MOS Field-Effect
Transistors (MOSFETs)
1
BJT – Bipolar Junction Transistor
MOSFET – Metal Oxide Semiconductor Field Effect Transistor
É o transistor mais utilizado, principalmente em circuitos integrados
• Requer menor área no circuito integrado
• Processo de fabricação mais simples
• Consumo de energia menor
Circuitos Integrados VLSI – Very Large Scale Integration
200.000.000 transistores em um único circuito integrado
Tipos de MOSFETS:
• JFET – Junction FET
• Depletion - Depleção
• Enhancement - Crescimento
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tox = 2 a 50 nm
W = 0.2 a 100 μm
L = 0.1 a 3 μm
Figure 4.1 Physical structure of the enhancement-type NMOS transistor: (a) perspective view; (b) crosssection. 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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„
Operação do transistor sem tensão no gate
Resistência do canal = 1012 Ω
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„
Criação do canal
Vt – tensão de limiar ou threshold voltage
Vt = 0,5 a 1 V
Figure 4.2 The enhancement-type NMOS transistor with a positive voltage applied to
the gate. An n channel is induced at the top of the substrate beneath the gate.
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„
Operação com baixa tensão vDS
Figure 4.3 An NMOS transistor with vGS > Vt 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 shown (for simplicity).
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„
Operação com baixa tensão vDS
Qual o valor da resistência entre dreno
e fonte em cada reta?
vGS – Vt - tensão efetiva de gate
Figure 4.4 The iD–vDS characteristics of the MOSFET in Fig. 4.3 when the voltage
applied between drain and source, vDS, is kept small. The device operates as a linear
resistor whose value is controlled by vGS.
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Figure 4.5 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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Figure 4.6 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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Figure 4.7 Increasing vDS causes the channel to acquire a tapered shape. Eventually, as vDS
reaches vGS – Vt’ the channel is pinched off at the drain end. Increasing vDS above vGS – Vt has little
effect (theoretically, no effect) on the channel’s shape.
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Figure 4.8 Derivation of the iD–vDS characteristic of the NMOS transistor.
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ε
Cox = ox
tox
ε ox = 3.45 × 10−11 F / m
tox
Capacitância por unidade de área na região do canal
Permissividade do óxido de silício
Espessura da camada de óxido de silício
A capacitância da faixa de largura dx é igual a CoxWdx
A quantidade de carga no canal, nesta região é igual a capacitância desta faixa
multiplicada pela tensão efetiva no canal neste ponto [vGS − v( x ) − Vt ]
dq = −Cox (Wdx )[vGS − v( x ) − Vt ]
O campo elétrico produzido pela tensão vDS no ponto x é igual a:
E( x) = −
dv( x )
dx
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O campo elétrico E(x) faz com que a carga dq se mova em direção ao
dreno com uma velocidade
dx
dv( x )
= − μn E ( x ) = μn
dx
dt
A corrente de drift resultante pode ser calculada como
i=
dq dq dx
dv( x )
=
= − μnCoxW [vGS − v( x ) − Vt ]
dt dx dt
dx
A corrente de dreno é então
iD = −i = μnCoxW [vGS − v( x ) − Vt ]
dv( x )
dx
Rearranjando esta equação
iD dx = μnCoxW [vGS − v( x ) − Vt ]dv( x )
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Integrando os dois lados desta equação de x = 0 até x = L correspondendo
a v(0) = 0 até v(L) = vDS
L
v DS
0
0
∫ iD dx = ∫ μnCoxW [vGS − v( x ) − Vt ]dv( x )
Temos a equação do FET na região de triodo
iD = ( μ nCox )(
1 2
W
)[(vGS − Vt )vDS − vDS
]
2
L
Para a região de saturação tem-se vDS = vGS − Vt
1
W
iD = ( μnCox )( )(vGS − Vt )2
2
L
K n' = μnCox
Parâmetro de transcondutância do processo
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Figure 4.9 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. Not shown are the connections made to the p-type
body and to the n well; the latter functions as the body terminal for the p-channel device.
