ECE 255: BJT Small Signal Model - nanoHUB.org › ... › uploads › L23_BJT_ss_model.pdfThe small...
Transcript of ECE 255: BJT Small Signal Model - nanoHUB.org › ... › uploads › L23_BJT_ss_model.pdfThe small...
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ECE 255:
BJT Small Signal Model (Sedra and Smith, 7th Ed., Sec. 7.2.2)
Mark Lundstrom School of ECE
Purdue University West Lafayette, IN USA
Lundstrom: Fall 2019
ECE 255: Fall 2019 Purdue University
2) AC analysis
2
+υo
−
RC = 5 kΩic
υi
We need an ac small signal model for the BJT
Lundstrom: Fall 2019
Outline
3
1) Small signal model for BJT 2) Small signal amplifier analysis 3) NPN vs. PNP 4) T-model
Lundstrom: Fall 2019
ac collector current
4
N P N
IC + ic
IB + ib
IC = ISeVBE VT → iC = ISe
VBE+υbe( ) VT
iC = ISeVBE VT eυbe VT
IC + ic = ISeVBE VT 1+υbe VT( )
ic = ISeVBE VT υbe VT( ) = IC υbe VT( )
ic =ICVT
υbe = gmυbe Ohm’s Law
Lundstrom: Fall 2019
Summary: s.s. collector current
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N P N
ic
ib ic = gmυbe
gm = ICVT
+υbe
−
“transconductance”
Note that the ac model parameter, gm, depends on the dc bias current, IC.
Lundstrom: Fall 2019
s.s. base current
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N P N
ic
ib
ic = gmυbe
gm = ICVT
ib =icβ= gm
βυbe =
υbe
β gm= υbe
rπ
ib =υbe
rπ
gmrπ = β
+υbe
−
Lundstrom: Fall 2019
s.s. eqv. circuit model: gm form
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icib
B
E
C
gm = IC VT gmrπ = β
+υbe
−E
C B
ib ic
rπ gmυbe
+υbe
−
“hybrid pi model”
s.s. eqv. circuit model: beta form
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gm = ICVT
gmrπ = βE
C B ib ic
rπ gmυbe
+υbe
−
gm = β rπ
ic =βrπυbe = βib
βib
ic = gmυbe
VCCS
CCCS
Lundstrom: Fall 2019
s.s. eqv. circuit model: vce dependence
9
E
C B ib ic
rπ gmυbe
+υbe
−
This model says that the collector current does not depend on the collector-emitter voltage.
Lundstrom: Fall 2019
Output resistance
10 E
VCE
IC
IC = ISeqVBE kBT 1+
υCE
VA
⎛
⎝⎜⎞
⎠⎟
dIC
dVCE
= ISeqVBE kBT 1VA
⎛
⎝⎜⎞
⎠⎟=
′IC
VA
ic =
υce
r0 ro ≈
VA
IC
VA = “Early Voltage”
dIC
dVCE
≈δ IC
δVCE
=icυceVBE1, IB1
ic =
dIC
dVCE
⎛
⎝⎜⎞
⎠⎟υce
Hybrid pi model
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gm = ICVT
gmrπ = β
ro =VA ICE
C B
ib ic
rπ gmυbe
+υbe
−ro
+υce
−
Lundstrom: Fall 2019
ic = gmυbe +υce r0
ib =υbe rπ
Doing it with math
12 Lundstrom: Fall 2019
f x, y( ) f x +δ x, y +δ y( ) = ?
f x +δ x, y +δ y( ) ≈ ∂ f∂x y
δ x + ...∂ f∂y x
δ y + ...
