## 1 Introduction  
Over the past several decades, high-power microwave (HPM) devices have transitioned from large scale laboratory systems to more practical, commercially available devices [1]. This progress has motivated the development of compact, solid-state equipment capable of generating HPM [1, 2, 3]. One such solid-state device under investigation for generating HPM is the nonlinear transmission line (NLTL) [2], which can achieve repetition rates above 1 kHz with consistent radiofrequency (RF) output [4, 5]. In tandem with their HPM generation capabilities, NLTL systems can also sharpen input pulses by using materials whose permittivity and/or permeability varies with electric field and/or magnetic field, respectively. For ferroelectric and ferromagnetic materials, the inverse relation between phase velocity and a medium's electromagnetic properties causes the crest of an electromagnetic pulse to propagate faster than the base, sharpening the pulse. HPM generation is realized by different means depending on topology. Gyromagnetic NLTLs (GNLTLs) use gyromagnetic precession to modulate incident pulses into RF waveforms as wideband sources [6]. One recent study used nonlinear coaxial transmission lines with magnesium manganese ferrite rings with a rectangular hysteresis loop to achieve a wide frequency range (-5.5-12.7 GHz) and peak microwave oscillations up to 350 kV [7]. This approach may potentially eliminate the need for an external biasing field and may achieve oscillation frequencies up to 20 GHz [7]. Another recent GNLTL system attained a maximum peak power of 110 MW at a central frequency of 1.3 GHz by periodically placing nickel zinc ferrite (NZF) saturated by an axial magnetic field produced by permanent magnets inside the NLTL [8]. More compact GNLTLs (60 cm) can generate a broad frequency spectrum from 200 MHz to S-band with RF conversion efficiency above 10% [9]. Alternatively, one may use nonlinear capacitance to modulate an input pulse and induce RF formation. While ceramic capacitors can be used, the resulting system frequencies are restricted to \(\sim\)100 MHz at high power due to parasitic inductances [10]. This has motivated the use of silicon carbide Schottky diodes to achieve frequencies up to 200 MHz [10]. Another modality leveraging nonlinear permittivity uses ferroelectric materials, such as barium titanate (BT) or barium strontium titanate (BST) [11]. An applied pulse moves an atom in the crystalline structure to another stable position, which rotates the atom's polarization vector [12,13]. The frequencies for ferroelectric NLTLs are generally on the order of tens of MHz, compared to GHz for ferromagnetic NLTLs, because the inertia of the atom in a ferroelectric line exceeds the inertia of the electron in a ferromagnetic line [14]. More recent studies have focused on hybrid NLTLs, which use both nonlinear capacitance and inductance [1]. One hybrid NLTL constructed using commercial off-the-shelf components produced RF between 55 MHz and 80 MHz for 5 kV and 8 kV pulse voltages, respectively, with 600 ns pulse durations [15]. A lumped element hybrid NLTL composed of BT dielectric nonlinear capacitors and ferrite bead inductors generated ten RF cycles with frequency \(\sim\)33 MHz for each input pulse [16], producing higher voltage modulation depth compared to NLTLs with a single nonlinear component [17]. In addition to nonlinear capacitors in the lumped element topology, other studies have assessed nonlinear resistances (as a function of voltage) with gas gap switches [18] or periodically placed high voltage silicon carbide Schottky diodes as switches [19]. An alternative approach to the lumped element topology is to construct a coaxial line made of a composite with both nonlinear dielectric and magnetic inclusions. Adjusting the volume loading of these inclusions provides tunability in both linear [20, 21, 22] and nonlinear [23] electromagnetic properties for adjusting NLTL output waveforms.