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We present the experimental demonstration of a traveling-wave tube (TWT) power amplifier operating in the ${W}$ -band (75–110 GHz) frequency range. The device is based on a serpentine waveguide (SWG) amplification circuit, a slow wave circuit type capable of high power and broad instantaneous bandwidth in the upper millimeter-wave range. A 20 kV, 140-mA round solenoid-focused electron beam powers the device. At 20 kV, we measure 215 ± 2 W peak RF output power at 93 GHz with 20.1 ± 0.15 dB saturated gain, pulsed at 0.1% duty. We observe 10-GHz instantaneous amplification bandwidth at 100-W minimum output power, covering the range 88–98 GHz. Operating at 20.8 kV, the TWT produces 285 ± 3 W at 91 GHz with 22.4 ± 0.15 dB gain, and 7 GHz, 3-dB bandwidth. The peak electronic efficiency measured is approximately 10%.

As is well known, a roadblock to realizing the full potential of GaN high-electron mobility transistors (HEMTs) for power amplifier applications is the peaked nature of the transconductance and the resulting power-gain roll-off exhibited by these devices. Motivated by promising work on compositionally graded HEMT designs, in this paper we explore this design solution using the numerical device simulation. Among other things, we examine the consequences of saturation velocity, grading profile, alloy scattering, and device scaling. In addition, lumped element modeling of the large-signal behavior is carried out to assess the power amplifier performance. We also compare the graded approach with another known method of linearity improvement in which the source resistance is reduced. In general, we find much to recommend in the graded-channel approach, especially for gate lengths greater than about 100 nm.

We present the fabrication and electromagnetic testing of serpentine waveguide traveling-wave tube amplifier circuits operating in the W-band (75-110 GHz) and D-band (110-170 GHz) frequency ranges. The circuit structures were fabricated in a split-block configuration in a photopolymer material using a commercial digital light processing (DLP) 3D printer and, subsequently, covered with a conducting layer by Au sputtering and Cu electroplating. Two-port S-parameter measurements of the W-band circuit demonstrate a transmission band from ~87-104 GHz, with a 26.7-dB return loss and a 0.55-dB insertion loss measured at 95 GHz. The D-band circuit demonstrates a transmission band from ~139 to 145 GHz, with a 21.5-dB return loss and a 2.4-dB insertion loss measured at 140 GHz.

We report on fabrication techniques for creating vacuum electron (VE) circuits from 30 GHz to 300 GHz. for devices up to 300 GHz, micro-CNC machining appears suitable.

We present fabrication and testing of RF components for a W-band serpentine waveguide TWT. Broadband ceramic RF windows and loads exhibit reflection lower than −20 dB across the TWT operating band, nominally 87–100 GHz. End-to-end cold test of the entire tube assembly, including interaction circuit, shows a clean passband better than −15 dB, in agreement with simulation. We discuss details of the fabricated components and electromagnetic cold test results.

When GaN HEMTs are used in power amplifier applications, their performance falls well short of ideal due to power-gain roll-off that results from having a peaked transconductance characteristic. A promising design solution involves compositionally grading the channel, and we here formulate a numerical device model to explore this approach that couples linear electroelasticity, diffusion-drift transport with new mobility models, and density-gradient theory. Lumped modeling of the large-signal behavior is also developed to explore the power amplifier performance. Preliminary results presented here indicate that the graded-channel idea has value, especially for gate lengths greater than about 100nm.

Millimeter and sub-millimeter wave vacuum electronic devices have been of great interest for a wide variety of applications, but fabrication of the sub-wavelength structures has been a persistent challenge. We present and compare fabrication approaches including CNC micromachining, 3D printed mold electroforming (3D PriME), and UV-photolithography for creating traveling wave tube circuits at 35, 95, 140 and 233 GHz, along with results. To date, CNC micromachining has yielded the best results up to 140 GHz.

We demonstrate 3D-printed mold electroforming (3D-PriME) fabrication of a W-band serpentine waveguide TWT circuit. The method allows the creation of a solid copper circuit, suitable for a vacuum electron device, beginning with a plastic inverse mold built on a commercial 3D printer. We present details of the fabricated circuit and electromagnetic cold test results.

