njit ece271 dr. serhiy levkovchap 4-1 topic 4 field-effect transistors ece 271 electronic circuits i
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-1
Topic 4Field-Effect Transistors
ECE 271
Electronic Circuits I
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-2
Chapter Goals
• Describe structure and operation of MOSFETs.• Define FET characteristics in operation regions of cutoff, triode and
saturation.• Develop mathematical models for i-v characteristics of MOSFETs.• Introduce graphical representations for output and transfer
characteristic descriptions of electron devices.• Define and contrast characteristics of enhancement-mode and
depletion-mode FETs.• Define symbols to represent FETs in circuit schematics.• Investigate circuits that bias transistors into different operating
regions.• Explore FET modeling in SPICE.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-3
Intro (1)
• Solid state transistor is the main building block of microelectronics. • It performs two major functions used in electronic devices:
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-4
Intro (1)
• Solid state transistor is the main building block of microelectronics. • It performs two major functions used in electronic devices:
- amplifications (in analog)
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-5
Intro (1)
• Solid state transistor is the main building block of microelectronics. • It performs two major functions used in electronic devices:
- amplifications (in analog) - switching (in digital)
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-6
Intro (1)
• Solid state transistor is the main building block of microelectronics. • It performs two major functions used in electronic devices:
- amplifications (in analog) - switching (in digital)
• There are two basic types of solid state transistors: BJT (bipolar junction transistor) and FET (field effect transistor).
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-7
Intro (1)
• Solid state transistor is the main building block of microelectronics. • It performs two major functions used in electronic devices:
- amplifications (in analog) - switching (in digital)
• There are two basic types of solid state transistors: BJT (bipolar junction transistor) and FET (field effect transistor).
• FET: electric field is used to control the shape and the conductivity of the channel of one type charge carrier (p or n) in semiconductor device.
• They are also called unipolar to contrast their single-carrier-type operation with the dual-carrier-type operation of bipolar (junction) transistors (BJT).
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-8
Intro (1)
• Solid state transistor is the main building block of microelectronics. • It performs two major functions used in electronic devices:
- amplifications (in analog) - switching (in digital)
• There are two basic types of solid state transistors BJT (bipolar junction transistor) and FET (field effect transistor).
• FET: electric filed is used to control the shape and hence the conductivity of the channel of one type charge carrier (p or n) in semiconductor device.
• They are also called unipolar to contrast their single-carrier-type operation with the dual-carrier-type operation of bipolar (junction) transistors (BJT).
• FET can be of two major types MOSFET (metal oxide semiconductor field effect transistor (mostly used)), and JFET (junction field effect transistor).
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-9
Intro (2)
• Metal Oxide Semiconductor Field Effect device was first solid state device conceived (Lilienfield, 1928), however it took very long to develop a successful commercial application of such devices. The first successful device was fabricated in 1950, however the reliable commercial fabrication did not start until decade later.
• Today, the CMOS technology based on MOSFET is the dominant technology in electronics.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-10
Intro (2)
• Metal Oxide Semiconductor Field Effect device was first solid state device conceived (Lilienfield, 1928), however it took very long to develop a successful commercial application of such devices. The first successful device was fabricated in 1950, however the reliable commercial fabrication did not start until decade later.
• Today, the CMOS technology based on MOSFET is the dominant technology in electronics.
• BJT devices were first introduced in 1948 and quickly became commercially available. The first IC with logic gates and operational amplifiers that appeared in early 1960s, were based on BJT technology. They are still widely used, particularly in applications requiring high speed and high precision.
• BJT device is based on pn-junction structure, while MOSFET is utilizing the MOS capacitor structure.
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NJIT ECE271 Dr. Serhiy Levkov
Metal Oxide Semiconductor Field-Effect Transistors
(MOSFET)
Chap 4-11
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-12
MOS Capacitor Structure
• Metal Oxide Semiconductor capacitor is the core structure of the a Metal Oxide Semiconductor Field Effect Transistor.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-13
MOS Capacitor Structure
• Metal Oxide Semiconductor capacitor is the core structure of the a Metal Oxide Semiconductor Field Effect Transistor.
• Consists of two electrodes and insulator in between.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-14
MOS Capacitor Structure
• Metal Oxide Semiconductor capacitor is the core structure of the a Metal Oxide Semiconductor Field Effect Transistor.
• Consists of two electrodes and insulator in between.
• First electrode (Gate): low-resistivity material such as metal or polycrystalline silicon.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-15
MOS Capacitor Structure
• Metal Oxide Semiconductor capacitor is the core structure of the a Metal Oxide Semiconductor Field Effect Transistor.
• Consists of two electrodes and insulator in between.
• First electrode (Gate): low-resistivity material such as metal or polycrystalline silicon.
• Dielectric - Silicon dioxide: stable high-quality electrical insulator between gate and substrate.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-16
MOS Capacitor Structure
• Metal Oxide Semiconductor capacitor is the core structure of the a Metal Oxide Semiconductor Field Effect Transistor.
• Consists of two electrodes and insulator in between.
• First electrode (Gate): low-resistivity material such as metal or polycrystalline silicon.
• Dielectric - Silicon dioxide: stable high-quality electrical insulator between gate and substrate.
• Second electrode (Substrate, Body): n- or p-type semiconductor.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-17
MOS Capacitor Structure
• Metal Oxide Semiconductor capacitor is the core structure of the a Metal Oxide Semiconductor Field Effect Transistor.
• Consists of two electrodes and insulator in between.
• First electrode (Gate): low-resistivity material such as metal or polycrystalline silicon.
• Dielectric - Silicon dioxide: stable high-quality electrical insulator between gate and substrate.
• Second electrode (Substrate, Body): n- or p-type semiconductor.
• The semiconductor body has limited supply of holes and electrons, and substantial resistivity.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-18
MOS Capacitor Structure
• Metal Oxide Semiconductor capacitor is the core structure of the a Metal Oxide Semiconductor Field Effect Transistor.
• Consists of two electrodes and insulator in between.
• First electrode (Gate): low-resistivity material such as metal or polycrystalline silicon.
• Dielectric - Silicon dioxide: stable high-quality electrical insulator between gate and substrate.
• Second electrode (Substrate, Body): n- or p-type semiconductor.
• The semiconductor body has limited supply of holes and electrons, and substantial resistivity.
The concentration of carriers being dependant on voltage, the capacitance of this structure therefore is a nonlinear function of voltage applied.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-19
Substrate Conditions for Different Biases
• Accumulation : VG<<VTN
The majority carriers (holes) accumulate in a very thin layer below the negative gate (like in capacitor)
We consider the conditions of the semiconductor region (p-type) below the gate electrode under three different voltage bias: accumulation, depletion, inversion.
Those conditions are determined by VTN (0.5 - 2.0 V) the threshold voltage, at which the electron inversion layer is just starting to form.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-20
Substrate Conditions for Different Biases
• Accumulation : VG<<VTN , VG<0The majority carriers (holes) accumulate in a very thin layer below the negative gate (like in capacitor)
• Depletion: 0<VG<VTN The small positive charge of the gate wipe out the holes from the layer below (depletes free carriers) creative a negative charge of ionized atoms
We consider the conditions of the semiconductor region (p-type) below the gate electrode under three different voltage bias: accumulation, depletion, inversion.
Those conditions are determined by VTN (0.5 - 2.0 V) the threshold voltage, at which the electron inversion layer is just starting to form.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-21
Substrate Conditions for Different Biases
• Accumulation : VG<<VTN
The majority carriers (holes) accumulate in a very thin layer below the negative gate (like in capacitor)
• Depletion: 0<VG<VTN The small positive charge of the gate wipe out the holes from the layer below (depletes free carriers) creative a negative charge of ionized atoms
• Inversion: VG>VTN The larger positive charge of the gate attracts electrons whose concentration in the very thin layer exceeds that of holes – inversion of p-type into n-type.
