Hindawi Publishing Corporation
EURASIP Journal on Wireless Communications and Networking
Volume 2006, Article ID 93712, Pages 1–12
DOI 10.1155/WCN/2006/93712
Modeling and Characterization of VCOs with
MOS Varactors for RF Transceivers
Pedram Sameni,1 Chris Siu,2 Shahriar Mirabbasi,1 Hormoz Djahanshahi,3 Marwa Hamour,1
Krzysztof Iniewski,2 and Jatinder Chana3
1 Department
of Electrical and Computer Engineering, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z4
of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 2V4
3 PMC-Sierra, Burnaby, British Columbia, Canada V5A 4X1
2 Department
Received 1 September 2005; Revised 8 March 2006; Accepted 17 May 2006
As more broadband wireless standards are introduced and ratified, the complexity of wireless communication systems increases,
which necessitates extra care and vigilance in their design. In this paper, various aspects of popular voltage-controlled oscillators
(VCOs) as key components in RF transceivers are discussed. The importance of phase noise of these key blocks in the overall
performance of RF transceivers is highlighted. Varactors are identified as an important component of LC-based oscillators. A new
model for accumulation-mode MOS varactors is introduced. The model is experimentally verified through measurements on LCbased VCOs designed in a standard 0.13 µm CMOS process.
Copyright © 2006 Pedram Sameni et al. This is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly
cited.
1.
INTRODUCTION
In the recent years, the demand for wireless communications has increased considerably. Wireless communication
systems encompass a wide variety of standards. Such systems
include cellular phones (e.g., GSM, CDMA), wireless local
area networks (WLANs), wireless personal area networks
(WPANs), wireless metropolitan area networks (WMANs),
and so forth. The adoption of any of these technologies depends on many variables such as cost and market demand.
Over time, the implementation cost of the technologies goes
down, which further accelerates their adoption. The hightech market research firm, In-Stat, forecasts that the worldwide wireless market will grow to more than 2.3 billion subscribers by 2009.
Typical RF transceivers have a built-in frequency synthesizer, namely local oscillator (LO), to generate a signal
with the desired frequency used for up and down conversions. Wireless standards strictly specify the minimum level
of the received signal, the maximum level of unwanted signal, the channel bandwidth, and the spacing between two adjacent channels. Using these specifications and targeting the
required signal-to-noise ratio (SNR) after downconversion,
the maximum amount of acceptable phase noise on the LO
can be calculated. This procedure is conceptually depicted in
Figure 1 for the GSM-1800 standard. Using the information
provided in the figure and knowing the desired SNR (e.g.,
9 dB after downconversion), the maximum acceptable phase
noise at 600 kHz offset from the carrier (which is at the center of the adjacent channel) is calculated to be 121 dBc/Hz
[1].
Figure 2 illustrates the problems that may arise if the
LO spectrum extends to the adjacent channel with relatively
high-power spectral density: after downconversion, there
will be an overlap between the spectra of the desired signal
and the unwanted adjacent channel. Unless a special technique is used, the recovery of the data becomes almost impossible.
LOs are usually in the form of voltage-controlled oscillators (VCOs) and are placed inside a feedback loop as part
of a phase-locked loop (PLL) system. As a result, they constantly align their zero-crossings with the reference clock.
The amount of generated phase noise, within the bandwidth
of the PLL, can be reduced by the loop characteristics. Table 1
compares the maximum allowable phase noise of some of the
wireless standards at their nominal frequencies.
Figure 3 shows the block diagram of a PLL-based frequency synthesizer typically used in integrated wireless
transceivers. This synthesizer comprises of phase (and usually frequency) detector (PD or PFD), charge pump, lowpass
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EURASIP Journal on Wireless Communications and Networking
Unwanted signal of the
adjacent channel with
maximum of 43 dBm
Desired channel with
minimum allowable GSM
signal of 102 dBm
Unwanted signal of
the adjacent channel
White noise floor
1.8 GHz
200 KHz
600 KHz
200 KHz
200 KHz
Figure 1: GSM channel around 1.8 GHz.
Unwanted signal in
the adjacent channel
Desired signal
fRF
Local oscillator (LO)
fLO
Desired signal overlaps
with interference after
downconversion
fRF
LO
Figure 2: Channel interference in the case of larger-than-expected phase noise.
filter, voltage-controlled oscillator (VCO), reference, and
feedback divider blocks (/M and /N). The output frequency
of the block is N/M times the reference frequency. Therefore,
by adjusting the N/M ratio, different multiples (integer or
fractions) of the reference frequency can be generated.
The phase transfer function from the reference to the
output of this system exhibits a lowpass characteristic. As
a result, high-frequency phase noise1 of the reference clock
is attenuated by the loop, while its low-frequency (close-in)
noise passes through the system to the output. On the other
hand, phase jitter of the VCO will see a high-pass function
to the output, which means that low-frequency jitter of the
VCO is suppressed within the bandwidth of the phase-locked
system.
The total output phase noise is a function of the phase
noise of each of the PLL blocks, the input phase noise generated by the reference clock, and noise shaping characteristics
of the loop. While there are different techniques for optimizing the performance of the synthesizers to reduce the total
phase noise, VCO plays a key role in total phase noise of the
system. This is because high-frequency perturbation on the
VCO control line tends to appear at the output in the form of
phase variations. In addition, any high-frequency (a.k.a. outof-band) phase noise generated by the VCO due to supply,
substrate, or device noise cannot be suppressed by the loop
and directly travels to the output. In this paper, our main focus will be on VCO as a key block of RF transceivers.
1
The time-domain counterpart of phase noise is jitter, which is a more
common term in wireline applications.
Frequency synthesizer circuits have been predominantly
implemented in technologies such as III-V, silicon bipolar, or
SiGe BiCMOS due to their high-speed and low-noise characteristics. However, circuits implemented in these technologies are still expensive, and are not very area efficient. Moreover, they are not suitable for system-on-chip integration.