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Símbolos do MOSFET
Figure 4.10 (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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Carracterística iD x vDS
i D = K n' (
W
1
iD = K n' ( )(vGS − Vt )2
L
2
1 2
W
)[(vGS − Vt )v DS − v DS
]
2
L
iD = K n' (
W
)(vGS − Vt )vDS
L
Figure 4.11 (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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Característica iD x vDS
1
W
iD = K n' ( )(vGS − Vt )2
2
L
iD = K n' (
1 2
W
)[(vGS − Vt )vDS − vDS
]
L
2
iD = K n' (
rDS =
W
)(vGS − Vt )vDS
L
1
K n'
W
(VGS − Vt )
L
VOV = VGS − Vt
=
1
W
K n' VOV
L
Gate to source overdrive voltage
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Região de saturação
1
W
iD = K n' ( )(vGS − Vt )2
2
L
Figure 4.12 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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Circuito equivalente para grandes sinais do MOSFET
Figure 4.13 Large-signal equivalent-circuit model of an n-channel MOSFET operating in the saturation
region.
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Figure 4.14 The relative levels of the terminal voltages of the enhancement NMOS transistor for
operation in the triode region and in the saturation region.
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Modulação do Comprimento do Canal
1
W
iD = K n' ( )(vGS − Vt )2
2
L
Figure 4.15 Increasing vDS beyond vDSsat causes the channel pinch-off point to move slightly away from
the drain, thus reducing the effective channel length (by DL).
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VA
Tensão de Early (J. M. Early)
ro =
VA
VA
=
I D 1 K ' (W )(v − V )2
n
GS
t
2
L
1
W
I D = K n' ( )(vGS − Vt )2
2
L
iD = I D +
1
1
ID
1
W
vDS = I D (1 +
vDS ) = K n' ( )(vGS − Vt )2 (1 +
vDS )
2
VA
VA
L
VA
Figure 4.16 Effect of vDS on iD in the saturation region. The MOSFET parameter VA depends on the
process technology and, for a given process, is proportional to the channel length L.
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ro =
VA
VA
=
I D 1 K ' (W )(v − V )2
n
GS
t
L
2
Figure 4.17 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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Figure 4.18 (a) Circuit symbol for the p-channel enhancement-type MOSFET. (b) Modified symbol with an
arrowhead on the source lead. (c) Simplified circuit symbol for the case where the source is connected to
the body. (d) The MOSFET with voltages applied and the directions of current flow indicated. Note that vGS
and vDS are negative and iD flows out of the drain terminal.
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Equações do FET canal P
Região de Triodo:
vGS ≤ Vt
iD = K 'p (
vDS ≥ vGS − Vt
1 2
W
)[(vGS − Vt )vDS − vDS
]
2
L
Região de Saturação: vGS ≤ Vt
iD = K 'p (
vDS ≤ vGS − Vt
W
)(vGS − Vt )vDS
L
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Figure 4.19 The relative levels of the terminal voltages of the enhancement-type PMOS transistor for
operation in the triode region and in the saturation region.
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Exercício 4.8
Vt = -1 V
Kp = 60 μA/V2
W/L = 10
Figure E4.8
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Body Effect
Em um circuito integrado do tipo NMOS o substrato é conectado à
tensão mais negativa do circuito, impedindo assim a condução do diodo
de substrato para fonte.
Esta polarização reversa (VSB) tem como efeito, a redução da
profundidade do canal, afetando portanto a corrente de dreno.
O efeito de VSB é geralmente representado como uma alteração na
tensão de limiar. Vt cresce com o aumento de VSB.
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Efeitos da Temperatura
Vt – cai 2 mV para cada 1oC de aumento da temperatura.
K’ – diminui com o aumento da temperatura.
A corrente de dreno diminui com o aumento da temperatura.
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Breakdown (Avalanche)
1 – A junção pn entre dreno e substrato entra em avalanche para tensões
entre 20 V e 150 V.
2 – Quando a tensão entre gate e fonte atinge 30 V, rompe-se a rigidez
dielétrica do óxido de silício na região canal, danificando definitivamente
o dispositivo. Isto pode ocorrer mesmo com eletricidade estática.
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Table 4.1
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Exemplo 4.2
Faça ID = 0,4 mA e VD = 0,5V
Dados:
Vt = 0,7 V
μnCox = 100 μA/V2
L = 1 µm
W = 32 µm
Figure 4.20 Circuit for Example 4.2.
