Characteristics of a four element gyromagnetic nonlinear transmission line array high power microwave source Free

Originally, nonlinear transmission lines (NLTLs) were operated exclusively as pulse sharpening devices utilizing spin reversal of the material’s magnetic domains.¹ However, it was found that significant oscillations, as well as an order of magnitude reduction in pulse risetime, could be produced by manipulating the NLTL to induce gyromagnetic precession of the material’s magnetic moments.^2–4 So far, continuous media gyromagnetic NLTLs, out of all types of NLTLs, have produced the highest power oscillations (gigawatt) while also achieving the highest emission frequency (5 GHz).^5,6

The highest power experiments using gyromagnetic NLTLs were conducted at the Institute for High Current Electronics (IHCE) in Tomsk, Russia where peak powers reached above 1 GW at 1.2 GHz using a two element array.⁷ Pulse repetition frequencies (prf’s) of around 10 Hz were achieved at these power levels. Additionally, a higher prf was achieved with lower power: 200 Hz, 1000 shot pulse train, 260 MW RF power at 1.2 GHz.⁸ The power emitted in these experiments rivals that of vacuum tube based high power microwave (HPM) sources, and the possibility of beam steering capability for radar applications⁹ makes it a viable solid-state successor. However, some inherent drawbacks to this high power NLTL HPM source include difficulty in achieving high pulse repetition frequencies and lower emission frequency (L-band) due to the radially larger coaxial geometries.

Work done at the Center for Pulsed Power and Power Electronics (P³E) at Texas Tech University, utilizing NLTL technology in an effort to produce a compact and portable HPM source, has led to the highest frequency emission of any NLTL in the C-band as well as extreme prf capability (65 MHz) for short bursts using photoconductive solid-state switching.¹⁰ Inherent drawbacks to this smaller NLTL system include relatively underpowered output emission and peak electric field irradiation. In an effort to mitigate these deficiencies, experiments on implementing an array of NLTLs were conducted to demonstrate an increase in output power, taking advantage of greater directivity and gain. The first NLTL driven antenna array began with Bragg and Reale with a two element array¹¹ and more recently continued by Romanchenko et al. where a two element array was also implemented.⁹ 

With the results shown in Sec. IV, the system presented here is comparable, in terms of RF power, to another solid-state NLTL HPM source by Seddon¹² where nonlinear lumped element transmission lines (NLETLs) were used to achieve 20 MW of emitted RF power at 1 GHz, operating at a prf of 1 kHz.

The NLTL described in this system produces oscillations due to gyromagnetic precession. Two necessary requirements must be met before precession can occur. First, an incident pulse with sufficient amplitude and risetime (dV/dt) must be injected into the line in order to generate an electromagnetic shockwave (pulse) that will propagate down the line. The pulse’s leading edge generates a magnetic field and rapidly saturates the magnetic medium. The crest following the leading edge travels with a higher velocity in the saturated medium and “catches up” to the leading edge. This results in both pulse sharpening and voltage overshoot. Oscillations are formed only when precession occurs, and these undulations are superimposed on the incident pulse. Since a pulse’s rising edge may not be accelerated to the point of an infinite slope, the limiting factor is the material’s relaxation time or switching time;¹³ subsequently, this is also what determines the maximum RF frequency possible for a given ferrite material in an NLTL HPM system.

Second, orthogonal magnetic fields, with respect to bias and injected pulse, must interact. This is accomplished in this system through an externally applied axial bias field via solenoid inductor (assuming coaxial geometry and cylindrical coordinates) and an azimuthal field generated from the input pulse. The bias places the magnetic domains of the material in a state of full or partial saturation in the axial direction. Then, as an incident pulse propagates down the line, the azimuthal magnetic field forms, rapidly saturating the material in the azimuthal direction, and the magnetic moments precess or switch in a coherent manner around an effective magnetic field (H_eff) which is mainly comprised of the axial and azimuthal magnetic fields. The precession is damped because the magnetic moments eventually align with H_eff, and as a result, the precession ceases. Both the voltage amplitude of the incident pulse and axial bias determine the output frequency, and since the charging voltage is held constant, axial biasing is adjusted to control the output frequency.