Recent advances in CMOS technologies have made CMOS an
attractive alternative for implementing high-speed systems,
including their oscillators. Advantages of CMOS implementation include lower cost, higher manufacturing yield, lower
power, and higher levels of integration, with the possibility
of integrating analog and digital circuits on the same chip.
Therefore, there is a growing trend in industry to extend the
use of CMOS circuits to high-speed integrated digital and
mixed-signal systems, system-on-a-chip (SoC), and systemin-a-package (SiP) designs. However, designing high-speed
mixed-signal circuits (e.g., multi-gigahertz systems) in advanced CMOS technologies is very challenging. Issues such
as speed, substrate noise coupling, reduced voltage headroom, and increased leakage current pose many difficulties
in the design of high-speed CMOS circuits.
In the following sections, first, various aspects of some
of the well-known VCO architectures, including their phase
noise performance, are compared. LC VCO is identified as
having the best performance in terms of phase noise. In
Section 3, the building components of various LC VCOs are
investigated and their effects on overall phase noise are studied. To facilitate this investigation, three forms of LC VCOs
are used that are implemented in a standard 0.13 µm CMOS
process. In addition, some varactor test structures are used
to characterize the tuning curve of the LC VCOs and their
Pedram Sameni et al.
3
Table 1: Comparison between phase noises of different wireless standards.
Wireless standard
GSM
WLAN
WPAN
850
900
1800
1900
Frequency
850 MHz
900 MHz
1800 MHz
1900 MHz
802.11a
5 GHz
802.11b
2.4 GHz
802.11g
2.4 GHz
ZigBee (802.15.4)
900 MHz
2.4 GHz
95 dBc/Hz at 5 MHz
Bluetooth (802.15.1)
2.4 GHz
94 dBc/Hz at 100 KHz [2]
Crystal osc. Ref.
M
Phase noise
121 dBc/Hz at 600 KHz
121 dBc/Hz at 600 KHz
121 dBc/Hz at 600 KHz [1]
121 dBc/Hz at 600 KHz
Many WLAN transceivers specify “integral”
noise in degrees rms over a frequency range,
for example, integral of phase noise from 10 K
to 10 M < 1.2Æ rms for the whole TX path, or
0.8Æ rms for the synthesizer. This may also be
translated to an average phase noise spec,
like P.N. < 90 dBc/Hz at < 100 KHz
(in-band, or close-in)
Phase/
freq.
detector
Charge
pump
N
Lowpass
filter
VCO
Output
Figure 3: A block diagram of a frequency synthesizer.
relationship with the C-V curve of varactors. A new practical
model for accumulation-mode MOS varactors is then introduced. Experimental results follow in Section 4 and concluding remarks in Section 5.
2.
Vin
+
+
H(s)
Vout
+
COMPARISON OF POPULAR VCO ARCHITECTURES
VCOs are one of the main building blocks of RF transceivers.
They are utilized inside PLL-based circuits (e.g., frequency
synthesizers as part of LO) to generate a clean and low-jitter
clock signal for the operation of other blocks of the frequency
synthesizer or transceiver. Typical oscillator circuits require
some form of positive feedback around a gain stage in order to sustain their oscillation. This concept is illustrated in
Figure 4. The closed-loop system (oscillator) has to fulfill the
following two Barkhausen conditions at all times for continuous oscillation:
H( jω) 1,
∠H( jω) = 360Æ .
(1)
Three common categories of oscillator circuits are relaxation (Figure 5), ring (Figure 6), and LC-based (Figure 7) os-
Figure 4: A gain stage with a positive feedback loop.
cillators. In a relaxation oscillator (a.k.a., multivibrator), the
oscillation relies on nonlinear switching that charges and discharges a capacitor with a time constant. The oscillation frequency is tuned by varying this time constant (e.g., through
a current source). Relaxation oscillators are usually limited
to moderate frequencies. Ring oscillators (Figure 6) are normally designed by cascading an odd number of inverters in a
loop. Alternatively, an even number of differential delay cells
can be used with an explicit polarity inversion in the feedback
connection. A variable delay element (e.g., variable resistor
or current source) is used for tuning. The frequency range
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EURASIP Journal on Wireless Communications and Networking
VDD
VDD
Vbias
R1
R2
M1
M0
VDD
M2
L1
L2
C
C1
Vcontrol
M1
M2
C2
L
Itune
C1
M1
Vcontrol
C2
M2
M3
Figure 5: Relaxation oscillator.
Vbias
Inverters with
controllable
delay
M4
M0
(a) Simple LC VCO
(b) LC VCO with a
PMOS current source
VDD
M1
M2
Figure 6: Ring oscillator.
L
C1
can also be adjusted by digitally adding or removing inverters
from the chain (coarse tuning). On the downside, the ring
and relaxation oscillators suffer from a poor frequency stability, which manifests itself as higher phase noise.
LC-based oscillators are usually made with a differential pair amplifier, using LC tank as the load. By connecting the outputs to the inputs, the amplifier starts to amplify the noise at its inputs around the resonance frequency
of the tank, provided that its open loop gain is greater than
one (first of the two Barkhausen conditions). Noise at other
frequencies gets filtered out by the LC tank. This filtering
characteristic of LC-based oscillators has made them the best
in terms of phase-noise performance. Furthermore, compared to the other two oscillator architectures, LC oscillators
typically operate more reliably at higher frequencies, provided an LC tank of moderate- to high-quality factor. However, they suffer from their inherently narrower tuning range.
Moreover, the integration of LC-based oscillators is more
costly due to the large space allocated to on-chip inductors.
It should be noted that, as technology advances, achieving
higher frequencies becomes more feasible, which in turn requires smaller (less spacious) inductors. Table 2 summarizes
the advantages and disadvantages of the three oscillator architectures [3].
3.