We consider the conditions of the semiconductor region (p-type) below the gate electrode under three different voltage bias: accumulation, depletion, inversion.
Those conditions are determined by VTN (0.5 - 2.0 V) the threshold voltage, at which the electron inversion layer is just starting to form.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-22
Low-frequency C-V Characteristics for MOS Capacitor on P-type Substrate
• MOS capacitance is non-linear function of voltage.
• Total capacitance in any region is dictated by the separation between capacitor plates.
• Total capacitance can be modeled as series combination of fixed oxide capacitance and voltage-dependent depletion layer capacitance.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-23
NMOS Transistor: StructureA N-MOSFET is formed by adding two heavily doped n-type (n+ , about one of 100 of silicon atoms is replaced with donor), regions to the MOS capacitor. The resulting diffusions provide a supply of electrons that can rapidly form the inversion layer and easily move under the gate, and also make terminals to apply a voltage and create a current in the channel region.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-24
NMOS Transistor: Structure
• 4 device terminals:
Gate(G)
A N-MOSFET is formed by adding two heavily doped n-type (n+ , about one of 100 of silicon atoms is replaced with donor), regions to the MOS capacitor. The resulting diffusions provide a supply of electrons that can rapidly form the inversion layer and easily move under the gate, and also make terminals to apply a voltage and create a current in the channel region.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-25
NMOS Transistor: Structure
• 4 device terminals:
Gate(G)
Drain(D)
A N-MOSFET is formed by adding two heavily doped n-type (n+ , about one of 100 of silicon atoms is replaced with donor), regions to the MOS capacitor. The resulting diffusions provide a supply of electrons that can rapidly form the inversion layer and easily move under the gate, and also make terminals to apply a voltage and create a current in the channel region.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-26
NMOS Transistor: Structure
• 4 device terminals:
Gate(G)
Drain(D),
Source(S)
A N-MOSFET is formed by adding two heavily doped n-type (n+ , about one of 100 of silicon atoms is replaced with donor), regions to the MOS capacitor. The resulting diffusions provide a supply of electrons that can rapidly form the inversion layer and easily move under the gate, and also make terminals to apply a voltage and create a current in the channel region.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-27
NMOS Transistor: Structure
• 4 device terminals:
Gate(G)
Drain(D),
Source(S)
Body(B)
A N-MOSFET is formed by adding two heavily doped n-type (n+ , about one of 100 of silicon atoms is replaced with donor), regions to the MOS capacitor. The resulting diffusions provide a supply of electrons that can rapidly form the inversion layer and easily move under the gate, and also make terminals to apply a voltage and create a current in the channel region.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-28
NMOS Transistor: Structure
• 4 device terminals:
Gate(G)
Drain(D),
Source(S)
Body(B).• Source and drain regions form
pn junctions with substrate.
A N-MOSFET is formed by adding two heavily doped n-type (n+ , about one of 100 of silicon atoms is replaced with donor), regions to the MOS capacitor. The resulting diffusions provide a supply of electrons that can rapidly form the inversion layer and easily move under the gate, and also make terminals to apply a voltage and create a current in the channel region.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-29
NMOS Transistor: Structure
• 4 device terminals:
Gate(G)
Drain(D),
Source(S)
Body(B).• Source and drain regions form
pn junctions with substrate.• vSB,= vS – vB , vDS = vD - vS and vGS
= vG - vS are typically nonnegative during normal operation.
A N-MOSFET is formed by adding two heavily doped n-type (n+ , about one of 100 of silicon atoms is replaced with donor), regions to the MOS capacitor. The resulting diffusions provide a supply of electrons that can rapidly form the inversion layer and easily move under the gate, and also make terminals to apply a voltage and create a current in the channel region.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-30
NMOS Transistor: Structure
• 4 device terminals:
Gate(G)
Drain(D),
Source(S)
Body(B).• Source and drain regions form
pn junctions with substrate.• vSB,= vS – vB , vDS = vD - vS and vGS
= vG - vS are always positive during normal operation.
• vB <= vD and vB <= vS , to keep pn junctions reverse biased.
A N-MOSFET is formed by adding two heavily doped n-type (n+ , about one of 100 of silicon atoms is replaced with donor), regions to the MOS capacitor. The resulting diffusions provide a supply of electrons that can rapidly form the inversion layer and easily move under the gate, and also make terminals to apply a voltage and create a current in the channel region.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-31
NMOS Transistor and Variable Resistor
• A transistor is a three (or four) terminal device, in which one terminal controls the voltage or current between other two terminals
• In certain way it is similar to a variable resistor, in which the movement of the middle terminal controls the voltage.
+
-
+
-
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-32
NMOS Transistor: Qualitative Behavior @ vDS =0
• VGS<<VTN (VGS <0): Two back to back reverse biased pn junctions btw S and D. Only small leakage current flows.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-33
NMOS Transistor: Qualitative Behavior @ vDS =0
• VGS<<VTN (VGS <0): Two back to back reverse biased pn junctions btw S and D. Only small leakage current flows.
• VGS<VTN (VGS >0): Depletion region formed under gate merges with source and drain depletion regions. No current flows between source and drain.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-34
NMOS Transistor: Qualitative Behavior @ vDS =0
• VGS<<VTN (VGS <0): Two back to back reverse biased pn junctions btw S and D. Only small leakage current flows.
• VGS<VTN (VGS >0): Depletion region formed under gate merges with source and drain depletion regions. No current flows between source and drain.
• VGS>VTN: Channel is formed between source and drain by electrons in inversion layer. If VDS>0, finite iD flows from drain to source.
• iB=0 and iG=0.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-35
Since the induced inversion layer is formed by electrons, it’s called N-channel MOSFET.
NMOS Transistor: Qualitative Behavior @ vDS =0
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-36
NMOS Transistor: Triode Region
vDSi K v V vnD TNGS DS2
where
Kn= Kn’W/L – the gain factor
Kn’=mnCox’’ (A/V2)
Cox’’=ox/Tox
ox= oxide permittivity (F/cm)
Tox = oxide thickness (cm)
for 0 v v VTNDS GS
Applying a small vDS creates a flow of electrons in the induced inversion layer between source and drain - current iD (iD = iS , since iB=0 and iG=0).
This is the triode region (linear region, ohmic mode). MOSFET operates like a resistor, controlled by the gate voltage relative to both the source and drain voltages.
smallvDS
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-37
N-MOS Transistor: Triode Region(derivation of the source-drain current)
' ''( ) / cm for ,
where '' / oxide capacitance per area, oxide permittivity(F/cm), oxide thickness (cm)ox ox TN ox TN
ox ox ox ox ox
Q W C v V C v V
C T T
Since currents iB and iG both are zero, and there is no path for drain current to escape: iS = iD.
To find it, we consider the transport of the charge. The linear density of the electron charge at any point in the channel is:
dx
xdvEx
)(
dx
xdvVxvvWCxi TNGSoxn
)()('')(
22" DS
TNGSnDSDS
TNGSoxnD
vVvKv
vVv
L
WCi
The voltage vox is the function of position x in the channel: . For inversion layer to exist, should be vox > VTN , so Q’ = 0 until vox > VTN . At the source, vox = vGS and it decrease to vox = vGS - vDS at the drain.
