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6.002 Spring 2020 Lecture 21 1
6.002 CIRCUITS ANDELECTRONICS
Lecture 21 – MOSFET, MOSFET amplifier
April 30, 2020
Contents:1. Review of amplifiers2. MOSFET i-v characteristics3. MOSFET amplifier4. Small signal response (probably next week)
Reading Assignment:Agarwal and Lang, Ch. 7 (§§7.3-7.6)
Handouts:Lecture 21 notes
Announcements:This lecture is being recorded and it will be posted in the certificates-protected part of the 6.002 website
6.002 Spring 2020 Lecture 21 3
1. Review of amplifiers• In the past, we studied this circuit:
• Transfer characteristics:
Circuit behaves as amplifier if: RLG>1
2
6.002 Spring 2020 Lecture 21 4
• Key device needed to make an amplifier: voltage-controlled current source
• Is there a device that exhibits this behavior?
Yes! The MOSFET! (and other transistors)
Ii
Iv
Oi
Ov+
–
+
–IGv
6.002 Spring 2020 Lecture 21 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 conduction• A modern microprocessor contains ~109-5x109 MOSFETs
Inte
l 14
nm
MO
SFET
8 nm
Samsung 14nm MOSFET
3
6.002 Spring 2020 Lecture 21 6
How does a MOSFET work?
http://www-g.eng.cam.ac.uk/mmg/teaching/linearcircuits/mosfet.htmlhttps://www.youtube.com/watch?v=tz62t-q_KEc&start=230
Demo
6.002 Spring 2020 Lecture 21 7
https://www.researchgate.net/figure/FET-Conventional-symbol-types_fig3_277095691
And many more…
4
Julius Lilienfeld and the first MOSFET
6.002 Spring 2020 Lecture 21 8
https://www.computerhistory.org/siliconengine/field-effect-semiconductor-device-concepts-patented/
The first transistor (1947)…
6.002 Spring 2020 Lecture 21 9
http://www.computerhistory.org/revolution/digital-logic/12/273/1364
5
6.002 Spring 2020 Lecture 21 10
https://mixedsignal.wordpress.com/2015/12/14/the-transistor-symbol/
https://hackaday.com/tag/point-contact-transistor/https://www.elprocus.com/different-types-of-transistor-and-their-functions/
6.002 Spring 2020 Lecture 21 11
1947: John Bardeen and Walter Brattain, with support from colleague William Shockley, demonstrate the transistor at Bell Laboratories in Murray Hill, New Jersey.
AB
C
6
6.002 Spring 2020 Lecture 21 12
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
6.002 Spring 2020 Lecture 21 13
• MOSFET as voltage-controlled current source ( ~analog electronics):
• MOSFET as switch ( ~digital electronics):
7
6.002 Spring 2020 Lecture 21 14
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)
6.002 Spring 2020 Lecture 21 15
• 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
8
6.002 Spring 2020 Lecture 21 16
3. MOSFET amplifier• In analogy with:
• Consider this circuit:
6.002 Spring 2020 Lecture 21 17
• 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
9
6.002 Spring 2020 Lecture 21 18
• Sketch the transfer characteristics:
• When MOSFET in saturation, transfer characteristics steep à high voltage gain!
Vo=Vs-RL.iD
Demo
6.002 Spring 2020 Lecture 21 19
• High voltage gain region suitable for amplifier:
10
6.002 Spring 2020 Lecture 21 20
• Cutoff and linear regions unsuitable for amplifier: low gain and distortion
Demo
6.002 Spring 2020 Lecture 21 21
• In saturation, MOSFET operates as current source à equivalent circuit:
How to quantitatively calculate transfer characteristic?
11
6.002 Spring 2020 Lecture 21 22
• Amplifier transfer characteristics:
Node equation for node vO:
Then, transfer characteristics:
Note: transfer function is quadratic à distortion!!
6.002 Spring 2020 Lecture 21 23
4. How to minimize distortion: Small-signal
• Transfer characteristics of MOSFET amp are not linear:
à distortion!
• Key insight: if magnitude of signal is small relative to VS, transfer characteristics around bias point look fairly linear à low distortion.
12
6.002 Spring 2020 Lecture 21 24
• If one can linearize, what are the vo-vi small-signal transfer characteristics?• Large-signal transfer characteristics:
• Input is of form:
• Output should then be of form:
• Identify terms:– Bias terms:
– Small-signal terms:
6.002 Spring 2020 Lecture 21 25
• Small-signal terms:
• Linearizing means keeping only the linear term:
• Small-signal gain:
slope: -KRL(VI -VT)
13
6.002 Spring 2020 Lecture 21 26
• When is this approximation good?
quadratic term << linear term
Or:
• The higher the bias, the easier it is to deliver this condition.
6.002 Spring 2020 Lecture 21 27
• 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.
14
6.002 Spring 2020 Lecture 21 28
• 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]
6.002 Spring 2020 Lecture 21 29
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)