LC-BASED VCOs
Figure 7 illustrates three forms of typical LC VCO implementations in CMOS. Figure 7(a) represents the simplest implementation, with an nMOS current source and an nMOS dif-
Vcontrol
M3
Vbias
C2
M4
M0
(c) LC VCO with an
nMOS current source
Figure 7: Different versions of LC-based oscillator.
ferential pair as the gain stage (also referred to as “negative
resistance”), which cancels out the loss of the tank. A pair
of varactors has been used for frequency tuning. The use
of differential signaling is another advantage compared to
single-ended VCOs (e.g., ring oscillator in Figure 6). It results
in higher oscillation swing in a constantly shrinking supply
voltage environment, and less susceptibility to environmental noise due to rejection of the common-mode component
of the noise.
Figures 7(b) and 7(c) represent two other popular implementations of LC VCOs, which result in lower overall
phase noise compared to simple LC VCO in Figure 7(a). They
have two differential pairs that generate negative transconductance to cancel the tank loss. According to [4], if the
Pedram Sameni et al.
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Table 2: Comparison of existing popular oscillator architectures [3].
LC oscillator
Speed
Phase noise
Integration
Tunability
Stability
Ring oscillator
Technology dependent (0.01–10 s of GHz)
Good
Poor (inductor and varactor)
Narrow/slow
Good
oscillation waveform is symmetrical (i.e., equal rise and fall
times), the DC component of the phase noise gets eliminated, which is the component that also carries flicker (1/ f )
noise. As a result, the two architectures shown in Figures 7(b)
and 7(c) potentially have lower phase noise compared to the
architecture in Figure 7(a), which has asymmetrical rise and
fall times. The use of nMOS or pMOS current sources creates a level of shielding between substrate (ground) or power
supply (VDD), respectively, which subsequently lowers the
phase noise due to substrate or supply noise. In technologies where larger supply voltages are available, using voltage
regulators is recommended for the VCO to further reduce
the oscillator phase noise resulting from substrate and supply noise.
Other than noise components contributed by the oscillator’s active elements (as well as supply and substrate),
there are other sources of noise resulting from the losses in
nonideal passive elements (inductors and varactors), which
further degrade the overall phase noise performance of the
LC oscillator. To reduce the noise floor due to the lossy inductors, inductors with higher quality factors (Q) need to
be used, since they result in lower resistive loss and subsequently lower thermal noise and lower power dissipation.
To some extent, however, this is limited by the technology,
as the thickness of the metal layers and substrate losses are
technology dependent, leaving the designer with fewer degrees of design freedom (e.g., increasing the width of inductor wires to lower the loss would degrade the self-resonance
frequency). Various solutions are limited by other criteria,
such as silicon-area usage. Although design of high-Q onchip inductors is a topic of active research, our focus in the
following sections remains on varactors as the tuning element of LC VCOs. The design, characterization, and modeling of the varactors significantly affect the overall performance of the LC VCO.
3.1. Varactors
Varactors are a principal component of LC VCOs used for
frequency fine tuning. Digitally controlled switched varactors or switched capacitors could also be used for coarse tuning in some designs. Traditionally, reversed-biased pn junction diodes acted as the varactor for LC VCOs (this is still true
in the case of bipolar VCOs). However, MOS-based varactors
are gaining popularity over the reverse-biased diodes due to
wider tuning range and higher Q factor, both of which improve with every new process generation. Higher doping levels in silicon, which in turn result in lower resistive losses
Multivibrator
Poor
Excellent
Wide/fast
Poor (needs acquisition aid with a PLL)
A
B
Figure 8: An nMOS transistor configured as a varactor.
and lower phase noise, have driven this improvement. It has
become more evident in recent designs in advanced CMOS
technologies (e.g., 0.18 µm, 0.13 µm, 90 nm) as implementation of monolithic high-speed VCOs becomes feasible.
An nMOS varactor can have the same structure as an
nMOS transistor, with gate as the first terminal and drain,
source, and bulk connected together to form the second terminal (Figure 8). MOS varactors operate in four main regions, based on the biasing point (voltage across the varactor terminals): accumulation, depletion, weak inversion,
and strong inversion. Accumulation and strong inversion
are two regions where most varactors are designed to operate in. Furthermore, a study on accumulation-mode and
inversion-mode varactors reveals that LC oscillators based
on accumulation-mode varactors demonstrate lower power
consumption and lower phase noise at large offset frequencies from the carrier, compared to those based on strong inversion varactors [5].
In most applications, designers would like to ensure that
the capacitance of the varactor is a monotonic function of the
biasing voltage. For instance, in an LC VCO, it would be desirable, as mentioned earlier, to have the varactor operating
predominantly in accumulation mode. However, using a regular nMOS, as in Figure 8, does not warrant this, as the operation region is voltage dependant. It is also worth noting that
the C-V curve of a regular nMOS is frequency dependant.
Figure 9 illustrates the cross-section of a varactor structure.
It may seem similar to an nMOS transistor, however, the n+
regions have been buried in n-well, instead of p-well. This
configuration guarantees that the device does not enter the
inversion-mode at all; hence the name accumulation-mode
MOS (AMOS) varactor.
The C-V characteristics of an MOS varactor can be predicted using 2D/3D numerical simulators. Unfortunately,
these simulation tasks require precise knowledge of the underlying doping profiles, which usually are not readily available. An alternative is to perform capacitance measurements.
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EURASIP Journal on Wireless Communications and Networking
7
Gate (G)
Bulk (B)
p+
n+
n-well
6.8
n+
p-substrate
Figure 9: Cross-section of an accumulation-mode MOS (AMOS)
varactor.
Oscillation frequency (GHz)
Sub
6.6
6.4
6.2
6
5.8
5.6
5.4
5.2
5
However, measuring subpico Farad capacitances is difficult
and requires a fairly expensive S-parameter RF measurement
setup. It is, therefore, very useful to predict the tuning characteristics of LC oscillators using standard foundry-supplied
models for MOSFETs.
