80 Design of CMOS Millimeter-Wave and Terahertz Integrated Circuits
Table 4.6: Performance Summary for Different Loaded Transformer
Topologies Based on Numeric Analysis
Loaded Trans-
former
R-loaded C-loaded L-loaded Proposed
Tuning Range Large Small Large Large
Linearity Low H igh Medium High
Quality Factor
Degradation
High Medium Medium Low
Band Numb er Large Large Small Medium
coupling between different portions on the secondary coil is much weaker. As
Figure 4.10(d) shows, a linear tuning curve is obtained with a large FTR, and
with low degradation on the quality factor in the whole tuning range at 60
GHz by the proposed inductor-loaded transformer.
The performances of different loaded transformers are summariz ed in Table
4.6. The numeric simulations confirm our observations in Section 4.3.1 that
the prop osed new inductor-loaded transformer can realize a wide FTR with
high linearity and low K
V CO
and also can achieve multiple sub-bands with
compact size. Furthermore, low de gradation on LC-tank quality factor and
hence better VCO phase noise performance can also be maintained in the
whole tuning range by the proposed inductor-loaded transformer. As shown
in Figure 4.1 0(e), a 20% FTR with linear tuning curve is achieved with a Q
factor above 10 for all sub-bands.
4.3 Frequency Tuning by CRLH T-Line
As mentioned in Section 4.1, Mobius-ring RTW-VCO is often utilized to gen-
erate multi-phase or quadrature output for many millimeter-wave applica-
tions such as big-data communication and imaging. Conventional RTW-VCO
is mostly tuned by varactor and capac itor bank due to the RH topology
[141, 142, 143]. Due to constrained tuning ability of varactor and capaci-
tor bank in the millimeter -wave region, the achieved FTR in quite limited
[141, 1 42, 143]. CRLH T-line, on the other hand, provides more choices of
tunable elements to achieve a wide FTR in RTW-VCO design, but is not well
explored at the millimeter-wave region [144]. In this s ection, a tunable CRLH
T-line biased in the LH region is studied for RTW-VCO to achieve compact
size and wide FTR. Assisted with the inductive tuning techniques presented
in the above sections, a much wider FTR can be obtained.
4.3.1 CRLH T-Line-Based RTW-VCO
The topology for Mobius-rang RTW-VCO is shown in Figure 4.11. A Mobius-
ring is evenly divided into N stages, with each stage loaded with a cross-
Oscillator 81
Figure 4 .11: CRLH T-line-based Mobius-ring RTW-VCO.
coupled transistor pair. As a wave travels along the Mobius-ring, certain phase
delay must be fulfilled to create a positive feedback for VCO oscillation. At
the same time, cross- coupled transistors should generate enough power to
compensate the loss from the T-line. In summary, the start-up conditio n of
Mobius-ring RTW-VCO is
g
m
>
2exp(αl)
Z
o
; βl =
Mπ
N
(4.10)
where g
m
is the transconductance of the cross-coupled pa ir, z
o
, l, α, β are
T-line characteristic impedance, physica l length, attenuation constant, and
phase constant, respectively. N is the stage number, and M =±1, ±3,... is an
odd integer numb er.
In this sec tion, a negative-phase CRLH T-line is deployed in the Mobius-
ring RTW-VCO for both compact size a nd wide FTR. Assuming a bala nc ed
condition for simplicity, with (4.7) and (4.10), the osc illation frequency for an
N -stage Mobius-ring RTW-VCO by CRLH T-line c an be obtained
ω
CRLH
=
π
2Nl
p
L
s
C
p
× (
v
u
u
t
1 +
4N
2
l
2
π
2
s
L
s
C
p
L
p
C
s
± 1). (4.11)
Here, only the fundamental resonant condition M =±1 is considered for
simplicity of illustration. The plus and minus signs in (4.11) correspond to
CRLH T-line working in the RH region and LH region, respectively.
Furthermore, phase noise is an important specification for VCO design.
Generally, for N -stage RTW-VCO, the phas e variation < Φ
2
(t) > is propor-
tional to 1/N [141, 14 8, 149, 150], which is reduced by 1/N when compared
to single s tage.
In this work, the LH operation is selected for compact size and superior
performance when implemented in multiple stages [144]. However, there is
no study of how to tune the CRLH T-line-based RTW-VCO, which will be
addressed in the ne xt part.
