312 IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 15, NO. 5, MAY 2005
Continuous Phase Shift of Sinusoidal Signals Using
Injection Locked Oscillators
J. M. López-Villegas, Senior Member, IEEE, J. G. Macias, J. A. Osorio, J. Cabanillas, Member, IEEE,
J. J. Sieiro, Member, IEEE, J. Samitier, Associate Member, IEEE, and N. Vidal
Abstract—This work presents an alternative to generate contin-
uous phase shift of sinusoidal signals based on the use of super har-
monic injection locked oscillators (ILO). The proposed circuit is a
second harmonic ILO with varactor diodes as tuning elements. In
the locking state, by changing the varactor bias, a phase shift in-
stead of a frequency shift is observed at the oscillator output. By
combining two of these circuits, relative phases up to
90 could be
achieved. Two prototypes of the circuit have been implemented and
tested, a hybrid version working in the range of 200–300 MHz and
a multichip module (MCM) version covering the 900–1000 MHz
band.
Index Terms—CMOS analog integrated circuits (ICs), injection
locked oscillators (ILOs), multichip modules (MCMs), phase
shifters.
I. INTRODUCTION
P
HASE Shifting is a key issue in modern communication
systems. Beam steering and beam forming in phase array
antennas, image rejection mixers, carrier recovery circuits or I/Q
modulation and demodulation, are examples where signals with
a precise phase shift are required. Different topologies of phase
shifters have been reported in the literature. For fixed amounts
of phase shift (i.e., multiples of 90
), poly-phase networks are
the preferred solutions [1]. When a digitally controlled phase
shift is required, phase shifters based on PIN or varactor diodes
and FET transistors are commonly used [2].
Another way to obtain sinusoidal signals with a precise phase
displacement is direct generation. Instead of having a signal
source connected to a phase shifter, the required signals are gen-
erated using a multiphase oscillator. Cross-coupled oscillators
and ring oscillators are examples of multiphase output circuits
[3]. In this case, a signal is forced to follow a closed loop and the
phase shift is accomplished by sampling the signal at the right
place. Depending on the loop elements different fixed values of
the phase shift can be achieved.
Sub-harmonic injection locking of oscillator circuits has also
been proposed as an alternative method to generate continuous
phase displacement of a sinusoidal signal [4]. Nevertheless, this
Manuscript received May 11, 2004. revised February 11, 2005. This work
was supported in part by the Spanish Ministry of Science and Technology under
project TIC2001-2947-C02-01. The review of this letter was arranged by Asso-
ciate Editor J.–G. Ma.
J. M. López-Villegas, J. G Macias, J. A. Osorio, J. Cabanillas, J. J. Sieiro, and
J. Samitier are with the Department of Electronics, Instrumentation and Com-
munication Systems, RF Group, University of Barcelona, Barcelona E-08028,
Spain (e-mail: josem@el.ub.es).
N. Vidal is with Escola Universitaria Salesiana de Sarrià (EUSS), Barcelona
E-08017, Spain (e-mail: nvidal@euss.es ).
Digital Object Identifier 10.1109/LMWC.2005.847690
Fig. 1. Circuit schematic of second harmonic ILO with varactor control.
method implies a phase noise degradation of the output signal,
when compared with the injected one. In this work an alterna-
tive scheme of phase shifting is reported. It is based on the phase
behavior of second harmonic ILOs [5]. When compared with
sub-harmonic injection, the proposed method allows continuous
phase shift in a shorter range, but improves the phase noise be-
havior. Consequently, the use of sub or super harmonic injection
will depend on the trade-off between the requirements of phase
tuning and phase noise.
II. C
IRCUIT FUNDAMENTALS
Injection is an usual way to synchronize an oscillator with an
incident signal. When the injected signal is close to a harmonic
of the oscillator free running frequency, the ensemble is known
as a super-harmonic ILO [5].
A possible implementation of second harmonic ILO is shown
in Fig. 1. The circuit is a cross pair oscillator, whose resonant
tank consists of an inverter transformer (inductive element) and
a pair of varactors. The second harmonic is injected at the centre
tap of the transformer. Ideally, under common mode excitation,
the transformer acts as a short circuit, thus the injected signal
is found without distortion at the varactors’ terminals. There,
due to the non linear behavior of the stored charge versus ap-
plied voltage, the injected signal at frequency
mixes with the
oscillator signal at frequency close to
. First-order harmonic
analysis gives for these signals
(1)
being
and the fundamental component of the oscillator
voltage and the injected signal, respectively,
and their
amplitudes and,
and the corresponding phases. Note that
phase
takes into account the dynamics of the oscillator
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LÓPEZ-VILLEGAS et al.: CONTINUOUS PHASE SHIFT OF SINUSOIDAL SIGNALS 313
Fig. 2. Measured output spectrum of a second harmonic ILO: dotted line is
the free running oscillation, continuous line is the forced oscillation when a
452-MHz signal is injected at the input.
frequency from the free running state, to the locked
state,
(i.e ).
By defining angle
, and after some
trigonometric calculations, the fundamental current
, passing
through the varactor diodes can be expressed as
(2)
where
and are the capacitance of the varactors and its
derivative versus the applied voltage, respectively, both at the
bias point
.
According to (2), the varactors’ capacitance
(i.e., term
between brackets) changes depending on the amplitude
and
angle
. As a consequence there is a change of the oscillator
frequency after the injection of the input signal. This change is
reflected in
and also in . Equilibrium is reached when
. Accordingly, the time derivative of should
also be zero and then, the final oscillator’s frequency will be the
locking frequency
. An example of this frequency synchro-
nization is shown in Fig. 2.
