26 Design of CMOS Millimeter-Wave and Terahertz Integrated Circuits
Figure 2.8: Equivalent circuit and layout diagrams for o ne unit cell
of differential CRLH T-line-based zero-phase shifter.
tor reduces the loss in return ground and also improves isolation. Parasitic
from transistors and connections form the RH T-line portion (L
s
and C
p
).
Connection lines and M1 shielding are used to adjust L
s
and C
p
values for a
zero-phase-shift at the targeted frequency ω.
Due to the differential des ign, the parallel inductor for the two differential
branches can be merged together with reduced area and improved isolation.
In addition, due to virtual ground on the central tap of the merged inductor,
de-coupling capacitor is removed with further reduced area. As a result, zer o-
phase-shift can be achieved at designed fre quency with compact area. For
example, the differential ZPS unit cell in Figure 2.8 further reduces the size
to only 61µm×81µm while achieving the same ZPS frequency point (60GHz)
as the sing le-ended design.
2.2.1.4 Tunable Negative-Phase CTLH T-Line
Another unique feature of CRLH T-line is the inverse relation between phase-
shift and T-line size in its LH r egion. As (2.7) a nd Figure 2.4 show, the
magnitude of pha se constant in CRLH T-line is inversely dependent on its
LH c omponents (L
C
and C
s
) and frequency. In contrast, the phase change in
RH T-line is linea rly dependent on the LC values and frequency and stays
positive. As such, the same phase shift in the RH T-line at a given frequency
can be realized by CRLH T-line in the negative-phase reg ion in Figure 2.4
with much sma ller LC values and thus T-line size. For example, as shown in
Figure 2.9, a λ/4 T-line can be realized by RH T-line at around 90GHz, but
can be replaced with a CRLH T-line with -90
◦
phase-shift at around 30GHz
CMOS Metamaterial Devices 27
Figure 2.9: Compact si ze for negative-Chase CRLH T-line to achieve
the s ame 90
◦
phase-shift compared to traditional RH T-line.
with similar lumped component values and thus similar size. As a result, the
required λ/4 T-line can be realized at the same frequency by -90
◦
CRLH
T-line biased in the LH region with much more compa ct size.
Though the negative-phase in the LH region shows a higher sensitivity to
frequency and thus smaller bandwidth compa red to ZPS, it does not impact
the frequency tuning range (FTR). In fact, except for compact size, another
bene fit for the negative-phased CRLH T-line is the potential to achieve a wide
FTR for VCO design. The tunability of CRLH T-line is analyzed here with
balanced condition as shown in Figure 2 .4 for simplicity, and similar analysis
and conclusion ca n be extended to more general conditions.
As discussed, T-line is normally used in VCO design to re alize traveling
wave to ge ne rate multi-phase and low-noise clock outputs, by achieving certain
phase-shift requirements (e.g., 360
◦
phase-shift forms a loop). According to
(2.7) in Sectio n 2.2, the total phase shift of one CRLH T-line unit cell (θ)
is contributed from two portions: the left-hand portion, and the right-hand
portion:
θ = β
R
p + β
L
p = ω
p
L
S
C
p
− (ω
p
L
S
C
p
)
−1
(2.12)
where p is the T-line’s physical length. Note that, different from (2 .7), lumped
components here are the normalize d value to consider the phase shift instead
of phase constant.
As shown above, CRLH T-line operating in the nonlinear LH region can
replace the traditional RH T-line to achieve the same phase-shift requirement
with much more compact size. When operating in nonlinear LH region, β
L
p
dominates. The formula can thus be simplified to
θ = β
L
p = −(ω
p
L
p
C
s
)
−1
= constant (2.13)
28 Design of CMOS Millimeter-Wave and Terahertz Integrated Circuits
ω = (−θ
p
L
p
C
s
)
−1
. (2.14)
By taking the product of the LH components (L
p
,C
s
) as P
L
, and the
product of the RH components (L
s
,C
p
) as P
R
, the tunability can then be
analyzed as
∂ω
∂P
L
=
1
2θ
(P
L
)
−
3
2
. (2.15)
The frequency tuning range (FTR) with CRLH T-line operating in non-
linear LH region can then be estimated as
F T R
LH
=
∆ω
ω
≈
1
ω
×
∂ω
∂P
L
× ∆P
L
=
∆P
L
2P
L
. (2.16)
Similarly, the FTR w ith traditional RH T-line can be estimated as
F T R
RH
≈
∆P
R
2P
R
. (2.17)
Based on (2.16) and (2.17), the FTR depends on the tunability of the
lumped component itself(∆P
e
/P
R
and ∆P
L
/P
L
). Conventional RH T-line
is mostly tuned by varactor and capacitor bank, where the tuning range is
limited by the parasitic capacitance from transistors and constraint tuning
ability of varactor and capacitor bank in millimeter-wave region. CRLH T-line,
on the other hand, provides more choices of tunable elements such as inductive-
loaded transformer [74] and avoids the effect of parasitic capacitance. As will
be explained in Chapter 5, a much w ide r tuning range can be achieved.
