IEEE Solid-States Circuits Magazine - Fall 2020 - 92

filter [20]. The parameters of the net-
work components can hence be cho-
sen to achieve any desired frequency
response for the filter. Note that the
additional capacitor can be explicit
or parasitic; e.g., it can be due to the
input pad. Moreover, note that the
balun can also be used to implement
some impedance transformation,
leveraging the intrinsic 1: nk ideal
transformer embedded in the equiva-
lent ladder network.
Coupling inductors is also use-
ful to decrease the footprint of the
magnetic devices. Coming back to
the inductively degenerated LNA

this arrangement allows one to easily
route signals to the transistors, simpli-
fying the overall floorplan of the LNA.
In the layout depicted in Figure 9,
the two identical gate inductors are
also coupled, making up a bifilar
transformer. This structure, singled
out in Figure 10(a), is interesting
because it shows a different behav-
ior in differential and common mode
operation. With reference to Figure 10(a),
in differential mode, I 2 = I 1 , and, for
each branch, we have a differential
mode inductance equal to

example, coupling the gate and
source coils helps save silicon area,
as illustrated in Figure 9 [21]. It is
easy to show [22] that the mutual
inductance due to the coupling
between L g and L s increases both
the inductive and real parts of the
input impedance of the amplifier in
Figure 9. Therefore, smaller wind-
ings can be used to achieve a target
level of series inductance and equiv-
alent resistance. Coupling L g and L s
also leads to a particularly compact
and convenient layout, especially
in a differential design, like the one
depicted in Figure 9 [21]. Moreover,

	

In common mode, instead, I 2 = - I 1 ,
and the common mode inductance is

k
Lg

M1 M2
k

k

k

Ls

	

Lg

L cm = L (1 - k) .(14)

The coils can be wound up to have
a positive magnetic coupling, as in
the layout presented in Figure 10(a),
or they can be wound up to have
k 1 0 , obtaining a larger inductance
in differential or common mode
operation, respectively. The sym-
metric bifilar transformer is useful
to implement differential artificial
transmission lines with a compact

Ls

[Padovan 16]
(a)

(b)
FIGURE 9: The coupling of the gate and source inductors in a CMOS LNA. (a) A die microphotograph and (b) the schematic and layout views.

I1

L dm = L (1 + k) .(13)

P2, Z01

Z0a
V1

+

-

λ /4

P3, Z03

2Z
Z01

L

λ /4
Z0a

k
L
V2

-

I2

+

C

I1
P1

I2
(a)

k

P1, Z01

L

L
C

L

P3

C

k

C

Section of
o Differential
Artificial t-Line
Artific

L

P2
(b)

FIGURE 10: The (a) symmetric bifilar transformer and (b) lumped-element implementation of an X-band Wilkinson divider.

92	

FA L L 2 0 2 0	

IEEE SOLID-STATE CIRCUITS MAGAZINE	



IEEE Solid-States Circuits Magazine - Fall 2020

Table of Contents for the Digital Edition of IEEE Solid-States Circuits Magazine - Fall 2020

Contents
IEEE Solid-States Circuits Magazine - Fall 2020 - Cover1
IEEE Solid-States Circuits Magazine - Fall 2020 - Cover2
IEEE Solid-States Circuits Magazine - Fall 2020 - Contents
IEEE Solid-States Circuits Magazine - Fall 2020 - 2
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