At the steady-state the oscillation frequency can be expressed
as follows:
(3)
where
is the steady state capacitance. By substituting in
(3) the term between brackets in (2), the steady state value for
angle
can be found
(4)
According to the above analysis the phase shift process can
be explained as follows. Let us consider a second harmonic ILO
in the locked state. The oscillator output frequency is
and
angle
is equal to . At this point let us consider the effect
of a modification in the varactors bias. The capacitance
,
its derivative
and the free running frequency will change.
Provided these changes are small (in practice the argument of
the arcsin function in (3) must be kept between
and 1), the
output frequency will still be
, and a new steady state condition
will be reached, corresponding to a new value of
. Finally,
(a) (b)
Fig. 3. Photographs of the second harmonic ILO circuits: (a) hybrid version
and (b) MCM version.
the modification of angle
before and after the bias change,
implies a change in the output phase .
This relationship between phases also explains the phase noise
improvement in super-harmonic ILO’s [5].
III. C
IRCUIT DESIGN AND FABRICATION
Two different versions of the second harmonic ILO circuit
have been fabricated and tested. First one is a hybrid version
working in the 200–300 MHz frequency band. The second is a
MCM version in the 900 MHz–1 GHz frequency band (Fig. 3).
The hybrid version has been implemented using lumped
components on a printed circuit board. Transformers have
been printed directly on board as interleaved square spirals.
Electromagnetic simulations tools have been used to optimize
their geometry in order to achieve good performance in both,
common and differential modes of operation.
The MCM version has been implemented using a Pyrex 7740
substrate carrier. Two 1.5-
m thick Al metal levels are used
as interconnects and to perform the required integrated trans-
formers. Polyimide, 4.5-
m thick, is used as intermetal dielec-
tric and passivation layer. RFIC’s die including the active part
of the oscillator has been fabricated using a 0.35-
m CMOS
process. This die has been flip-chipped on the carrier substrate
using Pb/Sn solder bumps over pads with a previous Ti/Ni/Au
metallization.
IV. E
LECTRICAL CHARACTERIZATION
In order to accurately measure the phase shift, two second
harmonic ILO circuits have been injected with the same input
signal. One of them is used as a reference while the other is
used as a test circuit. The output of the reference circuit is the
trigger for measuring the phase shift of the test circuit. Fig. 4
shows the obtained results for the hybrid version. Waveforms
corresponding to the reference circuit (bottom) and the test
circuit under three varactor bias conditions (top) are plotted.
A 444-MHz
6 dBm input signal is injected to both second
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314 IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 15, NO. 5, MAY 2005
Fig. 4. Measured output waveforms of the reference oscillator circuit (bottom)
and test circuit for three varactor bias conditions (top).
Fig. 5. Phase shift at test circuit output as a function of the varactors bias.
Outlined data points (
) correspond to 3 dBm injected power and 1.1 V for
the reference circuit varactors bias (
Vref
). Filled points correspond to 6-dBm
injected power and
Vref
:(
)1V,(
) 1.1 V and ( ) 1.2 V.
harmonic ILOs resulting in an output locking frequency of
222 MHz.
In Fig. 5, the phase shift between the outputs of the test
and reference circuits is plotted as a function of the varactors
bias of the test circuit. Four different sets of phase/bias values
are represented corresponding to different values of the refer-
ence circuit varactors bias and the injected power. Ideally, the
achievable phase shift ranges from
90 to 90 . Any further
intent to increase the phase shift would unlock one or both
second harmonic ILOs. In practice, the useful phase shift range
is more restricted due to inaccuracies in the phase control.
According to expression (4) the phase sensitivity is, in a first
approach, inversely proportional to the injected amplitude
.
Consequently, the phase-shift/Bias slope should decrease as the
injected power increases. This fact is clearly observed in Fig. 5.
Finally, particularly interesting is the existence of a range of
phase/bias values showing a nearly linear behavior, which will
allow direct analogue phase modulation.
In order to investigate the dynamic behavior of the phase
shifting process, the outputs of the reference and test circuits
have been added to perform a phase modulation (PM) to am-
plitude modulation (AM) conversion. The process is depicted
schematically in Fig. 6. The output phasor of the reference ILO
is combined with the output phasor of the test ILO for two dif-
ferent varactor biases. The resultant phasor changes its ampli-
tude according to the phase shift of the test ILO. Fig. 7 shows the
measured amplitude modulation pattern obtained using this pro-
cedure with two MCM second harmonic ILOs. The varactor bias
for one of them is kept constant while for the other it changes ac-
Fig. 6. Phasor diagram showing the amplitude modulation resulting after
adding the test and reference ILO’s outputs.
Fig. 7. Amplitude modulation pattern generated adding the outputs of two
MCM second harmonic ILO circuits.
cording to a 1-MHz square wave. In this case the output locking
frequency is 940 MHz.
V. C
ONCLUSION
Continuous phase shifting using second harmonic Injection
locked oscillators have been demonstrated in this work. Both
static and dynamic phase shift behaviors have been investi-
gated using two circuit prototypes. One hybrid version and
a MCM version intended to work in the frequency ranges of
200–300 MHz and 900 MHz–1 GHz, respectively. The pro-
posed circuits could be used as a direct narrow band analog or
digital phase modulator.
R
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