Sam PalermoAnalog & Mixed-Signal Center
Texas A&M University
ECEN326: Electronic CircuitsFall 2017
Lecture 2: Transistor Models & Single-Stage Amplifiers
Announcements
• Lab• Lab 1 begins on 9/14• Check the updated Lab 1 on website
• TA Noah Yang’s office hours are on Tuesday 10AM-12PM
• HW1 is posted on the website and due 9/18
2
BJT Circuit Symbols
3
NPN PNP
• BJTs are 3 terminal devices• Collector, Base, & Emitter
• 2 complementary BJT devices: NPN & PNP
MOSFET Circuit Symbols
4
NMOS PMOS
• MOSFETs are 4-terminal devices• Drain, Gate, Source, & Body
• Body terminal generally has small impact in normal operation modes, thus device is generally considered a 3-terminal device• Drain, Gate, and Source are respectively similar to the Collector, Base,
and Emitter of the BJT
• 2 complementary MOSFETS: NMOS, PMOS
NPN “Large-Signal” (DC) Output Characteristic
5
• For analog applications, we generally desire the BJT to operate in the “Active” region
VVV satCECE 3.0,
NPN “Large-Signal” (DC) Model
6
• Exact equation
• However, VBE doesn’t change much over large values of IC. So, for hand calculations we assume a fixed VBE and use the following
NMOS “Large-Signal” (DC) Output Characteristic
7
• For analog applications, we generally desire the MOSFET to operate in the “Saturation” region
tnGSOVDS VVVV
Saturation
NMOS “Large-Signal” (DC) Model
8
Saturation
oxnn Ck ' where
PNP “Large-Signal” (DC) Output Characteristic
9
• Similar operation to NPN transistor, except• IC flows out of the device• Flip the terminal voltages in calculations
• For analog applications, we generally desire the BJT to operate in the “Active” region VVV satECEC 3.0,
PNP “Large-Signal” (DC) Model
10
• Exact equation
• However, VEB doesn’t change much over large values of IC. So, for hand calculations we assume a fixed VEB and use the following
• Similar operation to NMOS transistor, except• ID flows out of the device• Flip the terminal voltages in calculations
• For analog applications, we generally desire the BJT to operate in the “Saturation” region
PMOS “Large-Signal” (DC) Output Characteristic
11tpSGOVSD VVVV
Saturation
PMOS “Large-Signal” (DC) Model
12
Saturation
oxpp Ck ' where
Large-Signal “DC” Response
13
Large-Signal “DC” + Small-Signal “AC” Response
14
• For small-signal analysis, we “linearize” the response about the DC operating point
• If the signal is small enough, linearity holds and the complete response is the summation of the large-signal “DC” response and the small-signal “AC” response
CH5 Bipolar Amplifiers 15
DC Analysis vs. Small-Signal Analysis
First, DC analysis is performed to determine operating point and obtain small-signal parameters.
Second, sources are set to zero and small-signal model is used.
NPN & NMOS Small-Signal T-Models (ro=)
16
Formal PNP & PMOS Small-Signal T-Models (ro=)
17
• While these are the formal models, for both the PNP and PMOS device you can use the exact same model as the NPN and NMOS device• This is easier to remember• Obtained by flipping the current sources in the formal model
CH5 Bipolar Amplifiers 18
Input/Output Impedances
The figure above shows the techniques of measuring input and output impedances.
Small signal analysis is used
x
xx i
VR
BJT Node AC Resistances (ro=)
19
• Using T-model, base AC resistance is the resistors connected from base through the emitter to ground multiplied by (+1)
• If ro is , then collector AC resistance is
• Using T-model, emitter AC resistance is re plus the base resistor divided by (+1)
BJT Amplifiers AC Gain (ro=)
20
CE Amp CC Amp CB Amp CE Amp w/ RE
MOSFET Node AC Resistances (ro=)
21
• Gate input impedance is capacitive, which is assumed to be infinite resistance at low frequencies
• If ro is , then drain AC resistance is
• Using T-model, source AC resistance is the 1/gm resistor
MOSFET Amplifiers AC Gain (ro=)
22
CS Amp CD Amp CG Amp CS Amp w/ RS
NPN Small-Signal Model & Introducing Finite ro
23
PNP Small-Signal Model w/ Finite ro
24
• While this is the formal model, you can use the exact same model as the NPN device• This is easier to remember• Obtained by flipping the small
signal veb and the current source in the formal model
MOSFET – Impact of Body Voltage
• Before we go over the MOSFET -model, lets consider the impact of the 4th terminal, the Body, on the drain current ID
• The MOSFET Vtn is a function of the Body-Source voltage VBS• If the threshold voltage changes, then so does ID
25
[Razavi] DStnGSoxn
D VVVLWCI
12
2
000 22 SBVtnFSBFtntn VVVV
• The small-signal drain current changes with VBS modulation due to changes in Vtn
Body Transconductance, gmb
26
[Razavi]
SBF
m
Qbs
tn
QtnGS
effOX
Qbs
Dmb V
gvVVV
LWC
vig
22*
Effects)g(NeglectinSaturationIn
NMOS Small-Signal Model w/ Finite ro & Body Transconductance gmb
27
000 22 SBVtnFSBFtntn VVVV
SBF V
22 where • Note, gmb is generally a weak effect (~0.1gm).
Thus, we often ignore it.• In problems/assignments I’ll make it clear when
we need to consider it
PMOS Small-Signal Model w/ Finite ro & Body Transconductance gmb
28
000 22
SBVtpFSBFtptp VVVV
SBF V
22 where
• Note, gmb is generally a weak effect (~0.1gm). Thus, we often ignore it.
