EENG 3510 Chapter 4
Metal-Oxide- Semiconductor (MOS)
Field-Effect Transistors (MOSFETs)
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Chapter 4 Homework 4a
4.5, 4.7a&b, D4.14, D4.34, 4.36,
4.42(a for Figures (a) & (b),
assume saturation in (a)),
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Chapter 4 Homework 4b
4.51, 4.59, 4.58, 4.64a, 4.69, 4.99
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Introduction
• From Diode to Transistor
– Two terminals to three terminals
– Use of the voltage between two terminals to control the current
flowing in the third terminal
• Two types of Transistors
– MOSFETs: metal oxide semiconductor field effect transistors
(chapter 4)
– BJT: bipolar junction transistor (chapter 5)
• Topics
–
–
–
–
Physical structure and operations
Terminal characteristics
Circuit models
Basic circuit applications: amplifier and logic inverter
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Metal-Oxide- Semiconductor (MOS) FieldEffect Transistors (MOSFETs)
• MOSFET
– Most important component in modern digital
integrated circuits
– Used in microprocessors
– Used in computer memory
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4.1 Device Structure and Physical Operation
(Physical structure of the enhancement-type NMOS transistor)
perspective view
cross-section
Typically L = 0.1 to 3 mm, W = 0.2 to 100 mm, and the thickness
of the oxide layer (tox) is in the range of 2 to 50 nm.
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4.1 Device Structure and Physical Operation
• 4.1.1 Device Structure
• Source (S) connects to Body (B), Drain (D) is at a positive
voltage relative to S, two pn junctions are cut off
• Substrate: no effect on device operation →3 terminals device
• Source and drain can be interchanged
+5 V
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4.1.4 Applying a Small VDS
An NMOS transistor with vGS (gate voltage) > Vt (threshold voltage)and with a
small vDS applied. The device acts as a resistance whose value is determined
by vGS. Specifically, the channel conductance is proportional to vGS – Vt’ and
thus iD is proportional to (vGS – Vt) vDS. Note that the depletion region is not
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shown (for simplicity).
4.1.4 Applying a Small VDS (Cont.)
The iD (drain current) – vDS (drain voltage) characteristics of the MOSFET
in the above slide when the voltage applied between drain and source,
vDS, (drain source) is kept small. The device operates as a linear resistor
whose value is controlled by vGS (gate source).
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4.1.5 Operation as VDS Is Increased
Operation of the enhancement NMOS transistor as vDS is increased.
The induced channel acquires a tapered shape, and its resistance
increases as vDS is increased. Here, vGS is kept constant at a value > Vt.
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4.1.6 Derivation of the ID –VDS relationship
The drain current iD versus the drain-to-source voltage vDS for an
enhancement-type NMOS transistor operated with vGS > Vt.
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4.1.8 Complementary MOS or CMOS
Cross-section of a CMOS integrated circuit. Note that the PMOS
transistor is formed in a separate n-type region, known as an n well.
Another arrangement is also possible in which an n-type body is used
and the n device is formed in a p well.
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Symbols for enhancement-type MOSFETs
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4.2 Current-Voltage Characteristics
4.2.1 Circuit Symbol
(a) Circuit symbol for the n-channel enhancement-type MOSFET. (b) Modified
circuit symbol with an arrowhead on the source terminal to distinguish it from the
drain and to indicate device polarity (i.e., n channel). (c) Simplified circuit symbol
to be used when the source is connected to the body or when the effect of the
body on device operation is unimportant.
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4.2.2 The ID –vDS Characteristics
• There are three distinct regions of operation:
– The cut-off region
– The triode region
– The saturation region
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4.2.2 The ID –vDS Characteristics (Cont.)
(a) An n-channel enhancement-type MOSFET with vGS and
vDS applied and with the normal directions of current flow
indicated. (b) The iD–vDS characteristics for a device with
k’n (W/L) = 1.0 mA/V2.
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4.2.2 The ID –vDS Characteristics (Cont.)
Cut off region
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4.2.2 The ID –vDS Characteristics (Cont.)
Triode region
The N-channel enhancement-type MOSFET
Operates in the triode region when vGS is greater
than Vi and the drain voltage is lower than the
gate voltage by at least Vt .
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Triode Region Example
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Triode Region Example (Cont.)
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Problem 4.7c&d
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Problem 4.7c&d (Cont.)
ox for silicon = 3.45x10-11
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4.2.2 The ID –vDS Characteristics (Cont.)
Saturation region
The N-channel enhancement-type MOSFET
Operates in the saturation region when vGS is
greater than Vi and the drain voltage does not
fall below the gate voltage by more than Vt .
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Saturation Region Example
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4.2.2 The ID –vDS Characteristics (Cont.)
Saturation region
The iD–vGS characteristic for an
enhancement-type NMOS transistor in
saturation (Vt = 1 V, k’n W/L = 1.0 mA/V2).
