Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
Biasing in MOSFET Amplifiers
• Biasing: Creating the circuit to establish the desired
DC voltages and currents for the operation of the
amplifier
• Four common ways:
1. Biasing by fixing VGS
2. Biasing by fixing VG and connecting a resistance in the
Source
3. Biasing using a Drain-to-Gate Feedback Resistor
4. Biasing Using a Constant-Current Source
MOSFETs 1
Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
Biasing in MOSFET Amplifiers
•
I D = 12 k n′
k n′ = μ n
VDD
Biasing by fixing VGS
ε ox
t ox
W
(VGS − Vt )2
L
= μ n Cox
VGG
VG
RD
VD
RG
M1
VS
RS
-VEE
When the MOSFET device is
changed (even using the same
supplier), this method can result in
a large variability in the value of
ID. Devices 1 and 2 represent
extremes among units of the same
type.
MOSFETs 2
Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
Biasing in MOSFET Amplifiers
•
Biasing by fixing VG and connecting a resistance in the Source
Degeneration Resistance
MOSFETs 3
Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
Biasing in MOSFET Amplifiers
• Biasing using a Drain-to-Gate Feedback Resistor
Large Resistor
MOSFETs 4
Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
Biasing in MOSFET Amplifiers
• Biasing Using a Constant-Current Source
Current Mirror
Used in Integrated Circuits
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.
MOSFETs 5
Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
Current Mirror DC Analysis
• The width and length (the W/L aspect
ratio) and the parameters of the two
transistors can be different
• We can choose W/L freely
• In this circuit, consider W/L of both
MOSFETs are the same and transistors
are identical. The Gate-Source voltages
W1
are also the same, then
L1
I REF
= k n′
I = 12 k n′
1
2
I
W1
(VGS − Vt )2
L1
W1
(VGS − Vt )2
L1
I
I REF
W1 L1
=
⋅
=1
L1 W1
-
VGS
+
+
W1
L1
VGS
-
I = I REF
MOSFETs 6
Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
Current Mirror DC Analysis
• Designing IREF
I REF
VDD − VGS + VSS
=
R
I REF =
1 ′
k
2 n
W1
(VGS − Vt )2
L1
• It is often needed to find the value of R in order to
achieve a desired IREF
MOSFETs 7
Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
Biasing of MOSFET Amplifier
•
•
•
•
•
•
•
•
•
1- Intro to MOS Field Effect Transistor (MOSFET)
2- NMOS FET
3- PMOS FET
4- DC Analysis of MOSFET Circuits
5- MOSFET Amplifier
6- MOSFET Small Signal Model
7- MOSFET Integrated Circuits
8- CSA, CGA, CDA
9- CMOS Inverter & MOS Digital Logic
MOSFETs 8
Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
MOSFET Design Space
• Modern integrated circuits use MOSFETs
extensively
– Very high densities of transistors – up to 109
transistors/cm2 in some ULSI memory arrays.
– Off-chip discrete resistors and capacitors are NOT
commonly used
– On-chip resistors and capacitors generally small
– Multistage amplifiers are usually DC-coupled
• Transistors used wherever possible to implement
current sources, resistors, capacitors,
MOSFETs 9
Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
Using MOSFETs to implement R’s and C’s
• Resistors:
Active Loads (large R’s)
Diode-connected loads (small R’s)
MOSFET Triode-Region (moderate R’s)
• Capacitors
Most obvious is the gate-body capacitor
Can be used to have variable-capacitors as well
• Current Mirrors
MOSFETs 10
Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
MOSFET Active Loads
• MOSFETs used as an active load for high resistances:
– MOSFET is held in saturation with the source and gate
held at a constant DC voltage
1
r
=
– Drain connected to circuit
o
λ ⋅ ID
– ro is inversely proportional to ID
vgs = 0
gmvgs = 0
Rin=ro
Rin= ?
MOSFETs 11
Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
Diode-Connected MOSFETs
• A Diode connected MOSFET can be used to achieve
small resistances:
– The Drain is directly connected to Gate, and therefore it
can only be operated in saturation (or cutoff)
Source Absorption Theorem
MOSFETs 12
Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
MOSFET Current Mirrors
• Used extensively in
MOSFET IC applications
• Often ro,is neglected. Since
there is no gate current, the
drain currents of M1 and M2
are identical
• In practice, IREF ≠ I due to
finite ro. (Not included in EC1)
1 W1
2
I REF = k n′ (V X − Vt ) (1 + λV X )
2 L1
V X = VGS 1 = VDS 1
VX
0
-
VGS
+
I
0
+
VGS
-
The current I will also depend on VDS2
MOSFETs 13
Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
Current Mirror DC Analysis
• The width and length (the W/L
aspect ratio) of MOSFETs can
be designed almost freely
• Since the W/L of M1 and M2
need not be the same, the size
ratios can affect current ratios
I REF = 12 k n′
W1
(VGS − Vt )2
L1
W2
(VGS − Vt )2
I = k n′
L2
1
2
I
I REF
=
W2 L1
⋅
L2 W1
I
W1
L1
W2
L2
-
VGS
+
+
VGS
-
MOSFETs 14
Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
Current Scaling (Steering)
W
L
W
L
W
L
W
L
• Ratio of
aspect ratios
can be
selected to
achieve
nearly any
scale factor
I/IREF
Note: All gates are connected
MOSFETs 15
Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
Current Mirroring – Pushing and Pulling
MOSFETs 16
Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
Small Signal
• Transistor M1 is diode
connected and acts like a
resistor to s.-s. ground.