Other components of (H_eff) are the demagnetizing field, exchange field, and anisotropy field. The demagnetizing field opposes the field generated by the magnetic moments and may be represented as circular eddy currents; the anisotropy field is present from inconsistencies within the ferrite and also between butted ferrites; and lastly, the exchange field is a result of the material’s many finite magnetic dipoles acting upon one another to push themselves into alignment with the application of an external magnetic field. Exchange fields are indicative of ferrimagnetic, ferromagnetic, and ferroelectric materials. The anisotropy field and exchange field are negligible and may be ignored due to the high isotropic nature of the ferrite used in the experiments conducted within this system, and the coherent (unison) motion of the magnetic domains greatly reduces the effects of the exchange field. The magnetic dynamics taking place within the ferrite may be accurately represented by taking into account only the external bias, pulsed azimuthal, and demagnetizing fields as shown from simulations performed by Dolan et al.,^13–15 

The Landau-Lifshitz expression for gyromagnetic precession may be seen in Eq. (1). This equation represents the magnetic dynamics taking place within the ferrite that produces pulse sharpening and RF oscillations. The first term describes the precession of the magnetic moments around H_eff, and the second term describes the damping action which eventually ends the precession and relaxes the magnetic moments to H_eff. γ represents the gyromagnetic ratio which is equal to −2.21 (s ⋅ A/m)⁻¹, and α represents the empirical damping factor which is typically a small percentage for suitable materials. M_s is the magnetization magnitude while the magnetic material is in saturation.

Desirable characteristics in a ferrite include high resistivity to reduce eddy currents, low dielectric and magnetic loss tangents, and high initial permeability and saturation magnetization.¹⁶ The longer a lossy transmission line, the more a propagating wave is reduced; however, there exists an ideal line length for pulse sharpening applications where the risetime of the propagating shockwave has reached its smallest value.¹⁷ Past this length only a lossy linear effect is imposed on the propagating wave. At the time of writing this manuscript, there exists no theoretically derived optimum line length only empirical results for NLTLs in RF generation applications.

The prime power source for the system is an 8 kW, constant current, negative polarity, high voltage supply with a maximum output of −50 kV. This charges a 5.2 nF capacitor bank, which is integrated into the main discharge switch, to −40 kV in approximately 800 μs. The main discharge switch is a center pin trigatron spark-gap where the electrode spacing is adjustable and ports are present for gas flow through the gap. Pressurized dry air along with electrode spacing sets the spark switching conditions, and the flowing air removes ionized particles to enable rapid succession operation. The spark-gap is custom made in-house and may be seen in its proper place in the system diagram in Fig. 1.

The high power switch is closed using a high voltage pulse trigger generator. This trigger generator, which is referred to in the following as simply the “pulser,” is what allows the system to fire in rapid succession. The main characteristics of the pulser output are 20 kV peak, 20 ns 10%-90% risetime, modular design for adjustable output voltage or current, electrical isolation from the load, RF shielding, and a maximum prf of 7 kHz. See Ref. 18 for a detailed description of the pulser. The only differences with the pulser used in this system as opposed to that described in the reference are insulated-gate bipolar transistors (IGBTs) in place of thyristors and resizing of the magnetic pulse compression circuitry to optimize the new discharge circuit. The change from thyristor to IGBT was done to decrease the risetime of the output pulse with the drawback being a lower current discharge capability. High voltage MOSFETs were also implemented yielding the fastest risetimes but would eventually fail from over-current operation. Positive polarity output from the pulser was chosen to compliment the negative charge of the capacitor bank. In the work done by MacGregor et al., it was shown that negative charging and positive triggering produced the fastest breakdown times due to the formation of positive polarity streamers.¹⁹ 