Recently, a lot of effort has been expended on modeling
the C-V characteristics of MOS varactors, partly due to the
increasing popularity of CMOS LC VCOs in which such varactors are used. One type of model is based on physically
meaningful parameters [6] that describe the characteristics
of the device with different equations for different regions
of operation. Another model based on the physical parameters of the device is reported in [7]. However, simulating
and using these types of models are not simple in SPICE
or similar simulators, as they require defining mathematical
functions inside the tool. Other models have been developed
based on subcircuits utilizing BSIM SPICE models [8]. These
models are suitable for simulator implementation within the
circuit-design environment and could be easily adopted for
future technologies. In the following sections, we introduce a
SPICE-like model that takes advantage of already developed
foundry models of transistors to create a practical model for
accumulation-mode varactors. First we take a closer look at
the tuning characteristics of LC VCOs, which further emphasizes the need for a good varactor model.
3.2. VCO design and tuning characteristics
For the following analysis, we used a standard LC VCO circuit with current source isolating the core of the oscillator
from the ground, as shown in Figure 7(b). The structure is
designed for 5–6 GHz operation. Inductance L is 1.5 nH, and
the total equivalent capacitance is in the range of 0.35 pF to
0.65 pF. It may seem that the modeling of the tuning characteristics is a straightforward task, as the oscillation frequency
is given by the following well-known formula:
fosc =
1
,
2π L C(V )
(2)
where L is the inductance and C(V ) is the equivalent capacitance for a given biasing point. However, a simple
test indicates that the modeling process is more involved
than it might initially appear. From the measured tuning
0
0.2
0.4
0.6
0.8
1
1.2
Control voltage (V)
Simulation
Measurement
Figure 10: Measured versus modeled VCO tuning characteristics
(extracted piecewise linear model).
characteristics (the experimental devices are described later
in the paper) the equivalent capacitance can be extracted using (2):
C(V ) =
1
4π 2 f
osc
2
L
(3)
.
Having determined C(V ) values (3), an extracted piecewise
linear model of the voltage-dependent capacitance is reconstructed and fed back to SPICE for simulation. The results of
this comparison, shown in Figure 10, indicate discrepancies
up to 7%.
These discrepancies can be attributed to the effective varactor capacitance. The varactor capacitance gets modulated
in time depending on the signal swing of the oscillator output, which in turn changes the effective capacitance of the
tank [9–11]. We have used a method similar to that reported
in [9] to calculate the effective capacitance. In our calculations, we neglect the current components at harmonics of
fosc as they play only a small role in determining the frequency of oscillation. Equation (4) is the revised version of
(2), used to obtain the VCO’s tuning characteristic:
fosc =
1
2π L Cav (V ) + Cpar (V )
.
(4)
In this equation, Cpar is the equivalent parasitic capacitance
associated with input of the next buffer, interconnects, and
device capacitances of M1–M4, the latter being somewhat
voltage dependent. Cav is the average capacitance of C1 and
C2 in series (Figure 7(b)), calculated according to the method
described in [9]. The average capacitance is the ratio of the
rms value of the varactor’s current, i(t), to the rms value of
dV/dt, where V (t) is the voltage across the varactor.
As shown in Figure 11, if the voltage swing is small (compared to nonlinearities of the C-V characteristics), then the
Pedram Sameni et al.
7
0.9
short structure, (b) the open structure, and (c) the device
under test (DUT), that is, varactor array.
Figure 13 shows the micrograph of some of the test structures on the die. These test structures from left to right are:
short, open (including dummy varactors), and the varactor
array (DUT).
0.8
Vpeak = 400 mV
0.6
Vpeak = 1.2 V
C1
av
(pF)
0.7
3.3.1. De-embedding technique
0.5
0.4
Vpeak = 800 mV
0.3
0.2
1.5
1
0.5
0
0.5
1
1.5
VBG (V)
Figure 11: C-V characteristics for three different values of the oscillator voltage swing (V peak).
equivalent large-signal C-V characteristic closely resembles
its small-signal counterpart. Here, C1 av refers to average capacitance of C1 calculated for different output swings. However, for large values of the voltage swing the equivalent
characteristics get smoothed or averaged over larger voltage
range. As a result, the tuning characteristic becomes dependent on the voltage swing, which in turn is affected by the
magnetic and resistive losses in the tank.
Calculation of the equivalent large-signal C-V characteristics depends on the shape of the oscillator’s output (rectangular, sinusoidal, etc.). However, at high frequencies the
current waveform can be approximated by a sinusoid due to
the finite switching time and limited gain [12]. Equation (5)
shows the relationship between the swing and tank losses in
this LC VCO:
VTank Itail Rloss ,
(5)
where Rloss is the equivalent parallel resistance of the tank and
Itail is the drain current of the current source transistor (M0
in Figure 7(b)). The effective C-V characteristics (Figure 11)
and their associated VCO tuning curves are obtained using
(4) and (5) and the method proposed in [9].
3.3. Characterization
Several accumulation-mode varactor test structures are
placed on a test chip. Other than varactors, a short structure
and an open structure are also placed on the chip to facilitate
the de-embedding procedure. For this experiment, two different varactors are characterized. Both varactors are made
up of multiples of a unit varactor cell: one has 100 multiples (m100 array) and the other has 60 multiples (m60 array). The unit varactor cell has a width of 7.9 µm and a gate
length of 0.13 µm. To reduce the effect of distributed gate resistance, contacts are used on both sides of the polysilicon
gates. Figure 12 illustrates the three test structures: (a) the
Agilent 8510C vector network analyzer (VNA) is used for
two-port RF characterization. S-parameters of the varactors,
open, and short structures are measured from 100 MHz up
to 6 GHz. The varactor voltage is varied from 1.5 V to 1.5 V,
with 100 mV resolution.
Different de-embedding techniques are currently used.
In [13], a three-step de-embedding technique is used that
employs two short structures, an open structure and a thrustructure instead of only short and open structures. A number of de-embedding techniques have been discussed in
[14]. We used two-step open/short de-embedding (OSD).