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4.2.2 The ID –vDS Characteristics (Cont.)
Large-signal equivalent-circuit model of an n-channel
MOSFET operating in the saturation region
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4.2.3 Finite Output Resistance in Saturation
IDEAL: a change vDS causes zero
change in ID , which means infinite
output resistance
Increasing vDS beyond vDSsat causes the channel pinch-off point to move slightly
away from the drain, thus reducing the effective channel length (by L).
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4.2.3 Finite Output Resistance in Saturation
Eq. 4.22
Eq. 4.24
Large-signal equivalent circuit model of the n-channel MOSFET in
saturation, incorporating the output resistance ro. The output resistance
models the linear dependence of iD on vDS and is given by Eq. (4.22).
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4.3 MOSFET Circuit At DC
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Example 4.2
Design the circuit of Fig. 4.20
so that the transistor operates
at ID=0.4mA and VD=+0.5V. The
NMOS transistor has Vt=0.7V,
μnCox=100 μA/V2, L = 1 μm, and
W=32 μm. Neglect the channellength modulation effect (i.e.
assume that λ=0).
RD= ?, RS = ?
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Example 4.2 (Cont.)
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Example 4.2 (Cont.)
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Another Design Example
Figure 1
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Example 4.4
Design the circuit in Fig. 4.22 to establish a drain voltage of
0.1 V. What is the effective resistance between drain and
source at this operating point? Let Vt=1 V, k’nW/L=1mA/V2.
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Example 4.4 (Cont.)
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Example 4.4 (Cont.)
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Another Design Example
Assume saturation
Figure 2
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Figure (c)
Assume saturation
ID = 2 = (½)(1)(Vov)2)
(Vov)2 = 4
Vov = 2 , However, Vov = -2 V since pmos circuit
VGS = Vt + Vov = -2 -2 = - 4
Thus Vs = 4 V = V4
V5 = -10 - ( - (2.5x103)(2x10-3)) = - 10 + 5 = -5 V
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Figure (d)
ID = 2 = (½)(1)(Vov)2)
(Vov)2 = 4
Vov = 2 , However, Vov = -2 V since
pmos circuit
VGS = Vt + Vov = -2 -2 = - 4 , Vs = 4
V6 = 10 – 4 = 6 V
V7 = 6 – 4 = 2 V
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4.4 The MOSFET As An
Amplifier and As A Switch
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4.4.1 Large-signal Operation –The Transfer Characteristic
• Common Source Amplifier (CS)
• To determine the voltage transfer
characteristic between vI and vO
VI = vGS
VO = vDS = VDD - RD iD
Graphically and analytically
Basic structure of the
common-source amplifier
Graphical construction to determine the
transfer characteristic of the amplifier in (a).
vDS= VDD-RDiD
iD= (VDD-vDS)/RD
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4.4.2 Graphical Derivation of the Transfer
Characteristic
Transfer characteristic showing operation
as an amplifier biased at point Q.
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4.4.3 Operation As Switch
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4.4.4 Operation as a Linear Amplifier
Two load lines and corresponding bias points.
Bias point Q1 does not leave sufficient room for
positive signal swing at the drain (too close to
VDD). Bias point Q2 is too close to the boundary
of the triode region and might not allow for
sufficient negative signal swing.
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4.4.5 Analytical Expressions for the Transfer
Characteristic
Cutoff-Region Segment, XA
vI< Vt, and vO= VDD
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4.4.5 Analytical Expressions for the Transfer
Characteristic (Cont.)
Saturation-Region Segment, AQB
Av = - 2 (VDD – VOQ) / VOV = - (2VRD) / VOV
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Example
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Example (Cont.)
Av = - 2 (VDD – VOQ) / VOV = - (2VRD) / VOV
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4.4.5 Analytical Expressions for the Transfer
Characteristic (Cont.)
Triode-Region Segment, BC
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4.5 Biasing In MOS Amplifier Circuits
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4.5.1 Biasing by Fixing VGS
Variability
Most straightforward
Device dependent
Temperature dependent
The use of fixed bias (constant VGS) can result in a large variability in the value
of ID. Devices 1 and 2 represent extremes among units of the same type.
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4.5.2 Biasing by Fixing VG and Connecting a
Resistance in the Source
Reduced Variability
Biasing using a fixed voltage at the gate, VG,
and a resistance in the source lead, RS: (a)basic
arrangement; (b)reduced variability in ID;
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4.5.2 Biasing by Fixing VG and Connecting a
Resistance in the Source (Cont.)
Biasing using a fixed voltage at the gate, VG, and a resistance in
the source lead, RS: (c) practical implementation using a single
supply; (d) coupling of a signal source to the gate using a
capacitor CC1; (e) practical implementation using two supplies.
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Example
6
Bias current does not change
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Example
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4.5.3 Biasing Using a Drain-to-Gate Feedback
Resistor
Biasing the MOSFET using a large drain-to-gate feedback resistance, RG.