The microwave dielectric properties of new aluminum-nitride-based microwave absorbing ceramic composites for use in vacuum electronics and particle accelerators are studied in the 0.5-18 GHz frequency band. The various physical mechanisms contributing to the dielectric loss and dispersion are identified. Thermal conductivity values in these materials are also reported, which in several of the formulations rival those of BeO-SiC composites.

Initial work is presented on novel monolithic integration of key components for 140 GHz traveling- wave tube arrays.

We present the application of UV-LIGA and CNC micromachining to development of a 233 GHz hybrid serpentine waveguide Traveling Wave Tube amplifier. Results compare achievable resolution and tolerances, and electromagnetic cold testing measurements. Output power from the TWT amplifier is predicted to exceed 140 W from a 20 kV, 124 mA electron beam.

We demonstrate a method for fabricating upper millimeter-wave TWT circuits and passive components, based on additive manufacturing and copper electroforming. The method allows the creation of a solid copper circuit, suitable for high-power vacuum electronic devices, beginning with a plastic inverse mold built on a commercial 3D printer. We present progress on W-band serpentine waveguide circuits fabricated in copper by this 3D-printed mold electroforming (3D-PriME) process.

We present the first vacuum electronic traveling wave amplifier to incorporate an interaction circuit fabricated by ultraviolet (UV) photolithography and electroforming, demonstrating over 60 W of output power at 214.5 GHz from a 12.1 kV, 118 mA electron beam. The tube also achieved an instantaneous bandwidth of ${\sim}{\rm 15}~{\rm GHz}$ in $G$ -band in the small signal regime. The all-copper circuit was fabricated in two layers using a UV-transparent polymer monofilament embedded in the photoresist to form the beam tunnel prior to electroforming. Effects arising from fabrication errors and target tolerances are discussed. This microfabrication technique and demonstration paves the way for a new era of vacuum electron devices that could extend into the 1–2 THz range with advances in high-current-density electron guns.

The design, fabrication, and electromagnetic cold testing results of an all-copper grating circuit intended for a G-band sheet-beam traveling-wave amplifier are presented. Fabrication was carried out via ultraviolet photolithography (UV-LIGA) using the SU-8 photoresists. Two cold test methods used to characterize the microfabricated circuits are reported and reveal excellent agreement with simulations. This type of all-copper grating also shows potential for use as a high-average-power sharp-cutoff filter.

We present development progress for a 233 GHz hybrid serpentine waveguide TWT amplifier employing microfabrication techniques based on UV-LIGA. Maximum output power from the circuit is predicted to exceed 140 W from a 20 kV, 124 mA electron beam. Updates include progress of the circuit microfabrication and testing, window tuning, and electron gun.

Microwave absorbing composites are of considerable importance in vacuum electronics, and therefore present an opportunity for further research. The synthesis and complex dielectric properties of new types of transition metal spinel-based microwave absorbing composites with unusual frequency responses are described. Also presented are improved dielectric measurements of more traditional BeO-SiC absorbers.

Fabrication of slow-wave circuits for TWTs is challenging at frequencies in the upper millimeter-wave range, due to size and geometry limitations of available methods. We describe fabrication techniques being developed for mmW circuits based on microfabrication and additive manufacturing. We present progress on W-band serpentine waveguide circuits fabricated by UV-LIGA, 3D printing, and CNC machining.

Nonlinear memory effects in a klystron and their impact on digital communications are investigated using a time-domain physics-based model. The simulation results are compared to an idealized block model based on the frequency response and amplitude/phase drive curves typically used in system design with vacuum electronic amplifiers. Significant departures in transient behavior are noted in the physics-based model in comparison to the block model when the klystron is at or near saturation, provided that the signal bandwidth is simultaneously large ( ges ~65% of the klystron output cavity bandwidth). Such nonlinear memory effects exist for pure amplitude, pure phase, and mixed transients of both the step and ramp variety. The effects of these nonlinear phenomena on 16-state phase-shift keying (16-PSK) digital communications waveforms (with preequalized symbols) are examined using symbol constellation diagrams and symbol error rate (SER) plots. Operation at saturation with signal bandwidths of 32%, 65%, and 93% of the klystron output cavity bandwidth, for a bit-energy-based signal-to-noise ratio of 18 dB, yields SER values of 2.0 times 10-5, 2.3 times 10-4, and 2.7 times 10-3 , respectively, in comparison to the ideal 16-PSK value of 1.1 times 10-5.