Figure 14 shows the equivalent circuit representation of the
parasitic series impedance and shunt admittance of interconnects and contact pads, respectively. Z1 and Z2 are the interconnection series impedances from pads to the varactor. Y1
and Y2 are the equivalent shunt admittances between the signal and ground (pad capacitance, substrate capacitance, and
resistance). We used signal-ground (SG or GS) probes. However, GSG probes are preferred, as they result in balanced
electrical characteristics.
Figure 15 illustrates a different lumped model for OSD,
as presented in [14]. Here Z1¼ and Z2¼ are the impedances between the probe tips and the pads on the CMOS chip as the
probe calibration is performed on an impedance-standardsubstrate (ISS). The ISS uses gold metallization instead of
typical aluminum traces, and has a lower resistance.
Both approaches to de-embedding shown in Figures 14
and 15 were carefully considered. However, we concluded
that in our setup, interconnection impedances are dominant.
Based on the parasitic lumped model of Figure 14, Y1 and Y2
are extracted from the following equations:
Y1 = Y11,open ,
Y2 = Y22,open .
(6)
Z1 and Z2 can then be calculated using the following equations:
1
,
Z1 =
Y11,short Y1
(7)
1
Z2 =
.
Y22,short Y2
Yii,open and Yii,short (i = 1, 2) are the input or output admittances of the open and short structures, respectively.
3.3.2. Parameter extraction procedure
Figure 16 shows the circuit model of the accumulation-mode
varactor [6]. In this figure, CS represents the main variable
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EURASIP Journal on Wireless Communications and Networking
Signal
Signal
Signal
Signal
Signal
Signal
DUT
Ground
Ground
Ground
Ground
(a)
Ground
Ground
(c)
(b)
Figure 12: Top-view of the test structures: (a) short, (b) open, and (c) DUT (varactor array).
Rs is equal to real part of Za (i.e., Re(Za )), and Cs is calculated
from
CS =
ω 2 Lg
1
,
ω Im Za
(10)
where Lg is also calculated at higher frequencies (e.g., 6 GHz)
using
Figure 13: Micrograph of the test structures in 0.13 µm CMOS,
from left to right: short, open, and the varactor array (DUT).
capacitance associated with the series capacitance of the gate
oxide and the depletion region under the gate. C f models the
fringing capacitance related to the sidewalls of the gate. Lg is
the inductance of the poly gate. Rs is the poly gate and channel resistance (the latter is voltage dependent), and Rnwell is
the resistance of the n-well. Cdep is the depletion capacitance
associated with the reversed biased p-sub/n-well diode. Rsub
and Csub are the substrate parasitics. Rsd is the resistance of
the n+ regions (bulk electrode).
In order to verify the model shown in Figure 16, we need
to characterize the de-embedded on-chip varactors (m60
and m100 arrays). Figure 17 shows the simplified form of
Figure 16. In this figure, we have neglected Rsd (Zc ), as the
impedance of the highly doped n+ regions is very small (less
than 1 Ω in these test structures).
Using the simplified circuit shown in Figure 17, we extract Za and Zb from the following two equations:
Za =
1
= Z11
Y11
Z12 ,
(8)
Zb = Z12 = Z21 = Z22 ,
where Z11 , Z12 , Z21 , and Z22 are the equivalent Z-parameters
of the two-port varactor (Figure 17) and Y11 is the input admittance (gate-side) of the equivalent Y-parameters.
Za can be written as (neglecting C f ):
Za = RS +
1
+ jωLg .
jωCS
(9)
Using (9) and employing numerical methods, we extracted
the elements of Za for both varactors (m60 and m100 arrays).
Lg =
1 + ωCS-Low Im Za
,
ω2 CS-Low
(11)
CS-Low is the capacitance at lower frequencies (e.g.,
100 MHz), where ω2 Lg is insignificant and can be removed
from (10).
The quality factor (Q) of the varactor, which is the ratio
of the stored energy to the dissipated energy (resistive loss)
in the varactor, can also be approximated by
Im Za
.
Q=
Re Za
(12)
The substrate effect (Zb ) is calculated using similar methods
described for Za .
3.4.
Varactor modeling
As indicated earlier, modeling of tuning characteristics using (2) is fairly complicated. Not only do the varactor C-V
characteristics have to be measured, but also the losses of the
tank have to be determined to properly find the oscillation
swing and hence the effective tank capacitance. An alternative
approach would be to use the equivalent circuit representation of the varactor created from foundry-supplied transistor
models and SPICE simulation to predict the tuning range.
If a varactor is operating in the strong inversion mode, an
nMOS transistor with tied source and drain can be used as a
primitive model, since the varactor structure is the same as
that of an MOS transistor. However, varactors that are working in the accumulation mode are usually laid out as shown
in Figure 9. This structure inhibits the formation of the inversion layer. Wider tuning range and lower parasitic resistance are other advantages of this implementation [5]. On
the other hand, the use of a plain transistor for modeling this
varactor is not viable because the device does not resemble a
transistor.
Pedram Sameni et al.
9
Z1
Z2
S2
pad
S1
pad
DUT
(varactor)
Y1
Y2
Ground
pad
Ground
pad
Figure 14: Equivalent lumped model of the varactor (DUT) with associated parasitics (open/short de-embedding).
Z1¼
Z2¼
DUT
(varactor)
S1
S2
Y1¼
Y2¼
Ground
Ground
Figure 15: Alternative lumped model for open/short de-embedding (OSD).
Za
Za
Cf
Gate
Bulk
Zc
Gate
Lg
Rs
Rsd
Cs
Bulk
Zb
Rnwell
Cdep
Sub
Csub
Rsub
Zb
Figure 16: Equivalent lumped model of the integrated varactor.
Figure 16 illustrates the model of this varactor constructed with passive circuit elements, and based on physical
parameters [6]. As mentioned above, this model requires the
implementation of nonstraightforward equations (e.g., hyperbolic tangent) in the circuit-design environment and may
involve other approximations as well. Moreover, the model
cannot be easily scaled to future technologies.
Sub
Figure 17: Simplified circuit of the two-port varactor in Figure 16.