The electron drift current is : , where
Combining everything: and integrating:
, we get
)(xvvv GSox
)()(''')( xnTNoxoxx EVvCWvQxi
)()(")(0 0
xdvVxvvWCdxxi TNGS
L v
oxn
DS
'''' and,where oxnnnn CKL
WKK
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-38
Triode (a bit of history)
A triode is an electronic amplification device having three active electrodes. most commonly it’s a vacuum tube with three elements: the filament (cathode), the grid (controlling element), and the plate or anode. The triode vacuum tube was the first electronic amplification device. It’s iv-characteristics was quite linear.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-39
N-MOSFET: Triode Region Characteristics• The expression for iD is quadratic in vDS
vDSi K v VnD TNGS 2
vDS
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-40
N-MOSFET: Triode Region Characteristics• The expression for iD is quadratic in vDS
with max reached at vDS = vGS - vTN = vOV
vDSi K v V vnD TNGS DS2
vDS
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-41
N-MOSFET: Triode Region Characteristics• The expression for iD is quadratic in vDS
with max reached at vDS = vGS - vTN = vOV
• For small vDS << vGS - vTN , the characteristics iD vs. vDS appear to be linear (triode region, linear)
vDS
vDSi K v V vnD TNGS DS2
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-42
N-MOSFET: Triode Region CharacteristicsUnder this condition, MOSFET behaves like a gate-source voltage-controlled resistor between source and drain,
1
onRi K v V v vnD TNGS DS DS
• The expression for iD is quadratic in vDS with max reached at vDS = vGS - vTN = vOV
• For small vDS << vGS - vTN , the characteristics iD vs. vDS appear to be linear (triode region, linear)
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-43
N-MOSFET: Triode Region Characteristics
( )
1
'0
1'
on
DS
R
Ron WK V V Vn GS TN DSL v
VGSWK V Vn TNGSL
Under this condition, MOSFET behaves like a gate-source voltage-controlled resistor between source and drain,
where on-resistance:
1
onRi K v V v vnD TNGS DS DS
• The expression for iD is quadratic in vDS with max reached at vDS = vGS - vTN = vOV
• For small vDS << vGS - vTN , the characteristics iD vs. vDS appear to be linear (triode region, linear)
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-44
MOSFET as Voltage-Controlled ResistorExample: Voltage-Controlled Attenuator
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-45
MOSFET as Voltage-Controlled ResistorExample: Voltage-Controlled Attenuator
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-46
MOSFET as Voltage-Controlled ResistorExample: Voltage-Controlled Attenuator
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-47
MOSFET as Voltage-Controlled ResistorExample: Voltage-Controlled Attenuator
) , ) 1( (1
o GS s GSv v
v Ro onG V G V v R Rs K R V Von n TNGS
If Kn=500 A/V2, VTN=1V, R=2k and VGS = 1, 1.5, 2 V:
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-48
MOSFET as Voltage-Controlled ResistorExample: Voltage-Controlled Attenuator
) , ) 1( (1
o GS s GSv v
v Ro onG V G V v R Rs K R V Von n TNGS
If Kn=500 A/V2, VTN=1V, R=2k and VGS = 1, 1.5, 2 V:
( 1) 1 1
A1 500 2000 1 1 V
2V
GSG V
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-49
MOSFET as Voltage-Controlled ResistorExample: Voltage-Controlled Attenuator
) , ) 1( (1
o GS s GSv v
v Ro onG V G V v R Rs K R V Von n TNGS
If Kn=500 A/V2, VTN=1V, R=2k and VGS = 1, 1.5, 2 V:
( 1) 1 1
A1 500 2000 1 1 V
2V
GSG V
( 2) 1 0.5
A1 500 2000 2 1 V
2V
GSG V
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-50
MOSFET as Voltage-Controlled ResistorExample: Voltage-Controlled Attenuator
) , ) 1( (1
o GS s GSv v
v Ro onG V G V v R Rs K R V Von n TNGS
( 1.5) 1 0.667
A1 500 2000 1.5 1 V
2V
GSG V
To maintain triode region operation,v V Vo GS TN
or
vDSvGS VTN
If Kn=500 A/V2, VTN=1V, R=2k and VGS = 1, 1.5, 2 V:
( 1) 1 1
A1 500 2000 1 1 V
2V
GSG V
( 2) 1 0.5
A1 500 2000 2 1 V
2V
GSG V
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-51
NMOS Transistor: inversion layer change
VOV - overdrive voltage
If we increase vDS , and it’s no more vDS << VGS - VTN = VOV (triode region limit), it starts influencing the depth of induced inversion layer, for which we need VGS > VTN.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-52
NMOS Transistor: inversion layer change If we increase vDS , and it’s no more vDS << VGS - VTN = VOV (triode region limit), it starts influencing the depth of induced inversion layer, for which we need VGS > VTN.
vDS = VOV - pinch-off voltage, saturation region begins
VOV - overdrive voltage
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-53
NMOS Transistor: Saturation Region
is also called saturation or pinch-off voltage.
v v VTNDSAT GS
What is the current in saturation region?
• When vDS increases above triode region limit, channel region akmost disappears, MOSFET also said to be pinched-off.
• Current saturates at (almost) constant value, independent of vDS.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-54
NMOS Transistor: Saturation Region
' 2
2
K Wni v VD TNGSL
for DS GS TN
v v V
Substituting vDS = vGS - VTN into previous equation for drain current, we get
Example here
• Saturation region operation mostly used for analog amplification.
is also called saturation or pinch-off voltage.
v v VTNDSAT GS
• When vDS increases above triode region limit, channel region akmost disappears, MOSFET also said to be pinched-off.
• Current saturates at (almost) constant value, independent of vDS.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-55
NMOS Transistor: iv-characteristic
( )GS po TN
v x Vv
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-56
NMOS Transistor: Region Summary• If vDS << VGS - VTN MOSFET is in linear
portion of the triode region
Triode
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-57
NMOS Transistor: Region Summary• If vDS << VGS - VTN MOSFET is in linear
portion of the triode region • If vDS < VGS - VTN MOSFET is in quadratic
portion of the triode region
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-58
NMOS Transistor: Region Summary• If vDS << VGS - VTN MOSFET is in linear
portion of the triode region • If vDS < VGS - VTN MOSFET is in
quadratic portion of the triode region • If vDS < VGS - VTN MOSFET is in saturation
region and current saturates at (almost) constant value, independent of vDS.
Discuss how to build the iv graph
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-59
Transconductance of a MOS Device
• Transconductance is the important characteristics that relates the change in drain current to a change in gate-source voltage
gmdiD
dvGS Q pt
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-60
Transconductance of a MOS Device
• Transconductance is the important characteristics that relates the change in drain current to a change in gate-source voltage
• Taking the derivative of the expression for the drain current in saturation region,
gmdiD
dvGS Q pt
gmKn'WL
(VGS VTN)2I
DV
GS V
TN
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-61
Transconductance of a MOS Device
• Transconductance is the important characteristics that relates the change in drain current to a change in gate-source voltage
• Taking the derivative of the expression for the drain current in saturation region,
• The larger the device transconductance, the more gain we can expect from the amplifier that uses the transistor.
• Transconductance is inverse to the Ron defined earlier and slightly differently.
gmdiD
dvGS Q pt
gmKn'WL
(VGS VTN)2I
DV
GS V
TN
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-62
Channel-Length Modulation• On the previous iv-characteristics, the
saturation part was horizontal (the current was constant, as vDS increases). However, it’s not exactly so.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-63
Channel-Length Modulation• On the previous iv-characteristics, the
saturation part was horizontal (the current was constant, as vDS increases). However, it’s not exactly so.
• As vDS increases above vDSAT , length of depleted channel beyond pinch-off point, DL, increases and actual L decreases.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-64
Channel-Length Modulation• On the previous iv-characteristics, the
saturation part was horizontal (the current was constant, as vDS increases). However, it’s not exactly so.
• As vDS increases above vDSAT , length of depleted channel beyond pinch-off point, DL, increases and actual L decreases.
• Since L is in denominator of the current expression, it compensate slightly the general increase of resistivity, which normally makes the curve flat.
