Ultrasonic Phased Arrays
This work represents the lion share of my institutional research to date, excepting the continued work building ultrasonic communications systems for the U.S. Navy. The goal of this work was to reduce the delay spread present in traditional ultrasonic communications channels (UCC), as delay spread is a direct contributor to inter-symbol interference.
Channel model
In most UCC's, piezoelectric transducers are directly aligned across the medium of communication (along thick line in figure). When data is sent, reflections from the far wall/receive side of the channel generate reverberant standing waves between the transmit and receive elements which drastically reduce the achievable data rates. This work used phased arrays to steer the beam across an angle, theta, such that the far wall reflections would be directed array from the communication elements.
theoretical model
We began with a theoretical model in MATLAB, using the propagation mathematics of a baffled rigid piston in water (see references in paper below). As can be seen in the output figure, the number of primary beams and directivity of each is a function of element width (and element spacing, as will be discussed below), when holding the speed of sound constant. In this case, the 2mm (approximately half wavelength) and 5mm (approximately one wavelength) element widths produced the fewest primary and secondary beams, which are desirable in a channel where the objective is to reduce multipath interference. We were looking to optimize both beam magnitude as well as directivity, and as such both the 2 and 5mm elements were further investigated
Phased vs. unphased simulation
The next step was to simulate these channels using Comsol to better understand the physics of beam directivity, which was done under low-reflecting boundary conditions to preserve steering information. As can be seen in the phased vs. unphased figure, the unphased channel has a much higher pressure magnitude, while the phased channel steers the beam across an angle at lower pressure.
2mm vs. 5mm
When beam steering in a UCC, the steering angle and incident energy are both critical criteria for channel efficiency. As can be seen in the 2mm vs. 5mm simulation, the 5mm elements created a higher pressure wavefront than the 2mm, however the 5mm also generated side lobes that have the potential of impacting the channel's communications. Focusing on the 2mm simulation, it is apparent that the dead space generated normal to the array is much quieter than the 5mm.
transient simulation
Using Comsol, we conducted a transient simulation to visualize the channel operation in real time, implementing both phased and unphased conditions with timescales of 100µs. Comparing the two cases, the phased channel produces steady state beams in under 30µs, whereas the unphased case produces a standing reverberant field in much the same time frame.
While the unphased case generates noise throughout the channel, the phased configuration creates well defined transit paths until far away from the transmission elements, as well as a low-pressure dead space directly normal to the array. These simulations powerfully display both the need to develop new strategies for traditional channels, as well as the potential efficacy of implementing phased arrays.
Simulation Delay Spread Results
Experimental Delay Spread Results
delay spread results
We analyzed the delay spread results in two ways: from simulation and from experimental data. After developing a Comsol model with a single transducer, I output the data to MATLAB and developed a script that analyzed every combination of phasing from 0 to pi by increments of 1/12pi, which was repeated for element spacings incremented by 1mm until no viable arrangements were found. The passable candidates (those with a steering angle of at least 30 degrees and a beam to dead space pressure ratio of at least 1.5) were then analyzed in the time domain by taking the inverse Fourier Transform and convolving the response with a carrier signal. The simulation delay spread results show a marginal reduction in delay spread (average of approximately 270µs) while producing a noisy signal.
The best candidates were then prototyped on a test channel. We used 2mm piezos, as they produced the most concise beams, steered at the greatest angle, with reasonable pressure magnitude. As can be seen in the experimental results, the 90% die-off from the RMS transmit voltage was reduced by 48 times, or nearly one and a half orders of magnitude.
Conference paper
With the hypothesis verified, we took the opportunity to write a conference paper to outline our experimental procedure and findings, due to be submitted for review in early to mid 2018. The draft conference paper can be found here.