Once the spark-gap switch has closed, the energy stored in the capacitor bank is discharged through a plasma channel into the NLTLs via the adjacent electrode and symmetrical aluminum current distribution plate. The distribution plate divides the input pulse four ways and excites each line equally. The incident pulse first reaches a 38 cm long NiZn NLTL delay line. This delay line NLTL is externally biased by an encompassing solenoid inductor to impose a propagation time on the incident pulse in order to achieve coherent irradiation from multiple outputs. With a fixed charging voltage of −40 kV, and using a NiZn ferrite, the delay line is capable of producing a maximum of 1.5 ns of delay when swept from 0 to 25 kA/m. Utilizing NLTLs as dynamic delay lines is not a new concept,¹⁵ although it is only recently that it has been implemented into HPM systems.^9,11,20,21 The external biasing affects the permeability of the material, and this, in turn, affects the propagation time of the line. The longer the line is, the greater the possible time delay. A sister paper was written comparing different ferrite materials in a fixed line length to determine which had the greatest possible delay as well as consistency.²² The NiZn1 material used in that paper is also used here. The delay line and axial biasing solenoid inductor may be seen in their proper place in Fig. 1.

Fig. 2 depicts the basic geometry of the different layers that makeup both the delay and main NLTLs. The inner and outer conductors are both brass, and the ferrites fit snugly over the inner conductor rod. Both the delay and main NLTLs use the same NiZn1 ferrite. A layer of Kapton® tubing, 264 μm thick is slid over the ferrites as the first of two insulators. The last insulator is pressurized sulfur-hexafluoride (SF₆) gas filling in the remaining space. Encompassing the NLTL is the solenoid inductor which biases the ferrites with an axial magnetic field as DC current passes through the inductor. Fig. 2 is an accurate representation of both the delay and main NLTLs as well as the solenoid inductor; however, its dimensions are not to scale. The delay and main NLTLs and the solenoid are custom made in-house.

After the pulse exits the delay NLTL the main 76 cm NLTL is excited. This NLTL is externally biased to emit whatever frequency the user desires in the span from 2 to 4 GHz. After gyromagnetic precession, the waveform exiting the main line has been transformed into microwave frequency oscillations set by the user. These are measured by a custom made “in-line” D-dot probe that is used to measure voltage in the line through capacitive coupling to the inner conductor. The measurements taken from this probe help the user to determine what biasing levels should be applied to each delay line to achieve phase alignment. Eight 1500 W programmable DC supplies bias the lines through a large solenoid coil placed around the NLTL. These supplies have a maximum output current of 38 A equating to 45 kA/m of magnetic field bias, and typical bias values for delay range anywhere from 5 kA/m to the maximum. These supplies also monitor themselves for internal and external errors, and these errors are sent to the control system for the user to readily observe. The main NLTL, solenoid inductor, and D-dot probe may be seen in Fig. 1.

The overall NLTL HPM system is depicted in Fig. 3, and Table I gives an overview of all the described subsystems therein excluding probes and diagnostics.

Since a TEM horn antenna is used in this system, a special type of conversion component must be implemented in order to transition from coaxial to parallel plate geometry. A custom made “zipper” balun is used with a linear taper of the outer conductor that opens up to parallel plate with an appearance similar to a zipper. Due to this gradual tapered transition, the impedance transitions very nearly continuously to match that of the antenna, minimizing reflections. Rexolite is the insulating material for the balun. More information on the “zipper” balun may be found here.²³ 

The TEM horn was chosen as the system’s radiating antenna due to its large bandwidth (1.5-4 GHz) in order to maintain the frequency agility of the NLTLs and to match the TEM waves propagating from the coaxial NLTLs. This antenna is custom made and also uses Rexolite insulation. Integrated into the end of the antenna is a RL low pass filter that shunts undesirable DC or low frequency components of the signal to minimize the chance for voltage buildup and electrical breakdown across the parallel plates. The horn and balun are shown in their proper place in Fig. 1.