ro2
MOSFETs 17
Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
Outline of Chapter 5
•
•
•
•
•
•
•
•
•
1- Intro to MOS Field Effect Transistor (MOSFET)
2- NMOS FET
3- PMOS FET
4- DC Analysis of MOSFET Circuits
5- MOSFET Amplifier
6- MOSFET Small Signal Model
7- MOSFET Integrated Circuits
8- CSA, CGA, CDA
9- CMOS Inverter & MOS Digital Logic
MOSFETs 18
Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
DC and AC - Body-Effect / CLM
Three types of analysis:
Neglect DC Body-Effect & DC CLM
Use DC Body-Effect / Neglect DC CLM
Use DC Body-Effect / Use DC CLM
Three types of analysis:
Neglect AC Body-Effect & AC CLM
Use AC Body-Effect / Neglect AC CLM
DC Analysis
Use whatever
DC values for
V and I in the
small-signal
analysis
AC Analysis
(small-signal)
Use AC Body-Effect / Use CLM
MOSFETs 19
Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
Common Source Amplifier (CSA)
• Current source I implemented
with current mirror.
• Current mirror provides
active load at drain
• Source terminal grounded –
no DC or AC Body effect
MOSFETs 20
Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
CSA with Current Mirror
ro2
CSA
MOSFETs 21
Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
CSA Small Signal Analysis
• From MOSFET
Current-Mirror:
only ro2 appears in
analysis
v gs1 = vi
vout = − g m1 (ro1 ro 2 )v gs1
vout
AV =
= − g m1 (ro1 ro 2 )
vi
MOSFETs 22
Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
CSA Input/Output Resistance
• Input Resistance
RIN ⇒ ∞
• Output resistance
vgs1 = 0
gm1vgs1 = 0
ROUT = ro1 ro 2
MOSFETs 23
Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
CSA Calculations
• In practice, difficult to keep all
transistors operating in saturation
VOUT is hard to control, and
sensitive to: W/L, VG, and
CLM
λ1 = λ2 = 0.01V −1
Vt1 = Vt 2 = 1V
k ′p = 50μ AV
Hand:
SPICE:
VG = 2.567V
VG = 2.58V
I = 2.596mA
k n′ = 125μ AV
VOUT = 3.855V
I = 2.57mA
VOUT = 2.895V
W2
W
= 50, 1 = 40
L2
L1
g m1 = 5.192m AV
AV = −102.4 V V
VDD = 5V ,VSS = −2V
RREF = 1kΩ
ro = 38.52kΩ
AV = −100 V V
MOSFETs 24
Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
Common Gate Amplifier (CGA)
• A pMOS current mirror is used
as IREF including the output
resistance.
• The gate terminal held at a DC
voltage. (AC Ground)
• Since source terminal not at
signal ground, the body effect is
present.
Typically used as second stage of a
multi-stage amplifier circuit
MOSFETs 25
Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
CGA – DC Analysis
• Current mirror is assumed to be ideal
during the DC analysis, thus IREF=I
• DC voltage at the source terminal (VS)
must be obtained from driving the
current IREF through the transistor.
• This assumes that the input voltage
source VI is set to zero
• RI is part of the source voltage
• Solve for VO, with VS and VG known,
and including CLM
2
1 ′W
I = 2 k n (VG − VS − Vt ) [1 + λ ⋅ (VO − VS )]
L
MOSFETs 26
Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
CGA
• Replace with a current source
including output resistance ro2
ro2
Choice of analysis:
Neglect AC Body-Effect & CLM
Use AC Body-Effect / Neglect CLM
Use AC Body-Effect / Use CLM
MOSFETs 27
Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
CGA – No Body Effect or CLM
vo = − g m v gs ⋅ ro 2
i=0
v gs = −
Non Inverting
AV =
1
g m1
1
+ RI
g m1
vI
vo
ro 2
=
1
vI
+ RI
gm
MOSFETs 28
Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
CGA – RIN & ROUT, No Body Effect or CLM
RIN
1
=
g m1
ROUT
vI = 0
RIN
ROUT = ro 2
MOSFETs 29
Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
CGA – With Body Effect & no CLM
Solve at vx first:
vX
RIN
vbs1 = v gs1 = −v x
vo = −(g m1v gs1 + g mb1vbs1 )ro 2
vo = −( g m1v x + g mb1v x )ro 2
vo
AV = = ( g m1 + g mb1 )ro 2
vx
Include RI and
vo vo v x
R IN
solve for total
AV − total =
=
⋅
= ( g m + g mb )ro 2 ⋅
voltage gain in
vi v x vi
R IN + R I
term of RIN
MOSFETs 30
Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
CGA – RIN With Body Effect & no CLM
iX
vX
iIN
RIN
vbs1 = v gs1 = −v x
ix = ( g m1 + g mb1 )v x
iin = ( g m1 + g mb1 )v x
Neglect Input
Voltage Source
RIN
1
=
g m1 + g mb1
MOSFETs 31
Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
CGA - With Body Effect & CLM
iX
iX
vX
Neglect Input
Voltage Source
v x = −v gs
vo = ix ⋅ ro 2
v x − vo
i x = ( g m1 + g mb1 )v x +
ro1
⎛1
⎞
vo
AV = = (ro1 ro 2 ) ⋅ ⎜⎜ + g m1 + g mb1 ⎟⎟
vx
⎝ ro1
⎠
MOSFETs 32
Department of Electrical and
Computer Engineering
ECSE-330B Electronic Circuits I
CGA – RIN With Body Effect & CLM
iX
vX
vo = ix ⋅ ro 2
RIN
v x − vo
ix = ( g m1 + g mb1 )v x +
ro1
1+
Neglect Input
Voltage Source
RIN =
ro 2
ro1
vx
=
1
ix
+ g m1 + g mb1
ro1
MOSFETs 33