' 2
2
K Wni v VD TNGSL
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-65
Channel-Length Modulation• On the previous iv-characteristics, the
saturation part was horizontal (the current was constant, as vDS increases). However, it’s not exactly so.
• As vDS increases above vDSAT , length of depleted channel beyond pinch-off point, DL, increases and actual L decreases.
• Since L is in denominator of the current expression, it compensate slightly the general increase of resistivity, which normally makes the curve flat.
• As a result, iD increases slightly with vDS
instead of being constant and we can rewrite equation in the form:
' 2
2
K Wni v VD TNGSL
' 2
12
K Wni v V vDSD TNGSL
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• On the previous iv-characteristics, the saturation part was horizontal (the current was constant, as vDS increases). However, it’s not exactly so.
• As vDS increases above vDSAT , length of depleted channel beyond pinch-off point, DL, increases and actual L decreases.
• Since L is in denominator of the current expression, it compensate slightly the general increase of resistivity, which normally makes the curve flat.
• As a result, iD increases slightly with vDS
instead of being constant and we can rewrite equation in the form:
NJIT ECE271 Dr. Serhiy Levkov Chap 4-66
Channel-Length Modulation
where lis the channel length modulation parameter, depends on manufacturing and L.
Va – Early voltage.
' 21
2
K Wni v V vDSD TNGSL
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-67
Enhancement and Depletion Mode MOSFETS• The MOSFETS transistors can be of two types:
enhancement mode when VTN > 0
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-68
Enhancement and Depletion Mode MOSFETS• The MOSFETS transistors can be of two types:
enhancement mode when VTN > 0 depletion mode when VTN < 0
(the NMOS transistors considered so far were of enhancement type.)
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-69
Enhancement and Depletion Mode MOSFETS• The MOSFETS transistors can be of two types:
enhancement mode when VTN > 0 depletion mode when VTN < 0
(the NMOS transistors considered so far were of enhancement type.) • The depletion mode devices are fabricated by ion implantation process
used to form a built-in n-type channel in device to connect source and drain by a resistive channel.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-70
Enhancement and Depletion Mode MOSFETS• The MOSFETS transistors can be of two types:
enhancement mode when VTN > 0 depletion mode when VTN < 0
(the NMOS transistors considered so far were of enhancement type.) • The depletion mode devices are fabricated by ion implantation process
used to form a built-in n-type channel in device to connect source and drain by a resistive channel.
• In such case, a non-zero drain current exists for vGS=0, and a negative vGS required to turn device off.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-71
Enhancement and Depletion Mode MOSFETS• The MOSFETS transistors can be of two types:
enhancement mode when VTN > 0 depletion mode when VTN < 0
(the NMOS transistors considered so far were of enhancement type.) • The depletion mode devices are fabricated by ion implantation process
used to form a built-in n-type channel in device to connect source and drain by a resistive channel.
• In such case, a non-zero drain current exists for vGS=0, and a negative vGS required to turn device off.
Depletion mode – because negative voltage has to be applied to the gate to deplete the n-type channel and eliminate the current path between the source and the drain.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-72
Output and Transfer Characteristics of MOSFETS• A MOSFET has one output variable – the drain-source current , that
depends on two input variables – drain-source voltage and gate-source voltage (VGS is usually is a control variable).
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-73
Output and Transfer Characteristics of MOSFETS• A MOSFET has one output variable – the drain-source current , that depends
on two input variables – drain-source voltage and gate-source voltage (VGS is usually is a control variable).
• Two types of iv-curves are used to describe a MOSFET device fully:
output (drain) curve (DS current vs. DS voltage for a fixed GS voltage)(the earlier considered characteristics were drain curves)
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-74
Output and Transfer Characteristics of MOSFETS• A MOSFET has one output variable – the drain-source current , that depends
on two input variables – drain-source voltage and gate-source voltage (VGS is usually is a control variable).
• Two types of iv-curves are used to describe a MOSFET device fully:
output (drain) curve (DS current vs. DS voltage for a fixed GS voltage)(the earlier considered characteristics were drain curves)
transfer curve (DS current vs. GS voltage for a fixed DS voltage, f.i. sat.)
Curves show that the enhancement mode device turns on at VGS = 2, while the depletion mode device turns on at VGS = -2.
Example here
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-75
Body Effect or Substrate Sensitivity
• Non-zero vSB changes threshold voltage.
• This is called substrate sensitivity and is modeled by
where
VTO - zero substrate bias for VTN (V)
gbody-effect parameter ,determines the intensity of the body effect
2FF - surface potential parameter (V), typically 0.6V.
VTNVTO
g vSB2F 2F
V
So far it was assumed that the source-bulk voltage vSB , is zero, which means that a MOSFET is a three terminal device. Quite often vSB , especially in ICs is not zero..
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-76
NMOS Summary (output characteristics)
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-77
PMOS Transistors Structure (Enhancement-Mode)
• p-type source and drain regions in n-type substrate.
00
DI
• n-type source and drain regions in p-type substrate.
NMOSPMOS
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-78
PMOS Transistors Structure (Enhancement-Mode)
• P-type source and drain regions in n-type substrate.
• vGS < 0 required to create p-type inversion layer in channel region
00
DI
• N-type source and drain regions in p-type substrate.
• vGS > 0 required to create n-type inversion layer in channel region
NMOSPMOS
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-79
PMOS Transistors Structure (Enhancement-Mode)
• P-type source and drain regions in n-type substrate.
• vGS < 0 required to create p-type inversion layer in channel region
• For current flow, vGS<vTP
00
DI
• N-type source and drain regions in p-type substrate.
• vGS > 0 required to create n-type inversion layer in channel region
• For current flow, vGS > vTN
NMOSPMOS
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-80
PMOS Transistors Structure (Enhancement-Mode)
• P-type source and drain regions in n-type substrate.
• vGS < 0 required to create p-type inversion layer in channel region
• For current flow, vGS<vTP
• To maintain reverse bias on diodes of source-substrate and drain-substrate junctions: vSB < 0 and vDB < 0
00
DI
• N-type source and drain regions in p-type substrate.
• vGS > 0 required to create n-type inversion layer in channel region
• For current flow, vGS > vTN
• To maintain reverse bias on the diodes of source-substrate and drain-substrate junctions: vSB >0 and vDB >0
NMOSPMOS
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-81
Enhancement-Mode PMOS Transistors: Output Characteristics
• For the PMOS transistor, all parameters and behavior are inverse of NMOS transistor.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-82
Enhancement-Mode PMOS Transistors: Output Characteristics
• For the PMOS transistor, all parameters and behavior are inverse of NMOS transistor.
• Thus the output characteristics of PMOS are the complete inverse of those of NMOS
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-83
Enhancement-Mode PMOS Transistors: Output Characteristics
• For the PMOS transistor, all parameters and behavior are inverse of NMOS transistor.
• Thus the output characteristics of PMOS are the complete inverse of those of NMOS
• Often, they are shown in the inverted scale and then they look very similar to the characteristics of NMOS
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-84
Enhancement-Mode PMOS Transistors: Output Characteristics
• For , transistor is off (note that on the diagram it’s vSG = - vGS).
VGSVTP
• For the PMOS transistor, all parameters and behavior are inverse of NMOS transistor.
• Thus the output characteristics of PMOS are the complete inverse of those of NMOS
• Often, they are shown in the inverted scale and then they look very similar to the characteristics of NMOS
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-85
Enhancement-Mode PMOS Transistors: Output Characteristics
• For , transistor is off (note that on the diagram it’s vSG = - vGS).
• For more negative vGS, drain current increases in magnitude.
VGSVTP
• For the PMOS transistor, all parameters and behavior are inverse of NMOS transistor.
• Thus the output characteristics of PMOS are the complete inverse of those of NMOS
• Often, they are shown in the inverted scale and then they look very similar to the characteristics of NMOS
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-86
Enhancement-Mode PMOS Transistors: Output Characteristics
• For , transistor is off (note that on the diagram it’s vSG = - vGS).
