A Low-Voltage High-Frequency CMOS LC-VCO Using a ...

A Low-Voltage High-Frequency CMOS LC-VCO
Using a Transformer Feedback
RTU4B-4
Chih-Hsiang Chang and Ching-Yuan Yang
Department of Electrical Engineering, National Chung Hsing University
250, Kuo-Kuang Road, Taichung, Taiwan 40254
Abstract — The paper describes a 0.18-μm CMOS
8.5-GHz LC-tank VCO using a technique of reducing
parasitic capacitances. Compared to the traditional crossed
coupled method with more parasitic capacitances, in this
work a symmetry transformer introduced by a transformer
on feedback currents from the active components is
employed to reduce parasitic capacitances in the VCO. The
proposed oscillator can easily arrive at the requirement for
high-frequency operation with the tuning range of 8.32 to
8.75 GHz (5%) at 0.7 V supply. With operating at 8.5-GHz
frequency, the measured phase noise is -121.6 dBc/Hz at
1-MHz offset under the power dissipation of 6 mW.
M n1
0 0
Mn2
I. INTRODUCTION
LC-tank voltage-controlled oscillators (VCOs) are
widely used in RF communication systems, particularly
in applications of phase-locked loops (PLLs). The
performance of LC-based oscillators heavily depends on
the quality of inductors and capacitors. A general
oscillation frequency of LC topologies is equal to
( 2π
LC )
f osc
= 1/ , suggesting that only the inductor and
capacitor values can be varied to tune the frequency.
Since it is difficult to vary the value of monolithic
inductors, we simply change the tank capacitance to tune
the oscillator. Thus, the resonant capacitances of the LC
tank can be simplified to be regarded as the sum of
constant capacitances and tunable ones. The former are
mainly made of the parasitic capacitances of the inductor,
the varactor and the transistors, and further limit the
tuning range even reduce the operation frequencies
because they cannot be varied by the control voltage. In
order to maximize both the tuning range and the
operating frequencies, constant capacitances in the tank
must be minimized.
In this paper, a technique to reduce parasitic
capacitances is developed for a high-frequency low-noise
LC-VCO design by using a symmetry transformer. In this
way, the limitation between the dynamic range and the
operating frequency can be mitigated while extracting a
higher frequency output signal.
II.
PROPOSED LC-VCO IMPLEMENTATION
A. Traditional LC Oscillator
A general LC-oscillator circuit scheme is shown in
Fig.1 [2],[3],[4]. The cross-connection of an NMOS
(M n1
-M n2
) differential pair in positive feedback generates
Fig. 1 One traditional LC-VCO
a negative resistance to compensate the parasitic parallel
resistance of LC tank for oscillation to occur. The
capacitances of the tank can be formed from an effective
parasitic capacitor (C p
) and a varactor. The frequencytuning
varactor is represented as a voltage-controlled
variable capacitor (C V
) in shunt with a non-variable
capacitor (C 0
).
With the transistor dimensions and tank inductance
value known, the capacitance in the varactor can be
calculated. Since:
ω = 1/ L× C
(1)
osc
and all contributions to C toto
can be identify as:
toto
( 4
0 )
C = C + C + C + C + C + C , (2)
if follows that
toto GS DB GD p V
1
C = − ( C + C + 4 C + C ) −C
. (3)
V GS DB GD 0 p
ωosc
× L
Thus, the resonant capacitances of the LC tank can be
simplified to be regarded as the sum of constant
capacitances and tunable ones. These issues reveals an
important drawback of LC oscillators: the former are
mainly made of the parasitic capacitances of the inductor,
the varactor and the transistors, and further limit the
tuning range even reduce the operation frequencies
because they cannot be varied by the control voltage. It’s
interesting to note that to maximize the tuning range,
operating frequencies and constant capacitances, the
978-1-4244-1808-4/978-1-4244-1809-1/08/$25.00 © 2008 IEEE 545 2008 IEEE Radio Frequency Integrated Circuits Symposium

Fig. 3 LC oscillation circuit equivalent
Fig. 2 The proposed LC-VCO with transformer based inductors
constant part in the tank must be minimized. However, it
nevertheless suffers from a trade-off between the
dynamic range and the operating frequency. The parasitic
capacitances from the transistors and varactor constitute
a significant fraction of the overall capacitance, thereby
limiting tuning range [1].
B. Proposed LC-VCO Using a Transformer Based
Inductor
To exclude the effective parasitic capacitor, an
LC-based oscillator scheme with a symmetry
transformer-based inductor is shown in Fig. 2. The
symmetry transformer is placed between the gate and
drain of M 1
, the circuit with a feedback loop to oscillate.
In order to reduce the required supply voltage and to
eliminate additional noise contribution, the tail current in
a conventional cross-coupled VCO is replaced by a
system inductor L 5
-L 6
. The LC oscillation scheme formed
by inductor, the varactor and the transistors but without
effective parasitic capacitor (C p
). The total capacitance
seen from X to ground is equal to C toto
plus the Miller
multiplication of CGS + CDB + 2CGD + C + C , assumed
0 V
A
V
=− 1. Now the varactor capacitance can be calculated.
