Oscillator 77
Table 4.4: EM Extracted Parameters at 60 GHn for the Proposed
Loaded-Transformer Implementation
L
1
(pH) L
2
(pH) M
12
(pH) k
154.2 175.5 77.3 0.470
to the sizing and biasing of cross-coupled tr ansistors, a few design iterations
are required to meet the targ eted performance for all specifications.
4.2.2.5 Load ed-Transformer Simulation Results
4.2.2.6 Model Validation
The proposed model in Section 4.3.2 is used to analyze one asymmetrical
implementation for the proposed loaded transformer, whose topology will be
shown in Figure 4.14 in Sectio n 4.4.2. Tr ansformer parameters are extracted
from EM simulation, as summarized it Table 4.4. C
t
from Figure 4.1 is ad-
justed to be 92fF. C alculated VCO oscillation frequency and noise density
contributed by switches are plotted in Figure 4.9 both of which can roughly
fit the simulation results from Cadence . This validates the proposed model.
Note a larger deviation occurs at lower frequency bands, which is due to ne-
glect of flicker noise in the switch mo de l, as will be addressed in Section 4.4.1.2
and 4.4.2.2.
(a) (b)
Figure 4.9: Model validation: (a) o scillation frequency, (b) output
noise density contributed by switches.
78 Design of CMOS Millimeter-Wave and Terahertz Integrated Circuits
4.2.2.7 Comparison between Loaded Transformer Topologies
The four topologies in Figur es 4.2 and 4.5 are simulated numerically in MAT-
LAB for performance comparison. To achieve a fair comparison, while both
resistor and capacitor-loaded transformers are simulated by the equivalent
circuit shown in Figur e 4.1, the inductor-loaded transformers are simulated
based on more comprehensive models shown in Figures 4.3 and Figure 4.6 to
consider parasitic effects on the secondary coil. Parameters derived in Section
4.2.2.3 are used to assist numeric analysis for the proposed inductor-loaded
transformer topology. The same parameters are utilized to simulate resistor-
loaded transformer (Table 4.5), with its resistance linearly varies between the
on and off resistances (R
on
and R
off
) of the 50µm switch in Table 4.1. The
linear change can be achieved by splitting the switch into a parallel a rray
of smaller switches [131]. Similarly, for the ca pacitor-loaded transformer, a
switched capacitor bank can be used to obtain linear and large tuning range
than single varactor. The penalty is the parasitic from the switches in the
capacitor bank, which is also the major limitation for its tuning range. With
the extracted switch parameters in Table 4.1, the effective capacitance ratio
when the switch is on and off for each bank (p
datio
=C
off
/C
on
) is analyzed.
A va lue of 3.206 is obtained for C
ratio
and is used for this analysis.
All loaded transformers are desig ne d to provide the same oscillation fre-
quency in 60-GHz band. The adjusted parameters are summarized in Table
4.5, and the simulated tuning range and quality factor are shown in Figure
4.10. To have a direct view of the extra loss c oupled from the tuning elements
into the LC-tank, a simila r definition of quality factor as (4.6) is used. With
this definition, the quality factor represents how much degradation on the
whole LC-tank quality factor (o r phase noise performance) will be caused by
the tuning elements loaded on the transformer.
Firstly, as Figure 4.10(a) shows, the resister-loaded transformer has a
highly nonlinear tuning-curve with respect to tuning resistanc e. Most of the
frequency tuning is realized in a narrow region of the tuning resistance, whe re
the lowest qua lity factor is also located. Next, the capacitor-loaded trans-
Table 4 .5: Parameters for Different Loaded Transformers Biased for
60-GHz Band Oscillation
Loaded
Trans-
former
R-loaded C-loaded L-loaded Proposed
L
prim
(pH) 80 60 80 80
L
sec
(pH) 80 60 N.A. 80
Coupling
factor
k= 0.5 k= 0.5 k
12
=k
13
=0.5
k
23
=0.4
k= 0.5
L
ratio
N.A. N.A. 0.3 0→ 1
C
ratio
N.A. 3.206 N.A. N.A.
Oscillator 79
(a) (b)
(c) (d)
Figure 4.10: Numeric simulation for tuni ng range and quality factor of
different loaded transformers: (a) R-loaned transformer, (b) C-loaded
transformer, (c) traditional L-loaded transformer, (d) proposed new
loaded transformer.
former, a s Figure 4.10(b) shows, has a very linear tuning-curve. Besides its
quality factor degradation in the lower frequency region, its major limitation
is the narrow tuning range which comes from the limited tuning ability of
varactor or capacitor bank. Lastly, for the traditional inductor-loaded trans-
former shown in Figure 4.10(c), there are only 4 sub-bands within the tuning
range. Besides its limitation on the number o f sub-bands that can be achieved,
the inductor-loaded transformer also differs fr om high degradation on quality
factor in the middle region (mode 3) of its tuning range. Different from the
resistor-loaded transformer, this degradatio n comes from magnetic coupling
from L
3
to L
2
when L
2
is switched on and L
3
is off. Rec all that multiple trans-
formers needed by the traditional inductor-loaded transformer would cause
large area overhead as well.
In contrast, the proposed inductor-loaded transformer does not have this
degradation. Due to the single-loop topology adopted for the transformer, the
..................Content has been hidden....................
You can't read the all page of ebook, please click here login for view all page.