• In problems/assignments I’ll make it clear when we need to consider it
• While this is the formal model, you can use the exact same model as the NMOS device• This is easier to remember• Obtained by flipping the
small signal vsg and vsb and the current sources in the formal model
• It is often useful to model transistor amplifiers with a Norton-equivalent model consisting of a transconductancecurrent source and parallel output resistance
Two-Port Modeling of Amplifiers
29
Two-Port Modeling – Extracting Gm and Rn
30
• Short the output, apply an input voltage stimulus, and measure output current
• Short the input, apply an output voltage stimulus, and measure current into output node
Two-Port Modeling – Multi-Stage Amplifiers
31
Two-Port Modeling – Multi-Stage Amplifiers
32
• Note, Rn1 also includes the input resistance of Stage 2
Two-Port Modeling – Multi-Stage Amplifiers
33
• Repeat procedure stage by stage
Two-Port Modeling – Multi-Stage Amplifiers
34
• Repeat procedure stage by stage• This procedure will be useful for analyzing multi-stage transistor
amplifiers
BJT Amplifiers AC Gain (ro=)
35
CE Amp CE Amp w/ RE
Cn
emm
e
CCm
i
o
RRr
gG
rRRg
vv
Cn
EeEm
mm
Ee
C
Em
Cm
i
o
RR
RrRggG
RrR
RgRg
vv
1
1
BJT Amplifiers AC Gain (ro=)
36
CC Amp CB Amp
Een
em
Ee
E
i
o
RrRr
G
RrR
vv
1
Cn
Bm
m
emitterBem
emitter
C
Bm
Cm
i
o
RR
Rgg
RRrG
RR
RgRg
vv
11
1
MOSFET Amplifiers AC Gain (ro=)
37
CS Amp CS Amp w/ RS
Dn
mm
Dmi
o
RRgG
Rgvv
Dn
Sm
mm
Sm
Dm
i
o
RRRg
gG
RgRg
vv
1
1
MOSFET Amplifiers AC Gain (ro=)
38
CD Amp CG Amp
Sm
n
mm
Sm
Sm
i
o
Rg
R
gGRg
Rgvv
1
1
Dn
sourcemm
source
DDm
i
o
RRR
gG
RRRg
vv
1
3-Stage BJT Amplifier Example
39
• This multi-stage amplifier consists of common-emitter, common-base, and common-collector amplifier
• The first two common-emitter and common-base stages are commonly used together, and are called a “cascode amplifier”
• The cascode stage provides all the voltage gain of the circuit, while the output common-collector circuit allows driving of a low-resistance load
Cn
EeEm
mm
Ee
C
Em
Cm
i
o
RR
RrRggG
RrR
RgRg
vv
1
1
3-Stage BJT Amplifier Example – 1st Stage Av
40
CE Amp w/ RE
• Using the common-emitter amplifier equations, the gain from the input to VE2 is
GEe
iv
ein
GEeGEm
mm
nmin
ev
RRrRA
rRR
RRrRRggG
RGvvA
1
21
221
11
11
112
1
1
3-Stage BJT Amplifier Example – 2nd Stage Av
41
• Using the common-base amplifier equations, the gain from VE2 to VB3 is
2
32
332
222
2
222
32
1
11
i
LeCv
LeCiCn
mie
m
nme
bv
RRrR
A
RrRRRR
gRr
G
RGvvA
CB Amp
Cn
Bm
m
emitterBem
emitter
C
Bm
Cm
i
o
RR
Rgg
RRrG
RR
RgRg
vv
11
1
3-Stage BJT Amplifier Example – 3rd Stage Av
42
• Using the common-collector amplifier equations, the gain from VB3 to Vout is
Le
Lv
Len
em
nmb
outv
RrRA
RrRr
G
RGvvA
33
33
33
333
3
1
CC Amp
Een
em
Ee
E
i
o
RrRr
G
RrR
vv
1
Le
L
GEe
iC
Le
L
i
iC
GEe
i
vvvin
outtotv
RrR
RRrRR
RrR
RRR
RRrR
AAAvvA
31
3
32
3
1
2
321,
3-Stage BJT Amplifier Example – Total Av
43
• The total gain is equal to the product of the individual stage gains
CH5 Bipolar Amplifiers 44
Amplifier Example I
The keys in solving this problem are recognizing the AC ground between R1 and R2, and Thevenin transformation of the input network
Then the common-emitter amplifer equations can be used
C1 acts as an AC short
CH5 Bipolar Amplifiers 45
Amplifier Example I
11
1 RRRRR
Rvv SThevS
inThev
• Find the input Thevenin equivalent
Ee
C
Em
Cm
i
oRr
RRg
Rgvv
1
CH5 Bipolar Amplifiers 46
Amplifier Example I
• Use the common-emitter amplifier equations CE Amp w/ RE
• As there is a base resistance (RThev), this must be reflected into the emitter by dividing by (+1) to use the derived equation
S
EeS
C
i
oRR
R
RrRR
RRvv
1
1
1
2
1
CH5 Bipolar Amplifiers 47
Amplifier Example II
Again, AC ground/short and Thevenin transformation are needed to transform the complex circuit into a simple stage with emitter degeneration.
Se
S
C
i
oRR
R
RrRR
Rvv
1
1
21
1
CH5 Bipolar Amplifiers 48
Amplifier Example III
The key for solving this problem is first identifying Req, which is the impedance seen at the emitter of Q2 in parallel with the infinite output impedance of an ideal current source
1211
211
12
111
1
RrrRrrRrR
RrR
eeeqein
eeq
11
21
Rrr
Rvv
ee
D
i
o
Next Time
• Differential amplifiers• Razavi Chapter 10
49
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