## Ahmed Kord

PhD Candidate, the University of Texas at Austin

# PhD Thesis

## Magnetless Circulators Based on Linear Time-Varying Circuits, 2015-Present

The realization of high-performance magnetless circulators is crucial to enable full-duplex communication which would revolutionize the wireless industry for it doubles the capacity of the entire EM spectrum compared to currently deployed TDD and FDD systems in addition to offering many benefits at the network and physical layer levels. These three-port non-reciprocal components not only can provide the first critical 20-30 dB of the total required self-interference cancellation, thus significantly relaxing the design of the following layers of isolation based on mixed-signal and DSP techniques, but they also permit the use of a single antenna for both the TX and the RX nodes while maintaining an aggregated insertion loss less than 3 dB. Since 2015, I have been leading the efforts in Prof. Andrea Alu's research group at the University of Texas at Austin to develop magnetless circulators (and other non-reciprocal components) based on linear time-varying circuits. Our efforts since then have led to many new discoveries, gaining the interest of several companies, funding agencies, and research groups at top-tier universities. These efforts are summarized as follows:

*Single-Ended STM Circulators*

In this project, we developed two entirely-new magnetless circulator circuits from basic physics to optimal implementation at radio frequencies. These circuits are based on connecting three bandpass or bandstop resonators in either a wye or a delta topology, respectively, and modulating their natural oscillation frequencies with signals having the same frequency and amplitude but their phases increase by 120 deg in a particular direction. Such modulation scheme provides a preferred sense of precession for the rotating modes supported by the resonant network, thus lifting their degeneracy and allowing them to destructively interfere at one port and sum up at the other in a cyclic-rotating fashion, which yields the operation of a circulator. The experimental validation of the bandstop/delta, or delta for short, topology resulted in the first watt-level magnetless circulator thus enhancing the power handling of such components by orders of magnitude compared to previous works.

*Differential STM Circulators*

The main challenge with the single-ended STM circulators is that they suffer from strong IM products resulting from mixing between the RF and modulation signals. These products not only pose an interference problem to neighboring channels but they also enforce a bound on the lowest possible IL and effectively reduce the circulatorâ€™s overall power handling since they could saturate or destabilize the cascaded frontend blocks. In order to overcome this problem, we developed a differential architecture that combines two single-ended delta or wye circuits with a constant 180 deg phase difference between their modulation signals in either a voltage- or a current-mode topology, respectively, in analogy with passive mixers. Interestingly, these differential circuits reject the IM products at all ports for input excitation at any frequency, thus making them the first-of-their-kind pseudo-linear time-invariant networks which synthesize a truly continuous angular-momentum bias even though they are implemented using a discrete number of resonators (three per each single-ended circuit). This is analogous to magnetic-biased circulators, where the aligned electron dipole moments imitate a continuous rotation of the ferrite disk at a macroscopic level although they are in fact a collection of quantized spins. This, in turn, allows the differential STM circulators to achieve remarkable performance in all metrics while drastically reducing the required modulation parameters. In order to prove this, the voltage-mode topology was built and experimentally characterized, resulting in unprecedented performance in all metrics compared to the current state of the art, including large isolation (>20 dB), low insertion loss (<2 dB), excellent matching (>20 dB), small IM products (<-30 dBc), high P1dB (>+28 dBm), high IX20dB (>+28 dBm), low noise figure (<2.7 dB), all over a sufficiently large bandwidth (>30 MHz) and a relatively small form factor (2x11x13 mm2), while using a small modulation frequency of only 10% at a center frequency of 1 GHz.

*Broadband STM Circulators*

The 20 dB IX BW of both the single-ended and differential STM circulators discussed above is limited to about 4% at best. Interestingly, this is comparable to the performance of magnetic circulators when the ferrite cavity is directly terminated with 50 Ohm ports. However, the BW of such magnetic devices can be increased to more than 10% by adding bandpass filters at each arm of the non-reciprocal junction. These filters are essentially matching circuits that reshape the frequency response of the junction to increase the BW of the combined network by trading off peak IX. In order to extend this technique to magnetless circulators, two conditions must be met: (i) the narrowband circuit must be cyclic-symmetric and (ii) the IM products must be sufficiently small (at least â€“20 dBc). Fortunately, both conditions are satisfied by the differential topologies of STM circulators. Therefore, a broadband circuit was built by connecting three identical *LC* filters at the ports of a current-mode STM circulator resulting in a 20 dB IX of 14%. While this value was 3.5 larger than all our previous results, an important question that remained was '*what is the maximum BW that can be achieved?'* In order to answer this question, we developed a rigorous analytical model using N-port network parameters and control theory, then we applied the Bode-Fano criterion to derive a global bound on the maximum possible BW that maintains a certain IX level.