We have considered a number of different equivalent
models reported in the literature and developed a new model
that closely approximates the measured characteristics of the
VCO [15]. This improved model is shown in Figure 18, and
is a modified version of that proposed in [8]. The overlap
capacitance Cov , a voltage source Voffset , and a voltage source
(dashed lines) between the bulk and drain/source have been
added in the new model.
To model the varactor capacitance, the equivalent circuit
contains a voltage source Voffset , a capacitor Cov , and a pMOS
with its source and drain connected to the ground with a
high impedance (e.g., 1 GΩ resistors) to resemble floating
(nonexisting) source and drain. The open circuit for the
10
EURASIP Journal on Wireless Communications and Networking
Voffset = 1.1 V
Gate
+
Cjunction is scaled
down (e.g., by 10 6 )
or a negative power
supply is used
Rg
Cav
+
5V
Bulk (n-well)
Sidewall and area
diode (n-well/p-sub)
Ra
Rarea and Rsidewall
Sub
Figure 19: Micrograph of a VCO test structure in 0.13 µm CMOS.
50
Figure 18: SPICE model developed for the varactor.
60
4.
EXPERIMENTAL RESULTS
Three different VCO structures have been fabricated in a
standard 0.13 µm CMOS process with a 1.2 V power supply. No special mixed-signal process options have been used.
The micrograph of the chip is shown in Figure 19. Varactors
are implemented as n+ accumulation-mode MOS capacitors
with no additional mask required. Thus, the obtained designs are portable to various CMOS processes of different
foundries.
The three implementations have similar architectures as
those depicted in Figures 7(b) and 7(c), but with different varactor values. The tail current in all three versions
is 1.5 mA; hence the DC power consumption is 1.8 mW,
excluding output driver and biasing circuits. The one that
70
Phase noise (dBc)
source/drain terminal is required to eliminate the inversion
layer capacitance present in the channel of the pMOS but
absent in the varactor structure (see Figure 9). As a result,
the gate to n-well (bulk) capacitance of pMOS represents
the varactor capacitance properly with an additional channel length correction for LDD (lightly doped source/drain)
regions. Unfortunately in this configuration, the gate-source
and gate-drain overlap components of the varactor get neglected; as a result, they have to be added back by using
the fixed capacitor, Cov Voffset represents a difference of the
metal-semiconductor work function φMS , as the pMOS has
p+ poly gate doping while the varactor has n+ poly doping due to their different source/drain diffusion. As doping
levels in the polysilicon layer are typically close to degeneration, the Voffset is close to silicon bandgap (Eg (T)/q), which
is about 1.1 V at room temperature. Finally, the junction capacitance of the pMOS transistor has to be scaled down. This
can be done either by changing the scaling factor inside the
SPICE model or adding a negative power supply between
source/drain and the bulk (e.g., 5 V) to enlarge the depletion area and reduce the junction capacitance.
80
90
100
110
120
130
105
106
107
108
Frequency
Figure 20: Measured phase noise of the VCO with pMOS tail current (Figure 7(b)) at three different supply voltages (1.2 V, and 1.2 V
5%).
incorporates an nMOS tail current source (Figure 7(c)) exhibits higher sensitivity to the power supply noise, while the
one with a pMOS tail current source (Figure 7(b)) has the
best power-supply-rejection ratio (PSRR), due to the extra
isolation from the power supply by the current source.
In addition to the three VCO circuits, a biasing circuit
and an output driver stage were added to drive external
50 Ω load. Individual varactor and inductor test structures
were also included for S-parameter measurements. Open
and short de-embedding structures were added for proper
extraction of the equivalent circuit, as explained earlier in
Section 3.3.1.
The phase noise of all three VCOs was measured using
a spectrum analyzer with a phase noise module. Figure 20
compares the phase noise of the VCO with the pMOS
tail current shown in Figure 7(b), for three different supply voltages (1.2 V, and 1.2 V 5%) at the nominal
temperature with the control voltage set to the mid-point
Pedram Sameni et al.
11
6
REFERENCES
Oscilliation frequency (GHz)
5.8
[1] J. Craninckx, M. Steyaert, and H. Miyakawa, “A fully integrated spiral-LC CMOS VCO set with prescaler for GSM and
DCS-1800 systems,” in Proceedings of the IEEE Custom Integrated Circuits Conference, pp. 403–406, Santa Clara, Calif,
USA, May 1997.
[2] C. Samori, S. Levantino, and V. Boccuzzi, “A -94 dBc/Hz@100
kHz, fully-integrated, 5-GHz, CMOS VCO with 18% tuning
range for Bluetooth applications,” in Proceedings of IEEE Custom Integrated Circuits Conference, pp. 201–204, San Diego,
Calif, USA, May 2001.
5.6
5.4
5.2
5
4.8
4.6
4.4
4.2
0
0.2
0.4
0.6
0.8
1
1.2
Control voltage (V)
Measurement
Simulation
Figure 21: Measured versus modeled tuning characteristics (new
SPICE model).
(600 mV). The phase noise at 1 MHz offset from the carrier
is 95.8/ 95.5/ 95.5 dBc/Hz, respectively.
The tuning characteristics were simulated using the varactor model described in Section 3.4. Excellent agreement
between the model and the measurement was obtained, as
shown in Figure 21. The results in Figure 21 are for a VCO
test structure with an increased number of varactor fingers
(varactor with 100 fingers) and hence lower center frequency
compared to the results shown in Figure 10.
5.
CONCLUSION
VCOs are among the critical building blocks of wireless RF
transceivers since their performance and phase noise potentially affects the overall transceiver performance. Among
various VCO architectures, LC VCOs have superior phase
noise performance and therefore are extensively used in RF
transceivers. Varactors are the main tuning component of LC
VCOs and play an important role in the phase noise performance and tuning capability of these types of VCOs. A
new model for CMOS accumulation—mode varactors is presented. The model is used to predict the tuning curve of the
LC VCOs. The shape of the tuning curve and the effective
varactor capacitance were shown to depend on the losses of
the tank and the magnitude of the tail current. The model is
SPICE-based and has been verified experimentally in a standard 0.13 µm CMOS process with different VCO structures.
