# Novel Composites for Nonlinear Transmission Line Applications

Nonlinear transmission lines (NLTLs) provide a solid state
alternative to conventional vacuum based high power microwave (HPM) sources.
The three most common NLTL implementations are the lumped element, split ring
resonator (SRR), and the nonlinear bulk material based NLTLs. The nonlinear
bulk material implementation provides the highest power output of the three
configurations, though they are limited to pulse voltages less than 50 kV;
higher voltages are possible when an additional insulator is used, typically SF_{6}
or dielectric oil, between the nonlinear material and the outer conductor. The
additional insulator poses a risk of leaking if structural integrity of the
outer conductor is compromised. The desire to provide a fieldable NLTL based
HPM system makes the possibility of a leak problematic. The work reported here develops
a composite based NLTL system that can withstand voltages higher than 50 kV and
not pose a risk of catastrophic failure due to a leak while also decreasing the
size and weight of the device and increasing the output power.

Composites with barium strontium titanate (BST) or nickel zinc ferrite (NZF) spherical inclusions mixed in a silicone matrix were manufactured at volume fractions ranging from 5% to 25%. The dielectric and magnetic parameters were measured from 1-4 GHz using a coaxial airline. The relative permittivity increased from 2.74±0.01 for the polydimethylsiloxane (PDMS) host material to 7.45±0.33 after combining PDMS with a 25% volume fraction of BST inclusions. The relative permittivity of BST and NZF composites was relatively constant across all measured frequencies. The relative permeability of the composites increased from 1.001±0.001 for PDMS to 1.43±0.04 for a 25% NZF composite at 1 GHz. The relative permeability of the 25% NZF composite decreased from 1.43±0.05 at 1 GHz to 1.17±0.01 at 4 GHz. The NZF samples also exhibited low dielectric and magnetic loss tangents from 0.005±0.01 to 0.091±0.015 and 0.037±0.001 to 0.20±0.038, respectively, for all volume fractions, although the dielectric loss tangent did increase with volume fraction. For BST composites, all volume fraction changes of at least 5% yielded statistically significant changes in permittivity; no changes in BST volume fraction yielded statistically significant changes in permeability. For NZF composites, the change in permittivity was statistically significant when the volume fraction varied by more than 5% and the change in permeability was statistically significant for variations in volume fraction greater than 10%. The DC electrical breakdown strength of NZF composites decreased exponentially with increasing volume fraction of NZF, while BST composites exhibited no statistically significant variation with volume fraction.

For composites containing both BST and NZF, increasing the volume fraction of either inclusion increased the permittivity with a stronger dependence on BST volume fraction. Increasing NZF volume fraction increased the magnetic permeability, while changing BST volume fraction had no effect on the composite permeability. The DC dielectric breakdown voltage decreased exponentially with increased NZF volume fraction. Adding as little as 5% BST to an NZF composite more than doubled the breakdown threshold compared to a composite containing NZF alone. For example, adding 10% BST to a 15% NZF composite increased the breakdown strength by over 800%. The combination of tunability of permittivity and permeability by managing BST and NZF volume fractions with the increased dielectric breakdown strength by introducing BST make this a promising approach for designing high power nonlinear transmission lines with input pulses of hundreds of kilovolts.

Coaxial nonlinear transmission lines are produced using composites with NZF inclusions and BST inclusions and driven by a Blumlein pulse generator with a 10 ns pulse duration and 1.5 ns risetime. Applying a 30 kV pulse using the Blumlein pulse generator resulted in frequencies ranging from 1.1 to 1.3 GHz with an output power over 20 kW from the nonlinear transmission line. The output frequencies increased with increasing volume fraction of BST, but the high power oscillations characteristic of an NLTL did not occur. Simulations using LT Spice demonstrated that an NLTL driven with a Blumlein modulator did not induce high power oscillations while driving the same NLTL with a pulse forming network did.

Finally, a composite-based NLTL could be driven directly by a high voltage power supply without a power modulator to produce oscillations both during and after the formed pulse upon reaching a critical threshold. The output frequency of the NLTLs is 1 GHz after the pulse and ranged from 950 MHz to 2.2 GHz during the pulse. These results demonstrate that the NLTL may be used as both a pulse forming line and high power microwave source, providing a novel way to reduce device size and weight, while the use of composites could provide additional flexibility in pulse output tuning.