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Exemplo 4.3
Faça ID = 80 µA. Calcule R e VD.
Dados:
Vt = 0,6 V
μnCox = 200 μA/V2
L = 0,8 µm
W = 4 µm
Figure 4.21 Circuit for Example 4.3.
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Exercício 4.12
Como continuação do exemplo
anterior, com R = 25 KΩ, ID = 80 µA
em Q1.
Calcule a corrente de dreno em Q2.
Dados:
Vt = 0,6 V
μnCox = 200 μA/V2
L = 0,8 µm
W = 4 µm
Figure E4.12
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Exemplo 4.4
Faça VD = 0,1V e projete o circuito.
Qual a resistência entre dreno e
source neste ponto de operação?
Dados:
Vt = 1 V
K’n(W/L) = 1 mA/V2
Figure 4.22 Circuit for Example 4.4.
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Exemplo 4.5
Analise o circuito.
Dados:
Vt = 1 V
K’n(W/L) = 1 mA/V2
Figure 4.23 (a) Circuit for Example 4.5. (b) The circuit with some of the analysis details shown.
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Exemplo 4.6
Projete o circuito para que o transistor
opere na região de saturação com VD = 3 V
e ID = 0,5 mA.
Qual a máxima resistência RD que ainda
mantém o transistor na região de
saturação?
Dados:
Vt = -1 V
K’p(W/L) = 1 mA/V2
Figure 4.24 Circuit for Example 4.6.
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Exemplo 4.7
Calcule iDN, iDP e vo para:
vI = 0 V, 2,5 V e -2,5 V.
Dados:
- Vtp = Vtn = 1 V
K’n(W/L) = K’p(W/L) =1 mA/V2
Figure 4.25 Circuits for Example 4.7.
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Exercício 4.16
Calcule iDN, iDP e vo para:
vI = 0 V, 2,5 V e -2,5 V.
Dados:
- Vtp = Vtn = 1 V
K’n(W/L) = K’p(W/L) =1 mA/V2
Figure E4.16
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Característica de
Transferência
iD =
VDD
1
−
vDS
RD RD
Reta de carga
Figure 4.26 (a) Basic structure of the common-source amplifier. (b) Graphical construction to
determine the transfer characteristic of the amplifier in (a).
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Característica de
Transferência
Av =
dvo
dt vi =VIQ
Ganho do Amplificador
Figure 4.26 (Continued) (c) Transfer characteristic showing operation as an amplifier biased at point Q.
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Figure 4.27 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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Figure 4.28 Example 4.8.
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Figure 4.28 (Continued)
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Polarização do MOSFET fixando a tensão VGS
1
W
I D = μ nCox (VGS − Vt )2
2
L
Vt, Cox, W e L variam de dispositivo
para dispositivo da mesma família
Vt, e μn variam com a temperatura.
Figure 4.29 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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Polarização com VG constante e resistor de fonte
ID =
VG − VGS
RS
Figure 4.30 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; (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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ID =
VSS − VGS
RS
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Projete o circuito para
ID = 0,5 mA
Dados:
VDD = 15 V
Vt = 1 V
K’n(W/L) = 1 mA/V2
Qual a variação de ID quando o MOSFET é trocado por outro com Vt = 1,5 V?
Figure 4.31 Circuit for Example 4.9.
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Polarização com resistor de realimentação entre dreno e gate
ID =
VDD − VGS
RD
Figure 4.32 Biasing the MOSFET using a large drain-to-gate feedback resistance, RG.
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Polarização com fonte de corrente constante
I REF =
VDD + VSS − VGS
R
1 ⎛W ⎞
I D1 = K n' ⎜ ⎟ (VGS − Vt )2
2 ⎝ L ⎠1
1 ⎛W ⎞
I D 2 = K n' ⎜ ⎟ (VGS − Vt )2
2 ⎝ L ⎠2
I D 2 = I REF
(W / L )2
(W / L )1
Figure 4.33 (a) Biasing the MOSFET using a constant-current source I. (b) Implementation of the
constant-current source I using a current mirror.
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Análise C.C.