82 Design of CMOS Millimeter-Wave and Terahertz Integrated Circuits
4.3.2 Wide-Band Tuning for CRLH T-Line-Based
RTW-VCO
Note that in (4.11), there are 4 c omponents that may be used for tuning : L
s
,
L
p
, C
s
, C
p
. For easy analysis, we represent the product of the LH components
(L
p
,C
s
,) as P
L
; and represent the product of the RH components (L
s
,C
p
,) as
P
R
. Then, the o scillation frequency in the LH region becomes
ω
CRLH LH
=
π
2Nl
√
P
R
× (
s
1 +
4N
2
l
2
π
2
r
P
R
P
L
− 1). (4.12)
Conventionally, P
R
is used to realize FTR by varacto r as part of C
p
[144].
Unfortunately, with the omitted L
s
component and thus small P
R
value in
[144], the tuning ability by P
R
is very limited, not to mention the already
constrained tuning ability as well as the limited quality factor of varactor at
high frequency. In fact, for a small P
R
/ P
L
value, appr oaches the operation
frequency of a pure LH T-line- based RTW-VCO
ω
CRLH LH
|
P
R
P
L
→ 0 = ω
LH
=
Nl
π
√
P
L
(4.13)
which is independent of P
R
with poor tuning ability. Furthermore, a large
portion o f C
p
is contributed by transistor par asitic with a fixed value, which
severely limits tuning range of the whole C
p
value, not to mention the already
constrained tuning ability as well as the limited quality factor of varacto r in
the high-frequenc y region.
Intuitively, a wider FTR should be obtained by tuning P
L
since the LH-
components domina te in the LH region. Since
δω
CRLH
δP
L
stays positive for all
P
L
values, the FTR can be calculated:
∆ω
CRLH
LH
=
π
2Nl
√
P
R
× (
s
1 +
4N
2
l
2
π
2
r
P
R
P
L min
−
s
1 +
4N
2
l
2
π
2
r
P
R
P
L max
)
(4.14)
The extreme condition forms for a pure LH T-line with
F T R
LH
=
1
√
P
L min
−
1
√
P
L max
1
√
P
L min
+
1
√
P
L max
× 2 ≈
α
P
L
2
(4.15)
where α
P
L
=
∆P
L
P
L
measures the tuna bility of components in P
L
. As (4.15)
shows, F T R
LH
is directly proportional to α
P
L
.
However, since the loss in C
s
adds directly into the signal path, it is not
feasible to tune C
s
. On the other hand, one can realize a wide FTR by tuning
L
p
with a loaded transformer structure presented in the above s ections. More
sp ecifically, the inductive-lo aded transfo rmer can achieve a large α
P
L
, which
is adopted in this work.
Oscillator 83
Figure 4 .12: Layout implementation for in ductor-loaded transformer
where tuned inductance is determined by s tates of two switches.
The mechanism for the inductive-loaded transformer has been explained in
Section 4.2.2. As (4.3) indicates, a large α
P
L
can be easily obtained by imple-
menting a large c oupling factor k for the transformer. Furthermor e, multiple
inductors can be switched on and off to further increase α
P
L
with a wide FTR
achieved by creating multiple sub-bands.
The designed switched coupled- inductor for inductive tuning is shown in
Figure 4.12. Inductors are realized by the top Cu layer to guarantee a high
quality factor. Two tra nsformers loaded with two switches are used to realize 4
sub-bands. As summarized in the tables shown in Figure 4.12, the resulted L
eq
can be varied over a large range from 47 pH to 91 pH. As such, wide FTR can
be rea lized with 4 sub- bands: (75.67–8 3.11 GHz), (79.65–87.78 GHz), (86.18–
94GHz) and (93.89–102.01 GHz). To realize a continuous tuning, fine-tuning
by var actor is used in each sub-band. To increase the tuning ability of varactor
as (4.13) indica tes to fully cover each sub-band, a rela tively large L
s
value is
adopted in this design.
The resulting tuning mechanism for the proposed CRLH T-line-based
RTW-VCO can be explained in Figure 4.13. Inductive-loaded transformer
creates multiple sub-bands by shifting the dispersion curve to different reso-
nant frequency points. Each sub-band is then covered with fine-tuning by a
varactor.
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