4.3 MOSFET Circuits at DC
• We study a number of design and analysis examples
of circuits with DC voltages and currents only
• In the following examples, we will neglect the
Channel Length Modulation effect, i.e.
λ=0
• Recall that: VOV = VGS - Vt
- For NMOS transistors: Vt and VOV are +ve
- For PMOS transistors: Vt and VOV are -ve
Dr. Tamer ElBatt
4.3 MOSFET Circuits at DC
Example 4.2: Design the circuit shown so that
the transistor operates at ID = 0.4 mA and
VD = +0.5 V. The 0MOS transistor has Vt = 0.7 V,
µn Cox = 100 µA/V2, L = 1 µm, and W = 32 µm.
In Which Region Does the
0MOS Operate?
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MOSFET Circuits at DC cont.
Example 4.3: Design the circuit shown to obtain a
Current ID of 80 µA. Find the value required for R
and find the DC voltage VD. Let the 0MOS transistor
have Vt = 0.6 V, µnCox = 200 µA/V2, L = 0.8 µm,
and W = 4 µm.
In Which Region Does the
0MOS Operate?
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MOSFET Circuits at DC cont.
Exercise: From the previous example, let the voltage
VD be applied to the gate of another transistor Q2 as
shown in the Figure below. Assume that Q2 is identical
to Q1. Find the drain current and voltage of Q2.
In Which Region Does Q2
Operate?
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MOSFET Circuits at DC cont.
Example 4.4: Design the circuit in the Figure shown to establish a
drain voltage of 0.1 V. What is the effective resistance between
drain and source at this operating point? Let Vt = 1 V and
k’n(W/L) = 1 mA/V2
In Which Region Does the
0MOS Operate?
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MOSFET Circuits at DC cont.
Example 4.5: Analyze the circuit shown in (a) below to
determine the voltages at all nodes and the currents through
all the branches. Let Vt = 1 V and k’n(W/L) = 1 mA/V2.
In Which Region Does the 0MOS Operate?
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MOSFET Circuits at DC cont.
Example 4.6: Design the circuit below so that the transistor
operates in saturation with ID = 0.5 mA and VD = +3 V. Let the
PMOS transistor have Vt = -1 V and k’p(W/L) = 1 mA/V2.
What is the largest value that RD can have while
maintaining saturation-region operation?
S
G
D
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4.4 The MOSFET as an Amplifier and as a Switch
• We use MOSFET in the design of amplifier circuits since they
act as a voltage-controlled current source in the Saturation
region
- i.e. Changes in vGS gives rise to changes in iD
• How to achieve Linear Amplification? i.e. an amplifier whose
output signal (i.e. the Drain current iD) is linearly related to the
input signal (i.e vGS )
- We’ll have to find a way around the highly non-linear (square-law)
relationship of iD to vGS:
1 'W
iD = k n
(vGS − Vt ) 2
2 L
[
]
Dr. Tamer ElBatt
DC Biasing is a Fundamental Step towards designing a
Linear MOSFET Amplifier
• The technique we use to obtain linear amplification out of a
fundamentally non-linear device is called DC biasing
- Two Steps:
1. Bias the MOSFET to operate at a certain DC voltage VGS and
corresponding ID and then,
2. Superimpose a small AC signal to be amplified vgs, on top of the DC
bias voltage VGS
Before we study the Small-signal operation of the MOSFET
Amplifier, we need to understand its Large-signal operation
Dr. Tamer ElBatt
Large-Signal Operation
Common Source (CS) (grounded source) Amplifier
• Called Common Source since the
grounded source is common to both
the input port (between G and S) and
the output port (between D and S)
• Changes in vl = vGS, causes changes in
iD and we use a resistor RD to get an
output voltage vo:
vo = vDS = VDD – RD iD
• A DC power supply VDD is needed to
turn the MOSFET on and to supply the
necessary power for its operation
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Large-Signal Operation cont.
vDS = vGS - Vt
VDD/RD
vGS = Vt
• Governed by the intersection of the MOSFET iD-vDS characteristic
and the Load Line imposed by connecting the drain to VDD via RD
• For any given vl (=vGS), we locate the corresponding iD-vDS curve and
find vo from the point of intersection of this curve with the load line
• As vl=vGS is increased, the operating point slides on the load line
from point A (cutoff), through Saturation, to point C (Triode)
Dr. Tamer ElBatt
The Transfer Characteristics – Graphical Derivation
Operation as a Switch
SWITCH OFF
• Operate the MOSFET at the
Extreme points of the Transfer
Curve
• vl < Vt : switch is turned off and
vo = VDD (operate between X
and A)
SWITCH O0
• vl = VDD: switch is turned on
and vo is very small (operate at
point C)
MOSFET Operates as a
“Digital Logic Inverter”
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The Transfer Characteristics – Graphical Derivation
Operation as a Linear Amplifier
• We make use of the Saturationmode segment of the curve (A
Through B)
• The MOSFET is biased
somewhere in the middle, e.g.
point Q
• The AC signal to be amplified is
then superimposed on the DC
Voltage VlQ
• By keeping vi sufficiently small,
we restrict operation to the almost
linear region between A and B
• Gain (Av):
dvo
Av =
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The Transfer Characteristics – Graphical Derivation
Operation as a Linear Amplifier
• VDSQ should be of such value
to allow for the required output
signal swing
• VDSQ should be lower than VDD
by sufficient amount to allow for
the positive peaks of the output
signal (sufficient headroom)
• VDSQ should also be away from
the boundary of the Triode region
(point B) to allow for negative
peaks (sufficient legroom)
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How to Bias a MOSFET Amplifier?
• Bias Point Q1: does not leave sufficient room for positive
signal swing at the drain (too close to VDD)
• Bias Point Q2: too close to the boundary of the Triode region
and might not allow for sufficient negative signal swing
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Analytical Expressions for the Transfer Characteristics
• Derive vo = f(vl)
• Cut-off Segment:
Vl ≤ Vt and vo = VDD
• Saturation Segment:
1
W
vo = VDD − RD µ nCox (vl − Vt ) 2
2
L
W
Av = − RD µ nCox (VlQ − Vt )
L
• Triode Segment:
vo = VDD − RD µ nCox
W
L
1 2

v
V
v
vo 
−
−
(
)
t
o
 l
2 
Dr. Tamer ElBatt