A free-field D-dot probe is used to measure radiation in the far-field. The probe used has a cutoff frequency of 5.5 GHz, and its output is recorded utilizing a 12 GHz, 40 GSa/s digital oscilloscope. The “in-line” D-dot probes are sampled by a 50 GHz, 160 GSa/s digital oscilloscope to accurately resolve the spacing between NLTL lines for phasing purposes. And, lastly, the spark-gap voltages are sensed by a high voltage probe which is measured by a 600 MHz, 4 GSa/s digital oscilloscope to determine if the spark-gap is closed when it was triggered.

The control system has a LabVIEW based graphical user interface. Controllable parameters include individual biasing for each delay and main NLTL, charging time of the prime power high voltage source, and the prf of the system. LabVIEW communicates with a cRIO module which reads and writes logic pulses to manipulate and monitor the system. The cRIO writes to the current supplies’ registers to enable and set their output values. The logic controlling the prime power source simply enables the device to charge, the duration of which is set by the user. The charging voltage is set on the power supply itself. Lastly, the cRIO interfaces with an electrical to optical board that sends the logic pulses to the pulse trigger generator via fiber optic cables.

While field mapping tests were conducted, the NLTL system was elevated 3 m off of the ground in an effort to reduce ground reflections measured at the receiving antenna. Centerline tests were performed as well as steered. The free-field D-dot probe, seen in Fig. 1, has a vertical orientation that matches the linear polarization of the TEM horn antennas in the y axis. The coordinate axes as well as the method for field mapping are illustrated in Fig. 4. Some terms that will be used in Sec. IV are defined here: more than one measurement taken along the z axis (direction of propagation) will be known as a vertical measurement, and measurements along the x axis (H-plane) will be known as horizontal measurements. Steered beam measurements are taken at an angle of ±16.7° represented by the red lines in Fig. 4 with the normal axis being represented as the blue line. Taking measurements normal to the directivity vector of the beam is essential for finding the spot-size in space and RF power emitted.

Spot-sizes and subsequent power calculations are the primary results shown in this section, both centerline and steered. For the field maps shown in this section, each data point represents an average of the peak electric field over 100 shots. The prf of this 100 shot burst is 100 Hz. Although the system is capable of operating at 1 kHz, 100 Hz was implemented to achieve more consistent results for the purpose of data acquisition as well as lessened stress on the insulation of the NLTLs. The method for phasing the array for either steered or straight ahead scenarios is to select one line as the reference, place the probe where the peak field is desired and then phase all other lines to it.

Fig. 5 is a field map of the NLTL HPM system taken 10 m from the source along the z axis and ±4 m along the x axis. A Gaussian distribution curve fit was placed on the data along with all other electric field maps.

The spot-size in Fig. 5 is approximately 680 cm full-width-half-max (FWHM) with the peak electric field around 7.8 kV/m. In order to calculate the instantaneous peak power of the beam, first the power density is found expressed by Eq. (2) in watts per meter squared,

where η₀ is equal to the impedance of free space, 377 Ω, and E(x, y) is the Gaussian curve fit of the empirical data expressed by Eq. (3) in Volts per meter,

where

Next, the cross-sectional area of the Gaussian shaped beam must be calculated. The assumption is made based on the design and simulations of the array that the beam is symmetrical in the E-field plane (y axis) and H-field plane (x axis). Next, the power density curve is integrated over the entire width and height of the beam yielding power in Watts. Eq. (5) expresses this operation,

where ±X and ±Y are the range of integration for the beam in the x axis and y axis. Since the beam is symmetrical, X and Y will be equal, and by setting these variables to the full width and height (±10 m each) of the Gaussian distribution, the calculated instantaneous peak RF power at 10 m is approximately 4.2 MW. The gain of the array can also be found by comparing the power density of the array to the equivalent isotropic power density as expressed in Eq. (6),

where S_array is Eq. (2) when S(0, 0) and S_isotropic is Eq. (5) divided by 4πR₀², where R₀ is equal to X. Using Eq. (6) the approximate antenna gain is 17 dB. This is on the order of the simulated antenna gain of 19 dB.