• For more negative vGS, drain current increases in magnitude.
• PMOS is in triode region for small (absolute) values of VDS and in saturation for larger values (note that on the diagram it’s more negative to the right).
VGSVTP
• For the PMOS transistor, all parameters and behavior are inverse of NMOS transistor.
• Thus the output characteristics of PMOS are the complete inverse of those of NMOS
• Often, they are shown in the inverted scale and then they look very similar to the characteristics of NMOS
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-87
NMOS Summary (model)
For the enhancement-mode NMOS transistor, VTN > 0. For the depletion-mode NMOS, VTN < 0.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-88
PMOS Summary (model)
For the enhancement-mode PMOS transistor, VTP < 0. For the depletion-mode PMOS, VTP > 0.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-89
NMOS and PMOS Summary (regions of operation)
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-90
NMOS and PMOS Summary (terminal voltages)
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-91
Short Summary of MOSFET (1)• A MOSFET is a 3 terminal (Gate, Source, Drain) or 4 terminal (Gate, Source, Drain,
Body) electronic device -- it has input (usually vGS) and output (usually iD).
• The basic function of all transistors - an input voltage is used to provide the change in the output current (or voltage): – the change in output can be much bigger then the change in the input - amplifier– the change in output can be to turn it on or off – digital gate
• There are two types of MOSFET : PMOS and NMOS
• Both types exist in two modes: Enhancement and Depletion.• NMOS enhancement mode: the output current (the inversion channel) may exist only
when input (vGS ) is positive (>0).
• NMOS depletion mode: the output current (the inversion channel) may exist when input (vGS ) is zero, requires to apply vGS <0 to shut the current).
• PMOS is pretty much the complete inverse of NMOS.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-92
Short Summary of MOSFET (2)
NMOSBody: p-substrateSource, Drain: n+
Inversion (conduction) layer: n
E-NMOSChannel
(drain current exists
when vGS > 0)
VTN > 0
D-NMOSChannel
(drain current exists
when vGS = 0)
VTN <= 0
PMOSBody: n-substrateSource, Drain: p+
Inversion (conduction) layer: p
E-PMOSChannel
(drain current exists
when vGS < 0)
VTP < 0
D-PMOSChannel
(drain current exists
when vGS = 0)
VTP >= 0
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-93
Short Summary of MOSFET (3)• MOSFET is a symmetrical device – D and S are interchangeable.• MOSFET is fully described by two characteristics:
- input-output or transfer characteristic: (iD - vGS or vDS - vGS )
- output characteristic: (iD – vDS )
• All four types of MOSFET may operate in three regions:
- cutoff : output current is 0
- triode: output current almost linearly depends on output voltage vDS (like in resistor)
- saturation: output current almost does not depend on DS voltage vDS (like in diode)
Transfer characteristics Output characteristics
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-94
MOSFET Circuit Symbols
• (g) and (i) are the most commonly used symbols in VLSI logic design.
• MOS devices are symmetric.• In NMOS, n+ region at higher
voltage is the drain.• In PMOS p+ region at lower
voltage is the drain
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-95
MOSFET Analysis• Depending on the type of application, a MOSFET may be put into one of three
regions of operation by setting its operating Q-point .
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-96
MOSFET Analysis• Depending on the type of application, a MOSFET may be put into one of three
regions of operation by setting its operating Q-point.• For binary logic application the transistor acts like an “on-off” switch and the
Q-point is set in ether cut-off region (“off”) or in the triode region (“on”) for the output characteristic or at the ends of transfer characteristic.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-97
MOSFET Analysis• Depending on the type of application, a MOSFET may be put into one of three
regions of operation by setting its operating Q-point.• For binary logic application the transistor acts like an “on-off” switch and the
Q-point is set in ether cut-off region (“off”) or in the triode region (“on”) for the output characteristic or at the ends of transfer characteristic.
• For amplifier application, the Q-point is set in the saturation region for the output characteristic or in the middle (high) point of the transfer characteristic
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-98
MOSFET Analysis: logic inverter example
• For the low values of input vGS (binary 0) the MOSFET is off, iD =0 and vDS = vout = 5V binary 1.
=low
= 0
= 5
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• For vGS =5V (binary 1) the MOSFET is on, iD is high, and the output voltage vDS = vout = 0.65V binary 0.
NJIT ECE271 Dr. Serhiy Levkov Chap 4-99
MOSFET Analysis: logic inverter example
= 5
=high
=0.6
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-100
MOSFET Analysis: logic inverter example
• For the low values of input vGS (binary 0) the MOSFET is off, iD =0 and vDS = vout = 5V binary 1.
• For vGS =5V (binary 1) the MOSFET is on, iD is high, and the output voltage vDS = vout = 0.65V binary 0.
= 5
=high
=0.6
=low
= 0
= 5
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-101
MOSFET Analysis: amplifier example• For the amplifier, the Q-point created by
vGS = 2.5V is located at the high slope region of transfer characteristic and at the saturation region of the 2.5V curve.
=2. 5
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-102
MOSFET Analysis: amplifier example• For the amplifier, the Q-point created by
vGS = 2.5V is located at the high slope region of transfer characteristic and at the saturation region of the 2.5V curve.
• A small AC signal is added to vary the gate voltage about vGS = 2.5V, which causes the drain current to change significantly and amplified replica of the input appears at the drain.
=2. 5
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-103
MOSFET Analysis: load line example• From KVL for the right loop:
vDD - vDS - iD RD = 0 iD = (vDD - vDS )/RD
• Setting two different values for vDS (5V and 3V for example) two points can be obtained and the load line drawn.
Nonlinearelement
Thevenin equivalent
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-104
MOSFET Analysis: load line example• From KVL for the right loop:
vDD - vDS - iD RD = 0 iD = (vDD - vDS )/RD
• Setting two different values for vDS (5V and 3V for example) two points can be obtained and the load line drawn.
• Intersection with the transistor iv-curve gives the Q-point, which, of course, depends on the input vGS.
Conclusion• The same device in the similar circuits may
behave differently depending on the ‘biasing‘ – DC voltages applied to different terminals of MOSFET. The ‘signal’ then, is actually comprised of relatively small changes in the DC current and/or voltage bias.
Nonlinearelement
Thevenin equivalent
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-105
Bias Analysis Approach• The previous examples shows the importance of biasing for the desired
operation of MOSFET.• Because of nonlinearity of characteristics and substantial difference in
operation region equations (different equations used), iterative approach is used:
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-106
Bias Analysis Approach• The previous examples shows the importance of biasing for the desired
operation of MOSFET.• Because of nonlinearity of characteristics and substantial difference in
operation region equations (different equations used), iterative approach is used:
• Assume an operation region (generally the saturation region)
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-107
Bias Analysis Approach• The previous examples shows the importance of biasing for the desired
operation of MOSFET.• Because of nonlinearity of characteristics and substantial difference in
operation region equations (different equations used), iterative approach is used:
• Assume an operation region (generally the saturation region)• Use circuit analysis to find VGS (left, input loop)
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-108
Bias Analysis Approach• The previous examples shows the importance of biasing for the desired
operation of MOSFET.• Because of nonlinearity of characteristics and substantial difference in
operation region equations (different equations used), iterative approach is used:
• Assume an operation region (generally the saturation region)• Use circuit analysis to find VGS (left, input loop)
• Use VGS to calculate ID, and ID to find VDS (right, output loop)
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-109
Bias Analysis Approach• The previous examples shows the importance of biasing for the desired
operation of MOSFET.• Because of nonlinearity of characteristics and substantial difference in
operation region equations (different equations used), iterative approach is used:
• Assume an operation region (generally the saturation region)• Use circuit analysis to find VGS (left, input loop)
• Use VGS to calculate ID, and ID to find VDS (right, output loop)
• Check validity of operation region assumptions• Change assumptions and analyze again if required.