ACKNOWLEDGMENTS
The authors would like to thank Roberto Rosales of the University of British Columbia and Mark Hiebert of PMC-Sierra
for assisting with the measurements. This research was supported in part by Natural Sciences and Engineering Research
Council of Canada (NSERC), PMC Sierra, CMC Microsystems, and Canadian Foundation for Innovation (CFI).
[3] R. Walker, “Clock and Data Recovery for Serial Digital Communication,” ISSCC short Course, February, 2002.
[4] A. Hajimiri and T. H. Lee, “A general theory of phase noise
in electrical oscillators,” IEEE Journal of Solid-State Circuits,
vol. 33, no. 2, pp. 179–194, 1998.
[5] P. Andreani and S. Mattisson, “On the use of MOS varactors in
RF VCOs,” IEEE Journal of Solid-State Circuits, vol. 35, no. 6,
pp. 905–910, 2000.
[6] S.-S. Song and H. Shin, “An RF model of the accumulationmode MOS varactor valid in both accumulation and depletion
regions,” IEEE Transactions on Electron Devices, vol. 50, no. 9,
pp. 1997–1999, 2003.
[7] A.-S. Porret, T. Melly, C. C. Enz, and E. A. Vittoz, “Design of
high-Q varactors for low-power wireless applications using a
standard CMOS process,” IEEE Journal of Solid-State Circuits,
vol. 35, no. 3, pp. 337–345, 2000.
[8] K. Molnár, G. Rappitsch, Z. Huszka, and E. Seebacher, “MOS
varactor modeling with a subcircuit utilizing the BSIM3v3
model,” IEEE Transactions on Electron Devices, vol. 49, no. 7,
pp. 1206–1211, 2002.
[9] R. L. Bunch and S. Raman, “Large-signal analysis of MOS varactors in C MOS -Gm LC VCOs,” IEEE Journal of Solid-State
Circuits, vol. 38, no. 8, pp. 1325–1332, 2003.
[10] E. Hegazi and A. A. Abidi, “Varactor characteristics, oscillator
tuning curves, and AM-FM conversion,” IEEE Journal of SolidState Circuits, vol. 38, no. 6, pp. 1033–1039, 2003.
[11] S. Levantino, C. Samori, A. Bonfanti, S. L. J. Gierkink, A. L.
Lacaita, and V. Boccuzzi, “Frequency dependence on bias current in 5-GHz CMOS VCOs: impact on tuning range and
flicker noise upconversion,” IEEE Journal of Solid-State Circuits, vol. 37, no. 8, pp. 1003–1011, 2002.
[12] A. Hajimiri and T. H. Lee, “Design issues in CMOS differential LC oscillators,” IEEE Journal of Solid-State Circuits, vol. 34,
no. 5, pp. 717–724, 1999.
[13] H. Cho and D. E. Burk, “A three-step method for the deembedding of high-frequency S-parameter measurements,”
IEEE Transactions on Electron Devices, vol. 38, no. 6, pp. 1371–
1375, 1991.
[14] T. E. Kolding, “On-wafer calibration techniques for giga-hertz
CMOS measurements,” in Proceedings of IEEE International
Conference on Microelectronic Test Structures (ICMTS ’99), pp.
105–110, Goteborg, Sweden, March 1999.
[15] P. Sameni, C. Siu, K. Iniewski, et al., “Modeling of MOS varactors and characterizing the tuning curve of 5-6 GHz of LC
VCO,” in Proceedings of IEEE International Symposium on Circuits and Systems (ISCAS ’05), pp. 5071–5074, Kobe, Japan,
May 2005.
12
Pedram Sameni received his B.S. (honors)
degree in electrical engineering from the
University of Tehran, Iran, in 1999 and the
M.A.S. degree in analog and mixed signal design from Simon Fraser University,
Canada, in 2002. He is currently pursuing
his Ph.D. in analog and mixed signal design in the System-on-Chip (SoC) Lab of
the University of British Columbia, Vancouver, Canada. His research interests include
clock and data recovery circuits for high-speed telecommunication
systems. During the summer of 2004 he was with PMC-Sierra, Vancouver, Canada, where he worked on MOS varactor modeling and
LC VCO characterization in CMOS 0.13 µm process. From August
2005 to March 2006 he was with Foveon, Inc., Santa Clara, USA
where he worked on characterization and modeling of circuits and
devices used in CMOS image censor circuits.
Chris Siu received the B.S. degree in electrical engineering from Simon Fraser University, Burnaby, Canada, in 1991, and the
M.S.E.E. degree from Stanford University,
California, in 1994. He has over 10 years
of experience in RF/Analog IC design and
management, having worked for companies
in both Canada and the US including PMCSierra, Philips, and Hewlett Packard. He was
a Ph.D. student at the University of Alberta,
Edmonton, Canada, involved in the research of RF transceiver circuits.
Shahriar Mirabbasi received the B.S. degree
in electrical engineering from Sharif University of Technology, Tehran, Iran, in 1990
and the M.A.S. and Ph.D. degrees in electrical and computer engineering from the
University of Toronto, ON, Canada, in 1997
and 2002, respectively. During the summer
of 1997, he was with Gennum Corporation, Burlington, ON, Canada, working on
the system design of cable equalizers for serial digital video and HDTV applications. From January 2001 to
June 2002, he was with Snowbush Microelectronics, Toronto, ON,
Canada, where he worked on designing high-speed mixed-signal
CMOS integrated circuits including ADC and serializer/deserializer
blocks. Since August 2002, he has been an Assistant Professor in the
Department of Electrical and Computer Engineering of the University of British Columbia, Vancouver, BC, Canada. His current
research interests include analog and mixed-signal integrated circuits and systems design for wireless and wireline communication
applications, biomedical implants, and sensor networks.
Hormoz Djahanshahi received the B.S.
