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6.002 Spring 2018 Lecture 7 1
6.002 CIRCUITS ANDELECTRONICS
Lecture 7 – MOSFET, MOSFET amplifier
March 1, 2018
Contents:1. Review of amplifiers2. MOSFET i-v characteristics3. MOSFET amplifier4. Small signal response
Reading Assignment:Agarwal and Lang, Ch. 7 (��7.3-7.6)
Handouts:Lecture 7 notes
Announcements:• Quiz on 3/14 (Wed) at 7:30-9:30PM in 10-250
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6.002 Spring 2018 Lecture 7 3
1. Review of amplifiers• Last time we studied this circuit:
• Transfer characteristics:
Circuit behaves as amplifier if: RLG>1
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6.002 Spring 2018 Lecture 7 4
• Key device needed to make an amplifier: voltage-controlled current source
• Is there a device that exhibits this behavior? Yes! The MOSFET!
Ii
Iv
Oi
Ov+
–
+
–IGv
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6.002 Spring 2018 Lecture 7 5
4. Transistors… The MOSFET• MOSFET=Metal-Oxide-Semiconductor
Field-Effect Transistor• MOSFET=three terminal semiconductor
device• In the MOSFET: Current through two
terminals (source and drain) controlled by voltage in third terminal (gate).
• Two different kinds: n-type and p-type• A modern microprocessor contains ~109-
5x109 MOSFETs
Inte
l 22
nm M
OS
FET
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6.002 Spring 2018 Lecture 7 7
• i-v characteristics of 2N7000
Satur
ation
Linea
r
Cut-off
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6.002 Spring 2018 Lecture 7 10
Three regimes of operation:– Cut-off: vGS ≤ VT
iD=0
– Linear or triode: vGS >VT, vDS ≤ vGS-VT
iD depends on vGS and vDS
– Saturation: vGS >VT, vDS ≥ vGS -VT
iD depends only on vGS
MOSFET i-v characteristics
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6.002 Spring 2018 Lecture 7 11
• MOSFET as voltage-controlled current source:
• MOSFET as switch:
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6.002 Spring 2018 Lecture 7 12
MOSFET equations
– Cut-off: vGS ≤ VT
– Linear or triode: vGS >VT, vDS ≤ vGS -VT
– Saturation: vGS >VT, vDS ≥ vGS –VT
Two parameters characterize the MOSFET in this simple model:– Threshold voltage: VT (in V)– �K factor�: K (in A/V2)
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6.002 Spring 2018 Lecture 7 14
• Compare behavior of MOSFET in saturation with that of voltage-controlled current source:
• In MOSFET in saturation, the gate-source voltage is the control voltage.
• Key to make MOSFET amplifier: use MOSFET in saturation!
iO
vO
vI
I=GvI
00
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6.002 Spring 2018 Lecture 7 15
3. MOSFET amplifier• In analogy with:
• Consider this circuit:
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6.002 Spring 2018 Lecture 7 16
• How does it work?• Use graphical technique first:
àdraw �load line� associated with RL
• Operating point of amplifier at intersection of load line with MOSFET characteristics.
Vo=VS-RL.iD
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6.002 Spring 2018 Lecture 7 17
• Sketch the transfer characteristics:
• When MOSFET in saturation, transfer
characteristics steep à high voltage gain!
Vo=Vs-RL.iD
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6.002 Spring 2018 Lecture 7 18
• High voltage gain region suitable for amplifier:
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6.002 Spring 2018 Lecture 7 19
• Cutoff and linear regions unsuitable for amplifier: low gain and distortion
Demo
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6.002 Spring 2018 Lecture 7 20
• In saturation, MOSFET operates as current source à equivalent circuit:
How to quantitatively calculate transfer characteristic?
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6.002 Spring 2018 Lecture 7 21
• Amplifier transfer characteristics:
Node equation for node vO:
Then, transfer characteristics:
Note: transfer function is quadratic
à distortion!!
Demo
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6.002 Spring 2018 Lecture 7 22
4. How to minimize distortion: Small-signal• Transfer characteristics of MOSFET amp
are not linear:
à distortion!
• Key insight: if magnitude of signal is smallrelative to VS, transfer characteristics around bias point look fairly linearà low distortion.
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6.002 Spring 2018 Lecture 7 23
• If one can linearize, what are the vo-vismall-signal transfer characteristics?
• Large-signal transfer characteristics:
• Input is of form:
• Output should then be of form:
• Identify terms:
– Bias terms:
– Small-signal terms:
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6.002 Spring 2018 Lecture 7 24
• Small-signal terms:
• Linearizing means keeping only the linear term:
• Small-signal gain:
slope: -KRL(VI -VT)
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6.002 Spring 2018 Lecture 7 25
• When is this approximation good?
quadratic term << linear term
Or:
• The higher the bias, the easier it is to deliver this condition.
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6.002 Spring 2018 Lecture 7 26
• Let’s put some numbers: use 2N7000 (VT=2 V, K=0.14 A/V2)
with RL=250 Ω and VS=5 V.Transfer characteristics look like:
If select VO=2.7 V, then VI=2.4 V, and:
Input waveform with Vi=80 mV [≈0.2(VI –VT )], gives output waveform with Vo=1 V.
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6.002 Spring 2018 Lecture 7 27
• More generally, obtain small-signal transfer characteristics by Taylor series expansion of large-signal transfer characteristics.
• If large-signal transfer characteristics are:
• Then, if vI=VI+vi, expand around (VI,VO):
• Small-signal transfer characteristics are:
• And small-signal gain is:
[check that from here, you get the same result as above]
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6.002 Spring 2018 Lecture 7 28
Summary
• Three regimes of operation to a MOSFET: cutoff, linear and saturation
• In order to make an amplifier, MOSFET must be used in saturation
• A simple MOSFET model provides adequate description of i-v characteristics and requires only two parameters:– Threshold voltage– �K factor�
• An amplifier can be constructed with one MOSFET and one resistor.
• Transfer characteristics are quadratic (some degree of distortion introduced)