IEEE Solid-States Circuits Magazine - Spring 2023 - 14

CIRCUIT INTUITIONS
Ali Sheikholeslami
Voltage Follower, Part III
W
Welcome to the 35th article in the
" Circuit Intuitions " column series.
As the title suggests, each article
provides insights and intuitions into
circuit design and analysis. These
articles are aimed at undergraduate
students but may serve the interests
of other readers as well. If you read
this article, I would appreciate your
comments and feedback as well as
your requests and suggestions for
future articles in this series. Please
e-mail me your comments at ali@
ece.utoronto.ca.
In the previous two articles [1], [2]
in this series, we reviewed the
general characteristics of a
simple voltage follower (SVF),
as shown in Figure 1(a), and
compared them against
those of a flipped voltage
follower (FVF) [3], [4], as
shown in Figure 1(b). An
SVF exhibits an infinite
input resistance, a small
output resistance, and a
voltage gain of slightly
less than 1 V/V. In contrast,
an FVF exhibits
a much-reduced output resistance
(by a factor of
transistor M1 with a bias current of
IB1 and an auxiliary PMOS transistor
M2 with a bias current of I .B2 For
simplicity, we assume both transistors
to have the same bias currents,
III ;BBB
== the same short circuit
transconductance, ggg ;mm m12
12
==
and the same output
rrr .ooo
12
resistance,
== That is, we assume that
In this article, we
look at another
variation of the
FVF, known as
the super source
follower, before
making detailed
comparisons
among the three
designs and
providing some
intuitions.
gr )mo while maintaining
the same voltage gain as that
of an SVF. In this article, we look at
another variation of the FVF, known
as the super source follower (SSF) [5],
before making detailed comparisons
among the three designs and providing
some intuitions.
Figure 1(c) shows a schematic of
an SSF, which consists of an input
Digital Object Identifier 10.1109/MSSC.2023.3269457
Date of current version: 22 June 2023
14
the bottom current source provides
twice the current of the top current
source. Further, we assume both
transistors to be in the saturation region.
Let us now find an expression
for the output voltage of this circuit
when we apply a
low-frequency smallsignal
voltage to the
input. In general, the
voltage of any node in
a linear time-invariant
circuit can be found by
multiplying its short cirwhere,
for simplicity, we have
assumed the two transistors to have
the same
g .m This equation is, in fact,
identical to what we found in the previous
article in this series [2] for the
FVF. That is, the short circuit currents
of both the FVF and the SSF are gr
mo
times larger than the short circuit current
of the SVF.
Let us now find the output resistance
of the SSF with the help of
the equivalent circuit shown in Figure
2(b). To find the output resistance,
we ground the input node,
apply an ideal signal source vx
to
the output node, and measure the
resulting signal current
x 12
.
=+#
i .x Again, for
the same reasons provided earlier,
ii ,i
=+ with i 01 = We observe
that ig vv rmd xo21 /. We find vd1
using the equivalent circuit of Figure
2(c) by multiplying the short
circuit current at the drain of
me
M ,1
and its output resistance gg g
[6]. To find the short circuit
current, we use the simplified
small-signal circuit of
Figure 2(a), where all of the
1
dc voltage and current sources are
zeroed. The short circuit current isc
is simply the sum of i1
and i .2 However,
i1 is zero because it leads to an
open circuit at the gate of M .2 The
voltage at the drain of M1
the product of its short circuit current
to the ground ()
equivalent resistance ().ro
fore, we have a voltage of gr vmo in
-
at the gate of M ;2 when we multiply
this by its g ,m
we find
ii ()
SPRING 2023
IEEE SOLID-STATE CIRCUITS MAGAZINE
sc 2in
== #gr gvmo m
is simply
R
-gvm in and its
Therecuit
current to the ground iv (/ )gr1xo1sc =+ and r ,o where
me mmb=+ is the effective short
circuit transconductance of the transistor,
including the body effect. In other
words, () ;vg rv1dmeo x
=+ # hence,
iv () .gg r
xx 1mmeo
=+ +
first term in ix
and we can write
vx
ix
r
v
o
x
If we assume gr ,1mo & only the
will be dominant,
out = .ccmm.
1
1
gr g
mo me
Again, this equation is identical
to what we found for the FVF. In both
cases, the output resistance is reduced
by a factor of gr
mo compared to the
SVF. Recall that this is the same factor
by which the short circuit current
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IEEE Solid-States Circuits Magazine - Spring 2023

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