NOTE : An enhancement-mode device with VDS = VGS is always in saturation.Why? For pinch off: VDS >= VGS - VTN . If VDS = VGS , then VDS >= VDS - VTN , or VTN >= 0, which is
always true for E-MOS device.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-110
Problem: Find Q-pt (ID, VDS , VGS) without and with the channel-length modulation ( and ).
Approach: Assume operation region, find Q-point, check to see if result is consistent with operation region.
0 102.0 V
Bias Analysis 1- Constant GS Voltage Biasing (1)
Do this example on the board
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-111
Problem: Find Q-pt (ID, VDS , VGS) without and with the channel-length modulation ( and ).
Approach: Assume operation region, find Q-point, check to see if result is consistent with operation region.
Assumption: 1. Transistor is saturated. 2. IG=IB=0.
0 102.0 V
Bias Analysis 1- Constant GS Voltage Biasing (1)
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-112
Analysis:
Simplify circuit with Thevenin transformation to find VEQ and REQ for gate-bias voltage.
Bias Analysis: Ex.1- Constant GS Voltage Biasing (1)
0 102.0 V
Problem: Find Q-pt (ID, VDS , VGS) without and with the channel-length modulation ( and ).
Approach: Assume operation region, find Q-point, check to see if result is consistent with operation region.
Assumption: 1. Transistor is saturated. 2. IG=IB=0.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-113
Analysis:
Simplify circuit with Thevenin transformation to find VEQ and REQ for gate-bias voltage.
Find VGS from the input loop, and then use this to find ID.
0 102.0 V
Problem: Find Q-pt (ID, VDS , VGS) without and with the channel-length modulation ( and ).
Approach: Assume operation region, find Q-point, check to see if result is consistent with operation region.
Assumption: 1. Transistor is saturated. 2. IG=IB=0.
Bias Analysis 1- Constant GS Voltage Biasing (1)
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-114
Analysis:
Simplify circuit with Thevenin transformation to find VEQ and REQ for gate-bias voltage.
Find VGS from the input loop, and then use this to find ID.
With ID, we can then calculate VDS using the output loop
0 102.0 V
Problem: Find Q-pt (ID, VDS , VGS) without and with the channel-length modulation ( and ).
Approach: Assume operation region, find Q-point, check to see if result is consistent with operation region.
Assumption: 1. Transistor is saturated. 2. IG=IB=0.
Bias Analysis 1- Constant GS Voltage Biasing (1)
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-115
0 3V I R V V V VEQ GS GS EQG EQ
The left (input) loop. Since IG=0:
A
TNV
GSVnK
DI
502V2132V
A
2
61025
2
2
Then, from the transistor equation:
Bias Analysis 1- Constant GS Voltage Biasing (1)
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-116
0 3V I R V V V VEQ GS GS EQG EQ
The left (input) loop. Since IG=0:
A
TNV
GSVnK
DI
502V2132V
A
2
61025
2
2
0V I R VDD D D DS
Check:VDS>VGS-VTN. Hence saturation region assumption is correct.
Q-pt: (50.0 mA, 5.0 V) with VGS= 3.0V
Discussion.
The obtained result is proportional to K and to the square of VTN , thus Q-pt. is quite sensitive to the parameter fluctuation of the device, so this circuit is not very used.
VKuAVDS
V 00.5 )100)(50(10
The right (output) loop:
Then, from the transistor equation:
Bias Analysis 1- Constant GS Voltage Biasing (1)
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-117
Check:VDS>VGS-VTN. Hence saturation region assumption is correct.
Q-pt: (54.5 mA, 4.55 V) with VGS= 3.00 V
IDKn2
VGS
VTN
2
1VDS
VDSVDD IDRD
VDS10V (100K)(2510 6)2
3 1 2 10.02 VDS
4.55 V
ID(2510 6)2
3 1 2 10.02 (4.55) 54.5 A
Now let’s repeat the same problem taking into account channel length modulation.
Bias Analysis 1- Constant GS Voltage Biasing (2)
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-118
Check:VDS>VGS-VTN. Hence saturation region assumption is correct.
Q-pt: (54.5 mA, 4.55 V) with VGS= 3.00 V
IDKn2
VGS
VTN
2
1VDS
VDSVDD IDRD
VDS10V (100K)(2510 6)2
3 1 2 10.02 VDS
4.55 V
ID(2510 6)2
3 1 2 10.02 (4.55) 54.5 A
Discussion.
The bias levels have changed by about 10%. Typically, component values will vary more than this, so there is little value in including effects in most circuits.
Now let’s repeat the same problem taking into account channel length modulation.
Bias Analysis 1- Constant GS Voltage Biasing (2)
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-119
Problem: Find Q-pt (ID, VDS , VGS)
Approach: Find an equation for the load line. Use this to find Q-pt at intersection of load line with device characteristic.
Assumptions: 1. IG=IB=0.
Do we need assumption for the transistor region of operation?
Load Line Analysis.
Bias Analysis 1- Constant GS Voltage Biasing (3)
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-120
Problem: Find Q-pt (ID, VDS , VGS)
Approach: Find an equation for the load line. Use this to find Q-pt at intersection of load line with device characteristic.
Assumptions: 1. IG=IB=0.
2. No need for region assumption, will find solution directly.
Load Line Analysis.
Bias Analysis 1- Constant GS Voltage Biasing (3)
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-121
Analysis: First, simplify circuit with Thevenin transformation to find VEQ and REQ for gate-bias voltage
Load Line Analysis.
Problem: Find Q-pt (ID, VDS , VGS)
Approach: Find an equation for the load line. Use this to find Q-pt at intersection of load line with device characteristic.
Assumptions: 1. IG=IB=0.
2. No need for region assumption, will find solution directly.
Bias Analysis 1- Constant GS Voltage Biasing (3)
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-122
Analysis: First, simplify circuit with Thevenin transformation to find VEQ and REQ for gate-bias voltage
Load Line Analysis.
0
3
V I R VEQ GSG EQ
V V VGS EQ
The left (input) loop. Since IG=0:
Problem: Find Q-pt (ID, VDS , VGS)
Approach: Find an equation for the load line. Use this to find Q-pt at intersection of load line with device characteristic.
Assumptions: 1. IG=IB=0.
2. No need for region assumption, will find solution directly.
Bias Analysis 1- Constant GS Voltage Biasing (3)
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-123
Check: The load line approach agrees with previous calculation. Q-pt: (50.0 A, 5.00 V) with VGS= 3.00 V
Discussion: Q-pt is clearly in the saturation region. Graphical load line is good visual aid to see device operating region.
@VDS=0, ID=100uA, @ID=0, VDS=10V
Plotting on device characteristic yields Q-pt at intersection with VGS = 3V device curve.
10ID100KVDS
Load Line Analysis.
