A Phase Noise Study on Coupled Oscillator Arrays
Jack Chao, University of Michigan – Ann Arbor
Advisors: Dr. L. Wilson Pearson, Chris Tompkins
Introduction
When antenna array elements are excited with signals of linear phase progression, array beam
steering is possible by changing the slope of the phase progression between elements. The
current method of accomplishing this entails using a phase shifter for each antenna, along with
complex control circuitry. This becomes difficult for large arrays at very short wavelengths.
This occurs because the size of a single array cell scales proportional to wavelength, and it is
difficult to fit phase control circuits into the small cell footprints that arise.
Equal-Phase Planes

Beam Axis

Broadside
(if all phases equal)

PhaseDelayed Input
Signals
Antenna
Array
Figure 1. Rotating the beam axis by creating a constant inter-element phase delay.
Coupled oscillator arrays are being investigated as a new and less complex method of beam
steering for antenna arrays at millimeter wavelengths. The output of several voltage-controlled
oscillators (VCOs) can be linked so that the entire array mutually oscillates at a single frequency.
Phase distribution between coupled oscillator array elements can then be manipulated in order to
perform antenna beam steering. This provides a simpler alternative to control circuitry currently
used for antenna arrays.
Antennas

Oscillators
Figure 2. A one-dimensional coupled oscillator array. The output of each
oscillator is coupled with adjacent oscillator outputs.
One important problem with any oscillator is random phase fluctuation, or phase noise, in its
output. A proposed solution to this is to injection lock oscillators at strategic points in the array.
VCOs have a narrow frequency locking range within which they can be injection locked by an
external signal. Upon being injection locked, oscillation will occur at the external frequency
instead of at the oscillator’s natural free-running frequency. Assuming the external signal has a
stable phase, injection locking will also stabilize the phase at the output of an oscillator. At each
injection point the injected signal’s phase will differ, conforming to the ideal phase progression
expected from the array.
Free Running
Oscillates at 0
More Phase Noise
Signal Injection
Injection Locked
External Signal at 1
(1 close to 0)
Oscillates at 1
Less Phase Noise
Figure 3. Injection locking a single voltage-controlled oscillator (VCO).
Array Implementation
A linear nine-element array was built at Clemson University in the summer of 2002 to test this
solution. The objective was to study various injection locking schemes and their effect in
reducing phase noise. The circuit consists of two layers with a ground reference plane
sandwiched in between. One layer contains the oscillators, which operate nominally at 10 GHz.
Packaged discrete transistors and passive components are used to implement the nine oscillators.
The output of each oscillator is passed to the other side by a signal wire through a via hole that is
drilled through the ground plane and both substrate layers.
Figure 4. The oscillator side of the circuit. The five transmission lines at photo top are used for
injection locking. The white and brown circular objects are transistors.
The transmit layer is on the other side of the ground plane from the oscillator layer. The output
of each oscillator is connected to the input of a packaged amplifier on the antenna layer. After
amplification, the signal is sent through a packaged monolithic microwave integrated circuit
(MMIC) frequency doubler to double the phase difference between adjacent elements. Doubling
the frequency also doubles the cell-to-cell phase shift and allows for a wider range of beam
steering. The output of each MMIC is then delivered to a patch antenna for transmission. A
mounting structure was used to avoid damage to the double-sided circuit during the assembly
process.
Figure 5. The transmit side of the circuit. The black circles are amplifiers. Via holes are
located to the right of each amplifier. To the left of each amplifier is a MMIC. Below each
MMIC is a patch antenna.
Because of the circuit’s small size, we encountered many problems that delayed the completion
of the array. Epoxy, a conductive glue used to attach components to substrate, was often
misplaced so that it short-circuited components. This occurred because of the difficulty in
applying epoxy on such a small scale. Capacitors were especially prone to these short circuits.
Another source of trouble was connecting the oscillator and antenna layers using via holes drilled
through the circuit. Placing components in these holes was more difficult than expected. In
addition, the painstaking process of gold wire bonding in the clean room consumed a fair amount
of time.
After the array was fabricated, the oscillator cells were tuned so that their individual free-running
frequencies agreed closely. In order for mutual oscillation to occur throughout the array, an
overlap in the free-running frequency ranges for all nine oscillators was necessary. Ideally, all
oscillators in the array would settle upon a common frequency that was within each of their
ranges.
However, a problem arose when the free-running frequency ranges of several oscillators did not
overlap with the others. These deviant ranges were higher or lower than intended, and
consequently these oscillators could not couple with the rest of the array. To address this,
component values and element configurations were altered to tweak frequency ranges. As a
result, all array elements are not perfectly identical. Ultimately, only the middle five of the nine
elements (elements 3-7) were suitable for coupling and phase noise testing by the time of this
writing.
Measuring Phase Noise
The coupled-oscillator array is a spatial power combining system, so its output was observed by
placing a horn antenna in the radiation field to capture the sum of the outputs from the five
radiating elements. Finding the free-running frequency of the five-element array was the first
undertaking after coupling the testable elements. This required tuning the individual frequency
of each oscillator until they locked together. When the oscillators are unlocked, one observes
several spectral lines in the radiated field. When the elements become locked, a single large peak
appears on the spectrum analyzer. The oscillator cells manifested frequency drift, and oscillators
frequently had to be re-tuned during the measurement process.
Since the array’s injection locking range was fairly narrow, finding the free-running frequency
also gave an approximate frequency with which to injection lock the array. Out of the five
elements, three injection locking points were available: the middle and both ends of the array
(elements 3,5, and 7). Phase noise was measured and compared for different injection locking
combinations of these three points. All measurements in this paper were taken with the beam
axis in the broadside direction. None were taken under beam steering conditions.
Antennas
Oscillators
3
5

