IEEE Solid-States Circuits Magazine - Fall 2021 - 118

the reciprocal phase shift of the transmission
line results in unidirectional
wave propagation. Additionally, a
three-port circulator can be realized
LO1(t)
V1
+
+
-
-V1
v1
+(t)
-v1
-v2
v2
+(t)
+(t-Td)
+(t-Td)
Tm
5Tm/4
tt
(a)
3Tm/2
Port 2
+
LO1(t)
Tm/4
Tm/2
3Tm/4
v1
v2
+(t-Td)
+(t)
-v2
-v1
+(t)
+(t-Td)
LO t
O1( )
Zo, Td = Tm/4
Zo, Td = Tm/4
by placing ports anywhere along the
loop as long as they maintain a /4m
circumferential distance between
them. The maximum linearity with
LO2(t)
LO2(t)
+
-
V2
+
LO2(t) -V2
+
respect to the Tx port is achieved
if the circulator is designed asymmetrically
and the Rx port is placed
adjacent to the N-path filter, since the
inherent Tx-Rx isolation suppresses
the voltage swing on either side of
the N-path filter, enhancing its linearity
to Tx signals [Figure 9(b)].
Switched-Transmission-Line-Based
Nonreciprocal Devices
Inspired by the N-path-filter-based
RF circulator discussed previously, a
generalized conductivity modulation
concept is proposed using switched
transmission lines [51]. This structure
consists of two sets of differential
mixer-quad switches on either
side of a differential transmissionline
delay (replacing the commutated
capacitors), as shown in Figure 10(a).
The switches are clocked at a modulation
frequency ,fm
of the line is equal to /T 4m
and the delay
(/ ).f41 m
The switches are clocked with 50%
duty-cycle square-wave clocks with
a relative phase shift of /.T 4m
As a
Port 3
Port 1
(b)
ANT
1.8 mm
LO Path
Switches
Switches
LO
(c)
FIGURE 10: (a) The switched-transmission-line concept. (b) A mm-wave circulator based on
the switch delay structure and (c) a chip photo of the implemented 45-nm SOI CMOS 25-GHz
mm-wave circulator [51], [52]. SOI: silicon-on-insulator.
118
FALL 2021
IEEE SOLID-STATE CIRCUITS MAGAZINE
result, waves traveling from left to
right experience the transmissionline
delay with no sign flips in both
halves of the clock period. On the
other hand, waves traveling from
right to left experience the transmission-line
delay along with one sign
flip. In this structure, transmission in
both directions is perfectly lossless,
but there is an infinitely broadband
180° nonreciprocal phase difference.
In other words, the structure realizes
an infinitely broadband gyrator. The
key aspect of this architecture is that
the infinite bandwidth of the gyrator
implies that the signal frequency and
the modulation frequency are completely
decoupled. An arbitrarily low
modulation frequency can be used,
with the only restriction being an
associated increase in the transmission
line length and hence, the loss.
This advantage has been leveraged to
implement circulators at mm-waves
while the modulation frequency is
still at RF [52] and to implement RF
circulators with high power handling
through the use of high-voltage
switches [53]. Another important
Tx
1.2 mm
Rx
−π/2
Clock 1
Clock 1
Clock 2
Gyrator
+π/2
Clock 3
Clock 4
Clock 3
λ0/4
λ0/4
λ0/8
λ0/8
IEEE Solid-States Circuits Magazine - Fall 2021

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