ic
gm =ICVBE VBE=VBE ,Q
=
VBEIS e
VBEVT
#
$%%
&
'((VBE=VBE ,Q
=IS e
VBE ,QVT
VT=IC,QVT
Again, we get: ic = gm vbe =IC,QVT
vbe
slope: gm
Linearizing the MOSFET Transfer CharacterisGc
MOSFET transconductance
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gm =IDVGS VGS=VGS ,Q
=
VGSk VGS VTH( )
2( )VGS=VGS ,Q
= 2k VGS,Q VTH( )(VGS,Q, ID,Q )
vgs
id
vGS =VGS,Q + vgsiD = ID,Q + id
slope: gm
We get the linear relaGonship:
id = gm vgs = 2k VGS,Q VTH( ) vbe
Does gm give us the complete picture?
What else changes ic or id?
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2N2222A
ZVN3306A
IB =10A
IB = 50A VGS = 9V
VGS =1V
IC = IS eVBEVT 1( ) 1+VCEVA
"
#$
%
&' ID = k VGS VTH( )
2 1+ VDS( )
BJT Transistor Output Resistance
What happens when there are small changes in VCE?
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2N2222A IB =10A
IB = 50A
ic =ICVCE VCE=VCE ,Q
vce
=
VCEIS e
VBEVT 1( ) 1+VCEVA
$
%&
'
()
$
%&&
'
())VCE=VCE ,Q
vce
=IS e
VBE ,QVT 1$
%&
'()
VA vce =
IC,QVA
vce = go vce =vcero
Output resistance: ro =VAIC,Q
MOSFET Transistor Output Resistance
What happens when there are small changes in VDS?
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id =IDVDS VDS=VDS ,Q
vds
=
VDSk VGS VTH( )
2 1+ VDS( )( )VDS=VDS ,Q
vds
= k VGS VTH( )2 vds = IDS,Q vds
= go vds =vdsro
Output resistance: ro =1
IC,Q
ZVN3306A VGS = 9V
VGS =1V
CompleGng the Picture: Transistor Input Resistance BJT Small signal base current
due to vbe
MOSFET Small signal gate current
due to vgs
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g =IBVBE VBE=VBE ,Q
=
VBEIC
"
#$
%
&'VBE=VBE ,Q
=1
ICVBE VBE=VBE ,Q
=gm
g =IGVGS VGS=VGS ,Q
= 0
r =1g
=gm
= VTIC,Q
r =1g
LinearizaGon Result: The Small Signal Model
BJT Total ic:
Total ib:
MOSFET Total id:
Total ig:
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ic =ICVBE VBE=VBE ,Q
vbe#
$
%%
&
'
((+
ICVCE VCE=VCE ,Q
vce#
$
%%
&
'
((
= gmvbe +vcero
id =IDVGS VGS=VGS ,Q
vgs#
$
%%
&
'
((+
IDVDS VDS=VDS ,Q
vds#
$
%%
&
'
((
= gmvgs +vdsro
ib =IBVBE VBE=VBE ,Q
vbe =vber
ig = 0
The BJT Small Signal Equivalent Circuit
KCL / KVL results in the small signal model
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ic = gmvbe +vcero
ib =vber
Linear! Fully describes the response of the BJT to small signal disturbances
about the quiescent point (no DC informaGon!) Dependent on the quiescent DC operaGng point
The MOSFET Small Signal Equivalent Circuit
KCL / KVL results in the small signal model
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id = gmvgs +vdsro
ig = 0
Large Signal vs. Small Signal
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IC,Q = IS eVBE ,QVT 1"
#$
%&' 1+VCE,QVA"
#$
%
&'
IB,Q =IC,Q
ic = gmvbe +vcero
ib =vber
IC,QVBE,Q ic
vbe
Small Signal Model ImplicaGons
Linear relaGonships! For small signals
Linear circuit analysis works! EEE 31 and 33 is useful amer all J Can use two-port network concepts
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gain input output
5V
voltage gain = 1,000
5mV input
Next MeeGng
Review of Two-Port Networks Single-Stage Ampliers
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