In summary, by using tunable negative-phase CRLH T-line in nonlinear
NH region to replace traditional RH T-line, the FTR can be largely improved
with more compact size. Note that the high nonlinea r dispersion curve in the
LH region can be also used to generate dua l-band or multi-band operation
[75], which can further extend the tuning range.
2.2.1.5 Active CRLH T-Line
Most of the time, transistors need to be loaded in T-line to achieve desired
functions. For example, in power combiner design for mm-wave PA, transistors
need to be periodically loaded in the combining network where the output
power of each tr ansistor is combined in phase. While in mm-wave RTW-VCO
design, transistors nee d to be distributed in the T-line loop to compensate the
loss and facilitate oscillation. When considering transistors a s a part of CRLH
T-line, an active CRLH T-line or T-line network is obtaine d.
Traditional active CRLH T-line loa ds active devices as neg ative re sistors
to compensate the propagation loss. As shown in Figure 2.10(a), by loading a
tunnel diode, negative resistance is introduce d. Simultaneous negative α and
negative β are demons trated in [76], indicating the loss is compensated with
maintained LH property. The same results can be obtained in a differential
manner by replacing the tunneling diode with a cross-coupled transistor pair,
CMOS Metamaterial Devices 29
(a)
(b)
Figure 2 .10: Traditional active CRLH T-line using tunnel diode or
cross-coupled transistor to compe nsate for the propagation loss, (a)
with tunneling diode, (b) with cross-coupled transistors.
as shown in Figure 2.10(b). The topology is used for CRLH T-line-based
RTW-VCO design in Chapter 5.
However, these active CRLH T- line topologies a re not feasible for PA de-
sign which requires signal amplification with maintained amplitude. Alterna-
tively, transistor output power can be in-phase combined by directly connect-
ing their outputs with zero-phase connections, which can be realized by the
zero-phase CRLH T-line with transistor parasitic absorbed into the T-line
design. Since zero-phase CRLH T-line can realize in-phase power combining
both in parallel and in series, a 2D active CRLH T-line network is introduced
in the following section, where a compact and high output power combining
can be achieved.
2.2.2 Magnetic Plasmon Waveguide
MPW with zero phase propaga tion can be introduced in the coupling net-
work design with 2k/N = 0 to largely improve the output power within a
compact area. It operates based on the inductive coupling between periodic
resonators. The equivalent circuit of an ideal 1D MPW is shown in Figure
2.11(a). The plasmon resonators are coupled by the magnetic flux between
adjacent resonators, which are represented by the LC networks with mutual
inductances (M). Assuming the magnetic coupling only exists between adja-
cent resonators, each unit-cell consists of two magnetic coupled resonators. As
30 Design of CMOS Millimeter-Wave and Terahertz Integrated Circuits
(a)
(b)
Figure 2.11: (a) Equivalent circuit of magnetic plasmon wavegui de
(MPW); (b) dispersion diag ram of MPW.
such, the dispersion relationship can be written as:
ω
2
0
/ω
2
− 1 =
2M
L
cos[(α + jβ)d] (2.18)
where j =
√
−1, ω
0
= 1/
√
LC is the self-resonance frequency of the L C
resonator, d is the dis tance between adjacent unit-cells, α and β are the at-
tenuation coefficient and phase constant, respectively. Figure 2.2.1.5 shows
the dispersion diagram. One can observe that both α and β are zero at the
lower s top bands boundary ω
L
with
ω
L
= ω
0
/
p
1 + 2M/L (2.19)
where the zer o phase propa gation exists. When multiple MPW unit-cells are
serially connected, the in-phase EM-energy can be stored in each unit-ce ll
in zero phase propagation mode. A zero phase propagation mode operation
is important for not only powe r combination but a lso phase noise reductio n.
The noise coupling network becomes reciprocal in the zer o phase propagation
mode, and the total phase noise will be reduced by N times when coupling N
free running oscillators [77].
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