All contributions to C toto
are identified as:
If follows that
C = C + C + 2C + C + C (4)
toto GS DB GD 0 V
1
C = − C + C + C + C
ω × L
[ 2
0 ]
V DB GD GS
osc
(5)
As expected, total capacitance (C toto
) in (2) is reduced
to (4) for proposed LC-VCO. The resonant circuit is
generally the type of parallel LC-tank, which is formed
by the equivalent inductance from the primary coil of the
transformer and the parasitic capacitances across the
Fig. 4 Half circuit equivalent
port.
III.
SIMPLIFIED LINEAR ANALYSIS
We exploit the LC oscillation scheme of Fig. 3 to
construct the equivalent circuit shown in Fig. 2. It is
composed of three mutual inductors L 1
-L 6
[5], a MOS
transistor pair. The inductors possess the coupling factor
K and coupling polarity is assigned by the dot convention
in the figure. The LC oscillation operation can be
explained by considering the half-circuit model of Fig. 4.
In the figure, R 1
and L 1
represent the series resistance and
inductance of the primary coil respectively while R 2
and
L 2
represents that of the secondary coil; C is the effective
tank capacitance. In this work, a symmetric structure of
the transformer is adopted, thereby L 1
= L 2
= L, and R 1
=
R 2
= R. By considering the resonator core’s loop in Fig. 4,
we have
1
+ × − × + × = 0 (6)
sC
( sL R) i2 i1 sKL i2
i = g × v
(7)
1 m1
vx
sg
1
=− i2
× (8)
sC
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Fig. 5 Die photo of the fabricated chip
Fig. 8 Measured output spectrum
Fig. 6 Measured phase-noise corner
Fig. 9 Measured phase noise
Fig. 7 Measured characteristics of tuning frequency range
ω = (10)
LC
2 1
osc
The oscillation frequency obviously depends on the
inductances and capacitances of the tank. In addition,
oscillate loss through the serial resistance R will be
cancelled while oscillating. By equations (9) and (10),
the transconductance must satisfy the following
condition for a sustained oscillation:
g
KL
m1
+ gm
1R5
C ≥ R
( 1 )
(11)
Substituting s = jω from above equations, we can get
i
2
R−
gm
1KL
gm
1R5
C
( 1+
)
1
+ jω
L− 0
2 =
ω C
(9)
Imaginary parts of the denominator must drop to zero
when oscillation occurs, and we have
and we get
g
m1
RC
≥
KL−
RCR
IV.
5
(12)
MEASUREMENT RESULTS
To verify the performance of the LC-VCO as
previously described, the proposed circuits were
fabricated in 0.18-μm CMOS technology. Fig. 5 shows
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the microphotograph of the test chip with an area of
830×910 μm 2 including the output buffers and I/O pads.
Each output signal is connected to an open-drain circuit
with an externally match resistance of 50 Ω. The VCO
was tested on an FR-4 PC board using Agilent E4407B
Spectrum analyzer for measurement. With a 0.7-V supply,
it consumes the power of 6 mW. Fig. 6 shows the
measured phase noise at 1-MHz offset. The measured
frequency tuning characteristic is shown in Fig. 7. As can
be seen, the tuning range is 5% (8.32 to 8.75 GHz). The
measured spectrum of 8.5 GHz is shown in Fig. 8, and
they prove that the resonant oscillation of the LC-tank
merely occurs in the primary of the transformers. Fig. 9
shows a plot of the measured phase noise of the 8.5-GHz
output is -121.5dB/c at 1-MHz offset.
A widely accepted figure of merit (FoM) for VCOs is
given by [6]:
f0 Pdiss
FoM = PN ( Δf
) − 20 log
+ 10 log
(13)
Δf
1mW
The FoM normalizes the phase noise at a given offset Δf,
the center frequency f 0
, and the power consumption
P in milliwatts. The best FoM of the VCO is −190
diss
dBc/Hz. Table 1 shows the FoM of several comparable
under around 1-V supply over the past years [7]-[10].
V. CONCLUSION
A high frequency and low voltage LC-VCO was
achieved by using a symmetric transformer-based
inductor. It is an interesting work covering the use of
Miller multiplication to reduce parasitic capacitances, for
building high-frequency VCOs. The prototype LC-VCO
can extend the operating frequencies at 8.32 to 8.75 GHz
in a standard 0.18-μm CMOS process at minimum
operating supply voltages of 0.7 V. The measured results
demonstrate the functionality of the LC-VCOs with the
proposed to reduce parasitic capacitances technique.
ACKNOWLEDGMENT
The authors would like to thank the National Science
Council, Taiwan, for the financial support and the Chip
Implementation Center (CIC), Taiwan, for the
infrastructure support. This work was sponsored by
NSC95-2220-E- 005-003
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Table 1 Comparison of performance with prior works
Technology Frequency
Refs
[μm]
[GHz]
Turing range
[GHz]
VDD
[V]
Power
[mW]
Phase Noise
[dBc/Hz]
FoM
[dBc/Hz]
This work 0.18 CMOS 8.5 0.4 0.7 6 -121.6 @ 1MHz -190
[7] 0.18 CMOS 2.4 4.4 1 2.6 -116.8 @ 1MHz -180.25
[8] 0.18 CMOS 5.8 0.198 0.8 - -100 @ 500KHz -
[9] 0.9 CMOS 1.77 0.07 1 6.26 -107 @ 1MHz -163.0
[10] 0.18 CMOS 4.8 0.4 1.5 3 -120 @ 1MHz -188.8
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