7

Phase-shifters
Clean Source Signal
Figure 6. Injection locking setup for obtaining phase noise measurements.
Results for Different Injection Schemes
The following are phase noise measurements for injection locking at one, two, and three ports.
Phase Noise for Different Injection Schemes (-4 dBm)
0
-20
Lf (dBc/Hz)
-40
-60
-80
-100
-120
-140
1.E+03
1.E+04
1.E+05
1.E+06
Frequency Offset from Carrier (Hz)
No injection
2-port (both ends)
Instrumentation noise
1-port (middle)
3-port (all)
Figure 7. Phase noise for one, two, and three port injection locking. Phase noise is measured in decibels
relative to the power of the carrier frequency (dBc/Hz).
The x-axis frequencies are with respect to their distance from the primary carrier frequency. On
the y-axis, phase noise (Lf) is measured in decibels relative to the power of the carrier (dBc/Hz).
At larger frequency offsets, phase noise associated with the signal tends to decrease. This
explains the general downward trend exhibited by each plot. Phase noise is highly sensitive to
ambient environmental factors, and this is shown in the power spikes at higher offsets, especially
between 100 kHz and 1 MHz from the carrier.
The top line is the array’s free-running frequency, and sets an upper limit to the phase noise that
can appear during injection locking. The bottom line is the phase noise from the experimental
setup, coming from signal generators and other factors not associated with the array itself. In
this case, the noise floor was a limiting factor in taking measurements for two and three port
injection, and must be lowered in the future in order to take more accurate measurements. This
is clearly seen in Fig. 7 between the frequency offsets of 5 kHz and 40 kHz.
Despite the high noise floor, it is still clear that increasing the array’s number of injection ports
will cause a corresponding decrease in phase noise across all frequency offsets. A phenomenon
of diminishing returns is also seen from the data in Fig. 7. The measurements at 1 kHz offset
will be analyzed to explain this. At 1 kHz offset, the free-running array had phase noise of
–21.05 dBc/Hz. Injection locking the middle port dramatically decreased this to –45.49 dBc/Hz,
over 24 dBc/Hz improved from before. Injection locking both ends brought the noise to –55.7
dBc/Hz. Adding this second port lowered the phase noise 10 dBc/Hz from one-port injection.
This improvement is less than the 24 dBc/Hz improvement from zero to one-port injection.
Injecting all three ports lowered the phase noise to –60.52 dBc/Hz, improving the phase noise by
less than 5 dBc/Hz over two-port injection.
Results for Different Injection Power Levels
The following are phase noise measurements at 1 kHz offset for different power levels of the
injection signal. High power was 1 dBm (yellow) and low power was –4 dBm (blue). These
power levels were estimated as seen by the array, accounting for loss from signal cables and
transmission lines.
Phase Noise at 1 kHz Offset vs. Injection Power
0
-10
1-port
2-port
3-port
Lf (dBc/Hz)
-20
-30
-40
-50
-45.49
-51.07
-60
-55.7
-58.13
-60.52
-60.92
-70
-4 dBm Injected
1 dBm Injected
Figure 8. Phase noise at 1 kHz offset for different power levels of the injection signal. Injection
power was increased from –4 dBm to +1 dBm for each injection-locking scheme.
The graph above shows that, in general, an increase in injection signal power will decrease phase
noise. This reduction in phase noise differs depending on how many ports are injected at the
time. For one-port injection (middle port), the drop in phase noise is over 5 dBc/Hz for an
increase of 5 dBm in the injection signal power. This improvement drops to below 3 dBc/Hz for
two-port (both ends) injection. When injecting all three ports, the improvement in phase noise in
response to a higher injection power is negligible.
Conclusions
The solution of lowering coupled oscillator array phase noise by multi-point injection locking,
proposed by H.-C. Chang, et. al., was experimentally verified by testing various injection locking
schemes. As the number of injection ports are increased, results show that phase noise is
correspondingly decreased. In addition, a phenomenon of diminishing returns on phase noise
improvement is seen as the number of injection ports increase.
Experimental results demonstrate that increasing the power of the clean injection signal also
helps in reducing phase noise. This occurred for all three injection-locking schemes previously
described. It is important to note that increasing injection power has a diminishing effect on
improving phase noise as the number of injection ports increase.
Future Work
Phase noise measurements for the five-element array under beam steering conditions do not fall
under the scope of this paper, and such measurements should be addressed in the future. In
addition, time needs to be spent on lowering the noise floor of the experimental setup in order to
take more accurate measurements for multi-port injection locking. The next step is to couple the
entire nine-element array by adjusting all nine free-running frequency ranges so that they
overlap. Once this is done, complete measurements can be taken for all nine elements. The
effect of injection locking schemes in reducing phase noise should then be investigated for a
more practical two-dimensional array.
Acknowledgments
The author would like to thank Dr. Jim Harriss for performing gold wire bonding on the circuit
and Xing Wang for providing miscellaneous help throughout the summer.
Bibliography
H.-C. Chang, et. al., “Phase Noise in Externally Injection-Locked Oscillator Arrays,” IEEE Trans.
Microwave Theory Tech., vol. 45, pp. 2035-2042, Nov. 1997.
Jinjin Shen, “A Study of the Design of Coupled Oscillator Phased Arrays,” Ph.D. Dissertation, Clemson
University, 2002.
R.A. York, “Nonlinear Analysis of Phase Relationships in Quasi-Optical Oscillator Arrays,” IEEE Trans.
Microwave Theory Tech., vol. 41, pp. 1799-1809, Oct. 1993.
R.A. York, Peter Liao, and Jonathan J. Lynch, “Oscillator Array Dynamics with Broadband N-Port
Coupling Networks,” IEEE Trans. Microwave Theory Tech., vol. 42, pp. 2040-2045, Nov. 1994.