(honors) and M.S. (honors) degrees in electrical engineering from Tehran Polytechnic
University, and the Ph.D. degree in electrical and computer engineering from the
University of Windsor, Canada, in 1998. In
1990–1992, he was with Fajr Microelectronics and developed biomedical instrumentation for patient monitoring in intensive
care units. While at VLSI Research Group
in Windsor, he worked on CMOS implementation of artificial neural networks and smart photosensors. In 1998 and 1999, he was
a postdoctoral fellow at the University of Toronto, Canada, and
EURASIP Journal on Wireless Communications and Networking
designed high-speed I/O, oscillators, and PLLs in CMOS and HBT
technologies. He received the Best Paper Award at 1999 Micronet
Symposium, Ottawa. Since 2000, he has been with PMC-Sierra,
Vancouver, Canada, where he is currently a Leader in Technology
Development Group. His work includes specification and design of
high-performance mixed-signal blocks for multi-Gigabit-per second wireline and wireless applications. He has designed to production numerous clock synthesizer, clock/data recovery and SerDes
components in 0.18 µm, 0.13 µm, and 90 nm CMOS. He has over
30 publications, one US patent, and is a Chapter Officer with IEEE
SSCS in Vancouver.
Marwa Hamour received her Bachelor’s of
electrical and electronic engineering from
the Imperial College of Science, Technology
& Medicine in 2000. She received her Master’s of applied science from the University
of British Columbia, Canada, and is currently reading for her Ph.D. at the same university.
Krzysztof Iniewski is an Associate Professor
at the Electrical and Computer Engineering
Department of the University of Alberta.
He is also the President of CMOS Emerging Technologies Inc., a consulting company in Vancouver. His research interests
are in advanced CMOS devices and circuits
for ultralow power wireless systems, medical imaging, and optical networks. From
1995 to 2003, he was with PMC-Sierra and
held various technical and management positions in Research &
Development and Strategic Marketing. Prior to joining PMCSierra, from 1990 to 1994 he was an Assistant Professor at the
University of Toronto, Electrical Engineering and Computer Engineering Department. He has published over 80 research papers in
international journals and conferences. He holds 18 international
patents granted in USA, Canada, France, Germany, and Japan. He is
a frequent invited speaker and consults for multiple organizations
internationally. He received his Ph.D. degree in electronics (honors) from the Warsaw University of Technology (Warsaw, Poland)
in 1988. Together with Carl McCrosky and Dan Minoli, he is an author of Data Networks—VLSI and Optical Fibre, Wiley, 2006. He is
also an editor of Emerging Wireless Technologies, CRC Press, 2006.
Jatinder Chana completed the Bachelor’s
and Master’s degrees in electrical engineering at University of Victoria, BC, Canada,
in 1992 and 1994, respectively. He joined
PMC-Sierra in 1995 and have since then designed and implemented delta-sigma A/D
converter, pipeline A/D converter, digital
filters, high-speed data and clock recovery
circuits for 3.125 Gbs, 2.5 Gbs Serdes, and
low-jitter CSUs for 4.25 GHz and 6.25 Ghz
Serdes. Prior to joining PMC-Sierra, he worked on a data acquisition and analysis system for coal, and researched digital video compression algorithms. Current interests include high-performance
mixed-signal circuits and DSP.
:: Open Access ::
EURASIP Journal on
Applied Signal Processing
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Special Issue on
Signal Processing for Applications in Healthcare Systems
Call for Papers
The cost of medical- and healthcare has been skyrocketing over the
past decades. This is mainly due to the rapid growth of the aging
population. To provide more comfortable and effective healthcare
services, a recent trend of healthcare has been directed towards deinstitutionalization, community care, and home care. On the other
hand, the technologies have witnessed an impressive evolution in
signal/image processing, computers, and network communications.
These technologies have facilitated the development of effective signal
processing techniques in consumer electronics to improve the quality
of community and home healthcare as well as many portable devices
with a wide variety of applications where signal processing-based software plays a pivotal role in their success. The goal of this special issue
is to provide most up-to-date and recent advances of signal processing techniques developed for system and network design of healthcare
applications. Hopefully, this special issue will serve as a forum and
venue for researchers in both academia and industries working in this
fascinating and emerging area to share their experience and findings
with the readers.
Chein-I Chang, Remote Sensing Signal and Image Processing
Laboratory (RSSIPL), Department of Computer Science and
Electrical Engineering, University of Maryland Baltimore County
(UMBC), 1000 Hilltop Circle, Baltimore, MD 21250, USA;
cchung@umbc.edu
H. K. Huang, Department of Radiology and Biomedical
Engineering, University of Southern California, 4676 Admiralty Way,
Suite 601, Marina del Ray, CA 90292, USA; hkhuang@aol.com
Chien-Cheng Lee, Department of Communications Engineering,
Yuan Ze University, 135 Yuan-Tung Road, Chungli, 320, Taiwan;
cclee@saturn.yzu.edu.tw
Major topics of interest include but are not limited to the following:
• Computer-aided diagnosis for various medical modalities
• Signal processing for vital signs monitoring and analysis
• Signal analysis in circuits and devices design for healthcare sys-
tems
• Signal processing and analysis in surveillance and home moni-
toring for healthcare systems
• Embedded system design for healthcare devices
Authors should follow the EURASIP Journal on Advances in Signal Processing manuscript format described at the journal site
http://www.hindawi.com/journals/asp/. Prospective authors should
submit an electronic copy of their complete manuscript through the
journal Manuscript Tracking System at http://mts.hindawi.com/, according to the following timetable:
Manuscript Due
December 1, 2007
First Round of Reviews
March 1, 2008
Publication Date
June, 2008
Guest Editors
Pau-Choo Chung, Department of Electrical Engineering, National
Cheng Kung University, Tainan 70101, Taiwan;
pcchung@ee.ncku.edu.tw
Hindawi Publishing Corporation
410 Park Avenue, 15th Floor, #287 pmb, New York, NY 10022, USA
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