1 W
I D = K n' (VGS − Vt )2
2
L
Introduzindo agora o sinal:
VD ≥ VGS − Vt
vGS = VGS − vgs
1 W
iD = K n' (VGS + v gs − Vt )2
2
L
1 W
1 W
W
iD = K n' (VGS − Vt )2 + K n' (VGS − Vt )v gs + K n' vgs 2
2
2
L
L
L
corrente c.c. de polarização: ID
amplificação
distorção
Figure 4.34 Conceptual circuit utilized to study the operation of the MOSFET as a small-signal amplifier.
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Condição de pequenos sinais:
K n'
1 W
W
(VGS − Vt )v gs >> K n' vgs 2
2
L
L
vgs << 2(VGS − Vt )
Desprezando o termo de distorção:
id = K n'
g m = K n'
vgs << 2VOV
iD ≈ I D + id
W
(VGS − Vt )vgs = g mvgs
L
W
W
(VGS − Vt ) = K n' VOV
L
L
ganho de transcondutância
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Interpretação gráfica do ganho de transcondutância
gm =
∂id
∂vGS
vGS =VGS
Figure 4.35 Small-signal operation of the enhancement MOSFET amplifier.
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vD = VDD − RDiD
vD = VDD − RD ( I D + id )
vd = − RDid = − g m RD vgs
Av =
vd
= − g m RD
vgs
Figure 4.36 Total instantaneous voltages vGS and vD for the circuit in Fig. 4.34.
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Modelo de pequenos sinais do MOSFET
id = g mvgs
g m = K n'
ro =
| VA |
ID
W
2I D
(VGS − Vt ) =
L
VGS − Vt
Figure 4.37 Small-signal models for the MOSFET: (a) neglecting the dependence of iD on vDS in saturation
(the channel-length modulation effect); and (b) including the effect of channel-length modulation, modeled
by output resistance ro = |VA| /ID.
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Analise o circuito e determine o
ganho, resistência de entrada e
máxima excursão do sinal de
saída.
Dados:
Vt = 1,5 V
K’n(W/L) = 0,25 mA/V2
VA = 50V
Figure 4.38 Example 4.10: (a) amplifier circuit; (b) equivalent-circuit model.
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Modelo T
Figure 4.39 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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Modelo T incluindo a resistência de saída
Figure 4.40 (a) The T model of the MOSFET augmented with the drain-to-source resistance ro. (b) An
alternative representation of the T model.
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Modelamento do Efeito Corpo (“Body”)
g mb =
∂iD
∂vBS
vGS = const .
v DS = const .
Transcondutância do corpo
Figure 4.41 Small-signal equivalent-circuit model of a MOSFET in which the source is not connected to
the body.
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Modelos de Pequenos Sinais
Table 4.2
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Amplificadores com MOSFET de estágio único
Polarização utilizada nos exemplos:
Figure 4.42 Basic structure of the circuit used to realize single-stage discrete-circuit MOS amplifier
configurations.
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Determine VOV, VGS, VS, VD.
Calcule gm e ro.
Dados:
Vt = 1,5 V
K’n(W/L) = 1 mA/V2
VA = 50V
Figure E4.30
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Table 4.3
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Amplificador fonte comum
Figure 4.43 (a) Common-source amplifier based on the circuit of Fig. 4.42. (b) Equivalent circuit of the
amplifier for small-signal analysis. (c) Small-signal analysis performed directly on the amplifier circuit with
the MOSFET model implicitly utilized.
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Análise direta no circuito
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Amplificador Fonte comum
com resistor de fonte
Figure 4.44 (a) Common-source amplifier with a resistance RS in the source lead. (b) Small-signal
equivalent circuit with ro neglected.
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Amplificador gate comum
Figure 4.45 (a) A common-gate amplifier based on the circuit of Fig. 4.42. (b) A small-signal equivalent
circuit of the amplifier in (a). (c) The common-gate amplifier fed with a current-signal input.
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(c) The common-gate amplifier fed with a current-signal input.
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Amplificador dreno comum
Figure 4.46 (a) A common-drain or source-follower amplifier. (b) Small-signal equivalent-circuit model.
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(c) Small-signal analysis performed directly on the circuit.
