The effective elastic moduli of a fluid-saturated solid containing thin cracks depend on the degree of interconnection between the cracks. Three separate regimes may be identified: (1) dry (drained), in which fluid in cracks can flow out of bulk regions of compression, (2) saturated isobaric, in which fluid may flow from one crack to another but no bulk flow takes place, and (3) saturated isolated, in which there is no communication of fluid between cracks. Transitions between these cases involve fluid flow, resulting in dissipation of energy. Relaxation of shear stresses in viscous fluid inclusions also results in dissipation. Viscoelastic moduli are derived, by using a self-consistent approximation, that describe the complete range of behavior. There are two characteristic frequencies near which dissipation is largest and the moduli change rapidly with frequency. The first corresponds to fluid flow between cracks, and its value can be estimated from the crack geometry or permeability. The second corresponds to the relaxation of shear stress in an isolated viscous fluid inclusion; its value may also be estimated. Variations of crack geometry result in a distribution of characteristic frequencies and cause Q to be relatively constant over many decades of frequency. Fluid flow between cracks accounts for attenuation of seismic waves in water-saturated rocks and attenuation observed in laboratory measurements on water-saturated rocks and partially molten aggregates. Attenuation in a partially molten upper mantle is probably due to fluid flow between cracks, although grain boundary relaxation in an unmelted upper mantle could also account for the seismic low-velocity zone. Grain boundary relaxation in the mantle may cause the long-term shear modulus to be around 20% less than that measured from seismic observations.

Viscoelastic properties of fluid-saturated cracked solids

THIS paper explores opportunities and challenges in power conversion in the VHF frequency range of 30-300 MHz. The scaling of magnetic component size with frequency is investigated, and it is shown that substantial miniaturization is possible with increased frequencies even considering material and heat transfer limitations. Likewise, dramatic frequency increases are possible with existing and emerging semiconductor devices, but necessitate circuit designs that either compensate for or utilize device parasitics. We outline the characteristics of topologies and control methods that can meet the requirements of VHF power conversion, and present supporting examples from power converters operating at frequencies of up to 110 MHz.

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Opportunities and Challenges in Very High Frequency Power Conversion

This paper presents a resonant boost topology suitable for very-high-frequency (VHF, 30-300 MHz) DC-DC power conversion. The proposed design features low device voltage stress, high efficiency over a wide load range, and excellent transient performance. Two experimental prototypes have been built and evaluated. One is a 110-MHz, 23-W converter that uses a high-performance RF lateral DMOSFET. The converter achieves higher than 87% efficiency at nominal input and output voltages, and maintains good efficiency down to 5% of full load. The second implementation, aimed toward integration, is a 50-MHz, 17-W converter that uses a transistor from a 50-V integrated power process. In addition, two resonant gate drive schemes suitable for VHF operation are presented, both of which provide rapid startup and low-loss operation. Both converters regulate the output using high-bandwidth, on-off hysteretic control, which enables fast transient response and efficient light-load operation. The low energy storage requirements of the converters allow the use of aircore inductors in both designs, thereby eliminating magnetic core loss and introducing the possibility of easy integration.

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Very-High-Frequency Resonant Boost Converters

A limitation of many high-frequency resonant inverter topologies is their high sensitivity to loading conditions. This paper introduces a new class of matching networks that greatly reduces the load sensitivity of resonant inverters and radio frequency (RF) power amplifiers. These networks, which we term resistance compression networks, serve to substantially decrease the variation in effective resistance seen by a tuned RF inverter as loading conditions change. We explore the operation, performance characteristics, and design of these networks, and present experimental results demonstrating their performance. Their combination with rectifiers to form RF-to-dc converters having narrow-range resistive input characteristics is also treated. The application of resistance compression in resonant power conversion is demonstrated in a dc-dc power converter operating at 100MHz

Resistance Compression Networks for Radio-Frequency Power Conversion

This paper presents a new switched-mode resonant inverter, which we term the inverter, that is well suited to operation at very high frequencies and to rapid on/off control. Features of this inverter topology include low semiconductor voltage stress, small passive energy storage requirements, fast dynamic response, and good design flexibility. The structure and operation of the proposed topology are described, and a design procedure is introduced. Experimental results demonstrating the new topology are also presented. A prototype inverter is described that switches at 30 MHz and provides over 500 W of radio frequency power at a drain efficiency above 92%. It is expected that the inverter will find use as a building block in high-performance dc-dc converters among other applications.

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A High-Frequency Resonant Inverter Topology With Low-Voltage Stress

This document describes several aspects relating to the design of dc-dc converters operating at frequencies in the VHF range (30–300 MHz). Design considerations are treated in the context of a dc-dc converter operating at a switching frequency of 100 MHz. Gate drive, rectifier and control designs are explored in detail, and experimental measurements of the complete converter are presented that verify the design approach. The gate drive, a self-oscillating multi-resonant circuit, dramatically reduces the gating power while ensuring fast on-off transitions of the semiconductor switch. The rectifier is a resonant topology that absorbs diode parasitic capacitance and is designed to appear resistive at the switching frequency. The small sizes of the energy storage elements (inductors and capacitors) in this circuit permit rapid start-up and shut-down and a correspondingly high control bandwidth. These characteristics are exploited in a high bandwidth hysteretic control scheme that modulates the converter on and off at frequencies as high as 200 kHz.

David D. Jackson

Papers

Design Considerations for Very High Frequency dc-dc Converters

Elastic relaxation model for seismic wave attenuation in the earth.