This paper presents 3-D thermal simulation studies of GaN-on-SiC monolithic microwave integrated circuits (MMICs) containing multifinger micrometer-scale high electron mobility transistors (HEMTs). The heat spreading effect of HEMT source, gate, and drain metallizations on peak structure temperatures is examined. The impacts of a realistic die attach material and rear-of-die heat transfer coefficient on structure temperatures, and in particular on temperature nonuniformity, are examined. Variable gate finger spacing, in which the gate spatial positions are described by polynomials as a function of gate number, is investigated as a means for optimizing the temperature uniformity from gate-to-gate. A thermal simulation code with a parametric MMIC geometry-based mesh generator and a deformable mesh consistent with sequential movement of gate finger positions during optimization is employed for all of the studies. The code is multiscale with a sufficient resolution range to handle a multifinger HEMT structure while also including the MMIC die, die attach metallization, and a realistic heat transfer coefficient associated with microchannel coolers. A variable gate pitch geometry based on an optimized cubic polynomial demonstrates considerable advantage in temperature uniformity.

Confocal μ-Raman was used to measure the operating temperatures in SiC MESFETS, AlGaN/GaN/SiC HEMT’s and 4H-SiC PiN diodes. Temperatures obtained from thermal imaging of the MESFETS compared well with those measured from Raman scattering. Operating temperatures were also obtained for large area PiN diode and it was shown that a single point at the center of the device can be used to measure the average temperature.

Experiments on removing high heat fluxes from GaN-on-SiC semiconductor dies using microchannel coolers are described. The dies contain an AlGaN/GaN heterostructure operated as a direct current resistor, providing a localized heat source. The active dimensions of the heat source are sized to represent the spatially-averaged heat flux that would appear in microwave power amplifiers. A wide variety of microchannel materials and configurations are investigated, allowing a comparison of performance and the resulting GaN temperatures. Silicon and AlN microchannel coolers exhibit good performance at lower power densities (1000–1200 W/cm2 over 3 × 5 mm2 to 2 × 5 mm2 active areas). Polycrystalline chemical vapor deposited (CVD) SiC microchannel coolers are found to be extremely promising for higher power densities (3000–4000 W/cm2 over 1.2 × 5 mm2 active areas with 120 °C GaN temperature). A hybrid microchannel cooler consisting of low-cost CVD diamond on polycrystalline CVD SiC exhibits moderately better performance (20–30%) than polycrystalline CVD SiC alone.

The vast preponderance of U.S. radar transmitters today use vacuum electronic amplifiers, spanning the spectrum from UHF to EHF. Enhancements to performance, reliability, and cost of ownership are being applied continuously to these systems; routine in-service life extensions mandate continuing vacuum electronics research and development to support system needs for the foreseeable future. In addition, exciting advances in vacuum electronics will provide dramatic improvements in millimeter-wave radar resolution, broadband low-noise power at microwave frequencies, compact high power sources operating at lower voltages, and life-cycle cost improvement. Recent progress in key enabling technologies, e.g., advanced device modeling and micro-fabrication, is expected to continue. This paper reviews the status and trends of vacuum electronics, with selected applications emphasizing recent advances in device performance in the microwave regime: multiple-beam klystrons (MBKs), microwave power modules (MPMs), and gyro-amplifiers in the millimeter-wave regime.

The principal challenge for creating vacuum electron devices in the millimeter-wave (mmW) frequency range is accurate fabrication of slow-wave circuits and other electromagnetic features with tight tolerance. Ultraviolet Photolithography and Electroforming (UV-LIGA) techniques are presented that allow tight tolerance control for slow wave circuits for the mmW and sub-mmW bands. We show how these techniques were applied at the W- and G-bands.

This paper presents finite-element thermo-mechanical simulation studies of microchannel-based techniques to cool AlGaN/GaN high electron mobility rf transistors grown on SiC substrates. A number of problems are considered, including standard thickness dies on both oxygen-free-high-conductivity (OFHC) copper and AlN microchannel coolers, as well as thinned dies on a hybrid diamond/silicon microchannel cooler. The active device sizes and cooling strategies selected are relevant to X-band (/spl sim/10 GHz) amplifiers dissipating 50-100 W of steady-state waste heat. The effects of die attach materials on device temperature and mechanical stresses are studied. The plastic yielding behaviors of the die attach material and other metallic portions of the package are incorporated into the analysis. The removal of 100 W of steady-state waste heat in an example X-band compatible device is found to be consistent with 140-185/spl deg/C maximum transistor junction temperatures and tolerable mechanical stresses.