(d) Circuit for determining the output resistance Rout of the source follower.
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Amp. fonte comum
Amp. fonte comum com resistor de fonte
Table 4.4
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Amp. gate comum
Amp. dreno comum
Table 4.4 (Continued)
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Figure 4.47 (a) High-frequency equivalent circuit model for the MOSFET. (b) The equivalent circuit for the
case in which the source is connected to the substrate (body). (c) The equivalent circuit model of (b) with
Cdb neglected (to simplify analysis).
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Figure 4.48 Determining the short-circuit current gain Io /Ii.
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Table 4.5
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Figure 4.49 (a) Capacitively coupled common-source amplifier. (b) A sketch of the frequency response
of the amplifier in (a) delineating the three frequency bands of interest.
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Figure 4.50 Determining the high-frequency response of the CS amplifier: (a) equivalent circuit;
(b) the circuit of (a) simplified at the input and the output;
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Figure 4.50 (Continued) (c) the equivalent circuit with Cgd replaced at the input side with the equivalent
capacitance Ceq; (d) the frequency response plot, which is that of a low-pass single-time-constant circuit.
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Figure 4.51 Analysis of the CS amplifier to determine its low-frequency transfer function. For simplicity, ro
is neglected.
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Figure 4.52 Sketch of the low-frequency magnitude response of a CS amplifier for which the three break
frequencies are sufficiently separated for their effects to appear distinct.
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Figure 4.53 The CMOS inverter.
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Figure 4.54 Operation of the CMOS inverter when vI is high: (a) circuit with vI = VDD (logic-1 level, or VOH);
(b) graphical construction to determine the operating point; (c) equivalent circuit.
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Figure 4.55 Operation of the CMOS inverter when vI is low: (a) circuit with vI = 0 V (logic-0 level, or VOL);
(b) graphical construction to determine the operating point; (c) equivalent circuit.
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Figure 4.56 The voltage transfer characteristic of the CMOS inverter.
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Figure 4.57 Dynamic operation of a capacitively loaded CMOS inverter: (a) circuit; (b) input and output
waveforms; (c) trajectory of the operating point as the input goes high and C discharges through QN; (d)
equivalent circuit during the capacitor discharge.
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Figure 4.58 The current in the CMOS inverter versus the input voltage.
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Figure 4.59 (a) Circuit symbol for the n-channel depletion-type MOSFET. (b) Simplified circuit symbol
applicable for the case the substrate (B) is connected to the source (S).
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Figure 4.60 The current-voltage characteristics of a depletion-type n-channel MOSFET for which Vt = –4
V and k¢n(W/L) = 2 mA/V2: (a) transistor with current and voltage polarities indicated; (b) the iD–vDS
characteristics; (c) the iD–vGS characteristic in saturation.
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Figure 4.61 The relative levels of terminal voltages of a depletion-type NMOS transistor for operation in
the triode and the saturation regions. The case shown is for operation in the enhancement mode (vGS is
positive).
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Figure 4.62 Sketches of the iD–vGS characteristics for MOSFETs of enhancement and depletion types, of
both polarities (operating in saturation). Note that the characteristic curves intersect the vGS axis at Vt. Also
note that for generality somewhat different values of |Vt| are shown for n-channel and p-channel devices.
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Figure E4.51
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Figure E4.52
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Figure 4.63 Capture schematic of the CS amplifier in Example 4.14.
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Figure 4.64 Frequency response of the CS amplifier in Example 4.14 with CS = 10 mF and CS = 0
(i.e., CS removed).
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Figure P4.18
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Figure P4.33
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Figure P4.36
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Figure P4.37
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Figure P4.38
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Figure P4.41
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Figure P4.42
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Figure P4.43
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Figure P4.44
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Figure P4.45
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Figure P4.46
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Figure P4.47
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Figure P4.48
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Figure P4.54
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Figure P4.61
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Figure P4.66
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Figure P4.74
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Figure P4.75
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Figure P4.77
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Figure P4.86
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Figure P4.87
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Figure P4.88
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Figure P4.97
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Figure P4.99
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Figure P4.101
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Figure P4.104
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Figure P4.117
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Figure P4.120
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Figure P4.121
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Figure P4.123
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