254 Design of CMOS Millimeter-Wave and Terahertz Integrated Circuits
Substituting Z
RLC
(s) into equation (11.6), the transfer function of the
proposed SRX can be expressed as
Z
NT V
(s, t) =
Z
0
ω
0
s
s
2
+ 2ζ
n
(t)ω
0
s + ω
2
0
(11.7)
where the new damping function ζ
n
(t) becomes
ζ
n
(t) = ζ
0
[1 − G
m1
(t) R
1 + e
jϕ
]. (11.8)
Note tha t the absolute value G
m2
(t) is equal to G
m1
(t), and a phase
difference ϕ is introduced due to the phase difference from the injected signals.
Therefore, when the damping signal is a ramping signal with slope β, the
damping function becomes
ζ
n
(t) = 1 − (1 + e
jϕ
)βt.
As a result, the gain function µ
n
(t) and the sensitivity function g
n
(t)
become
µ
n
(t) = κe
1
2
ω
0
β(1+e
jϕ
)t
2
(11.9)
g
n
(t) = κe
−
1
2
ω
0
β(1+e
jϕ
)t
2
. (11.10)
One can observe that the gain and sensitivity functions are both influenced
by the phase difference of the injected signal between two oscillators. When
the phase difference becomes zero, both the gain and the sens itivity functions
can be optimized.
We further compare the gain function and sensitivity function of the con-
ventional SRX w ith that of the proposed ZPS-coupled SRX by
U
C
=
µ
n
(t)
µ (t)
= e
1
2
ω
0
βt
2
(11.11)
G
C
=
g
n
(t)
g (t)
= e
−
1
2
ω
0
βt
2
. (11.12)
One can observe tha t the gain of the SRX enhancement is exponential
with ω
0
. When a signal frequency around ω
0
is injected into LC- tank-I, it is
amplified and injected into LC-tank-II in phase. Then, it is further amplified
by L C -tank-II and re -injected into LC-tank-I. Thus, a po sitive feedback loop is
established when in-phase coupling is realized by the ZPS, where the oscillator
amplification gain is increased with the improved detection sensitivity.
11.3 Circuit Prototyping and Measureme nt
11.3.1 SRX Circuit Design
The schematic of the proposed SRX is shown in Figure 11.3. It consists of
two ZPS-coupled LC-tank resonators, one common source input buffer and
In-Phase Detection 255
VDD
M
1
M
1
M
2
V
TUNE1
V
quench
M
2
L
Z
L
Z
C
Z
L
T
L
T
ZPS
LNA with
input matching
network
LC Tank-I
LC Tank-II
V
B
Output
R
D
R
B
M
5
Detector
V
B
M
5
L
1
L
2
V
G
M
3
M
3
M
4
M
4
M
3
M
3
R
B
Signal input
C
A
C
A
CON
M
dummy
M
6
V
TUNE2
Figure 11.3: Circuit diagram of propos ed SRX with ZPS-coupled os-
cillators.
one output e nvelope detector. Relatively small sized (2µm/100nm) NMOS
transistors (M3) are c onnected in both oscillator tanks, working as var actors
for freq ue nc y tuning. By tuning control voltages VTUNE1 and VTUNE2,
the process mismatch in two LC tanks is well cancelled to make sure that
the free-running fr equencies of two tanks are the same. As a result, CON
synchronization ma inly dep ends on the coupling network, which is ensured
by the ZPS given in this paper. The quench-controlled transco nductances are
implemented by cross-coupled transistor pairs (M
1
and M
2
), of which the tail
current is controlled by M
4
. Note that M
1
and M
2
have an identical size of
60nm length and 12µm width, and M4 has a size of 60nm length and 6 0µm
width. The input of LC-tank-I is connected to a common source buffer (M
6
),
of which the input is matched to 50 Ω by L
1
and L
2
. A dummy transistor
(M
dummy
) is introduced to compensate para sitic capac itor unbalance. The
output of LC-tank-II is connected to a differential envelope detector (M
5
).
The design of a pa ssive part such as ZPS [163] is shown in Figure 11.4. The
inductor is implemented in the top metal layer. The radius of the inductor
256 Design of CMOS Millimeter-Wave and Terahertz Integrated Circuits
L
T
L
Z
C
Z
0 50 100 150 200
55
60
65
70
75
80
85
12
14
16
18
20
22
24
Frequency (GHz)
Ind (PH)
Q
0 50 100 150 200
-35
-30
-25
-20
-15
-10
-5
0
-20
0
20
40
60
80
100
Frequency (GHz)
Phase (degree)
loss (dB)
0.4dB
131.5GHz
OI 3.3um
EA 0.9um
L
T
66PH
20
26um
ZPS
Figure 1 1.4: Layout of ZPS and simulation results of inductor and
ZPS.
is 26µm and the w idth is 10µm. The simulated inductanc e is 66pH, and the
quality factor is 20. The ZPS is implemented by a serial connection of two
inductors L
Z
and one capacitor C
Z
[163]. An EM simulation shows a zero-
phase-shift at 131.5 GHz with a small inse rtion loss of 0.4dB.
11.3.2 Measurements
The propos ed SSR is fabricated in 65nm CMOS process, and the die micro-
graph is shown in Figure 11.5 (a). The core are a is 0.06 mm
2
, and total area is
600 µm × 500 µm including input and output pads. The receiver is measured
on a probe station with RF signal provided by a microwave signa l generator
through GSG probe. A 12-MHz sinusoid quenching signal is applied by a func-
tion generator with 0.6-V DC level and peak-to-DC voltage swing is swept in a
range of 0 ∼ 300 mV. The receiver operates under 1-V power supply. T he cur-
rent consumption of each LC-tank is 3.8 mA, while the one of L NA is 0.5 mA.
The operating frequency of the SRX is measured at 131.74 GHz, which
is also the self-oscillation frequency, as shown in Figure 11.5 (b). A tuning
range of 1 GHz is observed when sweeping V
T UNE
in a range of 0 ∼ 1 V.
Good input power matching is a lso achieved for NF reduction and sensitivity
improvement. As shown in Figur e 11.6, S
11
is be low -10dB from 122 GHz to
140 GHz. The bandwidth is around 680 MHz. Note that the maximum gain
is 41 dB, which is almost 13 dB higher than c onventional SRX design [90].
In-Phase Detection 257
input
matching
LC-
tank_I
LC-
tank_II
ZPS
300um
200um
(a)
Frequency : 131.74GHz
Power : -23.10 dBm
(b)
Figure 1 1.5: (a) Chip photo o f 131.5 GHz S RX in 65 nm CMOS; (b)
measured self-oscillation frequency of 131 .74 GHz and output power
of −2 3.10 dBm.
Frequency
( GHz)
Gain (dB)
S
11
(dB)
Frequency
( GHz)
130.5 131.0 131.5 132.0 132.5 133.0
0
5
10
15
20
25
30
35
40
45
116 120 124 128 132 136 140 144
-20
-18
-16
-14
-12
-10
-8
-6
3 (dB)
680MHz
Figure 11.6: Measurement results: i) the maximum gain of 41 mB;
and ii ) input S
11
parameter.
In addition, as shown in Figure 11.7, the sensitivity of the rec eiver is
measured as -84 dBm. NEP is defined as the signal power in 1Hz band-
width of unity signal-to-no ise r atio, equivalent to S/
√
B, and measured as
0.615 fW/Hz
0.5
. Finally, NF is measured as 7.26 dB by S/KT B at a room
temperature. As shown in Table 11.1, the measurement re sults of the pro-
posed receiver are compared to recently published mm-wave imag ing receivers
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