The broadband (10 kHz–18 GHz) complex dielectric permittivity of electrically lossy aluminum silicate–pyrolytic carbon composites is studied as a function of carbon content. The composites are made from a commercial machinable ceramic that is treated by oxalic acid refluxing, followed by sucrose pyrolysis within the open porosity. The resulting composites have a slightly percolating conductor configuration that exhibits non-Debye dielectric properties. Such composites are useful as microwave absorbers in vacuum electronic amplifiers, for suppressing spurious oscillations, and for bandwidth control. Four contributions to the dielectric response were observed and analyzed. These consist of a direct current conductivity contribution that is significant only at frequencies below 1 MHz, an irregular low-frequency relaxation, a strong non-Debye, high-frequency relaxation with its upper portions extending into the microwave regime, and an underlying, broadband loss consistent with a universal dielectric response. The microwave behavior is dominated by changes in the position, intensity, and Cole–Cole exponent of the high-frequency relaxation as the carbon content increases.

We present electromagnetic cold-test measurements of BeO ceramic pillbox vacuum windows for a 220-GHz traveling-wave tube amplifier. Transmission and reflection measurements show better than 20 dB return loss over a 25 GHz bandwidth, with band centers in the range of 212-225 GHz. We observe tuning of the window response as the circular waveguide length is changed. High-power testing is performed at 2.5 W, 100% duty at 218 GHz.

Reliable and accurate temperature measurement during microwave processing of ceramic bodies is controversial. Although thermocouples are routinely used in conventional thermal furnaces, their presence in microwave furnaces can locally distort the electromagnetic field, conduct heat away from the sample, induce thermal instabilities and microwave breakdown, and lead to serious measurement errors. These thermocouple effects have been studied and found to be more pronounced in low- and medium-loss ceramic materials. To decrease the thermocouple effects during the processing of advanced ceramic materials, an optical, noncontact temperature sensing system has been developed, calibrated, and incorporated into a computer-controlled microwave furnace.

Current amplifier research at the Naval Research Laboratory Vacuum Electronics Branch emphasizes techniques to extend the bandwidth and average power capability of gyro devices for millimeter wave radar applications. This paper will discuss the implementation of a wideband high-gain gyro-traveling wave tube amplifier design, with a measured peak output power of 78 kW, gain /spl sim/60 dB, and a 3-dB bandwidth of 4.2 GHz (12%) at 52 kW in K/sub a/-band. The 3-dB saturated bandwidth at 70 kW is 6 GHz (17%), which is also the instantaneous bandwidth with appropriately tailored input power (e.g., gain equalizer). The amplifier operates in the TE/sub 11/ mode and for stabilization employs a high-average power compatible diffractive loading technique.

This paper describes the detailed design of an eight-beam electron gun for use in S-band multiple-beam amplifiers operating in the fundamental mode. The gun operating voltage is 45 kV with a total beam current of 32 A, evenly divided among the beamlets. Each individual beam has a perveance of 0.42 mpervs making a total beam perveance of 3.35 mpervs. The optimized electron gun is singly convergent using a four-fold symmetry with the four inner and four outer emitters interlaced 90/spl deg/ apart. The emitter current density has been kept below 10 A/cm/sup 2/ (space-charge limited). The cathode is magnetically shielded and the longitudinal magnetic field in the interaction region is in the range of 1.1-1.8 kG. The design of the magnetic focusing system minimizes beam corkscrewing as well as electron interception on the tunnel walls. Beam optics simulations of the gun indicate excellent beam transport characteristics with a final beam-to-tunnel radial fill factor of less than 0.45. The primary computational tools used in the design process were the three-dimensional gun code MICHELLE, and the magnetostatics code MAXWELL-3D.

In nearly any application of a microwave tube, noise characteristics are important figures of merit. This paper reviews and presents new results of recent studies of such noise. The areas discussed are ion noise in linear beam tubes, one of the oldest studied noise phenomena, and electron noise in gyroklystrons, one of the newest areas of interest.