From the KVL for the right loop, load line becomes
VDDIDRDVDS
Bias Analysis 1- Constant GS Voltage Biasing (3)
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-124
Bias Analysis 2 - Four-Resistor Biasing (1)
Problem: Find Q-pt (ID, VDS)
Approach: Assume operation region, find Q-point, check to see if result is consistent with operation region
Assumption: Transistor is saturated, IG=IB=0
Analysis: First, simplify circuit, split VDD into two equal-valued sources and apply Thevenin transformation to find VEQ and REQ for gate-bias voltage
Do this example on the board
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-125
0EQ GS D SV V I R
Left loop. Since IG=0,
STNGSn
GSEQ RVVK
VV 22
4VGS2510 6
3.9104
2V
GS 1
2
VGS20.05VGS 7.210
Bias Analysis 2 - Four-Resistor Biasing (1)
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-126
0EQ GS D SV V I R
Left loop. Since IG=0,
STNGSn
GSEQ RVVK
VV 22
4VGS2510 6
3.9104
2V
GS 1
2
VGS20.05VGS 7.210
V66.2,V71.2 GS
V
If VGS= -2.71 , VGS<VTN and MOSFET will be cut-off. Thus
VGS2.66V and ID= 34.4 mA
Solution:
Bias Analysis 2 - Four-Resistor Biasing (1)
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-127
0EQ GS D SV V I R
Left loop. Since IG=0,
STNGSn
GSEQ RVVK
VV 22
4VGS2510 6
3.9104
2V
GS 1
2
VGS20.05VGS 7.210
V66.2,V71.2 GS
V
If VGS= -2.71 , VGS<VTN and MOSFET will be cut-off. Thus
VGS2.66V and ID= 34.4 mA
( ) 0V I R R VDD D D S DS
V08.6DS
V
We have VDS >VGS-VTN .
Hence saturation region assumption is correct.
Q-pt: (34.4 mA, 6.08 V) with VGS= 2.66 V
Solution:
Right loop.
Bias Analysis 2 - Four-Resistor Biasing (1)
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-128
• Estimate value of ID and use it to find VGS and VSB
• Use VSB to calculate VTN
• Find ID’ using last equation
• If ID’ is not same as original ID estimate, start again.
In previous example, the body terminal was connected to the source, so VSB = 0. Now let’s consider the case with
VGSVEQ IDRS6 22,000ID
VSBIDRS22,000ID
VTN VTOg( VSB
2F 2
F)
VTN 10.5( VSB
0.6 0.6)
ID'2510 6
2V
GS V
TN
2
Iterative solution can be found by following steps:
Bias Analysis 2 - Four-Resistor Biasing (2) Body Effect
0VSB
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-129
The iteration sequence leads to ID= 88.0 mA, VTN = 1.41 V,
VDSVDD ID(RDRS)10 40,000ID6.48V
We obtained that VDS>VGS-VTN. Hence saturation region assumption is correct.
Q-pt: (88.0 mA, 6.48 V)
Check: VDS > VGS - VTN, therefore still in active region.
Discussion: Body effect has decreased current by 12% and increased threshold voltage by 40%.
Bias Analysis 2 - Four-Resistor Biasing (2) Body Effect
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-130
Do this example on the board
Assumption: 1. IG=IB=0. 2.Transistor is saturated since VDS=VGS
Bias Analysis 3 – Two Resistor (saturation)
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-131
Bias Analysis 3 – Two Resistor (saturation)
Assumption: 1. IG=IB=0. 2.Transistor is saturated since VDS=VGS
Analysis. No need for input loop: VDS=VGS
Output loop:
VDSVDD IDRD
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-132
VDSVDD IDRD
2
2 D
KnV V V V V RGS TNDDGS DS
21
2
4104106.23.3
GSV
GSV
V00.2,V769.0 GS
V
If VGS= -0.769 , VGS<VTN and MOSFET will be cut-off. Thus
V00.2DS
VGS
V and ID= 130 mA
We obtained VDS>VGS-VTN. Hence saturation region assumption is correct.
Q-pt: (130 mA, 2.00 V)
Assumption: 1. IG=IB=0. 2.Transistor is saturated since VDS=VGS
Analysis. No need for input loop: VDS=VGS
Output loop:
Bias Analysis 3 – Two Resistor (saturation)
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-133
Discussion of Four and Two-Resistor Biasing
Four resistor• Provide excellent bias for transistors in discrete circuits.• Stabilize bias point with respect to device parameter and temperature
variations using negative feedback.• Use single voltage source to supply both gate-bias voltage and drain
current.• Generally used to bias transistors in saturation region in amplifier circuits.
Two-resistor • Uses lesser components that four-resistor biasing and also isolates drain
and gate terminals.
• Feedback mechanism. Suppose, for some reason ID begins to increase. From it follows that VGS has to decrease, since Vg is constant. This will decrease the current ID due to current equation, thus restoring the existing state.
0EQ GS D SV V I R
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-134
Assumption: 1. IG=IB=0 2. Transistor is saturated.
Analysis.
Left loop: VGS=VDD=4 V
ID2502
AV2
(4 1)21.13mA
Bias Analysis 4 – One Resistor (triode)
Do this example on the board
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-135
Assumption: 1. IG=IB=0 2. Transistor is saturated.
Analysis.
Left loop: VGS=VDD=4 V
ID2502
AV2
(4 1)21.13mA
DSVDRDIDDV Right loop:
V19.2DS
V
DIDS
V 16004
Bias Analysis 4 – One Resistor (triode)
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-136
Assumption: 1. IG=IB=0 2. Transistor is saturated.
Analysis.
Left loop: VGS=VDD=4 V
ID2502
AV2
(4 1)21.13mA
2
A4 1600 250 (4 1 )
2VDS
DS DS
VV V
2.3, 8.7 = 2.3VDS
V and ID=1.06 mA
We obtained VDS<VGS -VTN, transistor is in triode region
Q-pt:(1.06 mA, 2.3 V)
Bias Analysis 4 – One Resistor (triode)
DSVDRDIDDV Right loop:
V19.2DS
V
DIDS
V 16004
We obtained VDS<VGS -VTN. Hence, saturation region assumption is incorrect.
Assume the triode region and use the triode region equation:
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-137
Bias Analysis 5 - Two-Resistor, PMOST
Assumption: 1. IG=IB=0
2. Transistor is saturated: VDS=VGS
Analysis.
Left loop: no need, VDS=VGS
Right loop: 15V (220k ) 0I VDSD
2A5015V (220k ) 2 02 2V
V VGS GS
0.369V, 3.45VVGS
Since VGS= -0.369 V is more than VTP= -2 V, we take VGS = -3.45 V
Then we can calculate ID = 52.5 mA.
Check:
Hence saturation assumption is correct.
Q-pt: (52.5 mA, -3.45 V)
VDS VGS VTP
Do this example on the board
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NJIT ECE271 Dr. Serhiy Levkov
Junction Field-Effect Transistors (JFET)
Chap 4-138
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NJIT ECE271 Dr. Serhiy Levkov
Junction Field-Effect Transistors (JFET)
n-channel JFET consists of:• n-type semiconductor block that houses
the channel region in n-channel JFET.• pn junction - forms the gate.• Source and drain terminals
Chap 4-139
• MOSFET devices are called FET because electric field is used to control the shape and hence the conductivity of the channel of one type charge carrier (p or n) in semiconductor device.
• There is another type of FET, which is not using MOS capacitor structure, however utilizes the electric filed effect: Junction Field-Effect Transistor.
• Less prevalent than MOSFET, JFET have many uses, especially in analog RF applications.• Can be of two types: n-channel and p-channel JFET.
Like a diode with enlarged n-type section and two n-terminals.
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NJIT ECE271 Dr. Serhiy Levkov
JFET Structure
• In triode region, JFET is a voltage-controlled resistor,
r - resistivity of channel
L - channel length
W - channel width between pn junction depletion regions
t - channel depth
• With no bias applied, a resistive channel exists. The current enters channel at the drain and exits at source.
• The resistance of the drain-source channel is controlled by changing the physical width of the channel through modulation of the depletion layers around pn-junctions (like squeezing a garden hose)
• Application of reverse bias to the gate-channel diodes causes the depletion layer to widen, reducing the channel width and decreasing the current.
• JFET is inherently a depletion-mode device – a voltage must be applied to turn the device off.
Chap 4-140
WL
tRCH
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NJIT ECE271 Dr. Serhiy Levkov
JFET: applying Gate-Source voltage
Chap 4-141
• vGS = 0. The channel width is W. It can conduct current well if vDS is applied.
