Circuits and Systems, 2011, 2, 281-285
doi:10.4236/cs.2011.24039 Published Online October 2011 (http://www.scirp.org/journal/cs)
Low Noise Phase CMOS Quadrature VCO with
Superharmonic Coupling Using Cross-Couple Pair*
Seyed Reza Hadianamrei, Masoud Sabaghi, Maziyar Niyakan Lahiji, Mehdi Rahnama
Research School of Nationa l Science & Technology Research Institute (N.S.T.R.I), Tehran, Iran
Received June 25, 2o11; revised July 27, 2011; accepted August 25, 2011
Abstract
This paper aims to introduce a quadrature VCO (voltage control oscillator) which applies superharmonic
coupling. The presented quadrature VCO is suitable to be used, both with 2 × subharmonic mixers, as well as
4× subharmonic mixers. It would be impossible to avoid the presence of harmonics in CMOS VCO circuits.
These harmonics are in general, undesirable signals which tend to accompany the desired fundamental signal.
There are common-mode nodes (similar to those in the two source nodes in a cross-coupled VCO) in defer-
ential VCO at which higher-order harmonics are present while the fundamental is absent in essence. We can
make use of these second-order harmonics which are present at the common-mode nodes of two VCO in or-
der to implement a quadrature connection between the fundamental outputs. The technique through which
this is done is called superharmonic coupling. This CMOS quadrature VCO which applies active superhar-
monic coupling puts an excellent performance in show, with an output power –0.942 dBm for fundamental
and –9.751 dBm for subharmonic, phase noise –107.2 dBc/Hz for fundamental and –114.8 dBc/Hz at a
1MHz offset. All of circuit applied are designed and simulated by ADS, 2008.
Keywords: Quadrature VCO, Cross-Couple, Phase Noise, CMOS
1. Introduction
Oscillators are fundamental components in wireless com-
munications systems that can be used for several applica-
tions. Communication systems that use phase shift key-
ing modulation frequently require a pair of LO signals
that are in quadrature, or 90˚ out-of-phase.
Quadrature VCO (voltage control oscillator) is one of
the most important components in direct conversion
transceivers. These VCOs are of a basic role in im-
age-rejection techniques which are based on the appro-
priate phasing of the signals. Furthermore, they eliminate
the immense and non-planar high-frequency filters. it
also should be added that, some digital radio communi-
cation systems (e.g. GSM and DECT) in which complex
digital modulation schemes are applied in order to reduce
the signal bandwidth to the possible minimum level,
need quadrature VCO [1]. In all the applications men-
tioned above, departures from the quadrature phase or
the existence of an amplitude imbalance between the two
signals leads to a damaging effect on the performance of
the whole system. There are a number of techniques
which can be applied to produce quadrature signals.
1) The first technique is a standard VCO which a
RC-CR phase-shift network follows. If the real values of
R and C are not accurate, it may result in errors in the
quadrature which, in turn, necessitate compensation of
some form [2].
The complete LO input circuit with balun and phase
shifters is shown in Figure 1 with relative phase shifts
indicated at the output for clarity. Using a reference 0˚
*This work was supported in part by N.S.T.R.I Tehran, Iran. Figure 1. RC-CR phase-shift ne twork.

S. R. HADIANAMREI ET AL. 282
phase of an LO input signal, the phase shift at the outputs
in Figure 1 would be –45˚, 45˚, 135˚, 225˚ from top out-
put to bottom relative to the input phase.
2) The second technique which can be applied is a
VCO which runs at double frequency and a digital fre-
quency divider based on flip-flops follows it. Here, the
sections of the circuit which work at the double fre-
quency may turn into a speed or power bottleneck.
3) Another technique is employing two cross-coupled
VCO’s [3].
4) Using active polyphase filters such as ring oscillator
designs is another technique in this list. In four-delay
stage ring oscillators, for example, taps at diametrically
opposite points yield quadrature phases [4].
An alternative method for obtaining quadrature VCO
based on the differential coupling at the second harmon-
ics of two differential VCOs is introduced in this paper.
As a matter of fact, if s 180-degrees phase shift occurs
between the second harmonics of two VCOs, their basic
frequency components will be in quadrature states.