IC VBE ,VCE( ) = ISeqVBE kBT 1+
υCE
VA
⎛
⎝⎜⎞
⎠⎟
IB VBE ,VCE( ) = IS
βeqVBE kBT
Outline
13
1) Small signal model for BJT 2) Small signal amplifier analysis 3) NPN vs. PNP 4) T-model
Lundstrom: Fall 2019
Small signal circuit
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+υo
−
RC = 5 kΩiC = IC + ic
υi
We now have an ac small signal model for the BJT
Lundstrom: Fall 2019
1) Use simple s.s. model
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gm = ICVT
gmrπ = β
E
C B ib ic
rπ+υbe
−gmυbe
Lundstrom: Fall 2019
Draw the s.s. equivalent circuit
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υOUT =VOUT+υo
VCC
RCiC = IC + ic
VBB+−
υi
Lundstrom: Fall 2019
Small signal circuit
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+υo
−
RC
icυi
C B ib
rπ+υbe
−
gmυbe
E
Same small signal circuit
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+υo
− RC
ic
υi
C B ib
rπ+υbe
−
gmυbe
E
Lundstrom: Fall 2019
ac analysis
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υo = −gmυbeRC
β = 100
RC = 5 kΩIC = 1mA
gm = ICVT
= 1mA0.026 V
= 38.5 mS
gmrπ = β
rπ = β gm = 100 0.039 = 2.6 kΩAυs
= −192
υo
υbe
= −gmRC
2) Use Hybrid pi model with output resistance
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gm = ICVT
gmrπ = βE
C B
ib ic
rbe gmυbe
+υbe
−ro
+υce
−
ro =VA ICLundstrom: Fall 2019
Draw the s.s. equivalent circuit
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υOUT =VO+υo
VCC
RCiC = IC + ic
RBB
VBE+−
υi
Lundstrom: Fall 2019
Small signal circuit
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+υo
− RC
ic
υi
C B ib
rπ+υbe
−
gmυbe
E
Lundstrom: Fall 2019
ro
ac analysis
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υo = −gmυbeRC || r0β = 100
RC = 5 kΩIC = 1mA
gm = ICVT
= 1mA0.026 V
= 38.5 mS
gmrπ = β
rπ = β gm = 100 0.039 = 2.6 kΩAυs= −183
υo
υi
= −gmRC || r0
VA = 100 V
ro =VAIC
= 100 kΩ
υi =υbe
Outline
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1) Small signal model for BJT 2) Small signal amplifier analysis 3) NPN vs. PNP 4) T-model
Lundstrom: Fall 2019
Hybrid pi model of BJT
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gm = ICVT
gmrπ = βE
C B
ib ic
rπ gmυbe
+υbe
−ro
+υce
−
ro =VA ICLundstrom: Fall 2019
Question: What does the small signal model for a PNP transistor like?
NPN DC to AC
26 Lundstrom: Fall 2019
N P N
IC = β IB
IB = IC β
IE =β +1β
IC
+VBE ≈ 0.7 V
-
ic = gmυbe
ib =υbe rπ
ie = gm +1rπ
⎛⎝⎜
⎞⎠⎟υbe
N P N
+υbe
-
+VCE > 0-
PNP DC to AC
27 Lundstrom: Fall 2019
P N P
IC = β IB
IB = IC β
IE =β +1β
IC
+VBE ≈ −0.7 V
-
ic = gmυbe
ib =υbe rπ
ie = gm +1rπ
⎛⎝⎜
⎞⎠⎟υbe
P N P
+υbe
-
+VCE < 0-
Small signal hybrid pi model for NPN or PNP
28 Lundstrom: Fall 2019
gm = IC VT
gmrπ = β
E
ro =VA IC
C B
ib ic
rπ gmυbe
+υbe
−ro
+υce
−
Outline
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1) Small signal model for BJT 2) Small signal amplifier analysis 3) NPN vs. PNP 4) T-model
Lundstrom: Fall 2019
Hybrid pi model
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E
C B
ib ic
rπ gmυbe
+υbe
−
+υce
−βib
Lundstrom: Fall 2019
ic = gmυbe
ib =υbe rπ
BJT T-Model
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E
C
B
ib
ic
ic = gmυbe
+υbe = iere
−
re =rπ
β +1
Lundstrom: Fall 2019
ic = gmυbe
ib =υbe rπ ?
ie
Question: Where does ro go?
Summary
32 Lundstrom: Fall 2019
The small signal model of a BJT consists of two resistors and one voltage-controlled current course. The values of the ac model parameters are determined by the dc bias current.
Circuit analysis consists of two steps: 1) dc analysis to determine the OP, and 2) ac small signal analysis using the ac circuit model.
We will stick with the hybrid pi model for MOSFETs and BJTs, but the book also uses the T model from time to time.
BJT s.s. model
Lundstrom: Fall 2019 33
1) Small signal model for BJT 2) Small signal amplifier analysis 3) NPN vs. PNP 4) T-model
Practice: Draw the s.s. equivalent circuit
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υOUT =VO+υo
VCC
RCiC = IC + ic
VBB+−
υi
RE
1) Hybrid pi w/o ro 2) Hybrid pi w ro 3) T-model w/o ro 4) T-model w ro