The gyro-traveling wave tube (gyro-TWT) is a microwave amplifier with simultaneous high power, high frequency, and broad bandwidth capabilities. Techniques for providing a controlled loading of the TE/sub 01/ cylindrical-guide operating mode of a 35 GHz gyro-TWT using monolithic, lossy ceramic structures are presented. The loading scheme, which also suppresses spurious backward-wave oscillations in the TE/sub 11/, TE/sub 21/, and TE/sub 02/ modes, is based on a sequence of alternating ceramic cylindrical shells and metal rings to form the electron beam tunnel. Design techniques for achieving optimal performance and methods for reducing the sensitivity to temperature-induced variations in ceramic dielectric properties are presented.

The results of a focused program to develop high-power W-band gyro-amplifiers, which culminated in the demonstration of record average output powers from amplifiers in this band, are described. Following an experimental and theoretical study of low-duty prototype amplifiers, two high-average power devices were designed, built, and demonstrated. The first high-average power amplifier achieved 10.1-kW average output power at 33% efficiency in the TE/sub 0.1/ mode at 93.8 GHz. The instantaneous bandwidth was 420 MHz and the saturated gain at the 10.1-kW point was 32 dB. The second high-average power gyroklystron, designed for improved bandwidth, demonstrated 10.2-kW average power at 31% efficiency with 700-MHz instantaneous bandwidth and 33-dB saturated gain. The measured results of the low-duty prototype amplifiers and the high-average power gyroklystrons are described in detail. In addition, theoretically predicted results for a high-average-power W-band gyrotwystron amplifier, which is currently in construction, are presented.

The design and experimental study of a 35-GHz gyrotron-traveling-wave tube (gyro-TWT) amplifier operating in the circular TE/sub 01/ mode at the fundamental cyclotron harmonic are presented. The interaction circuit in this experiment consisted of a new type of ceramic loading that provided the required loss for stable operation. A saturated peak power of 137 kW was measured at 34.1 GHz, corresponding to a saturated gain of 47.0 dB and an efficiency of 17%, with a -3-dB bandwidth of 1.11 GHz (3.3%). Peak output powers in the range of 102.1 to 148.6 kW with -3-dB bandwidths of 1.26 and 0.94 GHz, respectively, were measured by varying the operating parameters. The gyro-TWT was found to be zero-drive stable at these operating points, demonstrating that ceramic loading is a highly effective means of suppressing spurious oscillations in gyro-TWTs. This type of ceramic loading has the added advantage of being compatible with high average power operation.

Drive Induced Oscillations (DIO) manifest themselves as spurious oscillations at frequencies close to the edges of pass-band of periodic structure in vacuum electronic devices operating in the large signal regime. DIO in coupled cavity TWTs (CC-TWTs) is most known effect and it has been extensively studied experimentally1 since it is the major limiting factor of achievable power of wide band CC-TWTs. However, DIO appearance is not limited to CC-TWTs. Modeling of DIO both numerically and analytically is challenging problem due to strong non-linear electron beam bunching and severely different built-up times for processes at operating and DIO frequencies2. We are presenting a new multi-frequency hybrid approach to DIO modeling implemented in 2D design code TESLA-CC3 and discussing advantages and limitations of this approach. The comparison between simulated and measured1 onsets of DIO in CC-TWTs shows very promising agreement.

The design of a traveling-wave tube (TWT) amplifier chain capable of 2.5kW of peak RF output power and > 1.5 kW of power over the frequency band of 92 – 100 GHz will be presented. This amplifier configuration is comprised of a driver TWT and two serpentine TWT power boosters, which are cascaded in series. The driver TWT is driven by a 122 mA, 20 kV electron beam and is expected to yield an RF peak power of 245 W with >100 W of power over a 7 GHz band-width [1]. This driver tube is currently under development [2]. The booster amplifiers are driven by much more intense 533 mA, 20 kV electron beams formed via a novel beam forming approach. The beam is focused by a solenoidal magnetic field of 6 kG in a 420-µm diameter beam tunnel.