2. Design of a 4.8 GHz VCO
The cross-coupled VCO is the most frequently used mi-
crowave VCO topology in CMOS technology. We can
prepare a model of a LC VCO with the capacitor and
inductor, parallel with a resistor to simulate the losses in
the tank, and also a negative resistance to simulate the
active device. In order to produce the negative resistance
to compensate for the losses in the LC tank, employing a
cross-coupled differential pair, as shown in Figure 2,
would be a choice. The resistance, Rin looking into the
cross-coupled pair is obtained by:
2
in m
R
g
 (1)
gm is the transconductance of each of the BJTs in the
cross-coupled pair.
Therefore, by choosing a proper device size and bias-
ing, the value of negative resistance necessary to coun-
teract, we are able to find the losses in the tank.
R
in
Figure 2. Negative resistance generated from cross-coupled
BJT.
Figure 3 illustrates a frequently employed LC VCO
circuit using the cross coupled differential pair. A mod-
erately low supply voltage is possible to be used for this
implementation because there are only two levels of
transistors. However, it calls for two inductors, which
require considerable chip area.
The VCO topology illustrated in Figure 3 was applied
(with BJT transistor) in [5].
CMOS technology was applied to design fundamental
C band VCO for the present experiment. The Diode
varactor illustrated in Figure 2 allows the tuning of fre-
quency.
Simulation Results for Cross-Coupled VCO
The signal output power was about 0.942 dBm and the
phase noise at a 1 MHz offset was –107.2 dBc/Hz.
Figure 4 illustrates the phase noise graph. Figure 5
illustrates the output power spectrum and Figure 6 illus-
trates Time-domain VCO outputs.
Figure 3. Cross-coupled BJT VCO.
Figure 4. Phase noise 4.8 GHz VCO.

S. R. HADIANAMREI ET AL.283
10 2030 4050 60 70080
-80
-60
-40
-20
0
-100
20
freq, GHz
Output_powe
r
m1
m1
freq=
Output_power=-0.942
4.800GHz
Figure 5. Output power VCO.
Figure 6. Time-domain VCO outputs.
3. Concept of the Quadrature VCO
In most CMOS processes, resistors are particularly of
large tolerances. Hence, this method may result in a low
degree of accuracy in the quadrature signals that gene-
rated. In order to generate quadrature signals, another
method is to employ a digital frequency divider which
follows a VCO running at the frequency two times larger
than the fundamental frequency [6]. There are some es-
sential restrictions against using this technique at high
frequencies for it calls for a VCO operating at double the
desired frequency. A third frequent technique is to force
two VCOs to run in quadrature through applying cou-
pling transistors running at the fundamental frequency
[7]. The problem with this technique is a trade-off be-
tween quadrature accuracy and phase noise which is due
to the effects the coupling circuit imposes on the oscilla-
tion frequency. In order to overcome this problem, we
may take advantage of realizing a quadrature VCO thr-
ough superharmonic coupling. As shown in Figure 7(a),
quadrature signals are produced at the fundamental fre-
quency by using differential coupling at the common-
mode nodes where the second harmonic is predominant.
In order to implement the coupling of the second har-
monic with a 180˚ phase shift, the on-chip transformer
has been inverted [8-10] (Figure 7(b)).
The method of superharmonic coupling implements a
180˚ connection between the even-ordered harmonics of
the two VCO circuits, and this happens while both pas-
sive and active superharmonic coupling circuits are
achievable. The performance of the two individual def-
erential VCOs, as alongside with the coupling network
will determine the performance of a quadrature VCO
which applies the superharmonic coupling topology. This
results in an anti-phase relationship between the sec-
ond-order harmonics at the common-mode nodes.
4. Proposed Quadrature VCO
A frequently method used for implementing a CMOS
differential LC VCO is applying a cross-coupled pair for
generating the negative resistance needed for compen-
sating for the losses in the tank. Hence, by choosing the
proper device size and biasing, we are able to realize the
negative resistance needed to counteract the losses in the
tank. The core quadrature VCO circuit investigated in
this work is shown in Figure 8. It is made of two cross-
coupled VCOs connected through a cross coupled pair. It
has been shown that the phase noise of the VCO can be
enhanced notably by including cross-coupled inductor
above the cross-coupled NPN transistors, due to the
higher transconductance and faster switching speed of
the corresponding structure [10]. We can find the oscilla-
tion frequency for each VCO via the common formula
for finding the resonant frequency of an LC tank, in
which L is the value of the on-chip spiral inductor and C
is the total capacitance at the tank nodes. The inductors
employed in this circuit of the capacitance less than 1.1
nH. The overall capacitance, including the lumped ca-
pacitor, and adding the parasitic capacitance was 0.925
pF which provided oscillation at 4.8 GHz.
