IEEE Solid-States Circuits Magazine - Spring 2022 - 80

zero. Then, the start of the curve
is in the center. However, when ~
is infinite, the open-loop gain is
-A ,0
and its phase is -180. Briefly,
if the point of -1 had not existed in
the curve, the closed-loop function
would be stable.
Gaurav Agrawal
School: Interuniversity
Microelectronics
Centre-Vrije Universiteit
Brussel (IMEC-VU),
Brussels, Belgium.
Gaurav Agarwal received his bachelor
of technology (honors) degree in
electronics and communication enCF
gineering
from University College of
Engineering, Kota, India, in 2011 and
master of science degree (by research)
in analog/RFIC design from the Indian
Institute of Technology Madras, India,
in 2015. He was with Kilby Labs at Texas
Instruments (2015-2017) and Aura
Semiconductors (2017-2021), both in
India, working on analog/RFIC design
for subgigahertz radios, Bluetooth,
and LTE/5G FEM for base stations in
CMOS and III-V technologies. Since
mid-2021, he has been a Ph.D. candidate
at IMEC-VU Brussels in Belgium,
where he is currently working on millimeter-wave
CMOS transceivers beyond
100 GHz. He is the recipient of
the fall 2014 IEEE Microwave Theory
and Techniques Society Pregraduate
Award. Contact him at gaurav.agrawal@
vub.be.
R
Vin,A
RF
RL
Vout,A
A
RD
Vout,β RL
CF
Vin,β
RF
Im
β
FIGURE 5: A block diagram of the
proposed topology.
For the Positive-Feedback
-1
-A0
R
ω = ∞
φ = -180
Positive Gain Margin
FIGURE 7: The Nyquist plot of the proposed topology.
ω = 0
φ = 0
Student Circuit Contest Solution
A common-drain amplifier, dearly
known as a source follower or buffer,
provides an interesting example
of a circuit with a positive feedback
Now, consider an impedance ZF
connected between the input and
output (Figure 9). This impedance
represents the gate source capacitance
present in a real transistor. This
impedance introduces feedback from
the output to input. The sense of this
yet stable operation. The following
solution investigates this phenomenon
in detail.
Figure 8 shows an ideal transistor
connected in a common-drain
configuration. The input is applied
at the gate through a source resistance
^hR
.S
A load resistance RL^h
is connected at the output through
a large dc blocking capacitor. The
voltage gain Av^h from gate Vin
source Vout^h is given as
A
v==
V
V
out
in
gR
mL
1 gR+ mL
^h to
1 1
(12)
Note that the sign of this gain
is positive. Furthermore, this is always
less than unity, irrespective of
the values of gm
and R .L
M1
RS
vin
gm
vout
vs
I0
Source
FIGURE 6: Dr. Harry Nyquist, who did
important work on the stability of feedback
amplifiers [6].
80
SPRING 2022
Amplifier
FIGURE 8: A common-drain amplifier with the source and load.
IEEE SOLID-STATE CIRCUITS MAGAZINE
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RL

IEEE Solid-States Circuits Magazine - Spring 2022

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