*CMOS STM Circulators*

The single-ended, differential, and broadband implementations of STM circulators presented above, despite achieving remarkable performance in all relevant metrics, were all based on PCB technology and commercial off-the-shelf discrete components, which limits their size and cost reduction and prohibits their large scale production. In order to overcome this problem, we developed the first integrated-circuit STM circulator (and the second among all LPTV-based implementations) using a standard 180 nm CMOS process. The active silicon area of the fabricated chip was 0.2 mm2, the smallest among all magnetless circulators presented to-date, and it was mounted in a 5x5 mm2 QFN package and connected to six off-chip inductors on a PCB for testing. The total form factor of the circulator (IC+inductors) was 6x6 mm2 which is at least one order of magnitude smaller than our previous PCB prototypes, and as such represents a crucial step in our quest to commercialize this technology.

*MEMS STM Circulators*

The CMOS STM circulator presented above, despite reducing the form factor and the cost of such component significantly compared to discrete implementations, was still limited in its miniaturization by the fact that it requires six high-*Q* (>50) off-chip inductors. In order to overcome this problem, we developed the first inductorless implementation of all magnetless circulators based on LPTV circuits by replacing the *LC* tanks with compact chip-scale thin-Film Bulk Acoustic Resonators (FBARs) or Aluminum Nitride Contour Mode Resonators (CMRs) and modulating them using switched capacitors. The super high-*Q* (>1000) of the FBARs (or the CMRs) also permitted a drastic reduction of the modulation frequency to only 0.24% of the circulator's center frequency (6MHz/2.5GHz) resulting in a power consumption of only 6.8 uW, the lowest among all magnetless circulators reported to-date.

## Active Microwave Cloaking Based on Parity-Time Symmetric Satellites, 2015-2016

Can cloaking work? Not in our lifetime, I think! Nearly all cloaking devices presented to-date are based on passive metamaterial approaches which suffer from fundamental challenges related to their BW and the size of the object being concealed. This, in turn, casted a lot of doubt on whether cloaking can truly become a technological reality or it will remain a science fiction. A step on the right direction, however, to make invisibility *possibly* work as we envision it in the long term is to adopt an active approach. Towards this goal, we investigated a practical super stealth technology based on parity-time symmetric satellites which were realized using a combination of lossy materials that absorb the impinging signal on one side of the scattering object and active devices that re-emit it on the other side with the same phase and amplitude. Rigorous analysis and circuit/EM co-simulations show that such active technique can indeed overcome the limitations of passive metamaterial approaches and maintain a stable 10 dB reduction in the scattering cross-section over a fractional BW as large as 20% of the center frequency.

# M.S. Thesis

## Composite Right-/Left-Handed Metamaterials, 2013-2014

Composite right-/left-handed (CRLH) metamaterials are structures that exhibit simultaneous negative permittivity and permeability over a finite BW resulting in left-handed transmission within this band, in addition to the natural double-positive and right-handed characteristics far from it. These structures can be built using low-loss and high-power waveguide structures operating near their dominant mode cutoff and periodically loaded with stubs having a lower cutoff frequency. In order to optimize the design of the stubs, we developed a general form of asymptotic corrugation boundary conditions (ACBCs) that can be applied to any interface between two materials with arbitrary cross-sections. This, in turn, permitted a systematic design of several CRLH components with enhanced performance such as backward-to-forward leaky wave antennas with a wide beam-scanning range.

## Computational Electromagnetics, 2013-2014

Numerical codes were developed using FDTD, FEM, and MOM methods to analyze several RF circuits and EM scattering problems. All programs were written in Matlab and were validated by comparing the results mutually and to analytical solutions of standard problems. Further improvements in terms of speed, memory utilization efficiency, and post-processing capabilities were implemented later during my PhD. I have also built user-friendly GUI tools to facilitate the use of these codes in studying many RF and EM problems that are tedious to solve using commercial general-purpose 3D full-wave simulators such as Microwave Studio CST. These tools were also useful for illustrative educational purposes during my work as a teaching assistant and subsequently as an assistant lecturer at Cairo University.

# B.S. Thesis

## Implantable Pressure Sensor for Non-Invasive Biomedical Applications, 2010-2011

This was a senior-year project sponsored by Si-Ware Systems and it involved six students, including myself, in fulfillment of our B.S. degree requirements. The entire chip was designed from system-level to layout using a standard 130 nm CMOS technology. I was responsible for the energy harvesting unit which included a 1.8V Low Drop-Out (LDO) regulator, a 1.2V bandgap reference, an RF rectifier, an off-chip antenna, and a backscattering communication module. I also engaged in regular discussions with the group members on the design of all other analog blocks.