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Problem 4.64b
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4.5.4 Biasing Using a Constant-Current Source
Biasing the MOSFET using a
constant-current source I.
Implementation of the constantcurrent source I using a current mirror.
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4.5.4 Biasing Using a Constant-Current Source
(Cont.)
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4.6 Small-Signal Operation And Models
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4.6.1 The DC Bias Point
Set vgs to zero
Conceptual circuit utilized to study the operation
of the MOSFET as a small-signal amplifier.
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4.6.2 The Signal Current in the Drain Terminal
Conceptual circuit utilized to study the operation
of the MOSFET as a small-signal amplifier.
iD = the instantaneous drain current
ID = the DC Bias Current
To reduce nonlinear distortion, the input signal
should be kept small so that:
VO
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4.6.3 The Voltage Gain
Conceptual circuit utilized to study the operation
of the MOSFET as a small-signal amplifier.
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4.6.4 Separating the DC Analysis and the Signal
Analysis
Conceptual circuit utilized to study the operation
of the MOSFET as a small-signal amplifier.
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4.6.5 Small Signal Equivalent-Circuit Models
neglecting the dependence of iD
on vDS in saturation (the channellength modulation effect)
including the effect of channellength modulation, modeled by
output resistance ro = |VA| /ID.
VA = 1/ (where  = the channel-length
modulation effect)
r0 = 10K to 1000K
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4.6.6 The Transconductance gm
In contrast, gm for a bipolar
junction transistor (BJT) is
proportional to ID and is
independent of the physical size
And geometry of the device.
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Example
1
5
4
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Example a
= 10 V
= 4K
Vt = 1V
ID = (1/2) x 1 x (5 – 1)2
2ID = 42 = 16
ID = 8 mA
=5 V
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Example b
= 10 V
= 4K
Vt = 1V
Gm = 1 x (5 – 1) = 4 mA/V
=5 V
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Example c
= 10 V
= 4K
Vt = 1V
AV = - 4mA x 4K = -16 V/V
=5 V
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Example d
= 10 V
output resistance ro = |VA| /ID
VA = 1/ (where  = the channel-length
modulation effect)
= 4K
Vt = 1V
=5 V
rO = 1 / (0.01 x 8mA) = 1 / 0.08mA = 12.5 K
AV = - 4mA x (4K || 12.5K) = - 3.03 V/V
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4.6.7 The T Equivalent-Circuit Model
Development of the T equivalent-circuit model for
the MOSFET. For simplicity, ro has been omitted but
can be added between D and S in the T model of (d).
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4.6.7 The T Equivalent-Circuit Model (cont.)
The T model of the MOSFET augmented
with the drain-to-source resistance ro.
An alternative representation
of the T model.
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4.6.9 Summary
•
•
•
•
Small Signal Parameters
Transconductance:
Output Resistance:
Small Signal Equivalent Circuit Models
Hybrid-π model
T models
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4.7 Single-Stage MOS Amplifiers
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4.7.1 The Basic Structure
Basic structure of the circuit used to realize single-stage
discrete-circuit MOS amplifier configurations
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4.7.2 Characterizing Amplifiers
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4.7.2 Characterizing Amplifiers (cont.)
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4.7.2 Characterizing Amplifiers (cont.)
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4.7.3 The Common-Source (CS) Amplifier
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4.7.3 The Common-Source (CS) Amplifier (cont.)
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4.7.3 The Common-Source (CS) Amplifier (cont.)
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4.7.4 The Common-Source Amplifier with a
Source Resistance
Common-source amplifier with a
resistance RS in the source lead.
Small-signal equivalent circuit with ro neglected.
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4.7.4 The Common-Source Amplifier with a
Source Resistance
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Problem 77
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Problem 77a
a) VG = 15 x (5/15) = 5 V
VS = 3ID = VGS = 5 - 3ID
ID = (1/2)(2)(5 - 3ID - 1)2
0 = 16 -25ID + 9ID2
ID = 1 mA
VGS = 5 - 3ID = 2 V
VD = 15 – (7.5K x 1mA) = 7.5 V
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Problem 77b
Gm = 2 ID / VOV = (2 x 1) /(2 – 1) = 2 mA
rO = VA / ID = 100/1mA = 100K
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Problem 77c
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Problem 77d
x
x
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4.7.5 The Common-Gate (CG) Amplifier
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4.7.5 The Common-Gate (CG) Amplifier (cont.)
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4.7.6 The Common-Drain (CD) or SourceFollower Amplifier
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4.7.6 The Common-Drain (CD) or SourceFollower Amplifier (cont.)
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4.7.6 Summary and Comparisons
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4.7.6 Summary and Comparisons (cont.)
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4.7.6 Summary and Comparisons (cont.)
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4.7.6 Summary and Comparisons (cont.)
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