Fig. 6 is purely a vertical mapping with all measurements occurring on the z axis. It shows the reduction of the average peak electric field as the probe is moved outward from the source. Near the start of the far-field at 3 m, the peak electric field is approximately 25 kV/m, 7.5 kV/m at 10 m, and 3 kV/m at 30 m. All data points in this figure were from a single phasing of the array at 10 m.

A typical radiated waveform can be seen in Fig. 7. This is a single shot from a 100 shot burst where the system was phased on the z axis at 10 m. There are four oscillation cycles which contain all of the RF power where the peak electric field reaches approximately 8 kV/m.

The frequency characteristics of Fig. 7 are shown in Fig. 8 via fast Fourier transform (FFT). Here the primary frequency component is 3.1 GHz while the secondary frequency component is 3.5 GHz, even though the individual frequency of each line is 3.5 GHz. This shift in frequency is due to imperfect phasing and the wideband nature of the NLTL and TEM horn antenna. Additionally, a large amount of RF power can be seen in the lower frequency bands relative to the desired output emission frequency. This is to be expected with the rising and falling edges of the DC offset from the input pulse. The majority of the low frequency content from the spark-gap is shunted by the integrated high pass filter on the TEM horn, but as one can see, a significant amount of low frequency emissions still radiate out.

Fig. 9 is a steered beam at angles of ±16.7°. Here in Fig. 9, the steered beams have been placed in the same plane while maintaining their relative spacing from the z axis. Each steered waveform was measured at ±3 m normal (blue line) from the steered axis (red line) in Fig. 4.

Fig. 10 artificially removes the space offset between the steered beams while keeping them on the same plane in order to easily compare the shape and peak field qualities of each beam. The negative angle (□) beam has a peak field of 5.6 kV/m and a spot-size FWHM of approximately 5.6 m, and the positive angled (○) beam has a peak field of 5.9 kV/m with a spot-size FWHM of 5.8 m. The steered beams are nearly identical to one another. The power calculated for the negative angled beam using Eq. (5) is approximately 2.2 MW while the positive angled beam is approximately 2.4 MW. Both peak field measurements and peak power calculations are slightly lower than that of the centerline measurements as expected. This is primarily due to the static nature of the beam pattern from the individual antenna elements which limits the maximum amount of RF energy that can be combined in any given direction. Imperfect phasing of the individual NLTL’s may also play a role.

A solid-state, frequency agile, HPM system in the S-band has been demonstrated. Recorded power levels and prf are similar to those achieved by Seddon¹² using gyromagnetic continuous magnetic media NLTLs with higher output frequency and without compromising on size or power. The approximate peak power level is 4.2 MW with a peak field of 7.8 kV/m at 10 m correlating to 17 dB of antenna gain over an isotropic radiation pattern. The peak electric field of 25 kV/m is measured at 3 m, and beam steering of the array was demonstrated at ±16.7°. The steered peak electric fields are 5.6 kV/m (−16.7°) and 5.9 kV/m (+16.7°) with 2.2 MW and 2.4 MW, respectively. Although these measurements were taken with 100 shot bursts at 100 Hz prf, the system is capable of operating at 1 kHz prf.

Future work with coaxial gyromagnetic NLTLs at the Center for Pulsed Power and Power Electronics will focus on an eight element array and higher prf capability with a more consistent input than the spark-gap high voltage switch currently used to drive the NLTLs.

This work is supported by the Office of Naval Research.