There is a strong need for new types of traveling wave tubes (TWTs) in W-Band with improved power-bandwidth characteristics compared to traditional helix and coupled-cavity configurations. Three classes of alternative slow-wave structure for such TWTs are presently being investigated. The first is a dielectric TWT, which uses an annular dielectric liner surrounding the electron beam. It has been extensively modeled in the large-signal regime using an axisymmetric particle-in-cell code. A design using a 26 kV, 100 mA, 0.36 mm diameter beam inside a moderate dielectric constant liner (90% fill factor, 5.1 cm long) has been completed, and simulations indicate that it is capable of producing 115 W output power at 94 GHz with 10.3 dB large signal gain and a half-power bandwidth of 6 GHz. Extensive parametric studies will be presented. A second class of TWT, based on an all-metal serpentine waveguide geometry, has also been designed and thoroughly simulated with the large-signal particle-in-cell code Neptune. Using a 20 kV, 122 mA beam, an output power of 245 W at 95 GHz is predicted from a two-stage device, with a large signal gain of 30 dB and a half-power bandwidth of 5 GHz. When a variable input power (not exceeding 1 W) is allowed via equalization techniques, greater than 100 W of output power is predicted over the 92–99 GHz frequency range. Based on the highly encouraging simulation results, this serpentine-waveguide TWT is being fabricated for experimental hot tests, using multi-layer ultraviolet lithography and electroforming methods to fabricate the slow-wave structure. A third type of slow wave structure, which resembles a cavity-loaded helix, is presently being investigated with electromagnetic finite-element solvers to determine its dispersion characteristics. The essential idea is to use cavity loading (resonant slots or stubs) along a helix to further slow down the electromagnetic wave, which allows a coarser helix pitch than would normally be possible at W-band. This type of structure could potentially enable TWTs with operating characteristics intermediate between those of ordinary helix TWTs and coupled-cavity TWTs. Initial studies indicate a complicated mode spectrum with a variety of slow-wave, fast-wave, and coalesced modes; their variation with respect to geometry will need to be understood to optimize bandwidth and maintain stability.

Designs and simulated performance for W-band traveling wave tubes are presented for three slow wave structure types (dielectric, serpentine waveguide, and cavity-loaded helix). Output powers are 120 and 245 W at 94 GHz for dielectric and serpentine, respectively, with 5-6 GHz bandwidth (9 GHz in serpentine with equalization).

We present development plans for a 233 GHz, serpentine waveguide vacuum electron amplifier employing an embedded monofilament microfabrication technique based on UV-LIGA. Output power from the circuit is predicted to exceed 140 W in conjunction with a newly developed electron gun at 20 kV and 124 mA. Design, fabrication and integration progress will be discussed.

We report characterization of low-loss MgO-TiO 2 system ceramic materials in the 75-110 GHz (W-band) and 0.5-18 GHz frequency ranges. Measurements of the complex permittivity are used to study the dielectric constant, loss tangent, and DC conductivity (low-frequency) behavior of the materials for application in millimeter-wave vacuum electron devices. We investigate the effects of varying ceramic synthesis process parameters on the rf material properties.

The discrete nature of the electron charge gives rise to what is known as shot noise on electron beams. In this paper the spectrum of shot noise fluctuations on a spiraling electron beam is calculated. Particular attention is paid to the collective effects of the electron beam that can either decrease or increase the noise level. Shielding of the electron charge tends to decrease the noise level while the electrostatic cyclotron maser instability tends to increase the noise level. The formulation describes the competition of these effects for a radially inhomogeneous beam in a nonuniform magnetic field. Results of the calculations are compared with recently obtained experimental measures of the noise spectrum. The experiments indicate that noise is suppressed by collective effects. The calculations indicate that, while suppression is possible for a sufficiently cold electron beam, it is not expected for a beam with several percent velocity spread. The observed suppression is thus due to some collective ef...

The dependence of the permittivity of porous alumina on the microstructure was studied. Three different algebraic mixing laws inaccurately predicted the measured effective permittivity of the three-phase material, which was alumina, air, and water. Finite-difference electrostatic simulations of physically realistic microstructures accurately predicted the experimental results. The electrostatic simulations also provided physical insight into the arrangement of water in the material and its significant effect on the effective permittivity.

The effect of microstructure on the complex permittivity of alumina composites was studied. Three different algebraic mixing laws (Maxwell–Garnett, effective medium approximation, and the Landau–Lifshitz–Looyenga formula) inaccurately predicted the measured complex permittivities of alumina/silicon carbide and alumina/copper oxide composites. The imaginary part of the complex permittivity of the four-phase composites depends significantly on the absorbed water and microstructure. Accurate calculations require that the microstructure of the composite be examined and incorporated into the electrostatic model. Incorporating the general physical characteristics of the composites enabled a three-dimensional electrostatic model to accurately predict the permittivities of four-phase composites with different microstructures.