Figure 7. (a) Superharmonic coupling of the second har-
monic to enforce quadrature at the fundamental; (b) Cou-
pling using an inverting transformer; (c) Coupling using a
cross-coupled pair.

S. R. HADIANAMREI ET AL. 284
The network which is employed to implement the 180˚
phase difference in the second-order harmonics is a vital
component of the quadrature VCO. This anti-phase asso-
ciation is the factor which generates the quadrature phase
relationship at the fundamental frequency. Convenient
common-mode nodes which are used for coupling the
second harmonic are the common source nodes in each
of the cross-coupled differential pairs, which are signi-
fied by CM1 and CM2 in the comprehensive VCO cir-
cuit schematic illustrated in Figure 8. DC blocking ca-
pacitors were used so that transistors N5-N6 could be
biased for optimal coupling. Owing to the fact that any
practical use of a VCO requires connecting its output to
other circuitry, buffers are required to be employed in
order to guarantee that loading does not disrupt the os-
cillations. For each of the four outputs we have used
source follower buffers that we were able to measure the
VCO using equipment with 50 Ω input impedances. The
180˚ and 270˚ outputs were terminated on-chip with 50
Ω loads and the 0˚ and 90˚ were linked to CPW pads for
on-chip inquiring.
Simulation Results for Quadrature
Cross-Coupled VCO
In Quadrature VCO at subharmonic frequency (9.6 GHz)
the signal output power was approximately –9.751 dBm
and the phase noise at a 1 MHz offset was –114.8 dBc/
Hz.
Figure 9 shows spectrum of output power Figure 10
shows Graph of phase noise. And Figure 11 shows Ti-
me-domain VCO outputs. Table 1 shows result of fun-
damental and subharmonic VCO. Table 2 shows result
of compare with other VCO designs.
5. Conclusions
This paper represents a CMOS quadrature VCO which
was designed at 4.8 GHz by applying superharmonic
coupling. This technique focuses on coupling the sec-
ond-order harmonics between two VCO and obliges an
anti-phase connection, which, in turn, compels a quadra-
ture relationship at the fundamental. In order for this
coupling with a 180˚ phase shift to be implemented, a
cross-coupled differential NPN pair was employed at the
common-mode nodes. This CMOS quadrature VCO
which employs an active superharmonic coupling dem-
onstrates a very fine performance with an output power
of –0.942 dBm for fundamental and –9.751 dBm for sub-
harmonic, phase noise of –107.2 dBc/Hz for fundamental
and –114.8 dBc/Hz at a 1 MHz offset. it creates the 180˚
phase shift in the second-order harmonics by using a
cross-coupled differential pair.
Figure 8. Schematic quadrature VCO.
Figure 9. Output power quadratur e VCO.
0.20.40.60.81.01.21.41.61.80.0 2.0
-120
-100
-80
-60
-40
-20
0
20
-140
40
n oisef r eq, MHz
pnmx , dBc
m4
m4
noisefreq=
pnmx=-114.8 dBc
1.000MHz
Figure 10. Phase noise quadrature VCO.
Figure 11. Time-domain Quadrature VCO.

S. R. HADIANAMREI ET AL. 285
Table 1. Compare fundamental and subharmo nic VCO.
Fundamental Subharmonic
Freq 4.8 GHz 9.6 GHz
Output Power –0.942 dBm –9.751 dBm
Phase Noise –107.2 dBc/Hz –114.8 dBc/Hz
Table 2. Compare with other VCO designs.
Reference fc(GHz) Phase
noise(dBc/Hz) Device
[11] 8.7 –110 SiGe BiCMOS
[12] 2.2 –111 CMOS0.35 μm
[13] 11.02 –86.83 CMOS RF
[14] 1.6 –114.7 CMOS 0.18˚ μm
This Work 9.6 –114.8 CMOS 0.18˚ μm
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