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NJIT ECE271 Dr. Serhiy Levkov
JFET: applying Gate-Source voltage
Chap 4-142
• vGS = 0. The channel width is W. It can conduct current well if vDS is applied.
• VP < vGS <0. The depletion layers width is increased. The channel width W’ < W, and channel resistance increases. Gate-source junction is reverse-biased, iG almost 0.
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NJIT ECE271 Dr. Serhiy Levkov
JFET: applying Gate-Source voltage
• vGS = 0. The channel width is W. It can conduct current well if vDS is applied.
• VP < vGS <0. The depletion layers width is increased. The channel width W’ < W, and channel resistance increases. Gate-source junction is reverse-biased, iG almost 0.
• vGS = VP < 0. The depletion layer is max. Channel width – zero, region is pinched-off, channel resistance is infinite.
Chap 4-143
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NJIT ECE271 Dr. Serhiy Levkov
JFET: applying Drain-Source voltage
• With constant vGS, depletion region near drain increases with vDS
Chap 4-144
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NJIT ECE271 Dr. Serhiy Levkov
JFET: applying Drain-Source voltage
• With constant vGS, depletion region near drain increases with vDS
• At vDSP = vGS - VP , channel is totally pinched-off; iD is saturated. (the current does not stop: electrons are accelerated down the channel (V is large), are injected into the depletion region and swept to the drain)
Chap 4-145
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NJIT ECE271 Dr. Serhiy Levkov
JFET: applying Drain-Source voltage
• With constant vGS, depletion region near drain increases with vDS
• At vDSP = vGS - VP , channel is totally pinched-off; iD is saturated. (the current does not stop: electrons are accelerated down the channel (V is large), are injected into the depletion region and swept to the drain)
• JFET also suffers from channel-length modulation like MOSFET at larger values of vDS.
Chap 4-146
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NJIT ECE271 Dr. Serhiy Levkov
JFET: applying Drain-Source voltage
• With constant vGS, depletion region near drain increases with vDS
• At vDSP = vGS - VP , channel is totally pinched-off; iD is saturated. (the current does not stop: electrons are accelerated down the channel (V is large), are injected into the depletion region and swept to the drain)
• JFET also suffers from channel-length modulation like MOSFET at larger values of vDS.
Chap 4-147
http://www-g.eng.cam.ac.uk/mmg/teaching/linearcircuits/jfet.htmlhttp://learnabout-electronics.org/fet_03.php
Simulation:
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NJIT ECE271 Dr. Serhiy Levkov
N-Channel JFET i-v Characteristics
Transfer Characteristics Output Characteristics
Chap 4-148
The JFET iv-characteristics are remarkably similar to the MOSFET characteristics (virtually identical).
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NJIT ECE271 Dr. Serhiy Levkov
N-Channel JFET i-v equationsEquations are similar to MOSFET except written slightly differently • For all regions :• In cutoff region: • In Triode region:
• In pinch-off region:
Explanation:
iG0 for v
GS0
iD0 for v
GSV
P V
P0
2
2
2 for and 02DSDSS
GS PD DS GS P GS P DSP
vIi v V v v V v V VV
2
1 1 for and 0GSDSD DSS GS P DS GS P
P
vi I v v V v v V
V
Chap 4-149
2 2
2 2
2
( ) ( ) = ,2 2
where ( ) , [10μA, 10A], [ 25V, 0]2
1 1GS GSn nD GS P P DSS
P P
nP PDSS DSS
K KV V I
KI V I V
v vi v
V V
Typically: [10 , 10 ], [-25V, 0V]DSS P
A AI V
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NJIT ECE271 Dr. Serhiy Levkov
P-Channel JFET
• Polarities of n- and p-type regions of the n-channel JFET are reversed to get the p-channel JFET.
• Channel current direction and operating bias voltages are also reversed.
Chap 4-150
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NJIT ECE271 Dr. Serhiy Levkov
JFET Circuit Symbols
• JFET structures are symmetric like MOSFETs.• Source and drain determined by circuit voltages.
Chap 4-151
n-channel p-channel
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NJIT ECE271 Dr. Serhiy Levkov
JFET n-Channel Model Summary
Chap 4-152
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NJIT ECE271 Dr. Serhiy Levkov
JFET p-Channel Model Summary
Chap 4-153
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NJIT ECE271 Dr. Serhiy Levkov
Biasing JFET (1)
• Assumptions: Gate-channel junction is reverse-biased, reverse leakage current of gate, IG = 0
N-channel JFET Depletion-mode MOSFET
Chap 4-154
22 2400 /( ) ( 5) 5000 5
2 2n
PDSS
K A VI V A mA
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NJIT ECE271 Dr. Serhiy Levkov
Biasing JFET (2) DIY
Chap 4-155
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NJIT ECE271 Dr. Serhiy Levkov
Region Assumption: JFET is pinched-off (saturation)
GS
2 23
Input loop: 0,
1 5 10 A 1000 15V
1.91V, 13.1V
G S D D S
GS GSGS DSS S
P
GS
I I I V I R
V VV I R
V
V
Since VGS = -13.1 V is less than VP= -5 V , we take VGS = -1.91 V (n-channel type!)
and, ID = IS = 1.91 mA.
Output loop:
VDSV
DD I
D(R
DR
S)12 (1.91mA)(3k)6.27V
VDS >VGS -VP. Hence pinch-off region assumption is correct and gate-source junction is reverse-biased by 1.91V.
Q-pt: (1.91 mA, 6.27 V)
Chap 4-156
Biasing JFET (3)
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-157
Internal Capacitances in Electronic Devices
• Limit high-frequency performance of the electronic device they are associated with.
• Limit switching speed of circuits in logic applications
• Limit frequency at which useful amplification can be obtained in amplifiers.
• MOSFET capacitances depend on operation region and are non-linear functions of voltages at device terminals.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-158
NMOS Transistor Capacitances: Triode Region
Cox” =Gate-channel capacitance per unit area(F/m2).
CGC =Total gate channel capacitance.
CGS = Gate-source capacitance.
CGD =Gate-drain capacitance.
CGSO and CGDO = overlap capacitances (F/m).
CGSCGC
2CGSOW Cox"WL
2CGSOW
CGDCGC
2CGSOWCox"WL
2CGSOW
CSBCJASCJSW PS
CDBCJADCJSW PD
CSB = Source-bulk capacitance.
CDB = Drain-bulk capacitance.
AS and AD = Junction bottom area capacitance of the source and drain regions.
PS and PD = Perimeter of the source and drain junction regions.
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-159
NMOS Transistor Capacitances: Saturation Region
• Drain no longer connected to channel
CGS23
CGCCGSOW
CGDCGDOW
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-160
NMOS Transistor Capacitances: Cutoff Region
• Conducting channel region completely gone.
CGB = Gate-bulk capacitance
CGBO = gate-bulk capacitance per unit width.
CGDCGDOW
CGSCGSOW
CGBCGBOW
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NJIT ECE271 Dr. Serhiy Levkov
JFET Capacitances
• CGD and CGS are determined by depletion-layer capacitances of reverse-biased pn junctions forming gate and are bias dependent.
Chap 4-161
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NJIT ECE271 Dr. Serhiy Levkov Chap 4-162
SPICE Model for NMOS Transistor
Typical default values used by SPICE:
Kn or Kp = 20 mA/V2
g = 0
l = 0
VTO = 1 V
mn or mp = 600 cm2/V.s
2FF = 0.6 V
CGDO=CGSO=CGBO=CJSW= 0
Tox= 100 nm
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NJIT ECE271 Dr. Serhiy Levkov
SPICE Model for JFET
• Typical default values used by SPICE:
Vp = -2 V
l = CGD = CGD = 0
Transconductance parameter BETA
BETA = IDSS/VP2 = 100 mA/V2
Chap 4-163