IEEE Solid-States Circuits Magazine - Summer 2022 - 9

Digital
Input
Local Logic
fout
32 GHz
I1
fov
500 MHz
Local Logic
28 GHz
100 mV
(a)
850 mV Vcont
Digital
Input
(b)
FIGURE 5: (a) The desired continuous and discrete tuning characteristics and (b) the resulting layout complexity.
capacitor, Cu, into or out of the tank
at node X. If conducting, S1
off, S1
u
p=+ DB
displays
an on-resistance, Ru, limiting the
Q of this branch to /(1 RC ).uu 0~ If
still presents CC CGD
. That is, the " on/
in series with Cu
off capacitance ratio " is given by
/(
++ As the width of
S1 increases, so does the Q, but this
1 CC ).DBCGD
ratio drops. The reader can see that
this less-than-infinity ratio reduces
the vertical spacing between the
successive curves in Figure 5(a) or,
equivalently, raises the overlap, fov
achieve a Q comparable to that of the
inductor. This is an important issue
because, unlike the varactors, these
capacitors must constitute about 25%
of the tank capacitance, potentially
degrading the overall Q considerably.
With L = 53 pH, the tank capaci.
In
other words, 10 curves may not
suffice to cover a range of 4 GHz.
With the foregoing thoughts,
we ask whether it is possible for
the switched-capacitor branches to
X
X
Cu
Dj
S1
Cu
Ru
X
Cu
CGD
CDB
FIGURE 6: A switched-capacitor branch in
on and off conditions.
VX
Ron
(b)
VDD
tance should vary from 610 fF to
470 fF to yield the desired frequency
range. The total switched capacitance
then amounts to 140 fF. We begin with
the arrangement sho wn in Figure 7(a),
where all of the switched branches
are lumped into one. We select, as an
example, a W/L ratio of 10 μm/30 μm
for S1
and use ac simulations to
find the Q of the structure. Defining
Q as /( ){ }/ {},
1 RC ZZon aa a
~ =Im
on
/(
Re
we obtain Q 1. at 30 GHz! This
means that
10nn# =32 320
Note that
RC )144X...~
Thus, to approach the inductor Q of 32,
the width of the switch must increase
to mm.
with such a high Q, we have from
Figure 7(b)
V ()
V
X
N
=
on ++1
ap
a
on
.
Q
. 1
RC Cs
RC s
(4)
(5)
X Za
Ca
N
S1
10 µm
30 nm
(a)
Ca
VN
Cp
140 fF
Cp
-35
-30
-25
-20
-15
-10
-5
28
29
30
Frequency (GHz)
(c)
FIGURE 7: (a) A lumped representation of the entire discrete tuning network, (b) the simplified
model, and (c) the magnitude response for the on and off states.
IEEE SOLID-STATE CIRCUITS MAGAZINE
SUMMER 2022
9
31
S1 Off
S1 On
32
S1 On
S1 Off
VN/VX (dB)

IEEE Solid-States Circuits Magazine - Summer 2022

Table of Contents for the Digital Edition of IEEE Solid-States Circuits Magazine - Summer 2022

Contents
IEEE Solid-States Circuits Magazine - Summer 2022 - Cover1
IEEE Solid-States Circuits Magazine - Summer 2022 - Cover2
IEEE Solid-States Circuits Magazine - Summer 2022 - Contents
IEEE Solid-States Circuits Magazine - Summer 2022 - 2
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IEEE Solid-States Circuits Magazine - Summer 2022 - Cover3
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